Performing Knowledge: Twentieth-Century Music in Analysis and Performance [Illustrated] 019065354X, 9780190653545

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Performing Knowledge

OX F O R D S T U D I E S I N M U SIC   T H E O RY Series Editor Steven Rings Studies in Music with Text David Lewin Music as Discourse: Semiotic Adventures in Romantic Music Kofi Agawu Metric Manipulations in Haydn and Mozart: Chamber Music for Strings, 1787–​1791 Danuta Mirka Songs in Motion: Rhythm and Meter in the German Lied Yonatan Malin A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice Dmitri Tymoczko In the Process of Becoming: Analytic and Philosophical Perspectives on Form in Early Nineteenth-​Century Music Janet Schmalfeldt Tonality and Transformation Steven Rings Audacious Euphony: Chromaticism and the Triad’s Second Nature Richard Cohn Mahler’s Symphonic Sonatas Seth Monahan Beating Time and Measuring Music in the Early Modern Era Roger Mathew Grant Pieces of Tradition: An Analysis of Contemporary Tonal Music Daniel Harrison Music at Hand: Instruments, Bodies, and Cognition Jonathan De Souza Organized Time: Rhythm, Tonality, and Form Jason Yust Flow: Expressive Rhythm in the Rapping Voice Mitchell Ohriner Performing Knowledge: Twentieth-​Century Music in Analysis and Performance Daphne Leong

Performing Knowledge Twentieth-​Century Music in Analysis and Performance DA P H N E   L E O N G with

A L E JA N D R O C R E M A S C H I , H U N T E R EW E N , A DA M EW I N G , J U D I T H G LY D E , DAV I D KO R EVA A R , J O NAT HA N L E AT H WO O D, E L I Z A B E T H M C N U T T, R O B E RT M O R R I S , A N D T H E TA KÁC S QUA RT E T

1

3 Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and certain other countries. Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America. © Oxford University Press 2019 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by license, or under terms agreed with the appropriate reproduction rights organization. Inquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above. You must not circulate this work in any other form and you must impose this same condition on any acquirer. Library of Congress Cataloging-in-Publication Data Names: Leong, Daphne, author. Title: Performing knowledge : twentieth-century music in analysis and performance / Daphne Leong. Description: New York, NY : Oxford University Press, [2019] | Series: Oxford studies in music theory | Includes bibliographical references and index. Identifiers: LCCN 2019002768 | ISBN 9780190653545 (cloth : alk. paper) | ISBN 9780190653576 (oxford scholarship online) | ISBN 9780190653583 (companion website) Subjects: LCSH: Music—20th century—Analysis, appreciation. | Music—Performance. Classification: LCC MT90 .L413 2019 | DDC 780.9/04—dc23 LC record available at https://lccn.loc.gov/2019002768 1 3 5 7 9 8 6 4 2 Printed by Integrated Books International, United States of America

Acknowledgments I am grateful to George for his steady love and support, and deeply thankful to my parents, Che Kan and Theresa Leong, for nurturing my love of music and learning. Thanks to my collaborators on this volume for intrepidly accepting my invitations to work together, for pushing and challenging me, and for bearing with me! In some cases, performing together motivated our later co-​authorship; I would like to thank Erika Eckert and Judith Ingolffson, whose performance of the Schnittke Piano Quartet with Judith Glyde and me appears on the website for this book. Michiko Theurer and I collaborated in multi-​faceted ways on Crumb’s Four Nocturnes; the introduction to this book grows out of our rich interactions. My partners in crime (John Gunther, Michael Tetreault, Patrick Sutton) in the new-​music quartet Throw Down or Shut Up! unwittingly provided illustrations for collaborative theory; our rehearsals and performances have fed my musical soul. Bob Morris stimulated and challenged my thinking and hearing; it has been a boon to collaborate in new ways. Joel Lester provided advice and support on numerous occasions; I am grateful for his mentoring from my days as a young faculty member. Rick Cohn encouraged and guided me in my development of the book for the Oxford series, Steve Rings provided sage advice, and Suzanne Ryan helped the book come to fruition. It was Suzanne’s request to “provide a brief description of the collaborative process” that led me to delve into the question of collaboration itself. I thank all three for considering my book, despite its unusual hybrid structure, for a monograph series. Oxford’s anonymous readers provided valuable feedback and trenchant criticism that improved the final product immeasurably. I came to much of this music as a performer, and so my performance teachers—​ David Burge, Anton Nel, Douglas Humpherys, Robin Harrison, and Louise MacPherson—​have had a hidden but deep influence on this work. The community of musicians—​both scholars and performers—​at the University of Colorado Boulder, continue to stimulate my explorations in many ways. I particularly thank my theory colleagues Yonatan Malin, Steven Bruns, Keith Waters, and Philip Chang for the privilege of working together and for their suggestions on aspects of this book. Yonatan read drafts of various sections and bore the brunt of my thinking aloud about difficult topics. Ben Teitelbaum helped with ethnomusicological sources and feedback at an early stage. Exchanges with philosopher David Barnett and with communications scholar Matt Koschmann informed the book’s framework. As acknowledged in the following pages, many others influenced individual chapters.

viii Acknowledgments

I thank David Kirtley, who spent countless hours on musical examples, for his patience and attention to detail, and Kathryn Mueller, who assisted with the examples for the Messiaen chapter. Sara Corry was a cheerful and knowledgeable help with video and image matters. A generous subvention from the Society for Music Theory defrayed the cost of copyright permissions. I have benefited from support at the University of Colorado Boulder:  course releases provided by the Leadership Education for Advancement and Promotion Grant, a Kayden Research Grant, and several Graduate Committee on the Arts and Humanities Research and Creative Work grants. I thank my deans: Daniel Sher, who has supported me through many years, Robert Shay, and interim Dean James Austin. Finally, I am thankful for the opportunity and ability to make and explore music.

Acknowledgments: Individual Chapters We gratefully acknowledge assistance with individual chapters:

Theme Edward Klorman read a draft of the Theme; Brian Kane provided context for my thinking on musical structure. Counterpoint Scott Klingsmith, Robert Morris, Keith Waters, and Steven Bruns commented on drafts. Variation 1 The core of this chapter was first published as “The Performer’s Voice: Performance and Analysis in Ravel’s Concerto pour la main gauche” in Music Theory Online 11/​ 3 (2005). Joel Lester read an early version. Nicolas Waldvogel, conductor, articulated a “performer’s analysis” of the orchestral introduction to the Concerto; Laurie Sampsel helped track down recordings and manuscripts; and Kevin Harbison, Glenn Arndt, and Daryl Burghardt assisted with recording and technical matters.

Variation 2 Matthew Arndt critiqued the chapter and shared a draft of his analysis of Schoenberg’s Op. 19, No. 4. Variation 3 An early version of this material was presented as a keynote address, “A Rhythmic Problem in Bartók’s Fifth String Quartet,” at the Special Symposium on Performance and Analysis, Indiana University, February 21, 2009. Empirical analysis of recordings:  Hunter Ewen provided technical assistance with data extraction and display. Bryan Koerner carried out statistical analysis. Judith Glyde, Charles Wetherbee, Laura Eakman, Mei-​Mey Segura, and Michiko Theurer rated accent and articulation in the recordings. James Austin advised on methodology.

x  Acknowledgments: Individual Chapters

Variation 4 Peter Kaminsky read an early version of this chapter. Variation 5 Carlo Caballero commented on a draft of this chapter. Variation 7 “Virtuosity in Babbitt’s Lonely Flute” was first published in Music Theory Online 11/​1 (2005). That essay revised a paper presented at the Society for Music Theory National Conference, Seattle, 2004. Variation 8 Some of the ideas in Leathwood’s discussion of Changes were first presented at the Carter Colloquium at Wright State University in Dayton, Ohio, on October 25, 2008. Margaret Boland, Guy Capuzzo, Stephen Goss, and Andrew Mead provided generous and invaluable help. We thank Patrick Sutton for the interview in the Postlude.

Variation 9 Audience Response Experiment: Che Kan Leong carried out the statistical analysis and provided guidance on the project. Chelsea Reisner acted as research assistant, Hunter Ewen and Dustin Rumsey assisted with technical matters, and Kevin Harbison and John Truebger filmed the performance video and the AES and STR videos, respectively. Dave Rickels advised on experimental design and Elizabeth West Marvin commented on a draft reporting our results. Yayoi Uno Everett suggested the multi-​room experimental design. We thank our participants for their time and responses.

Permissions The following permissions to reproduce score excerpts and images are thankfully acknowledged.

Theme Crumb, George. Four Nocturnes (for violin and piano), “Notturno IV.” Copyright © 1971 by C. F. Peters Corporation. All Rights Reserved. Used by permission. Variation 1 Concerto pour la main gauche Musique de Maurice Ravel Copyright © 1937 Arima SCP /​Nordice B.V. /​Éditions Durand -​ Paris Tous droits réservés pour tous pays Reproduced by kind permission of Hal Leonard MGB s.r.l. Variation 2 Schoenberg, Sechs kleine Klavierstücke, Op. 19, No. 4: Reinschrift (seite 4). Used by permission of Belmont Music Publishers, Los Angeles. Variation 3 Béla Bartók String Quartet No. 5 © Copyright 1936 by Universal Edition A.G., Wien/​UE 34312 All rights in the USA owned and controlled by Boosey & Hawkes, Inc., New York String Quartet No. 5, SZ102 by Béla Bartók © Copyright 1936 Boosey & Hawkes, Inc. Copyright Renewed Reprinted by Permission of Boosey & Hawkes, Inc. Bartók, Fifth String Quartet:  “plan of the tonalities and structure of the work.” Reproduced from Béla Bartók Essays, edited by Benjamin Suchoff, by permission of the University of Nebraska Press. Copyright 1976 by Dr.  Benjamin Suchoff, Successor-​Trustee, The Estate of Béla Bartók. Bartók’s revised transcription of “Árvátfalvi kesergő.” Hungarian Institute for Musicology RCH HAS inv. no. ZTI_​BR_​12957.

xii Permissions

Photograph of Takács Quartet with Zoltán Székely, Banff, 1981. Courtesy of the Banff Centre for Arts and Creativity.

Variation 4 Klavierquartet based on a fragment by Gustav Mahler by Alfred Schnittke (1988) © With kind permission MUSIKVERLAG HANS SIKORSKI GMBH & CO. KG Karlheinz Stockhausen “rhythmic formants” from Die Reihe: Heft 3 –​Musical Craftmanship © With kind permission by Universal Edition A.G., Wien/​UE 26103E

Variation 6 Visions de l’Amen Music by Olivier Messiaen Copyright © 1950 Éditions Durand –​ Paris Reproduced by kind permission of Hal Leonard MGB s.r.l. “The Ladder of Virtue,” Suceviţa monastery, Romania. Image courtesy of RomaniaTourism.com Photograh of premiere of Messiaen’s Visions de l’Amen: Yvonne Loriod and Olivier Messiaen, pianists. Nigel Simeone, private collection.

Variation 7 Babbitt, Milton. None but the Lonely Flute. Copyright © 1993 by C.  F. Peters Corporation. All Rights Reserved. Used by permission. Variation 8 Changes by Elliott Carter © 1983 by Hendon Music, Inc. Reprinted by Permission of Boosey & Hawkes, Inc. Variation 9 Pure Tones among Hills and Waters, 1664. Xiao Yuncong (Chinese, 1596–​1673). Handscroll, ink and light color on paper; overall: 30.80 x 781.70 cm (12 1/​8 x 307 3/​ 4 inches). The Cleveland Museum of Art, John L. Severance Fund 1954.262

Note to Readers This book is intended for a varied audience of music theorists, performers, musicologists, and pedagogues. Its analytical chapters—​collaborations between a theorist, performers, and composers—​move among the languages of all three. Without stereotyping our discourses, we acknowledge differences in our values, interests, and ways of communicating. This note seeks to clarify vocabulary and paths through the book for different readers. Basic pitch-​class terminology is used. Pitch classes are labeled from 0 to 11: C = 0, ♯ C /​D♭ = 1, D = 2, D♯/​E♭ = 3, . . . , A = 9, A♯/​B♭ = 10, B = 11. Enharmonic equivalence is assumed. 10 and 11 are abbreviated as T and E. Standard set-​class labeling and terminology are employed. Pitches in register are labeled following the Acoustical Society of America: middle C = C4. Tn and TnI indicate transposition and inversion. {} represents unordered sets, < > ordered sets, and [] prime forms. Text in the book is complemented and supported by audio, video, and color illustrations online. In addition to fleshing out points made in the text, these media provide performer commentary, demonstrations and tips, complete performances, and primary sources. Many are integral to the line of argument. The reader is directed to them at the appropriate points by the web icon   . Data drawn from recorded performances is both “hard” and “soft”: the former empirical, and the latter qualitative. Both are valuable; hearing is determined not only by acoustic data but also by factors in combination. The following guidance is provided for those readers less interested in technical details and abstract treatments. The chapter on Schoenberg’s Klavierstück, Op. 19, No. 4, opens with a general discussion of scores and their affordances; practical readers may wish to skip to the discussion of the piece itself, beginning just before the heading “Schoenberg’s Klavierstück, Op. 19, No. 4.” The chapter on Bartok’s Fifth String Quartet contains a section of statistical analysis; this section is summarized in its last paragraph. The treatment of “Three Techniques” (rhythmic “formants,” expansion and contraction, and self-​similarity) in Schnittke’s Piano Quartet is slightly more technical than the rest of that chapter. Our analysis of Babbitt’s Lonely Flute jumps into all-​partition arrays and timepoints without preamble; an online tutorial introduces these compositional techniques. The Postlude on Carter’s Changes is directly pertinent for those interested in pedagogy. Finally, the chapter on Morris’s

xiv  Note to Readers

Clear Sounds differs from the others: it focuses on the listener, providing both experimental results and speculative discussion. We incorporate practical performance suggestions strategically, in chapters in which we advocate a particular interpretive approach. These include our treatments of Bartók’s Fifth String Quartet, Schnittke’s Piano Quartet, and Milhaud’s “Aurore.” Other chapters, such as those on Ravel’s Concerto pour la main gauche and Babbitt’s Lonely Flute, proffer performative options. For Carter’s Changes we supply exercises for internalizing its hexachords through improvisation. We avoid, in all cases, prescription, believing that interpretation is always open-​ended. Finally, the book is structured as a Theme and Variations. The Variations—​the analytical chapters—​cast light on the Theme, tracing it through different pieces, issues, and co-​authors. Vocal registers in the variations vary considerably. Depending upon the nature of each collaboration and the contributions and roles of each author, voices interact contrapuntally, harmonically, or even sectionally. Dialogue occurs in portions of the Ravel and Babbitt variations, while a joint voice speaks on Milhaud and Messiaen. Voices are distinct in the chapters on Schnittke, Carter, and Morris, as well as in those on Schoenberg (through the recordings) and Bartók (through the video). But voices do not transparently represent contributions: our roles as theorist and performer crossed fluidly, interchanging and interweaving as we worked. So those who expect clear theorist-​performer distinctions will be largely disappointed: our collaborative roles were much more nuanced and changeable than that. The voices build a progressively “thicker description” of the Theme, weaving various threads—​the concept of affordances, the role of metaphor, the nature of interpretation—​around it. These threads appear sometimes on the surface, sometimes underneath; the overall tapestry is interpreted in the book’s conclusion. The italicized introductions are not abstracts; they introduce the issues and set the context for each variation. They are appetizers to each course.

About the Companion Website www.oup.com/​us/performingknowledge​ Username: Music3 Password: Book3234 Text in Performing Knowledge is complemented and supported by audio, video, and color illustrations online. In addition to fleshing out points made in the text, these media provide performer commentary, demonstrations and tips, complete performances, and primary sources. Many are integral to the line of argument. The reader is directed to them at the appropriate points by the web icon  .

Contributors Daphne Leong is Associate Professor of Music Theory at the University of Colorado Boulder. Her research interests include rhythm, analysis and performance, and the music of twentieth-​ and twenty-​first-​century composers. Her publications appear in journals such as Journal of Music Theory, Perspectives of New Music, and Music Theory Online, as well as in edited collections on Bartók, Ravel, and the pedagogy of music theory. She is an active pianist and chamber musician, whose repertoire ranges from Bach to premieres of current music. Pianist Alejandro Cremaschi has recorded for the labels IRCO, Ostinato, Marco Polo, and Meridian Records. He was a prize winner at the International Beethoven Sonata Piano Competition in Memphis, Tennessee, in 2001. His research areas include Latin American music, student achievement, motivation and practicing strategies, and pedagogical technology. His pedagogical edition and recording of Alberto Ginastera’s Doce Preludios Americanos for piano was published by Fischer in 2016. He is Professor of Piano Pedagogy at the University of Colorado Boulder. Hunter Ewen is a composer and multimedia artist specializing in music technology. Formerly an instructor of Critical Media Practices at the University of Colorado Boulder, he currently directs the composer/​technologist team at Amper Music, an AI music composition company. His notable collaborations include works for SFMOMA, NCAR, ICMC, and SEAMUS with ensembles like the Beethoven Academy Orchestra, Cairo Symphony, Silesian Philharmonic, Verdant Vibes, and Third Coast Percussion. Lyric baritone Adam Ewing regularly sings with the Boulder Bach Festival, the Baroque Chamber Orchestra of Colorado, and the Denver Early Music Consort, as well as collaborating with Central City Opera, the Boulder Philharmonic, and the Colorado Symphony Orchestra. Ewing has appeared as a soloist at Franklin College, Pennsylvania State University, and the American University of Beirut in Lebanon. He was a NATS Artist Awards national finalist in 2018. Ewing currently serves as Affiliate Faculty of Voice at Regis University in Denver. Judith Glyde is Professor Emerita of cello and chamber music at the University of Colorado Boulder (1992–​2014). As a founding member of the Manhattan String Quartet, she appeared throughout the United States, Europe, Canada, Mexico, the former Soviet Union, and South America (1970–​92), playing over a hundred concerts a year. The Quartet’s discography comprises more than twenty-​five recordings for Naxos, Sony, Koch, Newport Classics, Centaur Records, and ESS.A.Y., including the first complete recording of Shostakovich’s fifteen string quartets by an American quartet. David Korevaar is Peter and Helen Weil Professor of Piano at the University of Colorado Boulder, where he was also named Distinguished Research Lecturer in 2016. He performs internationally as soloist and chamber musician, and has recorded numerous critically acclaimed CDs of

xviii Contributors repertoire from Bach to Lowell Liebermann on labels such as Decca, MSR, and Naxos. In addition to his teaching and performing activities, he writes on various musical topics, with a focus on French and early twentieth-​century music. Jonathan Leathwood is Associate Teaching Professor at the University of Denver’s Lamont School of Music. He performs on both six-​and ten-​string guitars and has appeared in Europe and both American continents at venues such as Wigmore Hall and the Cheltenham Festival. His collaborations include recordings with flutist William Bennett and cellist Rohan de Saram. He has worked closely with Harrison Birtwistle, and premiered and recorded works by composers such as Param Vir and Stephen Goss. As a pedagogue his focus is on helping students integrate different kinds of knowledge. Flutist Elizabeth McNutt primarily performs contemporary and electroacoustic music. She has premiered more than 200 works, performing in Europe, Asia, and the United States. Her recordings are on the CRI, Centaur, SEAMUS, Navona, and Ravello labels; her writing has been published in Organised Sound, Music Theory Online, and Flutist Quarterly. She directs the new music series Sounds Modern. McNutt is on the faculty of the University of North Texas, where she teaches flute and directs the new music ensemble Nova. Robert Morris has taught at the Eastman School of Music, University of Rochester, since 1980, where he is Professor of Composition with faculty affiliation within the music theory department. Morris has written over 180 compositions, including computer and improvisational music widely performed and recorded in North America, Europe, Asia, and Australia. He has also authored four books and over sixty articles and reviews. In 2017, the Society for Music Theory awarded Morris a Lifetime Membership “in recognition of truly outstanding contributions to the field of music theory.” Morris is presently co-​editor of the journal Perspectives of New Music. The Takács Quartet plays eighty concerts a year at the world’s leading venues. They were the first string quartet to win the Wigmore Hall Medal (2014) and the only string quartet inducted into Gramophone’s first Hall of Fame (2012). They were honored with the Award for Chamber Music and Song of the Royal Philharmonic Society in London (2011), and the Order of Merit of the Knight’s Cross of the Republic of Hungary (2001). Their extensive discography for Decca and Hyperion has garnered multiple international awards; their recording of the Bartók String Quartets received the 1998 Gramophone Award for chamber music. The Takács Quartet was formed in 1975 at the Liszt Academy in Budapest by Gabor Takács-​Nagy, Károly Schranz, Gabor Ormai, and András Fejér.

Performers, Structure, and Ways of Knowing Violinist Michiko Theurer and I  are preparing George Crumb’s Four Nocturnes for performance. We are struggling with the second system in Example 0.1. (Please view our performance on Video 0.1 .) For the pianist it requires a complicated ballet of motions from keyboard to mid-​register pizzicato to low-​register fingernail scrapes to the playing of harmonics: lateral movements among the piano’s registral extremes, in-​out and raised-​lowered motions into the strings (higher in height) and out to the keyboard (lower in height), and simultaneous combinations of all of the preceding. The music asks for nuanced control of timbre, from poco fz–​subito pp flickers, to the temporal and harmonic envelope of the pp fingernail scrapes, to the delicatissimo of the ppp staccato glints, to the balance and voicing of these one with the other. It requires coordination of the violinist’s and pianist’s gestures, the qualities of their sound, and the directions of their motions, as the violinist moves across the universe of a fugace, leggiero figure, a thematic motive marked p ma molto espressivo (possibly the most romantically expressive moment of the entire work), hairpin dynamics on a slow rise to pppp quasi niente, and a very slow, sospiroso, disappearing glissando. This passage comes from the fourth nocturne, which looks back on the other nocturnes “con un sentimento di nostalgia.” The passage is the entire work’s gravitational center. With its slow 7/​8 meter signature (eighth = MM 30),1 its interweaving of compound timbral and registral voices, its intense sonorous qualities and affective dimensions, and its temporal and spatial breadth, it embodies a plenitude. As I study the score after our rehearsal, I notice several structural features. The passage is clearly segmented into aggregates (labeled “U” on the example).2 Each aggregate, except the second, is initiated by the pianist’s poco fz grace notes, labeled with stars on the example. (The second aggregate consists of three [0167] sets—​a sonority characteristic of the work—​also articulated in this passage by the low bass scrapes on {G, C♯, C, F♯}.) Measures 2 and 3 contain repeating elements.3 The delicatissimo staccato /​pizzicato is immediately retrograded at pitch, legato, swooping down to a 1 This passage is one of only two in the entire work with a meter signature. 2 The aggregates of the passage under discussion (system 2) are labeled U1 through U5; I will refer to U1 as the first aggregate, U2 as the second, and so on. (The first system of the nocturne also completes an aggregate with the violin’s arrival on F6; that aggregate is not discussed here.) 3 Other material in this nocturne is unmetered, so I  have numbered only the measures of this second system.

Example 0.1. Crumb, Four Nocturnes, IV, systems 1–​2.

Example 0.1  (cont.).

6  Performing Knowledge

low F♯ fingernail scrape. The components of this legato gesture are retrograded in m. 3 . The final high poco fz grace note gesture (leading into m. 3) echoes the preceding the downbeat of m. 2, while its {A, D, C♯} restate the pitch classes of the poco fz gesture in the middle of m. 2. And the accented poco f {C, B} dyad, the penultimate sonority of the passage, recalls the low {C, B} dyad of m. 2.4 What, if anything, do these structural features, and the analytical process, have to do with embodied performance, with the rehearsal process, with performed interpretation—​and vice versa? That is the question addressed by this book. In it, a theorist and performers interact over issues of musical structure. The book in no way represents the many dimensions involved in performance itself or even the primary considerations of performers. Rather, it brings a theorist and performers together to illuminate questions of how analysis and performance do relate, do not relate, or might relate. * * * This book joins a fragmented discourse: on the one hand, the tradition of relating analysis and performance within the field of music theory, and on the other hand, the rapidly growing and widely diverse activities of musical performance studies. There is some overlap, but the points of intersection are few. Some of the obvious gaps are the paucity of performers directly involved (qua performers, and not primarily as scholars or study subjects) in analysis and performance, and the lack of attention to structural analysis in performance studies. Part of the debate concerns the nature of music itself, and hence the proper means of its study. Is musical ontology bound up with works? texts? performance? composition? society? structure? and so on. And depending upon the answer to the first question: How does one define performance? structure? and so forth. Another part of the debate concerns disciplinarity: What are the proper focuses for music analysis? for performance studies? To begin with the latter, the rise of musical performance studies (stimulated by multiple factors, including performance studies in theatre, the “new musicology,” writings such as Goehr (1992) and Small (1998), and, practically, by two multi-​ year multi-​institutional programs in the United Kingdom—​the Centre for the History and Analysis of Recorded Music, and the Centre for Musical Performance as Creative Practice) led to a new focus on “music as performance” and on the social nature of its construction.5 In these developments, attention fell initially

4 Which, incidentally, is the only time that Crumb writes a low fingernail scrape into something—​the pizzicato B. 5 See Cook (2013, 2018). Cusick (2004) provides a perceptive overview of two developments in North America: the new musicology’s interest in studying performance, and the emergence of the interdisciplinary field of performance studies.

Theme  7

upon recordings as the locus of empirical and historical study,6 and later turned to live performance and to aspects of music-​making unique to it.7 Most recently, the concept of distributed creativity (Clarke and Doffman 2017b) rehabilitates the composer (who had been in danger of disappearing in the focus on music as performance). Performers (and composers) participate actively in practice-​led or practice-​based research, which has gained momentum and academic standing. Attention to the term “performance” is relatively new in music scholarship; in Grove’s Dictionary of Music and Musicians it received its own entry (by Jonathan Dunsby) only in the second edition of The New Grove (2001). With the advent of the discipline of performance studies—​first in theatre and then in music—​ “performance” or “performativity” came to be defined in opposition to “text.”8 Performance is described as “an extreme occasion, something beyond the everyday, something irreducibly and temporally not repeatable, something whose core is precisely what can be experienced only under relatively severe and unyielding conditions” (Said 1991, 17–​18). Musical performance is thus a unique, irreproducible experience whose temporality is both immediate and bracketed from the everyday. Furthermore, it is a doing that enfolds sound in body, sight, and feel. It is in this sense that performance is “drastic” and not “gnostic”; gnostic disciplines (addressing “an abstract work’s formal shapes or representational implications”) are in large part irrelevant—​even counterproductive—​in the moment of performance (Abbate 2004, 530). And yet, as any musician knows, the moment of performance rests on many other moments less drastic in nature. Such moments include the hours necessary for developing technical skill, sharpening one’s ears, and shaping interpretations. They involve, at some level, analysis, whether that analysis investigates physical motions, affective implications, narrative arcs, or more traditional aspects of musical structure.9

6 See Philip (1992, 1994); Cook et  al. (2009); Leech-​Wilkinson (2009); Bayley (2010); and Doğantan-​ Dack (2008). Methods for the study of recordings have been both qualitative and quantitative. Approaches range from the close reading of a small number of recordings to studies of musical corpora of varying sizes. Features most frequently studied are timing and, to a lesser extent, dynamics, probably because these are variables that are relatively easy to measure. Findings are interpreted through the lenses of structural principles (Repp 1990; Ohriner 2012) or particular analyses (Dodson 2002, 2008; Leech-​Wilkinson 2015), interpretive traditions (Cook 2017) or performance practices (Benadon 2009; Butterfield 2011), stylistic norms (Komaniecki 2017) or individual characteristics (Barolsky 2007; Burns 2005), models of cognition and embodiment (Gotham 2018), listener perception (Martens 2007) or reception (Zayaruznaya 2017), and contemporary commentary (Kaminsky 2016). In some cases the detailed timing structure of recordings has been used as the basis for new compositions (Trottier 2013). The examples I have given here are only a small and somewhat arbitrary sampling of a large field of study. 7 See, for instance, Doğantan-​Dack (2008, 2011, 2012); Coessens (2014a); and Coessens and Östersjö (2014b). 8 Danuser (2015) provides a helpful history of the terms execution, interpretation, and performance, focusing on but not limited to German usage. 9 See Coessens (2014b) for her description of the five dimensions of an “artistic web of practice”: embodied know-​how, explicit and tacit knowledge, ecological affordances, cultural-​semiotic codes such as notation, and social interactions. Coessens and Östersjö (2014a, 334–​36) implicate purposeful training in the Aristotelian notion of hexis, comprising both ethos and techné, that is, virtue and skill.

8  Performing Knowledge

The discipline of music analysis itself has broadened greatly in recent decades. Relevant here are treatments of embodiment (Cusick 1994; Mead 1999; Le Guin 2002; Kozak 2015; Cox 2016), instrumental spaces (Rockwell 2009; Koozin 2011; De Souza 2017), and agency (Monahan 2013; Klorman 2016; Hatten 2018; Zbikowski 2018); empirical methodologies for the analysis of sound and movement (Gabrielsson 1999, 2003; Clarke and Cook 2004), and literary theories such as narrative theory applied to music (Abbate 1991; Almén 2008; Klein and Reyland 2013). So what results when performers and a theorist convene over questions of musical structure? Each chapter of this book is a case study on a particular twentieth-​ century work, co-​authored with a performer (or composer). We explore how instrumental and physical affordances affect structure, how interpreters create structure, how culture affects structure, how stories emerge from structure, how counterpoint delineates structure, how drama arises from structure, how performative insight and analytical structure intertwine or bypass one another, and how an audience responds to structural information.

Structure In this book I use the term structure in two senses. The first is that commonly accepted (but usually undefined) in the practice of music analysis, in which structure is constructed or interpreted from elements found in a score. Most theorists would include dimensions of perception and performance, broadly defined, in structure so interpreted.10 The second sense in which I use the term structure is much broader, and includes the first. It is the sense in which structure is created in the process of making music—​by composers, performers, listeners, and analysts. Structure in this broader conception explicitly includes perceived, performed, and even imagined elements. It can be active, fluid, and dynamic.11 This second sense of structure finds resonance in concepts of “structuration” as espoused by Roland Barthes in literary criticism and by Anthony Giddens in social theory.12 Barthes’ structuration (1970, 27) refers to the multivalent interweaving of voices in the interpretation of an open text. For Barthes (1975, 20), structuration does not result in a “unitary, architectonic, finite” form, but in a dissolved, fragmentary, overlapping network. Giddens (1976, 121)  defines structuration in the social sciences as “the dynamic process whereby structures come into being.” He highlights the “duality of

10 See Lewin (1986) for a pioneering phenomenological construction of structure, as well as a defense of the inseparability of perception, performance, and analysis. 11 While Rink (2015) addresses the role of performers in constructing musical structure, he seems to constrain it to choosing among existing structural potentials. It is not clear whether, in his conception, the performer may contradict or create beyond those potentials. 12 See also Lochhead’s (2016) “structuring.”

Theme  9

structure,” that is, the mutual constituting of social structures and human agents; objective structure and subjective agency are inextricably linked. For music we can expand the concept of agency to include non-​human actors: instruments, spaces, notations, traditions.13 Most frequently, such actors form hybrid agents with human actors; violinist-​violin-​sonic space might be one such agent, composer-​notation (in the case of a living composer interpreting or adapting her notation during rehearsal) might be another.14 Pieces themselves can also act as agents, during composition when material seems to demand a particular working out, for example, or in performance when a sounding-​physical-​visual trace seems to suggest a particular course of action.15 Like Giddens, I take structure to be interpreted and created through a dialogue of “objective” materials (acoustic facts, notated specifics, historical details) and “subjective” agency (human and non-​human). Such a dialogue eschews claims of immanence, truth value, and systematicity (claims sometimes associated with work concept) on the one hand,16 as well as radical focus on the individual interpreter as the source of structure and meaning on the other. It also leaves open questions of structure’s temporality, generality, and ontological status. At its basis is the common-​parlance definition of structure as relations among parts and whole.17 From this relatively agnostic definition, structure can be constituted in many ways, from different types of elements, and by diverse agents.18 The entities from which musical structure can be constituted include traditional elements of music analysis—​pitch, rhythm, motive, phrase, twelve-​tone rows, and so forth;19 perceived elements—​pulses to which one entrains, felt durations, surprising moments, and so on;20 and performed elements—​temporal and dynamic shaping,

13 On the agency of instruments, see De Souza (2017); De Souza refers to musical traditions in terms of Kirsch’s (2013, §2.6) “enactive landscapes” (52–​53, 63). 14 Following Cook (2018, 50–​51, 61), we could call such hybrid agents assemblages; Cook’s examples include “MAN-​HORSE-​STIRRUP” and “COMPOSER-​PERFORMER-​GUITAR.” An assemblage consists of self-​subsistent, heterogeneous parts that form an emergent whole (DeLanda 2006b, 10–​11, 14, 18); the concept was originated by Deleuze and Guattari and developed by DeLanda. In their original usage, assemblages are often quite complex and less discrete than the MAN-​HORSE-​STIRRUP example. The assemblages of Deleuze and Guattari are always “passing into . . . other assemblages” (1987, 323). DeLanda’s assemblages make up different levels of society: an individual’s subjectivity, social encounters such as conversations, interpersonal networks, and so on, up to the level of states (2006a). Agency is not a necessary feature of an assemblage. 15 On pieces as agents or personae see, for instance, Monahan (2013) and Cone (1974). 16 Adorno (1982) and Agawu (2004), for example, are concerned with the Wahrheitsgehalt, or “truth content,” of a work, revealed through analysis of immanent technical structure. “The truth content is not necessarily a literal, empirical truth but rather a dynamic, motivating truth designed partly to anchor listening in specific sociocultural and historical moments . . .” (Agawu 2004, 273). 17 Definitions of structure from the Oxford English Dictionary include: “2. The existing arrangement and mutual relation of the constituent parts of a material object, especially as determining its distinctive nature or character . . .” “3a. fig. The arrangement and organization of mutually connected and dependent elements in a system or construct.” “4a. The quality or fact of being organized in a particular manner; definite or purposeful arrangement of parts within a whole.” “7. A combination or network of mutually connected and dependent parts or elements; an organized body or system” (Oxford English Dictionary, 2018, s.v. “structure, n.”). 18 Unlike structuralism, then, I do not associate the idea of structure as a network of internal relations with the broader criteria of systematicity, formal concepts, and methodology (Culler 1975, 255–​56). 19 See Hanninen (2012). 20 See, for example, London (2012), Margulis (2007), and Huron (2006), respectively.

10  Performing Knowledge

tone color and voicing, physical actions, etc.21 These categories are not exclusive, and they intertwine in intricate ways.22 They give rise to emergent elements—​ metaphors of musical motion and process, affective and connotative associations, narrative dimensions, and so on,23 which also play into musical structure. In the sense, however, that both structure and its elements are interpretively constructed, all musical structure is emergent. Though afforded by perceptual information (acoustic, visual, physical, symbolic), cognitive processes, and embodied experience, structure is always understood within some cultural—​or even disciplinary—​context (consider the various ways in which the term “phrase” is understood), some temporal dimension (synchronic, diachronic, moment of performance, stretched time of rehearsal), and some human practice (analyzing, listening, dancing). Furthermore, structure may be explicitly constructed (in a compositional plan, analytical article, or pedagogical communication), but it may also be implicitly construed (understood or embodied by composer, performer, or listener). It may be articulated in words and diagrams, but it may also be expressed in other modes (sound, physical motion, visual analog). It can be understood synchronically or experienced diachronically. Thus, rather than hewing to the view that “a structure always presumes a centre, a fixed principle, a hierarchy of meanings  .  .  .” (Eagleton 2008, 116), this book decenters the concept of structure.24 It attempts to connect the first, narrower, sense of structure with the second, broader sense. It interlocutes the first with aspects of the second—​structure in embodied action, sounding structure as created by performers, structure implied by cultural practices, structure in narrative and drama—​and juxtaposes both with questions of performance preparation and of reception. Structure broadly defined is essentially plural. It constitutes open networks, in which various structures can interact and can be incongruent with one another. Its plurality arises in part from distinctions between musical process (composing, performing, listening, analyzing) and musical product. (I have argued elsewhere that musical states and processes can be considered transformations of one another.25) Structure is a means of making sense of music. It is a way of approaching sound and symbol, image and movement, and “hearing-​as” (“understanding-​as,” “seeing-​ as,” “feeling-​as”).26 In so doing, it gives flight to imagination. 21 See, for instance, Prior (2017), Lhevinne (1972), Doğantan-​Dack (2011), De Souza (2017), and Rockwell (2009). Rink et al. (2011), for example, considers motives as performed expressive patterns. 22 Bamberger (1996, 40) makes the point that we experience music holistically and contextually; it is only in analysis that we separate and name the components that give rise to our experience, “in a profound sense, bringing these components into existence.” 23 Marion Guck (2017) terms these “impressions,” as opposed to “perceptions.” See Cumming (2000, 241–​ 53) for a discussion of emergence in literature on aesthetics. 24 Compare to Dubiel (1997). 25 Leong (2016). 26 For discussion of Ludwig Wittgenstein’s treatment of hearing-​as or seeing-​as as it relates to music and music analysis, see Kramer (2012), Dubiel (2017), Guck (2017), and Parkhurst (2017).

Theme  11

This approach to structure suits it to the endeavor of relating analysis and performance. Rather than polarizing structure as something to be promoted or vilified, seen as edifying or as irrelevant (or perhaps oppressive), it draws from both viewpoints and, defining structure as (nontrivial) relations construed among parts and whole, allows interface among our experiences as composers, performers, listeners, and analysts. * * * To return to the passage from Crumb’s fourth nocturne: What specific effects does analysis have on Michiko’s and my hearing, feeling, and shaping of the passage—​ and vice versa? First, we had begun our learning process with a concept—​hueco (hollowed space), drawn from the poetry of Federico García Lorca—​that Michiko had developed to interpret Crumb’s extensive use of silence and sonic shadow (Theurer 2017). So I  understand the subito pp notes following the starred poco fz grace notes not as entities in themselves, but as traces of the poco fz openings. Second, there are four such gestures in the passage. The third of these differs from the others in rising rather than descending, and in rising to an extreme high note, C7. This transformed gesture initiates the violin’s slowly paced rising quintuplet, the opening out of its registral space, and the quiet but intense drama of this ascent. So it is significant. And changes in the quality of motion and in gestural repetition accompany the violin’s ascent. The piano begins its repeated {D♯, F, E} gestures, moving from the delicacy of ppp staccato and pizzicato notes, to the smoothness of a pp legato swing from high to low, and changing from duple rhythmic subdivisions to more fluid triple subdivisions,27 while the violin stretches out its quintuplet. These are qualities that Michiko and I wish to feel, embody, and convey. The violin suspends its sound at its highest point until the piano articulates the downbeat of m. 3—​the climax (pppp quasi niente) of the Four Nocturnes—​and then falls in an impossibly slow and soft glissando. Its vanishing fall is accompanied by the piano’s echoes, in retrograde, of preceding gestures and the sharp recall of the {B,C} dyad, accented.28 These references are anything but abstract; in playing the passage, the physical reversal of the oval gesture is immediately palpable and also translatable into a reversal of the weight of the gesture from swinging into the low F♯ to floating above it. In our performance of this passage, it would be impossible to say where the analysis ends and the performance begins, or where the performance ends and the analysis begins, for it is the process of hearing, rehearsing, performing, and analyzing that imbues these aggregates, motives, shapes, and interpretations with the meanings that we ascribe to them. It is not that analysis and performance are one

27 Duple subdivisions of the eighth note are used exclusively until the midpoint of m. 2. 28 This dyad references the {B,C} piano dyad that opens the work, and is followed immediately after this passage by the work’s opening sonority {F♯, F, C, B} in the violin.

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and the same, but that for us, the two processes intertwine—​each informing the other in real time—​so that it becomes impossible to view them as discrete activities. Michiko had interpreted the Nocturnes in terms of hueco before ever approaching them as a performer. I, on the other hand, began rehearsing them before analyzing them in any explicit way. But as pianist I quickly moved to examining the score because I found that the complex physical motions required me to memorize much of my part. Analysis helped with this and also led naturally to interpretive dialogue and performance decisions. In the other direction, experiences in rehearsal and performance fed into and altered analytical conclusions. And, as duo partners, the dialogue of analysis and performance was also our personal dialogue. We tried out, took over, and transformed one another’s ideas and sonic gestures—​just as usually happens in the act of making chamber music. Michiko Theurer responds: I think part of what makes this nocturne so rich and rewarding (and difficult) to perform is that its gestures can be traced on the basis of multiple non-​congruent layers of cues:  for example, if we listen to timbre, constellations of particular types of sounds emerge and suggest corresponding gestural maps; if we look at phrasing/​articulation marks, other gestural shapes become evident; and so forth with register, dynamic, pitch, harmony, etc. The second system in particular was disorienting to me because whereas other parts of the Four Nocturnes seem to divide neatly into chunks of associated pitch/​rhythm/​timbre material, this system seems to incorporate many different types of material in a carefully interwoven fabric. Your analytical approach is helpful as a way of finding larger wholes within this texture: if the score begins as a star-​field in which we as performers are trying to orient ourselves in order to guide a listener through it, these different approaches to analysis seem like cross-​sections taken from different angles and suggesting different constellations. The aggregate-​based approach you describe helps because it suggests compelling expressive relationships both within that line and with the rest of the fourth nocturne. One of the most interesting aspects to me is the way key notes overlap between adjacent aggregate divisions. Seeing the aggregate structure made the blurring of its edges audible to me as an expressive device. For instance, the low G fingernail scrape at the beginning of the second system: though it comes before the completion of the passage’s first aggregate, it clearly leads into the next aggregate; similarly, the poco fz gesture leading to the high C in m. 2 intrudes on the previous aggregate, intersecting with the resonance of the low C fingernail scrape. In this context, my high G straddling mm. 2–​3 is particularly interesting, since it completes both the fourth and the fifth aggregates. And yet, it’s pppp quasi niente, slipping away into that quavering glissando sigh. Your aggregate analysis prompted me to look again at the remaining two systems of the fourth nocturne (not shown), and I noticed that the only notes missing from the aggregate for each of the last two systems are G♯ (which is the note from

Theme  13

which the entire nocturne emerges, in your doubled pizzicato-​key opening) and G♮. Knowing, then, that my high G♮ (which I think you’re right to identify as the possible climax of all four nocturnes) is the last that will be heard invests it with greater meaning. In my performance, I want to hold on to it and let go of it as something precious, never to be retrieved. This also makes me aware of your G♮ scrape in aggregate 2 (the first of the scrape-​sounds in this nocturne) as connecting to my pppp G♮ peak, almost literally scraping open a space in which we hear its dying echoes two measures later. I noticed that in your sketch there were several points at which you drew arrows from one point to another on the basis of your analysis,29 and I found myself doing the same as I carried your analytical ideas into my interpretation of my own part. I think that part of what I want to do as a performer is this drawing of imaginary arrows from point A to point B, whether that’s through my physical embodiment of the gestures (speaking of the choreography of Crumb) or through my interpretation of dynamic relationships, timbral shifts, and so on. So I find this type of analysis extremely helpful as a key to my engagement as a performer and interpreter. On one level, it’s simply a deepening of my contact with the score, another organizational tool through which I can synthesize individual notes and markings into embodied gestures. Incidentally, I think there’s a key difference here, though, between linking analytical insights with a performative gesture and using analytical ideas as the basis of a written thesis. I was thinking about my relation to the piece as a performer (through our work together) compared with my relation to the piece in constructing a paper on the idea of hueco (or, hypothetically, any other analytical idea). In an academic discussion, to convey an idea clearly, it seems helpful to filter one’s examples and arguments so that they align well with the thesis, and to discuss contradicting ideas in such a way that they can be placed to the side of the central thesis (that is, at least temporarily, below it). What I find interesting about re-​entering the piece as a performer is that it opens up (even necessitates) investigation from different and sometimes contradictory angles and methodologies, because what we’re trying to produce together is a compelling experience, not a logical argument. What matters is that we are able to embody and connect our choices into a meaningful whole, and these connections are not always rational or logically explicable. So in the end, I think, analysis from many potentially contradictory angles has the potential to become a part of performative language, and the connection need not be traceable in the manner I’ve been attempting here (pivot points, constellations, etc.) in order to become a part of the performer’s contact with and interpretation of the music. In some senses, I think, analysis is just another way of living in the music. It’s a way to become more comfortable in the space of the score. Pitch-​class analysis, poetic interpretation, etc., all

29 DL: I showed, for example, how the piano’s grace notes in the first system anticipate the four melodic notes of the violin’s entry.

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serve as different ways to map relationships between sounds, and eventually one internalizes so many different types of maps that the maps become unnecessary and it’s possible to move freely together within the space of the music.30 At least that’s the goal, I think.

Ways of Knowing The book aims to bring about a meeting of cultures—​the distinct values, practices, and vocabularies of theorists and performers.31 It is true that the medium of discourse (primarily written language, though complemented by audio and video) and venue (a book published by an academic press) skews the dialogue. But there can be no conversation if two cultures go on speaking in their own languages exclusively, each on issues of concern to them alone. Imperfect as it is, then, this book seeks to bring these two cultures together, and to address an issue—​musical structure—​that bears on both. The intermingling of cultures also brings different kinds of knowledge into play. Borrowing from my essay (Leong 2016), I  end this introduction, and open the discussion, with an illustration of three ways of knowing. Example 0.2 shows my quartet, consisting of saxophone, guitar, percussion, and piano. We play cutting-​ edge new music. The piece after which we are named, Vineet Shende’s Throw Down or Shut Up!, opens as shown in Example 0.3. (Please listen to the audio online .) It’s a tricky opening, very syncopated. The notated pulse is nowhere present. The piano takes the lead, playing a rhythmic pattern for which the counting is written below the staves: 1 2 & 3 e & a 4 e & a 5 & 1. The other instruments each play a single accented note (or two in the case of the vibraphone) in unison with one of the piano notes. The attacks are extremely exposed, and must be hit simultaneously. We were not succeeding. Structurally what is happening is quite clear. It’s a subtractive rhythm: 6 then 5 then 4 then 3 then 2 sixteenth notes between attacks. Since we weren’t hitting the rhythm together, I (in my wisdom as theorist), aware of empirical studies that suggest that metric subdivisions (such as 3e&a) are less directly controlled than beats,32 proposed that we make the attacks the beats, that is, that we count the subtractive pattern in sixteenths (123456, 12345, 1234, 123, 12, 1). My fellow quartet members ignored me politely. It wasn’t until we had several performances in which we did not hit those notes together that I realized that I was the problem. Counting the subtractive pattern 30 Redundancy is at the foundation of so much of our performative training (for instance, memory techniques), and I think different approaches to analysis could be seen in a similar light. 31 Geertz writes that “culture consists of socially established structures of meaning” (1973, 12). Alternatively, Turino defines “cultural cohorts” as “social groupings that form along the lines of specific constellations of shared habit based on similarities of parts of the self,” such as age, interests, and occupation (2008, 111–​12). 32 See, for example, Shaffer (1984, 580): “. . . the theory assumes two degrees of freedom in producing musical rhythm, one in timing the metre and the other in timing notes in relation to the metre.”

Example 0.2.  Throw Down or Shut Up! (Patrick Sutton, guitar; Daphne Leong, piano; Michael Tetreault, percussion; John Gunther, saxophones, flute, clarinet)

Example 0.3. Shende, Throw Down or Shut Up! opening. (score in C)

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did not help my accuracy. And as a classically trained pianist, I was “placing” the syncopations. My fellow musicians, a jazz saxophonist, a guitarist with much crossover experience, and a percussionist, were all laying the subdivisions down exactly. When I finally took a mini-​lesson with my percussionist, and started playing the pattern metrically and precisely—​not as a subtractive pattern (in other words, not according to structure)—​we hit it right on every time. This example gives rise to several issues. The metrical strategy may have succeeded simply because we were all thinking of the pattern in the same way, rather than because it was, intrinsically, a better method. But my reasoning about metric structure was faulty: cognitively it is simpler to entrain to the notated beat (eighth = 160 bpm, or quarter = 80 bpm), than to make the sixteenth-​note subdivision (at sixteenth = 320 bpm) the only referent, especially with relatively large and constantly changing numbers of sixteenths.33 In any case, the strategy that worked for my quartet did indeed run against the motto’s subtractive structure. Was structural understanding then of no use? Or worse, was it a hindrance? As an ensemble strategy, it did not work. But as an interpretive one, it did. Playing the passage as metrically notated helped us align our attacks. But playing it as a converging gesture helped us point its energies and bind those attacks together. The complementary tools of practical notation and structural underpinning helped us articulate a spring-​loaded gesture releasing on its final note. In our endeavors as theorists and practicing musicians, there are different kinds of knowledge. We might represent three of these using the German words wissen (knowing that), können (knowing how), and kennen (knowing, as in knowing a person).34 In terms of knowing that, one understands that Shende’s opening motto, which recurs and is transformed throughout the work, is a subtractive rhythm. One also hears that it consists of descending and ascending perfect fourths that converge on the final G♯. In terms of knowing how, our playing together requires the ability to precisely attack the subdivisions within the notated 5/​4 meter.35 But if we bring these two simple aspects of knowing that and knowing how together, we find that each deepens the other: we know how to shape the individual attacks into a converging gesture that explodes on its final note, and this knowledge-​how in turn helps us inhabit our knowledge-​that in an embodied and experiential way. Our



33 See, for example, London (2012, 46–​47).

Furthermore, different readings of notation were involved: I initially understood the marks on the page to mean something different (“placed” syncopations) than did my fellow quartet members. (Shende’s indication, “With Rhythmic Precision,” should have informed me otherwise.) 34 Thanks to David Barnett for bringing this elegant encapsulation of three ways of knowing to my attention. The distinction between “knowing how” and “knowing that” is Gilbert Ryle’s (1949, 2009). John Rink (1994, 112) refers to the French savoir and connaître in connection to analysis and performance. These three ways are but one formulation of types of knowledge; Östersjö (2017), for example, identifies three domains of knowledge in artistic research: artistic, embodied, and discursive. 35 While closely related, knowing how and ability cannot be equated. See, for example, Carr (1981), or Fantl (2014, 2.1).

Theme  17

knowledge is enriched and made multi-​dimensional, much as it is when one gets to know a person more deeply.36 Counterpointing the views of theorists and performers can bring all three kinds of knowledge into play. Musical structure—​in this book—​then becomes a prism through which musical intuition, dynamic experience, practical strategies, and score analysis collide, reflect, and refract.

Performing Knowledge Performing Knowledge is structured as a Theme and Variations. The nine variations are the case studies, each focusing on a single twentieth-​century work, and each co-​authored with a performer of the work in question (or, in two cases, with composers). Each addresses questions of structure. The first variation, on Ravel’s Concerto pour la main gauche, considers embodiment as a source of musical structure; the second, on Schoenberg’s Klavierstück Op. 19, No. 4, investigates structure created in interpretation, by performers and analysts; the third, on Bartók’s Fifth String Quartet, explores cultural dimensions of notational and hence structural understanding. These three variations move from performance to analysis. The following three variations move in the opposite direction, from analysis to performance. We interpret Schnittke’s Piano Quartet in light of the composer’s metaphor of memory, Milhaud’s “Aurore” from Trois Poèmes en prose in the context of poetic structure, and Messiaen’s Visions de l’Amen as ritual and drama. All three of these are pieces that I performed with my co-​authors, the first and third prior to conceiving this book project, and the second as part of it. The final three variations present divergent views of the relation between analysis and performance. In the first, on Babbitt’s Lonely Flute, processes of analysis and performance are juxtaposed and contrasted. In the second, on Carter’s Changes for Guitar, analysis and performance are closely intertwined. In the last, on Morris’s Clear Sounds among Hills and Waters, questions of musical structure are broached in the context of audience response both to my performance of Clear Sounds and to new music more generally. This final variation closes the circle of theorist-​ performer viewpoints with those of composer-​listener. These variations represent separate collaborative projects, and were undertaken at different times. The variations on Ravel’s Concerto and on Babbitt’s Lonely Flute were the earliest; they were published initially in Music Theory Online. While they have been updated and recontextualized for this book, the reader will notice that

36 Schachter (1994) compares getting to know a piece to getting to know a person—​going beyond surface impressions to understand the piece’s or person’s unique qualities. Various dimensions of knowing—​affective understanding, embodied knowledge, and so on—​can be included in these three ways of knowing. Wissen, können, and kennen are not intended to represent a theory of musical epistemology; I use them as helpful representations of different aspects of analytical and performative understanding.

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aspects of the Babbitt variation seem to step back in time, to a point when my collaborative approach was less than ideal. We have kept this text intact; the progression from our original text to our later writing reflects developments within performance scholarship in general—​that is, the embracing of performers as equals. Our early collaborations were, in a sense, pioneering. Collaboration between scholars and performers in research remains a complex undertaking. The opening “Counterpoint: Cross-​Disciplinary Collaboration” section theorizes some of the issues; the closing “Counterpoint” revisits them in light of the book’s collaborations. The question of voice, in particular, is vexing. Performers speak in different ways in this book’s chapters. At times we simply write together, at others we write separate sections, and at still others we blend our separate contributions or I write as primary author. The presentation of voice in writings such as this is still being worked through; recent publications from the series Studies in Musical Performance as Creative Practice present performers’ contributions as separate “Interventions,” “Reflections,” or “Insights,” interspersed with other chapters.37 Both process and product can be challenging when co-​writing across disciplines. A note on our use of recordings: we read them, in part, as texts of performers’ interpretations, employing close listening and simple empirical methods. Recordings, of course, can be heard and used in many ways (see, for example, DeNora 2000 and Guck 2006). In light of this book’s focus, we consider how particular recorded interpretations express musical structure, broadly defined. Finally, the title of the book—​Performing Knowledge—​is multivalent. We invite the reader to consider how the book brings together the performance of knowledge and the knowledge of performance in colloquy over structure. Performing Knowledge, in a sense, charts my personal journey in the exploration of relations between analysis and performance. As such, it is the journey of my interactions with my collaborators, many of whom are friends as well as colleagues and co-​ performers. The book is less a theory of analysis-​performance relations than a series of particular instances of them. In their diversity and particularity, these variations demonstrate distinct manifestations of our theme—​the interactions of a theorist with performers over questions of musical structure. Each variation is a collaborative experiment. And each is an opportunity to do what both analysis and performance do well: to grapple with particular pieces and to convey meaningful interpretations of them.

37 “Interventions,” “Reflections,” and “Insights” appear in Clarke and Doffman (2017a), Leech-​Wilkinson and Prior (2017), and Rink, Gaunt, and Williamon (2017), respectively.

Cross-​Disciplinary Collaboration In this chapter I explore how things and people enable and motivate collaboration across disciplines. I will call the things shared items and shared objectives, and the people shared agents. These three concepts draw from literature on collaboration in the sciences and from research on intercultural communication. My shared items and shared objectives are equivalent to what the literature on scientific collaboration calls “boundary objects,” “activity objects,” and “epistemic objects,”1 and my shared agents adapt ideas from writing on “third cultures.” The collaborations in this book counterpoint voices from the disciplines of theory, performance, and (sometimes) composition. In them, shared items are exemplified by musical scores, shared objectives by the book’s chapters, and shared agents by scholar-​performers or performer-​scholars. Here is a real-​life situation that demonstrates how a score may act as shared item, a concert as shared objective, and an analyst-​performer as shared agent. I present the scene here without explanation, theorize the things and people mentioned in the foregoing, and then return to the scene to view it through the lenses of these concepts. My fellow quartet members and I were rehearsing a difficult passage in Shende’s Throw Down or Shut Up! (Example 0.4). The texture was extremely busy, and we were getting lost—​not arriving at rehearsal C at precisely the same moment. I mentioned aural markers in my part, attempting to demonstrate by playing the sfz riffs in m. 23 while saying the beats (1 and 2) on which they occurred. One of my colleagues responded by saying that if we tried to adjust to one another, it would throw everything off. So we played the passage (which begins a few measures before Example 0.4) several times through together, without success. By the next rehearsal, I had taken a closer look. I came with copies of the score page, marked to highlight the passage’s governing riffs and points of convergence. (As with most chamber music, my colleagues played from their parts only; they did not see the entire score. Per the usual notational practice, as pianist I played from the full score.) When I distributed my “handout” (Example 0.4) illustrating 1 Boundary objects and activity objects represent Nicolini, Mengis, and Swan’s “secondary” and “primary objects of collaboration” respectively (Nicolini et al. 2012, 625). I am grateful to Matt Koschmann for introducing me to this literature. It investigates collaboration on such processes as the development of a bioreactor in biomedical engineering, the building of a research natural history museum, automotive product design engineering, and responses to the failure of a medical infusion pump.

Example 0.4. Shende, Throw Down or Shut Up! mm. 23–​26: marked-​up score as shared item.

Example 0.4 (cont.).

24  Performing Knowledge

what I had been trying to communicate verbally, everyone saw what had previously been conceptually and aurally opaque: that the passage was meant to foreground characteristic “funky” riffs (in rectangles on the example). There was instant buy-​ in. Our percussionist pointed out one riff that I had missed, and one misinterpretation of notation on my part, and our guitarist remarked that the piano-​guitar motive of m. 23 had characterized the piece earlier. After this exchange and our mutual discoveries, we—​for the first time—​played the passage successfully and solidly together. Structural knowledge (wissen) had been translated into knowledge useful for performance (können) and also transformed into musical understanding (kennen). (Please listen to Example 0.4 online  .)

Shared Items Boundary objects, which I  call shared items, were first theorized by Star and Griesemer (1989). Boundary objects have inspired a substantial body of research, but, as far as I know, have not been applied to the study of musical collaboration.2 I call boundary objects shared items because each such item, while possessing an identity that transcends domains, functions differently from one domain to the next. It is thus “shared” in that each domain defines the item’s function differently, but none “owns” the item exclusively. Renaming boundary objects as shared items “reframes them as positive images of the intersections in which they form: as active, resonant openings into collaboration, rather than as the boundaries of established . . . practices” (Theurer and Leong, forthcoming). “Item” is not an ideal choice of words, but may have fewer associations with concreteness than “object.” A shared item may be material, but it may also be abstract (Star 2010, 602). A theory, for example, can be a shared item. A few examples of shared items from the sciences may be helpful. The Museum of Vertebrate Zoology at the University of California, Berkeley, a research natural history museum, brought together the concerns of scientists, amateur naturalists, philanthropists, government officials, university administrators, curators, and museum patrons to develop a collection that supported research into speciation, environment, and evolution. Specimens and field notes acted as shared items—​ items around which work could coalesce (both amateurs and scientists collected specimens for the museum) but that meant something different to each party. The state of California also functioned as a shared item—​an item, in this case with literal boundaries, that constrained the activities of all parties but that held different meanings (geographic, political, ecological, personal, pragmatic) for each of them (Star and Griesemer 1989, 408–​11). 2 Assis (2014) identifies various musical “objects” (compositional materials, recordings, literature, instruments, the performer’s approach, the performer’s body) as boundary objects, that is, “objects that change their . . . nature depending on the context in which they are used” (41, 46), without explicitly mentioning that boundary objects mediate between “different social worlds” (Star and Griesemer 1989, 393).

Counterpoint  25

In automotive engineering, assembly drawings (three-​ dimensional CAD representations) can function as shared items. Carlile (2002, 449–​50) describes the case of a manufacturing engineer proposing a new structure to design engineers. With only a two-​dimensional design drawing, discussion stalled. With a three-​ dimensional assembly drawing, which reified the specifics of the proposal and the concerns at stake for both sides, the engineers were able to collaboratively find a solution that met both manufacturing and design requirements. Scores are exemplary shared items. They mediate between the musical worlds of composition, performance, and scholarship. They fulfill different functions within each of these domains, yet are recognizable and accepted across all of them. The same score can be, for the composer, a means of working out compositional ideas and a medium for transmitting a musical product; for the performer, a set of instructions to be interpreted and a portrayal of the sounds of the composition; for the theorist, a text representing musical material and processes to be studied, interpreted, and explained. All three communities share a general understanding of the score’s symbols and what they denote. Put another way, shared items facilitate cross-​boundary communication by establishing a shared language (syntax) in which knowledge can be represented, one that affords different usages or meanings (semantics) across boundaries. Because they reify within-​boundary concerns, they allow collaborators to identify differences and dependencies across boundaries and to clarify the implications of these differences. Take, for instance, Example 0.3, the opening of Shende’s Throw Down or Shut Up! For us as performers, the score’s metric notation directed our conceptions of the passage, as well as our approach to playing it. For me as theorist, the metric notation itself was incidental, serving as a practical means to express a subtractive durational succession. These two interpretations of the “same” score passage informed können (knowing how), on the one hand, and wissen (knowing that), on the other. I argued earlier that the counterpointing of these two viewpoints led to kennen (knowing, as in knowing a person). Shared items facilitate joint transformation of knowledge in just such ways. From within-​domain knowledge, they generate new cross-​domain knowledge and hence new shared language (Carlile 2002, 451–​53). I view shared items performatively. This approach comes from “action-​net theory” in the organizational literature, which focuses on how actions, objects, and quasi-​objects (such as organizational units) connect. It sees shared items (“boundary objects”) as “objects-​in-​use—​not as stable entities, but as enacted ones. . . . There are no objects that are boundary ‘by nature,’ just objects which, in a particular time and place, function as boundary objects” (Lindberg and Walter 2012, 1–​2). So shared items are enacted and their meanings constructed; it is only when they are thus “performed” that they take part in the ongoing practices of composition, analysis, and performance. A slight aside here: while scores functioned as our main shared items, recordings also performed this role. In our chapter on Bartók’s Fifth String Quartet, for

26  Performing Knowledge

instance, multiple recordings of a single passage allowed me and members of the Takács Quartet to explore different interpretations of rhythmic notation. Other types of shared items have, historically, played significant roles in musical study, but these were not central to our work. For example, the musical “work” (a much contested concept) exemplifies what Star and Griesemer (1989, 410–​11) and Star (2010, 608) call an “ideal” or “Platonic” type of shared item. If the musical work is understood as a collection of objects (various versions of a score, performances through history, interpretive traditions passed down through generations, and so on), it is a “repository” type of shared item (Star and Griesemer 1989, 410). Shared-​item theory assumes that multiple domains are valuable and that collaboration among them is worthwhile. A shared item is a means of translation (Star and Griesemer 1989), mediation, or transformation of concerns or knowledge across boundaries. It is the interactions between domains that animate performance and analysis. Such interactions, of course, do not necessarily involve agreement. Star and Griesemer (1989, 404) pose six strategies for collaborating when views diverge. These include using various types of shared items, employing shared items in particular ways, and choosing certain working arrangements. From their list I extract the three strategies most pertinent to our discussion: (1) using versatile shared items adaptable to the purposes of each domain; (2) working in parallel except for limited interactions of standard types; (3) working in relatively independent stages. A crude illustration of strategy (1) is that scores can be viewed—​for analysis—​as texts, and—​for performance—​as scripts. Strategy (2) (working in parallel) characterized the process for our chapter on Babbitt; that is, as theorist and flutist, we each learned Babbitt’s Lonely Flute independently, analyzing it and preparing it for performance respectively. We then, however, attempted to go beyond the most limited and standard type of exchange by having our views and experiences interrogate one another as we co-​wrote the chapter. Strategy (3) can represent what some early performance and analysis writings are criticized for: analysis prior to, and directing, performance.3 Shared items can lessen the need to learn across boundaries; they allow each domain to operate in partial ignorance of other domains. “This is because they carry details that can be understood by both parties, but neither party is required to understand the full context of use by the other party because the object itself takes care of performing such mediation” (Nicolini et al. 2012, 617). A scholar and a performer, for example, can collaborate on analyzing a Beethoven sonata without the scholar needing to grasp the nuances of the pianist’s performance, and without the performer needing to understand the details of the theorist’s Schenkerian graph. 3 Other, less collaborative, strategies for managing differences include unilateral imposition, coercion, silencing, and fragmentation (Star and Griesemer 1989, 413).

Counterpoint  27

A corollary of this principle is that shared items allow cooperation without consensus (Star and Griesemer 1989, 413). The scholar and performer may have distinctly different interpretations, yet still be able to work together through the mediating function of the score. I theorize that shared items allow cross-​domain collaboration at three levels of convergence: (1) working in parallel; (2) “translating” or mediating different views such that the two domains influence one another; (3) transforming existing domain-​ specific knowledge to create new cross-​ domain knowledge. All three of these levels occur in this book.

Shared Objectives: Activity Objects and Epistemic Objects My shared objectives include both activity objects and epistemic objects. Activity theory conceives of activity objects as “prospective outcomes that motivate and direct activities, around which activities are coordinated, and in which activities are crystallized . . . when the activities are complete” (Kaptelinin and Nardi 2006, 66). The activity object—​the co-​authored chapter in our collaborations—​motivates and organizes the community that develops around it. “The division of labor, the rules and tools to be used, and the position and identity of each member . . . all depend on the particular object of work”; some members will be “more equal than others” (Nicolini et al. 2012, 621–​22). Activity theory considers the cultural, ideological, and discursive practices surrounding collaborations. For academics, publication is an obligatory goal. Carlile (2002, 446) writes about “objects” and “ends” in practice, ends being the outcomes that demonstrate success in the manipulation of objects. For academics, then, ends are published results. For performers, ends are performances or recordings.4 The end in our collaborations—​a published chapter—​is academic and not performative. Therefore it holds varying power as an extrinsic motivator for co-​authors. Performers who have deeper experience with and buy-​in to academic publishing more readily understand the principles and practices that govern it. It is only natural that among co-​authors, commitment to the publication process itself varies. For intrinsic motivation, I turn to another type of objective. Epistemic objects are objects of investigation. In the sciences, epistemic objects are material—​a sensor that

4 The landscape is shifting with the advent of artistic research.

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is being developed, for example.5 In our collaborations, they are the interpretations—​ analytical, performative, and in-​between—​that we develop of the pieces under investigation, and of the relations between analysis and performance and analyst and performers. Epistemic objects “embody what one does not yet know” (Rheinberger 1997, 28); their incompleteness fuels attachment and emotional investment (Knorr Cetina 1997, 12–​15). Generating questions and trying to answer them creates a collaborative community. But the degree of interest and hence investment generated by the epistemic object varies from collaborator to collaborator. We may compare our collaborative processes to experimental systems, used to model scientific practice. Experimental systems “are systems of manipulation designed to give unknown answers to questions that the experimenters themselves are not yet able clearly to ask. Such setups are . . . not simply experimental devices that generate answers; experimental systems are vehicles for materializing questions.” Experimental systems are not givens, but are arrived at laboriously. Further, “any simple case [in our situation, the chapter representing our collaboration] is the ‘degeneration’ of an elementarily complex experimental situation.” Our chapters “channel the noise produced by the research arrangement”; they oscillate between “density” and “articulation,” between messiness and definition.6 Returning to the activity object, each chapter of this book is a “problem space”: theorist and performers bring different skills and conceptual tools to its negotiation. The community created by the chapter is far from an “integrated whole,” “a smooth fusion of intents and goals” (Nicolini et al. 2012, 621–​22). Rather, it holds in tension conflicting interests and expectations. For us, conflicts included issues of content, voice, writing style; questions of role and contributions; points of procedure and timeline. The activity object itself is therefore inherently heterogeneous (being grounded in distinct professional practices), its methodologies at potential cross-​purposes and its contents conceivably contradictory. The contradictions keep the object in flux as the practices and expectations of participants evolve. Collaborative activity is “maintained around the pursuit of a partially shared, partially fragmented, and partially disputed object.” The object is partial, not visible as a whole to any single participant (Nicolini et al. 2012, 614, 621), socially constructed, and emergent. This was true of our collaborations: the content and shape of each chapter was never clear at the outset, expectations shifted constantly, and revisions were legion, negotiated, and sometimes contested. Our activity objects—​the chapters—​were thus partly given (as obligatory publication) and partly emergent (from the interests of participants). Because the chapters represent divergent interests, they contain “traces of multiple viewpoints, translations, and incomplete battles” (Star and Griesemer 1989, 412–​13). 5 Rheinberger (1997, 28) defines epistemic objects as “material entities or processes—​physical structures, chemical reactions, biological functions—​that constitute the objects of enquiry.” Rehding (2016), adapting Rheinberger’s “epistemic thing,” explores musical instruments as tools for music-​theoretic inquiry. 6 Rheinberger (1997, 28, 26, 106). Assis (2014) and Schwab (2014) discuss Rheinberger’s experimental systems in the context of music performance and artistic research.

Counterpoint  29

In the overall process, the exchange itself at first acted as motivator: “let’s collaborate and see what it will show us.” For an end to be achieved, however, this goal needed to be superseded by an epistemic object that would drive the search for knowledge. This emergent object became the attractor for attempts to understand, explain, and model—​the piece, relations between performance and analysis, or our collaborative processes. Our epistemic objects and activity objects worked in tandem, the one providing intrinsic motivation, the other supplying extrinsic motivation. Decisions about how to mediate divergent interests shaped not only the collaborative process and relationships, but also the content of our findings. This is a performative, action-​net, perspective on performance and analysis: collective actions (scores, performances, analyses, interpreters) continually connect and reconnect to one another, and become co-​constructed and enacted (Lindberg and Walter 2012, 1–​2). In the process, new syntaxes are developed, meanings translated and negotiated, and knowledges juxtaposed and transformed. I return to my rehearsal story, in which my score “handout” provided the key for ensemble success. The marked-​up score page acted as shared item between me, who could see the interrelations of parts, and my fellow quartet members, who could see only their individual parts. It also mediated between me, who (from my chamber-​ music and accompanying experience) was used to listening for and adjusting to various parts in coordinating an ensemble, and my colleagues, who were used to laying down a steady beat and following that as their guide. The marked-​up score allowed our ensemble to move from my first level of collaboration (collaborating by working in parallel) to my second level (translating or mediating different views such that the two domains influence one another), emerging at my third level (transforming existing domain-​specific knowledge to create new cross-​domain knowledge). At the first level, each individual played his or her part as faithfully as possible, hoping that we would line up in accordance with the (invisible) score. At the second level, my colleagues understood the riffs defining the passage’s structure, realized what the structure meant practically, and added to and corrected my observations; the marked-​up score had reified my previously opaque statements in concrete relationships that all could see. At the third level, the new conceptual knowledge allowed us to hear what we had not heard before, and to meaningfully sync our playing. This experience produced a sense of team triumph over what had been a persistent obstacle. We had surmounted the challenge collaboratively. The objects that had fueled this collaborative success were the shared item (the annotated score), the epistemic object (playing the passage well), and the activity object (the concert for which we were rehearsing). In classical music-​making, the score is so basic to what we do that its fundamental functions are almost invisible:7 performers learn pieces from scores or parts 7 Such invisibility of “means” has been described as constituting “the tacit dimension of activity” (Miettinen and Virkkunen 2005, 451).

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of scores, scholars study scores and their various instantiations. Modeling scores as shared items sheds new light on the functions that scores perform as they are enacted in composition, performance, and scholarship. But what about my personae as theorist and performer: What role did they play in our problem-​solving process?

Shared Agents I have already posited the worlds of theory and performance as different cultures. I now draw upon the concept of “third culture,” first theorized by Useem, Useem, and Donoghue (1963) and later developed by writers such as Casmir (1978, 1993) and Casmir and Asuncion-​Lande (1989). Useem et al. (1963, 169) defined the “third culture” as “the behavior patterns created, shared, and learned by men [sic] of different societies who are in the process of relating their societies, or sections thereof, to each other.” A third culture brings two cultures together and creates new, composite patterns of behavior by navigating underlying similarities and fundamental differences. It can be understood only by referencing its originating cultures, but it is more than the sum of its parts.8 With regard to performance and analysis, we can apply this concept on three tiers: (1) the meeting of disciplinary communities (of scholars and performers), (2) the scholarship or practice of relating performance and analysis, and (3) people who are themselves bicultural (scholar-​performers or performer-​scholars) or involved in ongoing interactions between the two cultures. Although all three tiers interconnect, this section focuses on the third tier. Toward the end of the book I will address the first and second tiers directly. I will use the term multicultural in lieu of bicultural, since it includes biculturalism without being restricted to only two cultures. (Some musicians are theorists, composers, and performers, for example). We can distinguish between people with multicultural competencies and those with deeper multicultural identities. For example, Heyward 2002 (16–​17) models intercultural literacy on a multilevel scale. On the first three levels, people are largely unaware of other cultures, interact with them superficially, or view them stereotypically and judgmentally. On the fourth level, they demonstrate meaningful cross-​cultural engagement, competencies, and regard for different cultures. And on the fifth level, they possess insider knowledge of multiple cultures, and profess a multicultural or transcultural identity.

8 Casmir and Asuncion-​Lande (1989, 289, 294). Yoshikawa (1987) provides a “double-​swing model” of intercultural encounter, depicted with a Möbius strip. He envisions two cultures meeting in a dynamic back-​ and-​forth process that retains and sharpens the uniqueness of each culture: a mutual relation that preserves a dynamic tension. Later writers also applied the term “third culture” to those who spend a significant part of their developmental years outside of their parents’ culture (Pollock and van Reken 2009, 13 [1999], and many following writers). This is a specific usage that I do not employ here.

Counterpoint  31

Multicultural people view themselves in complex ways that include blended and multiple cultural identities and behaviors. They can slip easily from one cultural frame to another, in attitude or in action.9 Adler (1977, 26, 37) describes such people as living “on the boundary,” characterized by “a fluid, dynamic movement of the self, an ability to move in and out of contexts, and an ability to maintain some inner coherence through varieties of situations.” One could call them boundary people, to relate the concept to that of boundary objects.10 Since I have called boundary objects shared items, however, I will call such individuals shared agents. One could think of them as double agents (or triple, or quadruple, agents), but for the fact that they do not generally act undercover. Like shared items, shared agents function both within cultures and across them. They meet role requirements within cultures, while possessing a recognizable identity across cultures. Their roles are more clearly defined within cultures, less so across cultures. Scholar-​performers and performer-​scholars, as well as those with high competencies in both theory and performance, are shared agents. Also like shared items, shared agents enable cross-​boundary translation, mediation, and knowledge transformation. “A critical role for this type of individual is to serve as a link, as a facilitator, and as a catalyst for contact and change within and between cultures. These individuals build bridges to connect segments of various cultures. . . . They serve as translators . . . and interpreters . . .” (Casmir and Asuncion-​Lande 1989, 295). But Useem et al. (1963, 170, 177, 179) note that “a bridge . . . is worthless unless pathways and roads link the bridge with segments of both societies.” That is, if shared agents act as bridges, people not expressly identified with the third culture, yet with affinities for it, can serve as pathways to more remote segments of their home cultures. Such people often have broader access to, deeper understanding of, and greater “social capital and credibility” in their home cultures than do third-​ culture individuals. Third-​culture persons may not accurately represent first and second cultures. Since their cultural makeup is hybrid, their views do not come from any single culture. This is why it is important, in relating performance and analysis, to consider the views of performers who are not also scholars or researchers, and to consider the views of theorists without performance proclivities.11

9 Moore and Barker (2012, 559, 557); see also Nguyen and Benet-​Martínez (2010, 97). Benet-​Martínez et al. (2002) distinguish between bicultural individuals who view their cultural identities as compatible and those who consider them to be in opposition. This perception significantly affects “cultural frame switching,” that is, how such persons shift between cultural interpretive frames and behaviors in response to contextual cues. The term “cultural frame switching” comes from Hong et al. (2000, 709–​10). 10 This boundary person differs from the boundary spanner of organizational literature. The essential characteristic of the boundary spanner is an ability to link two domains (see Williams 2002, 109–​13, for an overview of key traits), whereas that of a boundary person is competency in, or identification with, two domains. 11 In this book, the latter come into play through references to theoretical literature. I acknowledge, of course, that “pure” cultures of performance and theory, without the influence of one another, do not exist.

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Finally, third cultures, like other cultures, can be transmitted.12 In the case of performance and analysis, such passing on can occur through role modeling (by performers, by theorists, and by collaboration between them), implicit teaching (that links the two domains in the studio, in the classroom, and elsewhere), or explicit teaching (through performance-​ and-​ analysis courses, course units, and 13 workshops). I return once again to the rehearsal anecdote, where I was functioning—​perhaps?—​ as a shared agent. Certainly I  was using analytical knowledge (wissen) of the passage’s texture, its rhetoric, and its motivic interconnections, and communicating it to my fellow performers in a way that spoke to them and that enabled performative ability (können) and interpretive understanding (kennen). One might say that I was speaking as a theorist to my performer colleagues. But I wasn’t—​that wouldn’t have worked. I needed to speak in a language that made sense to my colleagues. Furthermore, the analytical knowledge demonstrated in Example  0.4 is very straightforward. There is nothing highly theoretical about it, and I  would guess that any competent musician looking at the score and aware of the piece’s general vibe, drive, and fabric, would make similar observations. A certain mindset and willingness to examine the score are required, but those are certainly not theorists’ prerogatives! Thus, Example 0.4 is not a clear-​cut illustration of a theorist-​performer shared agent, in the sense of demonstrating knowledge that clearly lies in one domain being translated into knowledge unambiguously in the other. And in fact, analysis and performance is just like this in real life. We do music and musicians of all kinds a disservice if we make black-​and-​white distinctions between Analysis and Performance, Theorists and Performers—​for performers analyze and theorists perform, if perhaps to different degrees and in different ways. So pursuing questions of analysis and performance means examining those questions on the boundary as well as those in the interior—​and all the grey areas in-​between. And it means involving those in the “third culture” per se and those in the first two cultures. Otherwise we understand only a narrow strip along the two domains’ boundaries, and not the interactions of the two cultures per se.



12 See Casmir (1993, 422); and Useem, Useem, and Donoghue (1963, 172), for example. 13 See Leong (2018).

1 Determination of Structure

Performers’ Voices on Ravel’s Concerto pour la main gauche Daphne Leong and David Korevaar

This chapter updates an article first published in Music Theory Online. The original article (2005) confronted the absence of the performer in performance-​and-​ analysis literature of the day—​still a problem that the current book addresses more systematically. We invite the reader to begin by viewing Video 1.1 , Daphne Leong playing the opening cadenza of Ravel’s Concerto for the Left Hand. At the time that we wrote this article, much of the performance and analysis literature fell into two categories: the first presented analyses and their implications for performance, and the second studied performances (usually sound or video recordings). In neither area were performers actively involved as producers of the research. We wrote, “With rare exceptions, existing analytical literature on performance studies texts: the score, recorded performances or experimental sessions, or even recorded performers’ interviews or commentaries. Performers, when included, are usually objects of study; rarely do they have a voice in the research that is produced.”1 Our article sought to turn the influence arrow in the opposite direction. In contrast to Janet Schmalfeldt’s (1985, 2) challenge to analysts to develop “a comprehensive critique of the value and the limitations of analysis for performance,” we wished to explore the value and limitations of performance for analysis. Rather than asking how an analyst could contribute to the performance of a work, we asked what a performer could contribute to its analysis.

1 Work was beginning to be done in this area. For example, Leong and McNutt (2005) explored Babbitt’s None but the Lonely Flute from the points of view of theorist and flutist; Eric Clarke and Nicholas Cook coauthored a study of Bryn Harrison’s être-​temps with the composer and the work’s commissioning performer, Philip Thomas (Clarke et al. 2005). More recently the issue of performers’ voices is raised in literature such as Doğantan-​Dack (2008). Daphne Leong and David Korevaar, Determination of Structure In: Performing Knowledge. Edited by: Daphne Leong, Oxford University Press (2019). © Oxford University Press. DOI: 10.1093/oso/9780190653545.003.0003

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We took the opening cadenza of Ravel’s Concerto for the Left Hand as a case study. (The one-​movement concerto contains two cadenzas; a second occurs near the work’s conclusion.) We were particularly interested in exploring the work as “something that you do” (Cusick 1994, 18).2 And we wanted to consider performers’ implicit analyses.3 In this case, performance considerations—​technical, visual, and affective elements—​wove warp and weft not only of the Concerto’s playing, but also of its structure and meaning. We were able to speak both from personal experiences of having performed the Concerto and from insights provided by historical recordings of the work. The Appendix to this chapter lists recorded performances of the Concerto by pianists with some association with Ravel: Jacqueline Blancard, Robert Casadesus, Alfred Cortot, Jacques Février, Vlado Perlemuter, and Paul Wittgenstein.4 The recordings are of particular interest because of their connections (although sometimes tenuous) with the composer.5 Asterisks indicate those recordings to which we had access, and to which we refer in the following analysis.6 Information on each pianist and his or her connection with Ravel is given at the end of the Appendix. We now explore the cadenza: visual and kinesthetic aspects, rhetorical and tonal function, form and structure, rhythmic features and performance issues. * * * On a fundamental level, the physical in this Concerto constrains the structural. Maurice Ravel felt that “the music of a Concerto . . . should be lighthearted and brilliant, and not aim at profundity or at dramatic effects” but, because “in a work of this kind [the Concerto for the Left Hand] it is essential to give the impression of a texture no thinner than that of a part written for both hands, . . . I resorted to a style which is much nearer to the more solemn kind of traditional Concerto.” “The 2 Mead (1999) extends the concept of works as products of physical actions to the experience of listener and composer. Le Guin (2002) explores embodied performance in Boccherini’s chamber music; Berry (2009) discusses physical gesture in Gubaidulina’s writing for low strings; Doğantan-​Dack (2011) focuses on the performer’s experience of bodily motion; Laws (2014) experiments with the interface between physical gesture and meaning. Physical gesture is investigated in Gritten and King (2011) and Godøy and Leman (2010). See also De Souza’s (2017) exploration of interfaces between instruments, bodies, and musical organization. 3 Writers such as Meyer (1973, 29) and Rink (1990, 323) have commented on “performer’s analysis.” Rink, for example, states that “good performers are continually engaged in a process of ‘analysis,’ only . . . of a kind different from that employed in published analyses. The former sort of ‘analysis’ is not some independent procedure applied to the act of interpretation: on the contrary, it forms an integral part of the performing process.” Chaffin, Imreh, and Crawford (2002) illuminate “performer’s analysis” in the course of a study of expert practice and memorization; Wise, James, and Rink (2017) explore creative processes in the practicing of advanced students. Bazzana (1997, 87–​89) provides insightful study of Glenn Gould’s approach to performance. For a sampling of performers’ writings on their processes of preparation, see Sherry (2002) on contemporary music, Hill (2002) on the role of score study, and Helffer (2010) on the music of Xenakis. 4 Touzelet (1990) provides a partial listing of such recordings, with a description of each performer’s relation to Ravel. See also Jozaki (2000, 342–​46) for a discography that includes historical recordings. 5 Clearly, the degree to which these (and any) recorded interpretations represent Ravel’s desires varies greatly. For example, Ravel objected strenuously to Wittgenstein’s performances of the Concerto because the pianist took flagrant liberties with the score (Touzelet 1990, 593–​95). Woodley (2000) discusses performance practice in Ravel. 6 We do not discuss Wittgenstein’s film clips.

Ravel’s Concerto pour la main gauche  37 Example 1.1. Ravel, Concerto pour la main gauche, opening cadenza, m. 57.1.

most formidable aspect of the problem . . . is to maintain interest in a work of extended scope while utilizing such limited means” (Orenstein 1990, 477, 396). The left-​handedness of the Concerto, then, dictated its dramatic affect (in stark contrast to the divertissement character of Ravel’s G major Piano Concerto, written at the same time) and its one-​movement length. The Concerto’s left-​handedness is essential. Ravel disapproved of Alfred Cortot’s two-​handed rendition (Orenstein 1990, 327), for the Concerto centers upon the particular challenge of playing with a single hand. It exploits the left hand’s capabilities and stretches them to their limits. Roland-​Manuel’s “aesthetic of imposture” is relevant here: “Pour que notre attente soit à la fois satisfaite et trompée, le musicien doit user de l’équivoque et l’ambiguïté.” “ ‘Quoi?’ . . . ne sert que de prétexte au ‘Comment?’ ”7 We expect two hands, and we hear them—​rendered by one hand. The Concerto is about the left hand masquerading as two hands, and hence about the distance between the physical and the musical. To no one is this more evident than to the performer. Example 1.1 (Video 1.2 ) shows the left hand leaping between two lines, playing the roles of two hands and maintaining the illusion of two contrapuntal lines. Example 1.2 displays one instance of the Concerto’s first theme. This example provides several illustrations of the left hand’s multiple roles. The performer must give the illusion of a legato singing line with the use of thumb-​only on the melody. A true legato is impossible using only one finger; this legato line is made even more impracticable by the left hand’s leaps to the bass register. The passage is further complicated by accompanying harmonies too wide for the average hand (circled); these chords must often be split. Yet Ravel also endows the passage with characteristics true to the left hand. The thumb-​only melody exploits the thumb’s ability to produce a rich full tone. The theme’s casting for one finger alone heightens the performer’s sense of the expanding leaps leading to the peak of the melody. And the physical motion between melody

7 So that our expectation can be fulfilled and fooled at the same time, the musician must use the equivocal and the ambiguous. ‘What?’ only serves as pretext for ‘how?’ (Roland-​Manuel 1925, 20–​21; DL’s translation). “Imposture” has taken on negative connotations of fakery, trickery, and superficiality in Ravel scholarship (see, for example, Kaminsky 2011 and Kelly 2011), but this is not the sense in which we use it. Rather, we emphasize the fulfillment of expectation with unexpected means, and the compositional and performance mastery implied by this challenge.

38  Performing Knowledge Example 1.2. Ravel, Concerto pour la main gauche, opening cadenza, Theme 1 (mm. 36–​44).

on beats one and three, and sarabande-​like bass on beat two, creates a palpable rhythmic “groove.”8 (Please view Video 1.3  .) These parallels and conflicts between physical and musical narratives create meaning for the performer, and, insofar as the (in)congruences are displayed, for the audience member as well.9 In the Vivo passage of the earlier Example 1.1, the visual contrast between physical motion and linear strands contributes to the drama of the passage. As the distance between the two contrapuntal strands increases, so does the physical demand on the performer and the visual drama for the audience member. Other incongruences, however—​the illusory (one-​fingered) legato and split chords of Example 1.2—​should be concealed. The physical and visual omission of the right hand brings aesthetic issues—​“unusualness” and the challenge of limitation—​into play. An analysis merely of the sounds represented by the score would surely bypass what lies at this Concerto’s heart: the left hand’s immensely successful portrayal of two hands at work.10 8 Ravel frequently borrowed from older dance forms—​menuet, pavane, forlane—​as well as more contemporary ones—​waltz, habanera—​as evidenced by his works Menuet antique, Pavane pour une infant défunte, “Forlane,” “Rigaudon,” and “Menuet” movements from Le Tombeau de Couperin, Valses nobles et sentimentales, and “Habanera” from Sites auriculaires. 9 Here we assume a live or video performance. Some sources, such as Cone (1974, 137), consider the visual aspect of a performance to be intrinsic to it. According to Stravinsky (1936, 114), “the sight of the gestures and movements of the various parts of the body producing the music is fundamentally necessary if it is to be grasped in all its fullness.” Schutz and Manning (2012) provide evidence for obligatory multimodal synthesis, such that what is seen affects what is heard. A sizable literature addresses concepts of embodied cognition, listener mimesis, or “kinesthetic empathy” between players’ physical efforts and listeners’ responses (Godøy 2018, Cox 2016, Mead 1999, Shove and Repp 1995, for instance). See also MacRitchie et al. (2013) on the relation of performers’ movements to musical structure, and Davidson (1993, 1995, 2007, 2012, for instance) on their expressive effects; Laws (2014) critiques inferred intention in empirical studies of musicians’ gestures. Gritten and King (2006, 2011) and Godøy and Leman (2010) address both physical gesture and its perception. 10 When I (DL) had students listen to multiple recordings of the work, several asked if it was indeed played with only one hand. Janina Fialkowska, a Canadian pianist who had severe left-​hand injuries, has performed this work with her right hand—​a feat that raises complicated interpretive issues.

Ravel’s Concerto pour la main gauche  39

Overview of the Cadenza The opening cadenza of the Concerto performs the rhetorical function of announcing the soloist and establishing his or her authority:  clarifying key, presenting and transforming thematic material, and establishing a wide keyboard range. The cadenza provides striking proof of the one-​handed pianist’s keyboard prowess: having one hand is no handicap, since this pianist can traverse the entire keyboard and make as wide a variety of noises as any two-​handed performer. (Compare this piano entrance to that in Ravel’s G-​major Concerto:  in the two-​ handed concerto, the soloist begins the piece as part of the orchestra and is initially confined to a high register.) We have divided the cadenza into four sections. (Please see Example 1.4, which is a continuous score of the complete cadenza. We refer to this example throughout our discussion.) With the Opening Gesture (OG) (Example  1.4a), the pianist arrives with a flourish. Then, the stage set, the soloist “sings” the lyrical Theme 1 (T1) (Example 1.4b), with its lush harmonies. Theme 1 transforms into the majestic and fanfare-​like Theme 2 (T2) (Example 1.4c), featuring full dynamic, octave doublings, and double-​dotting, and building to a virtuosic passage

Example 1.3. Ravel, Concerto pour la main gauche, orchestral introduction. (a) beginning

(b) end (orchestral reduction by Ravel)

40  Performing Knowledge Example 1.4. Ravel, Concerto pour la main gauche, opening cadenza. (Subdivisions of Ravel’s measures are numbered with decimal points for reference. Decimal places indicate ordering only, not proportional divisions of the measure.) (a) Opening Gesture (OG)

Ravel’s Concerto pour la main gauche  41 Example 1.4 (cont.). (b) Theme 1 (T1)

(c) Theme 2 (T2)

(Continued)

42  Performing Knowledge Example 1.4 (cont.). (c) (cont.)

Ravel’s Concerto pour la main gauche  43 Example 1.4 (cont.). (d) Closing Gesture (CG)

of dramatic leaps. The increasing intensity culminates with the Closing Gesture (CG) (Example  1.4d), comprising virtuosic scalar passages, noisy tremolandos, and a dramatic glissando. We now dissect this initial description. OG and CG bookend the cadenza, framing its thematic content (T1, T2) with virtuosic gestures. Example 1.5 compares and contrasts the OG and CG. Both are predicated on pitch class A, closing with a motion to D. OG inhabits the white-​key pentatonic {GABDE} exclusively, while CG presents a combination of A Mm7 (with flat 9) and black-​key pentatonic. Both OG and CG claim a large keyboard range and traverse their ranges with equivalent pitch contours: up-​down-​up, followed by a low register motion to D.11 The fast initial “up” establishes the range, the slower “down” explores it in a more leisurely

11 In the CG, the low register motion to D occurs in the orchestra.

44  Performing Knowledge Example 1.5.  Comparison of Opening and Closing Gestures (OG, CG) in Ravel, Concerto pour la main gauche, opening cadenza.

fashion, and the final “up” builds to the arrival of tonal center D.12 As rhetorical gestures, OG and CG differ: since the OG presents and establishes the soloist, it unfolds more expansively and more comfortably, on the white keys, while the CG, as the culmination of tension built up through T2, is more compressed in time and more awkward, with fast black-​key passagework. Tonally, the two gestures move from dominant to tonic in D. The “V”–​I motion of the OG is shown in Example 1.4a, mm. 35–​36. This arrival on the tonic D—​the first of the Concerto—​provides a strong sense of resolution after the harmonic 12 Wittgenstein (1937) ends his final glissando (CG) on pitch A7 rather than D7, ignoring the parallel between OG and CG, and undermining the drive to the work’s tonal center.

Ravel’s Concerto pour la main gauche  45

ambiguity of the preceding orchestral introduction. The resolution, however, is an “imposture,” on three counts. First, as mentioned earlier, the OG motion from A to D occurs entirely in a pentatonic collection {GABDE}; it thus lacks the force and leading tone (C♯) of a true V–​I cadence in D major. Second, the pianist appears to attack the arrival on D (m. 36, downbeat), but in fact does not. Rather, the pedal is cleared, allowing D to emerge from the clamor of the pedal A (much as the contrabassoon earlier emerged from the cello and bass murk of the opening). The downbeat D is thus revealed rather than actually being sounded. (Video 1.4 demonstrates this passage.) Third, the OG’s arrival on the tonic acts merely as an interior cadence, a way-​ station en route to the V7 of the CG (Example 1.4d, m. 57.2). This long-​awaited V7—​the work’s first complete dominant chord—​resolves to I  at the orchestral reentry (mm. 58–​59), combining tonal resolution with timbral, thematic, and formal emphasis.13 The result is a “structural downbeat” following on the heels of the “expanded upbeat” comprising the orchestral introduction and opening cadenza.14 The particular nature of this structural downbeat derives from the solo piano’s materials: the orchestra’s bass D arrives late just as the piano’s bass D did in T1. The lateness mandated by the pianist’s one-​hand limitation thus carries over to the orchestra, which has no such physical limitation. The underlying harmonic progression of the cadenza is thus “V”–​V7–​I. The cadenza clarifies the tonal function of the preceding orchestral introduction. As shown in Example 1.3a, the Concerto begins ambiguously, with a divisi sonority of stacked fourths {E,A,D,G} played softly by celli and double basses in their lowest registers. The sound emerges gradually, as if it has been going on for a while before the listener becomes aware of it.15 Thematic material (not shown) emerges slowly in the contrabassoon and passes eventually to upper winds, brass, and strings. Dynamic and texture build, culminating, as shown in Example 1.3b, in the final chord of the orchestral introduction, a re-​orchestration of the opening chord {E,A,D,G} over an E pedal. (Please listen to Audio 1.1 .) The pianist’s entry (Example 1.4), with its forthright articulation of the dominant, answers the harmonic ambiguity and timbral build-​up of the orchestral introduction. It is only here that the tonal function of the orchestral introduction—​supertonic—​becomes clear. The entire introduction to the Concerto (including the opening cadenza) articulates a large-​scale supertonic–​ dominant–​tonic progression: large blocks of pedal tones move from E (orchestral introduction) to A (cadenza’s OG and CG) to D (orchestral re-​entry).16 This E–​A–​D motion is foreshadowed by the opening arpeggio in the double basses. 13 This relatively traditional use of V7–​I is rare in Ravel’s oeuvre, and is more characteristic of late works such as the two piano concertos. In general Ravel avoids clear statements of dominant harmonies, or resolves them in other ways. (See Teboul 1987, 67–​84, for examples of Ravel’s resolutions by tritones or major thirds.) 14 These terms were introduced by Cone (1968, 24)  to explain the function of “integrated introductions.” 15 Ravel uses a similar strategy elsewhere, particularly when evoking water, as in Une Barque sur l’océan and Ondine. 16 The progression recalls the harmonic motion of a traditional Classical cadenza (cadential 6/​4 to V to I). Ravel’s cadenza also resembles Classical cadenzas by closing a formal section, in this case, the Concerto’s introduction. (In Classical works, of course, the cadenza generally concludes a section preceding the coda or final ritornello.)

46  Performing Knowledge

Pianistic Considerations The OG and CG frame an exposition of thematic material in which the piano takes over, clarifies, and transforms themes that had first appeared in the orchestral introduction. In the pianist’s version, the two themes differ markedly in melodic vocabulary. While the first theme (Example 1.6) moves primarily by major second, perfect fourth, and perfect fifth, the second theme (Example 1.7a) focuses on minor second, major second, and minor third. Since the melodies are played with the thumb only, each interval requires a corresponding arm motion, and the pianist experiences intervallic distances physically as well as aurally.17 The cadenza brings several interrelated pianistic considerations to the fore: dynamics, pedaling, and voicing. Example 1.4c shows one problem in dynamics. The second theme (see especially mm. 54–​56) increases in dynamic as it rises in register, contradicting the piano’s property of decreasing in resonance with rising register. The primary melody notes enter before their supporting bass notes, compounding the problem. The pianist must compensate for this contradiction between desired musical effect and instrumental properties by carefully rationing the crescendo; the strain of rising register and increasing dynamic also contributes to the building intensity of this passage. (Please view Video 1.5  .) The separation of bass and melody creates a need for pedal, and the added dilemma of how to pedal. As shown in Example 1.4, Ravel marks pedaling in OG and CG.18 In both OG and CG, the marked pedaling reinforces the underlying pedal A. In the OG (Example 1.4a), for example, a single sustained pedal holds the initial bass A0-​A1 through the entire opening cascade from A4-​A5 back down to A0-​A1. The pedal is then changed with each octave ascent so that the rising line is not lost amidst the more resonant lower sonorities. The passage’s penultimate pedal change at the return of A0-​A1 (m. 35) is held until A resolves to D (m. 36). Depending on the acoustics of the hall, however, the performer may have to clear the pedal (at least partially) more often than indicated by Ravel.19 In my

Ravel was fond of defining large musical sections with pedal tones. See, for example, “Le Gibet” in Gaspard de la nuit, which features a B♭ pedal throughout; also “Une Barque sur l’Océan” (Korevaar 2000, 117–​19). 17 Generally, pianists do not physically experience the traversal of intervals as directly as do string players or singers. This one-​handed work makes movement across intervallic distances explicit. 18 Ravel’s manuscript, held in the Lehman collection at the Pierpont Morgan Library, confirms Ravel’s authorship of these markings. The T1 pedal markings in the published edition are editorial additions. We are grateful to the Pierpoint Morgan Library for supplying a microfilm of this manuscript. 19 Performers of early twentieth-​century French piano works often face such pedaling dilemmas, in which notated pedaling, clarity of harmony and voice-​leading, and notated durations all compete as pedaling considerations. (See, for example, the pedal-​point A’s in the first movement of Debussy’s Pour le piano.) The problem is due in large part to the prevalence of sustained pedal points in this repertoire; it is exacerbated on modern pianos, which have a richer tone and longer sustain than period French instruments (Winter 1990, 28–​29). One solution is the use of the middle pedal, which appeared on some French pianos as early as the 1890s (Brody 1987, 181).

Example 1.6. Ravel, Concerto pour la main gauche, opening cadenza, Theme 1.

Example 1.7. Ravel, Concerto pour la main gauche, opening cadenza, Theme 2, reduction.(Bold bar lines indicate hypermeasures; regular noteheads indicate unmeasured durations.)

Ravel’s Concerto pour la main gauche  49

performances, I (DL) aim to carry the initial low A0-​A1 pedal through, at least conceptually. I (DK) sometimes use the piano’s middle pedal to sustain the bass A0-​A1 through the first OG descent, then release it and follow the marked pedaling for the rest of the passage. (Video 1.6 demonstrates the first descent.) Other performers, such as Blancard (1953) and Perlemuter (1955), do not carry the bass A0-​A1 through, clearing the pedal with the arrival of each long note, or even more often. In our opinion, this detracts from the momentum and drama of the passage. (Audio 1.2 provides Blancard’s playing of the passage.) Février (1957) presents an entirely different conception of the OG. He pedals very little in the opening descent (m. 33.1), playing the sixty-​fourth notes non-​ legato and at times detached. Then, rather than grouping the OG ascent (mm. 33.2–​ 34) according to the octave ascents of the bass A’s and Ravel’s pedal markings, he opts (as shown by brackets above the staff) for four-​“beat” groupings initiated by the rhythmic change to constant sixty-​fourth notes in the middle of m. 33.2. Février articulates the groupings by replacing Ravel’s indicated pedal changes with his own (particularly noticeable at the point marked *), accompanied with accentuation (at *) and slight pauses before the melodic B’s of the first “beat” of each group (marked with ~).20 He thus preserves the lower octave as bass for each succeeding move upward, and facilitates a focus on a long melodic line and forward motion. (The melodic line is circled; Février projects a continuously rising line by correctly playing E4 at the end of m. 33.2 rather than the published G4.21) The overall effect is that of a continuous build-​up of texture and momentum.22 (Février’s playing can be heard on Audio 1.3  .) In the first and second themes, a different kind of pedaling dilemma occurs. Here harmonies in the melody change above a bass line that remains static or changes at a different time than the melody. The pianist’s single hand cannot physically sustain both lines; the pedal must sustain the melody while the bass is being played, and vice versa. As a result, lifting the pedal for harmonic clarity in one line often breaks the flow of sound in the other line. In the first theme (Example 1.4b), for example, pedal changes can only be made on the downbeat if notes are to be sustained as written. This follows the published pedal indications and the notated rests. However, harmonic changes in the melody occur on both beats 1 and 3, leaving the pianist with the choice of clearing the pedal partially or entirely on beat 3 and shortchanging the bass D, or holding the pedal and bass D and blurring the third beat. A  third option is to pedal as indicated, voicing chords carefully with an ear to dissonance and consonance.

20 These pauses may be due in part to the physically wide stretch of these beats. 21 Musical context and Ravel’s manuscript (at the Pierpont Morgan Library) confirm that E4 is the correct pitch. 22 Since Wittgenstein’s (1937) top notes emerge only at the asterisk, he gives the impression (beginning at that point) of similar four-​“beat” groupings.

50  Performing Knowledge

The second theme (Example 1.4c) presents trickier problems.23 In mm. 47–​48, for example, one cannot sustain notes as written with any degree of clarity: the only “legitimate” pedal changes occur at the rests, with a long stretch of changing harmonies in between. In general, judicious voicing lessens the need for pedal changes, but occasionally, as in this last passage, the pianist must half-​pedal, or “sneak” pedals. And as with many other performance decisions, choices remain subject to the specific characteristics of piano and hall. (Video 1.7 demonstrates Example 1.4c, mm. 46–​48.) Because of the registral split between melody and bass, then, pedaling acquires a structural significance. More than merely providing color and timbre, the pianist’s pedaling choices determine harmonies, lines, and gestures heard. In performance we prefer to maintain the lines as much as possible, bringing out the melody and half-​pedaling where necessary for harmonic changes. Blancard (1953) and Casadesus (1947), on the other hand, value harmonic clarity over sustaining individual lines, and clear the pedal very frequently. Wittgenstein’s (1937) pedaling neither clarifies harmonies nor sustains individual lines; he holds the pedal through rests in first and second themes, creating unnecessary blurs. Some of the issues that we have been considering here (and one other—​“split beats”—​that we shall consider shortly) are common to other instruments. For the difficulty of sustaining bass against upper voices, or the impossibility of articulating bass and upper voice simultaneously, one need look no further than Bach’s sonatas for solo violin or suites for solo cello: we could take the Adagio of the G-​minor solo violin sonata or the Courante of the C-​major cello suite as examples. Two-​handed pianists, however, do not normally face such constraints; for pianists, they are notable in their departure from the norm.

Rhythmic Considerations We will discuss three rhythmic features of the cadenza. The first, “split beats,” arises from the physical limitations of a single hand. The second and third, iambic groupings and expansion/​contraction, direct a performer’s sense of momentum and affect. The single-​hand nature of the work decrees that registrally distant bass and melody be articulated separately. Thus beats “split” between melody and harmony, creating characteristic metric structures.24 The opening of the OG (Example 1.4a) illustrates a characteristic “split beat.” As shown by “beats” numbered below the staves, the passage consists of “measures” of four unequal “beats”; the fourth “beat” 23 Ravel provides no pedal indications here. Rather, as had become usual in French music, pedaling is implied through note values and rests. 24 See Rothstein (1989, 58–​63) for a discussion of successive downbeats that are articulated first in the accompaniment, then in the melody. Rothstein’s discussion deals with split hypermetric downbeats, rather than the simple split downbeats discussed here.

Ravel’s Concerto pour la main gauche  51

is frequently shortened (m. 33.1, m. 33.2, absent in m. 33.3), providing a sense of acceleration.25 The very first “beat” of the gesture (m. 33.1) falls in a strange place—​ at least one quarter note after the orchestral downbeat of m. 33.0.26 We interpret the pianist’s low A0-​A1 octave as the bass of the chord, with the top of the chord arriving at m. 33.1; the boxed notes all form part of a single verticality, broken out of physical necessity.27 We view the entire broken chord as part of the preceding orchestral downbeat, although it must follow the orchestral downbeat so that the pianist can be heard. This “split-​chord” interpretation affects the way that I  (DL) play the passage. Rather than waiting for the orchestra’s final chord to die down, I come in immediately, weighting the low A, and playing the high A5-​A4 as an extension of the bass A0-​A1. I (DK) approach it similarly, with the feeling that the momentum of the orchestra’s cutoff leads directly into the piano gesture. Other performers’ recordings reflect various interpretations. Wittgenstein (1937), Perlemuter (1955), and Blancard (1953) wait for silence before entering.28 (Audio 1.4 presents Blancard’s interpretation.) Blancard then lingers on the first of the ascending sixty-​fourth notes, and Perlemuter “places” the top chord. Casadesus (1947) and Février (1957), on the other hand, enter immediately, Casadesus lingering on the first of the sixty-​ fourth notes and Février “placing” the top chord. (Février’s rendition can be heard on Audio 1.5  .) A similar phenomenon occurs at the juncture between the pianist’s second theme and CG. As shown by numbers in diamonds between staves in Example 1.4c, the second theme expresses four-​measure hypermeter, with a bass arpeggio acting as the fourth-​measure anacrusis to each hypermetric downbeat. The Vivo passage ending the theme (m. 57.1—​a “stretched” fourth measure) leads to the hypermetric downbeat beginning the CG (Example  1.4d). This downbeat, articulated by the long-​awaited V7, “splits” three ways, between the bass arrival, the circled melodic arrival on A5 (ending the large-​scale melodic line ), and the beginning of the Strepitoso on A6 (which begins another 4-​”beat” measure). (Please see Video 1.8  .) The two large split beats that we have just discussed articulate analogous points in the cadenza’s structure (the openings of OG and CG), and dramatize the cadenza’s articulation of the dominant (“V” and V7 respectively). Ravel thus parlays physical limitations into articulators of tonal middleground. 25 The “measures” of four “beats” begin as hypermeasures of four 2/​4 measures, contracting by m. 33.3 to measures of quarter-​note beats. 26 As notated, the first “beat” falls 13/​64 quarter notes after the orchestral downbeat. Given the a piacere indication, however, the sixty-​fourth notes could be interpreted as “durationless” grace notes. 27 This kind of “split-​chord” writing is reminiscent of Bach’s solo sonatas for strings. Like many passages in those sonatas (Lester 1999, 31–​39), the split-​chord passages mentioned here ground themselves on harmonic rather than melodic bases. This parallel seems especially appropriate given other Baroque references in the Concerto’s opening cadenza (sarabande rhythm in Theme 1, French-​overture characteristics of Theme 2), and the many other references to earlier periods by Ravel (especially Le Tombeau de Couperin, Menuet antique) and his French contemporaries. 28 The silence in the Perlemuter recording, and part of that in the Wittgenstein recording, sound suspiciously like botched splices.

52  Performing Knowledge

Both of these cases feature bass arriving first, followed by melody. Beat “splitting” also occurs in the opposite order (melody first, harmonic filler second), as shown in Example 1.4a, mm. 35–​36. Here, the primary motion A to D is elaborated with a pentatonic descending line (circled); the pianist attacks this line first, then fills in the upper harmonic {A,G} dyad. In contrast to this interpretation, both Wittgenstein (1937) and Blancard (1953) interpret the lower notes as literally notated—​as grace notes to the upper ones. We have been describing beat-​splitting in the cadenza. Now we will look at iambic groupings and expansion/​contraction. The cadenza prominently features groupings in which metrically weak first parts precede metrically stressed second parts. These iambs and their transformations pervade the rhythmic structure of the cadenza at multiple levels.29 In the lyrical first theme (Example 1.4b), for example, successive expansion of the basic iamb X =  into gestures Y, Z, and Z' delineate the theme’s melodic contour and define its rhythmic shape. In the melody, Y highlights changes of direction in pitch contour, preceding both the arrival at the melodic peak (m. 38) and a departure from a strictly descending contour (m. 40); in the bass, Y (m. 39) and Z (m. 41) follow these two points. Z and Z' help expand the theme. They precede melodic echoes; their expanded length turns the melodic iambic pattern into relaxed triplet eighth notes, and delays the melodic long note that would normally occur on the downbeat. The second theme (Example 1.4c) takes over much of the rhythmic structure of the first (iambic patterns, second-​beat accompaniment, specific rhythmic motives), but transforms it to communicate a dramatically different affect. It sharpens iamb X =  to X' = , and transforms Z' into the dramatic descending flourish of Z''. These transformations, combined with octave doublings, expanded register, and arpeggiated sweeps, contribute to the majestic and powerful character of this second-​theme presentation.30 In his 1939 recording, Alfred Cortot conflates first-​theme iambs (X= ) and second-​theme iambs (X' = ): he tends to double-​dot first-​ theme iambs, and softens second-​theme iambs to .31 In so doing, he blurs this notated distinction between the two themes. 29 Though the iamb originally connoted short–​long, it has also acquired the meaning weak–​strong, and we use the term here primarily for the latter meaning. We specify that, on smaller scales, the second syllable of the iamb represents relative metrical strength, and on larger levels, a confluence of tonal and metric accent. 30 In the cadenza, the first and second themes resemble one another rhythmically, while differing from one another in intervallic vocabulary: as mentioned earlier, major second, perfect fourth, and perfect fifth in the first theme, and minor second, major second, and minor third in the second theme. In the orchestral introduction, the similarities are reversed: both themes feature melodic lines in dorian modes (E and G dorian respectively), beginning with the first three degrees of their modes ( and ); Theme 1 features iambs, short-​long patterns, and triple meter, while Theme 2 displays begin-​accented patterns, equal durations, and motivic rather than metric organization. 31 Perlemuter’s 1955 recording displays similar, though less marked, tendencies. Such a lack of distinction between different types of dotted rhythms was also reflected in much of the teaching I (DK) received from Paul Doguereau, a student of Marguerite Long, Jean Roger-​Ducasse, and Ravel. For example, melodic dotted rhythms in pieces as varied as Debussy’s Reflets dans l’eau and Ravel’s Le Gibet might be overdotted

Ravel’s Concerto pour la main gauche  53

Iambs also govern the cadenza’s rhythmic structure on deeper levels. In the OG (Example 1.4a), for example, each group of thirty-​second notes leads to the following long note (m. 33.1); the momentum of the entire opening cascade carries through to the arrival of the low A0-​A1 of m. 33.2, aided by the accumulation of sound, the shortening of the fourth “beat,” and the accents marked on the final thirty-​second-​note gesture.32 On a larger scale, the A pedal of mm. 33–​35 acts as upbeat to the D of m. 36, and on an even deeper level, the Concerto’s entire introduction (orchestral introduction and opening cadenza, Examples 1.3a through 1.4d) expresses an expanded upbeat to the orchestral re-​entry’s structural downbeat on the tonic (Example 1.4d).33 Although the listener expects the iambic downbeat to be strongest on the deeper levels, Ravel undercuts it: he fudges the arrivals on D in the OG (Example 1.4a, m. 36) and at the end of the cadenza (Example 1.4d) with evaded attacks and split beats. On larger levels, then, the iambic “downbeats” reify Ravel’s penchant for masquerade—​his “esthétique de l’imposture.” Iambs and their transformations significantly impact performers’ physical experiences of and affective projection of the cadenza. A  second rhythmic feature, expansion/​contraction, does the same. As we observed earlier, a process of iambic expansion occurs in Theme 1. Expansion—​motivic expansion—​also occurs in Theme 2, underlying a process of rhythmic contraction. Example 1.7a provides a rhythmic reduction of the second theme’s melodic line; bold bar lines indicate hypermeasures and rectangular noteheads represent unmeasured durations. As shown by upward stems, the theme traces an ascending stepwise trajectory . (In the score, each note of this ascent, except for the final A5, is marked by the iamb X' = .) As shown in Example 1.7b, the ascent breaks down into three sections, labeled AA'B at the top of the example.34 The two A sections follow each member of the ascent with a descending step (, ), while the B section comprises a steady rise through the tritone . Some pianists, such as Casadesus (1947), point out the change in pattern ( rather than ) by emphasizing the F5 agogically. to the point of making distinctions inaudible. Although Ravel occasionally asked for overdotting or other rhythmic performance interpretations, he was generally known for demanding adherence to “the text, only the text!” including rhythmic details. (See Perlemuter and Jourdan-​Morhange 1953, 66, 24, on overdotting in “Forlane” from Tombeau de Couperin, and on playing a bird call more quickly than written in Oiseaux tristes; and Février 1939, 892, and Grey 1938, 370, on adherence to the text.) 32 Although Ravel marks the OG a piacere, he notates rhythmic values precisely, usually adding up to units of quarter or eighth notes. Since he was known for demanding rhythmic exactitude (Grey 1938, 370), we suggest practicing the opening rhythms as written, and using them as a point of departure. Several pianists change Ravel’s notated rhythms measurably:  Casadesus (1947) and Blancard (1953), for example, shortchange the low A0-​A1’s in m.33.2 by an eighth note, and linger markedly (an eighth note) on the first A1 of each sixty-​fourth-​note group. This rhythmic trade goes against the function of A0-​A1 as pedal bass, of the peaks in the sixty-​fourth-​note runs as melody, and of the notes in between as harmonic filler. (Blancard further undermines the A0-​A1 pedal bass by not pedaling the sixty-​fourth notes.) 33 On these larger levels, the iambic stress results from a combination of tonal and metric factors. 34 Although Example 1.7b resembles a Schenkerian graph, it is not intended as one.

54  Performing Knowledge

With regard to the overall ascent, the B section contracts the A sections in several ways (Example 1.7a). The duration between successive ascending pitches decreases from 4 measures to 2 measures to 1 (), along with a decrease in the number of primary iterations of each pitch (), an elimination of the descending step found in the A sections, and a contraction of the 3/​4 meter of the A sections to the implied 2/​4 beginning the B section. This rhythmic contraction, along with rising register and increasing dynamic, heightens tension in the second theme, in sharp contrast to the rhythmic expansion, descending register, and level dynamic of the first theme. As shown in Example 1.7b, however, the rhythmic contraction of the pitch ascent conceals a deeper-​level motivic expansion: the descending steps and are answered and expanded by the “descending step” . What is initially heard as a process of contraction turns out to be an “imposture” hiding an expansion on a larger level. This view of the overall shape of the second-​theme section conditions our performance interpretations. We strive to project the underlying expansion by carrying the line from the B section through the arrival on the dominant (CG) to the final glissando up to the tonic pitch D7. Blancard (1953) does not do so. Contrary to Ravel’s indications, she makes a break between the first two chords of the Vivo (Example 1.4c, m. 57.1, G-​major triad and low G♯ octave), thus separating the Vivo passage and its arrival on the melodic A5 (m. 57.2, circled) from the < C5,D5,E♭5,F5,G5> line leading up to it.35 In addition, she slows at the end of the strepitoso run, and deliberately articulates the endpoints (A0–​D7) of the glissando (Example 1.4d); these features of her performance militate against hearing the larger melodic motion from E♭ to D. In general, Blancard’s interpretation of the cadenza displays surface-​level details clearly, at the expense of overall shape and drama. Finally, as we mentioned earlier, the two “frames” of the cadenza (OG and CG) exhibit both contraction and expansion in relation to one another. As shown in Example 1.5, the CG expands the OG’s pitch range upward by an octave, and compresses its temporal unfolding dramatically, for a showy gesture that is more complex both technically and harmonically. It provides a fitting culmination to the performer’s proof of prowess, to the rhetorical build-​up of the cadenza, and to the momentum of the Concerto’s introduction as a whole. * * * In our original conclusion, we said that “our exploration of the opening cadenza of Ravel’s Concerto has served as a vehicle for introducing another voice—​that

35 Breaking the line at this point emphasizes the anacrustic character of the Vivo, in parallel to the anacrustic arpeggios preceding hypermetric downbeats throughout Theme 2. The break also focuses attention on the harmonic importance of the bass G♯, which eventually leads to the dominant.

Ravel’s Concerto pour la main gauche  55

of the performer and not merely of his/​her performance—​into musical analysis, complementing the voice of the theorist in the study of score and performance. . . . Our perspectives as performers, in particular, have contributed specific insights into metric structure, pedaling as a structural determinant, and the purely visceral experience of the work in motion.” In a later reflection on the process of writing the article, DK wrote: the idea of understanding music kinesthetically makes a great deal of intuitive sense to a pianist. One can also apply the idea to compositional process. Many composers have worked at the piano, even if they were not primarily composers for the piano (Wagner and Stravinsky are two famous cases). Can we conclude that to some extent musical gestures relate to the way they feel on the piano? Regarding his Etudes for piano, György Ligeti has written: I lay my ten fingers on the keyboard and imagine music. My fingers copy this mental image as I press the keys, but this copy is very inexact: a feedback emerges between idea and tactile/​motor execution. . . . The result sounds completely different from my initial conceptions: the anatomical reality of my hands and the configuration of the piano keyboard have transformed my imaginary constructs. . . . The criteria are only partly determined in my imagination; to some extent they also lie in the nature of the piano—​I have to feel them out with my hand. For a piece to be well-​suited to the piano, tactile concepts are almost as important as acoustic ones; so I call for support upon the four great composers who thought pianistically: Scarlatti, Chopin, Schumann, and Debussy. A Chopinesque melodic twist or accompaniment figure is not just heard; it is also felt as a tactile shape, as a succession of muscular exertions. A well-​formed piano work produces physical pleasure. (Ligeti 1996, 8–​9)

Etudes and other works by composers such as Chopin, Liszt, Scriabin, Debussy, and Ravel often exhibit the compositional development of an intrinsically physical gesture. DK continues: This particular collaboration, and the one that followed (Leong and Korevaar 2011) brought home to me the power of that particular idea. While I was aware of the physical difficulty of performing Ravel’s Left-​Hand Concerto, I hadn’t given thought to the fact that Ravel would have composed a piece around that particular difficulty (even knowing that he had to some extent indicated that in his own writing: the idea of one hand posing as two). The pianist’s left hand becomes something like a solo cello: large chords and big registral spreads require time, as they always must be broken in some way in order to be playable. Physical gesture inhabits Ravel’s choice of thematic material and the way in which he develops it.36 36 DL: Domenico Scarlatti’s keyboard sonatas also come to mind as pieces in which physicality plays a defining role. The performer’s movements—​which incorporate digital dexterity, varied articulation and tone color, close hand positions, registral traversals, incisive chords, and sparkling ornamentation—​link intimately to topical references, instrumental timbres, and rhythmic character: they infuse these sonatas with meanings and identities.

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Of course, Ravel finds the left-​hand limitation intriguing enough that he also uses it in the cadenza of his two-​handed concerto. And, it is not a new idea, as plenty of eighteenth-​century sets of variations feature right-​hand trills with the left hand taking on the remaining texture—​see Mozart’s Gluck Variations, Beethoven’s Op. 34 Variations, and numerous other examples. Perhaps the most interesting aspect of this work for me is in how it has come full circle to something that I have thought and taught for many years: the attachment of musical shapes to the human voice. The physical act of performing the Left-​Hand Concerto of Ravel presents an analogue to the idea that melodic leaps, in order to be convincingly performed, require time in proportion to the size of the interval. A form of analysis that acknowledges the physicality of performance—​whether of vocal cords, string-​instrument shifts, or the leaps of a left-​handed pianist—​can be of immense practical value to performers and teachers of performance. Such an approach strives to be dynamic, and to intelligently join the too often separate strands of intellectual activity around music theory and music performance into a more integrated whole. We close with Video 1.9 , David Korevaar playing the opening cadenza of Ravel’s Concerto for the Left Hand.

Ravel’s Concerto pour la main gauche  57

Appendix: Historical Recordings of Ravel’s Concerto pour la main gauche * recordings to which we had access Blancard, Jacqueline. 1938. Charles Münch. Orchestre Philharmonique de Paris. Polydor. Blancard, Jacqueline. 1949. Ernest Ansermet. L’Orchestre de la Suisse Romande. Digitally remastered on Decca 4825193. Blancard, Jacqueline. * [1953.] Ernest Ansermet. L’Orchestre de la Suisse Romande. London LP LL797. Casadesus, Robert. *1947. Eugene Ormandy. Philadelphia Orchestra. Sony. Reissued 1999 on Philips Classics compact disc 456739-​2. Casadesus, Robert. *[1960.] Eugene Ormandy. Philadelphia Orchestra. Columbia Masterworks LP MS 6274. Cortot, Alfred. *1939. Charles Münch. Société des Concerts du Conservatoire. Victor Set M629 (2LA 3059/​62). Reissued 1993 on Pearl Gemm CD 9491. Février, Jacques. 1942. Charles Münch. Société des Concerts du Conservatoire. Reissued 1999 on Lys 270. Février, Jacques. *1957. Georges Tzipine. Orchestre National de la Radiodiffusion Française. Digitally remastered 1996 on EMI Classics CD2B 69464. Perlemuter, Vlado. *1956. Jascha Horenstein. Concerts Colonne Orchestra, Paris. Digitally remastered 1992 on VoxBox CDX2 5507. Wittgenstein, Paul. 1933. Maurice Ravel. L’Orchestre Symphonique de Paris. Film clips. *Clip at https://​ www.youtube.com/​ watch?v=FI7tnBmGnq4, accessed January 27, 2017. Wittgenstein, Paul. *1937. Bruno Walter. Amsterdam Concertgebouw Orchestra. Reissued 1999 on Urania URN 22.126. Wittgenstein, Paul. 1958. Max Rudolph. Metropolitan Opera Orchestra of New York. Orion ORS-​7028.Wittgenstein, Paul. *n.d. Film clips of excerpts from opening cadenza. https://​www.youtube.com/​watch?v=_​zQteXqbYas, accessed January 27, 2017. Blancard performed the four-​hand work Ma Mère l’Oye with Ravel; her score contains the dedication “in remembrance of our fine performance. M.R., Geneva, February 28, 1929.” Ravel coached, played with, and attended performances of Robert Casadesus; Casadesus also ghost-​recorded difficult pieces for Ravel on some putative Ravel piano rolls (Woodley 2000, 222). Cortot and Ravel were teenage classmates at the Conservatoire. Février studied the Concerto with Ravel, and was chosen by him as the first French performer of the Concerto in France and the United States. Perlemuter studied Ravel’s complete piano works with the composer, meeting with him several times a week for a period of six months, and performed

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the complete works in Paris in 1929. In Ravel d’après Ravel, he discusses Ravel’s piano works, focusing on personal communications from the composer. Austrian one-​handed pianist Wittgenstein commissioned the work (with exclusive performance rights for six years), and the Concerto is dedicated to him. He performed the work with several conductors, including Ravel. However, Wittgenstein took many liberties with the score, and Ravel objected to these (Touzelet 1990, 550, 551, 554, 559, 581–​82, 593–​95).

2 Creation of Structure

Interpreting Schoenberg’s Klavierstück, Op. 19, No. 4 Daphne Leong and Hunter Ewen

Here we question the role of the notated score in delimiting structure. Examining first the soundness of the published editions of Schoenberg’s Op. 19, No. 4, and then analyzing the score and recordings by three pianists associated with Schoenberg interpretation (Edward Steuermann, Maurizio Pollini, and Mitsuko Uchida), we demonstrate how structure can be defined by the interpreter—​analyst or performer. A view of interpretation as creation is set against a backdrop of a score’s affordances, including those of text or script. Central to this chapter is the tenet that interpretation is a creative act. Both analysis and performance take certain givens (the score being the most obvious) and bring something new into existence. In the process, structure is created. We explore this idea—​ the creation of musical structure by analyst and performer, alongside that of a score’s entailments—​its meanings and its affordances. We also consider the relation between score and interpreter. Let us begin with the score. (Our discussion refers primarily to traditional Western notation.) The information encoded in a score can perform diverse functions.1 A score may include only the information needed by a “native speaker” conversant with the style (notes inégales, figured bass, mnemonic notations in some of Mozart’s piano concertos). Or it may attempt to provide as thorough an accounting of musical elements as possible within its notational conventions (by necessity, still incomplete).2 Furthermore, this accounting may describe the intended sound and/​ or the method by which the sound is to be produced. Eleven of the variations in Bach’s Goldberg Variations, headed “a 2 Clav.,” are for two-​ manual harpsichord; the second movement of Webern’s Piano Variations, Op.  27, contains frequent hand-​ crossings; Ravel’s Concerto pour la main gauche is

1 This discussion draws from and amplifies that in Leong (2016). 2 We take this distinction from Bruno Nettl’s (2005, 82) discussion of transcription. Daphne Leong and Hunter Ewen, Creation of Structure In: Performing Knowledge. Edited by: Daphne Leong, Oxford University Press (2019). © Oxford University Press. DOI: 10.1093/oso/9780190653545.003.0004

60  Performing Knowledge Example 2.1.  Mid-​bar downbeat in Bach, French Suite No. 5 in G major, Gigue, mm. 1–​2, 14–​16 (Burkhart 1994, 18).

for the left hand alone. In all three of these cases, the physical method can be—​ and has been—​ contravened (played on the modern, single-​ keyboard, piano; played without hand-​crossings; played with both hands or even just the right hand).3 Intended instruments can be affected by historical developments (Baroque violins and bows versus modern ones) or arrangements (Stravinsky’s Rite of Spring has been played by saxophone ensemble and by jazz trio).4 Tablature notation, such as lute tablature of the sixteenth century, prescribes the actions for producing the sounds. Some new music goes further and prioritizes “performative actions over determinate sonic results” (Kanno 2007, 252). Cassidy’s The Crutch of Memory for indeterminate bowed string instrument (2004) notates three left-​hand parameters (strings and fingerings, hand “shapes” from closed to spread fingers, and position on the fingerboard) along with actions of the bow and right hand: “here it is physical states, the interface between the body of the player and the body of the instrument, and physical gestures that drive the sonic surface.”5 The accounting may obscure, or transparently represent, structural features. In the Gigue from Bach’s French Suite No. 5 (Example 2.1) and the first movement of Mozart’s Piano Sonata K. 331 (Example 2.2), the metric notation conceals mid-​ bar downbeats. Carter, in his first string quartet (I, mm. 22–​25), notates distinct 3 On mapping between instrument and body, see De Souza (2017). Mead (1999) exegetes meanings conveyed by Webern’s hand distributions; Crispin (2013, 54–​56) discusses ethical principles implicated in performers’ choices for these distributions. On Ravel’s Concerto for the Left Hand, see Variation 1 (p. 37 and p. 38 n 10). 4 By the Eastman Saxophone Project and The Bad Plus, respectively. See https://​www.youtube.com/​ watch?v=YtrCvdH_​Alk (accessed January 8, 2017)  for the former, and Sony Masterworks B00I89Y1XW (2014) for the latter. 5 Cassidy program note. A score excerpt and the program note can be found at http://​www.aaroncassidy.com/​ music/​crutchofmemory.htm (accessed February 24, 2017). A score may also call for actions without accompanying sounds; see, for instance, Berry (2009) on Gubaidulina’s music.

Example 2.2.  Mid-​bar downbeat in Mozart, Sonata K. 331, I (Cone 1968, 44).

Example 2.3. Messiaen, Quatuor pour la fin du temps, VI “Danse de la fureur.”

62  Performing Knowledge Example 2.4.  J. S. Bach, Kanon zu vier Stimmen, BWV 1074.

concurrent tempi pragmatically within a single common meter; Messiaen’s barring in the Quartet for the End of Time (VI, mm. 1–​13; see Example 2.3 for mm. 1–​6) bounds gestural units (ending with quarter or half notes), transmitting the expanding grouping structure. In some cases, scores inscribe concepts. Example 2.4, a puzzle canon from Bach’s Musikalische Opfer, encodes a four-​voice canon as written and then in inversion. Hunter Ewen, composer and co-​author of this chapter, frequently creates two scores for his pieces: one to display the sense of flow, narrative, and structure, and another, in more traditional notation, for the performers. The two scores evolve together as he composes, moving back and forth between them. Example 2.5 shows both scores for Ewen’s Circles on Quiet Water (2011), for viola and electronics. Example 2.5b linearizes the circles shown in Example 2.5a. But the circular score captures the main structural and metaphorical feature of the piece. The viola plays one circle at a time, moving from the inner circle toward the outermost circle, each circle taking one minute to traverse. The electronics process the material in one-​minute delays, so that when the viola plays material at “5:00 pm” on circle 3, sonic material from the “5:00 pm” angle of circles 2, 1, and 0 is heard—​ripples in the water. Further, a score can be used and understood in different ways by different actors, in different practical circumstances, within different stylistic milieux, and in the context of different interpretive traditions. Actors might include composers, musicologists, theorists, performers, or conductors. Practical circumstances could involve writing for oneself or for an external reader, publication venues or constraints, and solo, chamber, or orchestral performance situations. Stylistic milieux might span unmeasured preludes, symphonic poems, and new complexity. Analytic traditions could include formalist approaches, hermeneutics, and corpus studies; performance traditions might embrace historically informed performance, influences of great pedagogues, and aleatoric practices. According to one binary distinction, a score can function both as a “text, independently usable and analyzable” and “a text for performance (script).”6 In another binary, analysis interrogates texts, while performance enacts scripts. But in practice these distinctions between text and script, analysis and performance, blur. Lewin (1986, 385–​88) describes real or imagined enactment of the score as integral to perception and analysis; score then is script for analysis. More broadly, if a score is 6 De Marinis (1993, 31) is here referring to dramatic texts. Cook (2001, 15) applies these terms to musical scores.

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analyzed as imagined or heard (Westergaard 1977, 148), and any hearing (inner or otherwise) is predicated upon music as experienced (via performance of some kind) (Leech-​Wilkinson 2012), then analysis is ultimately based upon experiences of (performed) music. The art of rhetoric can serve as a further illustration of the overlap between script and text, performance and analysis. Rhetoric—​intrinsically compositional and performative in its classical origins—​became an analytical tool for German theorists of the seventeenth century, and informs aspects of both musical performance and analysis to the present day.7 In addition, the relationship between score and interpreter varies. Focus can shift from fidelity to the text (the score, the “work,” or the “composer’s intentions”) to concern with the brilliance of the interpreter, whether performer or analyst.8 Even given a primary concern with the text, interpreters may consider presentation of the “work” to override specifics of the score itself. In Schenkerian analysis, for example, the middle-​or background may supply literally absent but conceptually present notes. In performance, to take one example, Charles Rosen (1998, 72) states that “any liberty seems to me justified if it does not substantially alter the composer’s conception but makes it more effective.” According to Tom Beghin (2007, 132), who applies rhetorical concepts to the performance of Haydn, “. . . the notion of a ‘text’ is neither a goal nor a point of departure: it is an intermediate stage between invention and delivery. Delivery is of the ‘ideas’ rather than the words; conversely, the purpose of inventing ideas is not to have them reflected in elegant prose, but for them to be orally effective. . . . And . . . being effective might sometimes mean not adhering to one’s well-​prepared text. . . .” Charles Rosen, going further, says “the most successful performances  .  .  .  are those that only give the illusion of remaining faithful to the text while they hide a genuine and deeply rooted freedom of interpretation” (73). The shift here is from an “autocratic” (composer as authority) to an “allocratic” (composer and interpreter as collaborators) view of interpretation (Goehr 1993, 179) or, in more extreme terms, from the text as command from author to performer, to the text as “unsolicited advice” or “set of optional instructions” (De Marinis 1993, 42–​43). This under-​(or over-​)determination by the score makes each analysis and performance an interpretation, where to interpret is to explicate (explain the meaning of, present in understandable terms), to construe from a certain point of view (shaped by particular beliefs, circumstances, and so on), or to realize via artistic performance or presentation (to sound, show, embody).9 Each of these aspects of interpretation is creative, supplying what is not present in the score, shaping what

7 Burmeister’s (1606) use of rhetorical figures to analyze Lassus’s motet In me transierunt is frequently viewed as the first example of a Western music analysis; for modern-​day applications of rhetoric to both analysis and performance see, for example, Lester (1999), Beghin and Goldberg (2007), and Beghin (2007). 8 See Ayrey (1996, 6–​7). 9 The idea of musical performance as interpretation began in the mid-​1840s, gradually supplanting earlier views. (See Dreyfus 2007, which sketches the history of “performance as interpretation” in common-​practice music.)

Example 2.5. Ewen, Circles on Quiet Water. (a) circular score

(b) viola part, excerpt

Example 2.5 (cont.).

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is there, or contradicting it.10 If to create is “to bring into existence,”11 then an interpretation of a score, through analysis or performance, creates features not present in the score itself or in what is implied by the score’s symbols. We complement this idea of creative response with that of a score’s affordances. Affordances, a central concept in ecological psychology, were first theorized by James J. Gibson (1966, 1979) in his model of perception.12 When the constant properties of constant objects are perceived (the shape, size, color, texture, composition, motion, animation, and position relative to other objects), the observer can go on to detect their affordances. I have coined this term as a substitute for values, a term which carries an old burden of philosophical meaning. I mean simply what things furnish, for good or ill. What they afford the observer, after all, depends on their properties. The simplest affordances, as food, for example, or as a predatory enemy, may well be detected without learning by the young of some animals, but in general learning is all-​important for this kind of perception. The child learns what things are manipulable and how they can be manipulated, what things are hurtful, what things are edible, what things can be put together with other things or put inside other things—​and so on without limit. He also learns what objects can be used as the means to obtain a goal, or to make other desirable objects, or to make people do what he wants them to do. In short, the human observer learns to detect what have been called the values or meanings of things, perceiving their distinctive features, putting them into categories and subcategories, noticing their similarities and differences and even studying them for their own sakes, apart from learning what to do about them. All this discrimination, wonderful to say, has to be based entirely on the education of his attention to the subtleties of the invariant stimulus information. (1966, 285)

The environment, or an object in the environment, affords possibilities, both good and bad, relative to an agent. When affordances are perceived, they become opportunities for action. Affordances are therefore co-​defined by the object’s properties in relation to the agent’s abilities. As Clarke (2005, 37) explains, “To a person, a wooden chair affords sitting, while to a termite it affords eating. Equally, the same chair affords self-​defense to a person under attack—​an illustration of the way in which an organism can notice different affordances according to its own changing needs.” To perceive affordances, the agent must pick up invariants in the environment. That is, structural properties in available sensory information (optic, acoustic, and so on) maintain typical relations under changing circumstances. Light reflected off rippling water, for instance, presents certain characteristics that remain



10 “There are no interpretations but only misinterpretations . . .” (Bloom 1997, 95). 11 Oxford English Dictionary Online, s.v. “create,” accessed February 3, 2017.

12 Our discussion of affordances relies heavily upon Scarantino (2003).

Schoenberg’s Klavierstück, Op. 19, No. 4  67

constant under different wind conditions, allowing a perceiver to identify the sight as rippling water. In this way invariants specify an object’s properties and allow the perceiver to detect its affordances. Moreover, invariants lawfully specify properties; that is, some physical law links invariants to structural properties. For Scarantino (2003, 954) and Turvey et al. (1981, 260–​75), invariants lawfully specify both properties and affordances; Scarantino uses the terms somewhat interchangeably. Gibson (1966, 187), however, states that “a property of the stimulus is univocally related to a property of the object by virtue of physical laws.” Following Gibson, we prefer to say that invariants specify properties, which constrain affordances—​potential uses and meanings. How these affordances are interpreted in the human sphere is greatly influenced by culture. Norman (2013, 145) gives the example of a doorknob, which has the perceived affordance of graspability, due to its shape, size, and other features in relation to the characteristics of a human hand. But understanding that it is used to open a door is learned through cultural convention. To take another example, in 2014 the umbrella became a symbol for Hong Kong’s pro-​democracy protests. A physical object, meant to shade protesters from the sun, became a defense against tear gas and pepper spray and then rapidly an icon of protest. The umbrella’s invariant physical features allow it to be specified as such; its properties afford certain uses and by association the meaning of protest. We attempt here to interpret how affordances—​originally theorized to explain perception-​action couplings between a physical environment and an agent—​ might apply to symbol systems such as musical notation. In a literal sense we might consider a score’s symbols (in their particular arrangement) to constitute the object. This object’s invariants consist of various relations among its symbols. What these invariants specify is defined not by natural laws but by cultural practices.13 For instance, the symbol has no inherent meaning apart from that ascribed to it through cultural usage. In musical scores, it indicates two elements in rhythmic relationship, but depending upon cultural context it could imply nominally equal durations, “swung” eighth notes, or notes inégales. The symbol could also indicate metric structure and suggest a certain tempo range. As a scaffolding for improvisation, it could underlie embellishment of various kinds. And so on. In the general case, affordances come into play for an agent when they are perceived. In the musical case, the perception of a score’s affordances depend not only upon the cultural usages specifying its symbols’ meanings, but also upon the agent’s knowledge, understanding, skill, and compliance with those usages. In the next chapter, for example, the meaning of Bartók’s rhythmic notation comes into play. Furthermore, as suggested in our discussion of shared items (in the introductory section of this book on “Cross-​Disciplinary Collaboration”), a score affords compositional creation, audiation of sounds, performative action, analytical

13 See also Gjerdingen (2009) on the role of culture and schematic perception in affordances permitted by symbolic objects.

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interpretation, and responses of many kinds—​as well as affording communication and collaboration among composers, performers, theorists, and others. Scarantino (2003, 956–​57) theorizes affordances as “dispositions,” that is, as properties that are dependent upon the response of the agent. An object “X has affordance property A (at time t relative to an organism O in circumstances C),” if, given particular circumstances C, there is a probability of some manifestation M involving X and O. In the musical case, circumstances C could include the various circumstances for score usage described earlier (types of information encoded, reading conventions of the time, and so on). Circumstances, as Scarantino states, cannot be listed exhaustively since they constitute an undefinably large set. But neither can they be unrestricted since under some set of circumstances it is likely that almost any object would possess any given disposition. (“There are conditions under which bars of steel are soluble, pieces of diamond fragile, etc.”) To avoid both problems of undefinability and triviality, “we should rely on a tacit understanding of C as the set of normal ecological circumstances.” For musical scores we can understand C as constituting the set of generally accepted interpretive practices (for that score by a certain interpreter at a given time).14 Gibson’s theory of affordances entails a tension that is amplified by its application to musical notation. This tension stems from the interplay of objective and subjective, physical and phenomenal: Does the affordance actually reside in the object’s properties or in the agent’s response?15 Gibson stresses the complementarity of affordances, the corequisite of an object’s properties and an agent’s abilities: An affordance is neither an objective property nor a subjective property; or it is both if you like. An affordance cuts across the dichotomy of subjective-​ objective. . . . It is equally a fact of the environment and a fact of behavior. It is both physical and psychical, yet neither. An affordance points both ways, to the environment and to the observer.16

Yet he is at pains to ground affordances in the invariants of the object, independent of the agent’s response:

14 Compare to Fish’s (1980) discussion of situational norms determining the meanings of texts. De Souza (2017, 52) draws upon Kirsch’s (2013) term “enactive landscape” to explore how “artifact-​based skills” are “learned, culturally and technically situated, and directed towards goals.” While De Souza’s discussion focuses on the affordances of musical instruments, the contexts of habitus, sociality, and purpose apply equally well to the affordances of musical scores. 15 This tension goes back to the origin of the term in Kurt Lewin’s Aufforderungscharakter—​“invitation character” or “valence”—​referring to characteristics of an object that invite or demand behavior. Gestalt psychologists developed a phenomenal approach to valence, invitation, and demand, an approach from which Gibson distances himself (Gibson 1979, 138–​40). 16 “The Theory of Affordances,” in Gibson (1979, 127–​43). The quote is from p. 129. On the complementarity of affordances, see pp. 127–​29, 141; on the interpenetration of objective and subjective in affordances, see pp. 129, 138, 143. Greeno (1994, 338) discusses the complementary relations between affordances of the environment and abilities of the interacting agent.

Schoenberg’s Klavierstück, Op. 19, No. 4  69 The affordance of something does not change as the need of the observer changes. The observer may or may not perceive or attend to the affordance, according to his needs, but the affordance, being invariant, is always there to be perceived. An affordance is not bestowed upon an object by a need of an observer and his act of perceiving it. The object offers what it does because it is what it is. To be sure, we define what it is in terms of ecological physics instead of physical physics, and it therefore possesses meaning and value to begin with. But this is meaning and value of a new sort. (1979, 138–​39)

This tension between an affordance as something intrinsic to the object and as something bestowed upon it by the agent is a point of controversy in ecological psychology. In music it manifests in the tension between score as text and score as script; between music as “works,” composer’s intentions, and scores, and music as performance. Since the very conventions by which score symbols specify meaning develop through the practices of a musical community, including interpreters (performers, analysts, and others), we cannot separate a score’s affordances from agents’ interpretive and inventive responses. Affordances of a score’s symbols, beyond the fact that affordances are always relations between an object and an agent, are themselves created by the practices of agents. And so in the usage—​creation, development, establishment, interpretation—​of musical scores and their symbols, affordances meet creation in a way not possible in the world of physical affordances. What is created, in part, is structure. To speak in the broadest sense, performers, or analysts, give form or shape through their interpretations. In making explicit what is not present in the score (sounds—​in all their specificity of pitch, duration, timbre, envelope, and dynamic; relationships; concepts) performers and analysts delineate intelligible relationships among parts—​that is, structure. To create these relationships performers have recourse to timing, color, dynamic nuance, balance, voicing, and such factors as these in the aggregate to create metaphorical curves or energetic shapes; analysts may employ inner hearing or actual “playing through.” For performers, and sometimes analysts, the physicality of performance is integral to interpretation. Structure is embodied and in part defined through physical and instrumental affordances and constraints. Corollary to this is the component of risk and the unexpected in live performance. A note that sounds more softly than anticipated can change the interpretive trajectory and, by extension, the structure and/​or affect that is conveyed. Analysts, not having to analyze in-​time, tend to take a score’s notational particulars (or their implied meanings where these can be reasonably specified) as givens, although they also have the luxury of ignoring features not relevant to their analysis. (One can focus purely on pitch structure to the exclusion of rhythm, for instance.) Performers, on the other hand, cannot omit those dimensions that do not interest them. In the following we will demonstrate how an analysis and three performances shape Schoenberg’s Klavierstück, Op. 19, No. 4, giving it form, color, nuance, and

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style. In the analysis, the score’s elements are interpreted in abstractions—​schema that model processes and relationships. In the performances, the score is made concrete in sound, with attendant completions and contradictions. The chapter’s broader analysis is analysis of recordings, drawing out relationships within each performance and among performances and analysis.17 The structure we find in all cases is an interpretive construct, a creation of analyst and performers in response to the affordances of the score. Ultimately, structure is created by listener and reader as well, although we will not discuss that aspect in this chapter. The analysis is by Leong, and the recordings are by Maurizio Pollini, Mitsuko Uchida, and Edward Steuermann. We chose these three recordings because of the creative range that they represented. Fortuitously, all three pianists also turned out to have particular connections to Schoenberg and his music. Analysis of the recordings is by Leong and Ewen.

Schoenberg’s Klavierstück, Op. 19, No. 4 Score The published score of Schoenberg’s Op. 19 itself raises questions. Two autograph sources exist:  the first written copy (no sketches are known), and a holograph fair copy.18 Schoenberg probably intended the latter to be used for performance, as well as as an engraver’s copy. However, the first published edition (Universal Edition, 1913) took the first written copy as its source instead. Schoenberg wrote on September 14, 1913, that “. . . I sent off the corrections to the second series of piano pieces. Unfortunately I had to change quite a lot, because they had—​without consulting me—​used a manuscript in which I had not yet put in all the definitive corrections” (Meyer 2009, 22–​23). The corrections that Schoenberg sent to the publisher are lost. Schoenberg’s personal copy of the 1913 edition is extant, but contains (in his handwriting) only measure numbers and one indication, a 32nd-​ note stem with a question mark above the first note of No. 4 (Brinkmann 1975, 17–​18).19 Schoenberg’s Sämtliche Werke reproduces the score from the 1913 first edition (with only two minor editorial changes, in Nos. 5 and 6) (Brinkmann 1975, 19–​20). This version of Op. 19, No. 4, exhibits multiple discrepancies of detail with both the first written copy and the holograph fair copy. The first written copy, like many

17 For simplicity, we treat each recorded performance as a “performance,” although a recording differs from live performance in many respects. 18 In MS 19 in the Arnold Schönberg Center, Vienna. Both sources are reproduced in facsimile in Schoenberg (2009), as well as in electronic images at http://​www.schoenberg.at. 19 It is difficult to date the printing of this copy—​it is from 1914 at the earliest, and predates World War II. Schoenberg’s markings on the copy may be post-​1925 (Brinkmann 1975, 18–​19).

Schoenberg’s Klavierstück, Op. 19, No. 4  71

of Schoenberg’s first copies, presents incomplete performance indications, and the changes in the published edition primarily add or refine dynamics, accents, articulation, and other performance markings. The Sämtliche Werke critical commentary does not mention such variants (Brinkmann 1975, 52, 55). In several notable instances the holograph fair copy diverges from both the 1913 edition and the first written copy. For instance (Example 2.6), the poco rit. that occurs at the beginning of m. 7 in the printed version (and that, in the absence of another indication, seems to continue to the end of m. 9), occurs at beat 2 in the fair copy and continues only to the end of m. 7. The fair copy was thought to be lost at the time the Sämtliche Werke piano volume was published (Brinkmann 1975, 17). Thus, neither in the Sämtliche Werke, nor in the facsimile edition that reproduces the two autographs mentioned earlier, does critical discussion of textual variants for Op.  19, No. 4, exist. In the absence of such evaluation, the definitiveness of certain performance indications must be questioned.

A Question of Affordances Is the method by which the sound is to be produced part of the invariants of a score? Example 2.7 (also in color ) shows the fair copy of Op. 19, No. 4. It contains pencil markings, perhaps by Egon Petri, who played Op. 19 for Schoenberg on January 22, 1912, and was to give the premiere; more likely by Louis Closson, a Belgian pianist, who did give the premiere on February 4, 1912.20 In the last system, m.g. and m.d. (standing for main gauche and main droite, or left hand and right hand, respectively) indicate a redistribution of the line.21 A single line, originally for one hand (punctuated by two-​hand chords in mm. 11 and 12), is now shared between two. This redistribution makes the technically tricky phrase easier: it allows surer and clearer articulation of the fast notes in m. 10, and stronger definition of the m.g. eighths in mm. 11 and 13. It also makes a faster tempo possible. (When played with a single hand, the forte and martellato indications, articulation markings, series of short durations, and configurations on the keyboard limit the speed at which this passage, and hence the entire piece, can be played.) Is this redistribution of hands afforded by the score’s invariants? A line physically articulated by one agent (a single hand) is thereby split between two, losing an element of technical difficulty and requisite effort, and gaining the possibility of a quicker tempo, more forceful articulation, and technical assurance. Stuckenschmidt (1974, 147)  writes that at the premiere “Closson disappointed [Schoenberg]; he played the six little pieces much too quickly and without pauses.”22 In the case of

20 Meyer (2009, 23). For mention of Louis Closson as a pianist from Liège and student of Busoni, see Dwelshauwers (1912, 70). I thank Matthew Arndt for drawing my attention to these markings. 21 Two other hand redistributions occur: the fingerings “3 2” penciled in above mm. 1–​2 suggest that the pianist played the forte accented chord of m. 2 with the left hand, and the low E of m. 9 is marked m.g. 22 “Closson enttäuschte ihn; er habe die sechs kleinen Stücke viel zu schnell und ohne Pause gespielt” (translation by Leong).

Example 2.6. Schoenberg, Klavierstück, Op. 19, No. 4: poco rit. in 1913 published edition and in fair copy.

Example 2.7. Schoenberg, Klavierstück, Op. 19, No. 4: Fair copy.

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this fourth piece, two-​hand distribution of the last line may have allowed Closson to take a faster tempo than Schoenberg desired.

Analysis My analysis23 confronts questions of the piece’s form and shape, and these questions will thread their way through the remainder of the chapter. Despite its brevity, Op. 19, No. 4, presents a manifold form and trajectory. As shown in Example 2.8 (Audio 2.1  ), it contains three phrases, the first angular and presentational, the second lyrical and expansive, and the third martellato and conclusive.24 Each phrase divides into two subphrases: phrase 1a is marked with a slur, phrase 1b changes to straight 16th notes from the dotted rhythms of 1a; phrase 2a brings in an alto voice, which, after the longest inter-​onset duration within the phrase, continues alone in phrase 2b; phrase 3a consists of 32nd-​note flurries, leading to the repeated rhythmic patterns (mm. 11, 12) of phrase 3b. The subphrases of each phrase become ever more tightly connected as the piece progresses. I present three ways in which the piece’s form can be understood (Example 2.9): (a) as a three-​part form in which the second phrase contrasts with the first and last, (b) as a two-​part form in which the third phrase contrasts with the first two, or (c) as a two-​part form in which the final phrase summarizes the first two. As support for (a), the more lyrical and rubato-​like phrase 2 (with its triplet eighth notes and poco rit. at the beginning of phrase 2b) contrasts qualitatively with the more angular phrases 1 and 3. As support for (b), the third phrase differs dramatically from the first two in dynamics (forte to fortississimo versus piano and pianissimo), touch (martellato versus leicht), rate of activity (32nd notes versus longer note values), and direction (conclusive versus trailing off). Pitch and rhythmic relations support (c).25 Example 2.8 shows pitch relations.26 (Upper-​case letters in angle brackets < > label ordered pitch segments; upper-​case letters in curly brackets { } identify unordered pitch collections. Transposition subscripts indicate number of semitones lower or higher in pitch space.) I will begin with relations between the first two phrases, and then discuss those between the opening phrases and the final phrase.

23 My analysis uses the published score, simply because I analyzed the piece before becoming aware of the manuscript sources, and because I knew the piece as a pianist through that published score. 24 I define “phrase” here as a reasonably complete musical idea demarcated by some means of closure (cadence, cadence-​like progression, caesura, etc.). In size my phrases resemble Rothstein’s constructs (1989) more than Schoenberg’s (1967, 3–​7). Both Morris (1993) and Arndt (2018) read six or seven shorter phrases, Arndt differing from Morris only in the addition of an overlapping phrase at mm. 5–​6. According to Morris, “the piece is set in the manner of a recitative with six phrases of diverse character punctuated by chords and in one case, in mm. 5–​6, accompanied by a brief melodic figure marked leicht. . . . Phrase boundaries conform to traditional criteria: slurs and other forms of articulation, punctuating gaps, shape, and referential affinity” (209–​10). 25 These formal descriptions merely outline contrast and similarity; they do not posit formal functions. 26 See also Morris (1993, 209–​12) for discussion of pitch, set-​class, and contour relationships in the piece.

Example 2.8.  Phrases and pitch relations.

Example 2.9. Form.

76  Performing Knowledge Example 2.10.  Phrases 1 and 2: pitch relations.

Example 2.11.  Phrases 1 and 2: descent of bounding A/​E octaves.

Phrases 1 and 2 link closely. Phrase 1b’s opening pitch-​segment H begins phrase 2b at T-​7. Phrase 1b’s pitch-​sets {E} and {F} recur in phrase 2a, the latter with pitches in the same order.27 Pitch elements of phrase 1 reappear in the alto voice of phrase 2, an octave lower, as shown in Example 2.10. And the two phrases together descend through bounding octave A’s and E’s (Example 2.11).28 The soprano fragment (marked leicht) beginning phrase 2 further links the two phrases by fudging the boundary between them. As can be seen in Example 2.8, the boundary’s ambiguity results from voice-​leading, pitch structure, and texture. First, the melodic line of m. 4 continues its stepwise ascent past the fermata ending phrase 1 through the fragment beginning phrase 2 (). Second, as will be discussed later, directed motion from A♯ (or B♭) to B suggests melodic closure in this piece; the fermata on A♯ at the end of phrase 1 therefore implies a temporary halt (analogous to a half cadence) before continuing on to B. The A♯–​B movement is picked up in the tenor voice of m. 6 and brought to completion (B♭–​B) at the end 27 In phrase 1b, {F} occurs as three contiguous notes, and {E} as three notes, the first emphasized by a slur and metric placement, and the second and third emphasized by register. In phrase 2a, {E} forms the upper voice, while the notes of {F} associate through registral proximity. 28 E4 is implied by the line rising through mm. 7–​8 (), but Schoenberg substitutes E3 in m. 9 instead.

Schoenberg’s Klavierstück, Op. 19, No. 4  77

of the work. Third, the main (alto) voice of phrase 2 enters only in m. 6 after the fragment begins, overlapping with it. (Schoenberg marks the alto piano with tenuto markings, over the soprano’s pianissimo.)29 Phrases 1 and 2 link strongly not only with one another, but also with phrases 3a and 3b, respectively. In overview: phrase 1’s opening pitch-​segments and outline phrase 3a; phrase 2’s opening pitch-​sets {E} and {F}, pitch-​segment , and rhythmic pattern define phrase 3b; and pitch-​segments and , which span the boundary between phrases 1 and 2, recur to bridge the boundary between phrases 3a and 3b. In slightly greater detail: phrase 1a’s pitch-​segments and return at T-​12 and T-​13 respectively in phrase 3a, the latter defined by register. Phrase 2’s pitch-​sets {F} and {E} recur as phrase 3b’s alto voice (mm. 11–​12) and left-​hand accompanying chord respectively. Its tenor voice ( in m. 6) reappears in the right hand, in retrograded rhythmic values, to close the piece. Its opening rhythmic pattern (m. 6)  returns in phrase 3b (mm. 11 and 12), reversing the roles of chords and single notes. , the melodic segment that closes phrase 1 and begins phrase 2 (along with a prominent left-​hand pitch), occurs at T-​6 in mm. 10–​11, correspondingly split between phrases 3a and 3b. The melodic segment concluding phrase 1 and linking to phrase 2 recurs in phrase 3, an octave lower in the lower right-​hand register.30 Further evidence of phrase 3’s condensation of phrases 1 and 2 comes in the form of pitch classes F and B (Example 2.12). F5 begins phrase 1; B4 begins phrase 2; F4 moves to B3 over phrase 3 as a whole as well as over phrase 3b. The striking articulation of F-​B as an accented forte chord at the beginning of the piece is answered with B-​F in the sforzando chord at the end of the piece (these top two notes played by the right hand). Phrase 3 not only summarizes preceding pitch material but also brings together two rhythmic threads begun in phrases 1 and 2.31 To discuss this process of convergence, we will need several terms. My metric contour (Leong 2011, 113) assigns 0 to the measure level or downbeat, 1 to the next strongest level of pulses, and so on to faster pulse levels. Example 2.13 shows the piece’s basic 2/​4 metric contour (the larger the contour number, the weaker the metric position). Syncopes and offbeats represent two distinct aspects of syncopation. As discussed in Leong 2011 (113–​17), syncopes, following historical usage, consist of attacks on weak beats that sustain over following stronger beats (Example 2.14a). Offbeats, in 29 Arndt (2018) views the piece as a period (antecedent–​consequent) with interrupting episode; the episode is the alto voice in mm. 6–​9. He reads the antecedent as cadencing in m. 6 (overlapping with the episode in the alto voice). This reading disregards both the ritardando and the long caesura on the A♯ and accompanying chords in mm. 4–​5, and the leicht and pianissimo markings of the soprano fragment and accompanying chords in mm. 5–​6, where Schoenberg indicates a change in color, a new start. 30 Here the distribution between phrases 1 and 2 does not correspond to that between phrases 3a and 3b; rather, the pc pair A♯-​B splits at the “half cadence” between phrases 1 and 2, but joins to create the “full cadence” concluding phrase 3. 31 The rhythmic analysis that follows was first published in Leong (2011), an article on syncopation.

78  Performing Knowledge Example 2.12.  F-​B in phrases 1–​2, 3.

Example 2.13.  Metric contour.

Example 2.14. Syncopation.

contrast, consist of stressed events on weak beats that do not sustain over following stronger beats (Example 2.14b). Syncopes and offbeats will be labeled with their level in the metric contour, followed by their identity as syncopes (s) or offbeats (t). In Op. 19, No. 4, two independent rhythmic threads—​offbeats, and syncopes in relation to motivic pitch structure—​converge in phrase 3.32 The piece contains four short punctuating offbeat chords, shown (Example 2.15) in diamonds at measures 2, 8, 11, and 12. Example 2.16a lists the notated durations of the chords, their dynamics, and their levels in the 2/​4 metric contour. (The piece’s basic metric contour is shown at the bottom of the example for reference.) As the piece unfolds, the chords increase in duration (and dynamic), and make their way to deeper levels of the metric hierarchy. 32 Charles Morrison (1992) has written convincingly of syncopation as motive in this little piece without, however, addressing its relation to pitch, or the question of offbeats.

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At the same time, Schoenberg sets up syncopes on metric levels 2 and 1. The boxes in Example 2.15 mark the cadence of phrase 1 (m. 4), the opening of phrase 2 (m. 6), and the cadence of phrase 3 (mm. 11, 12). Within each box there are two levels of motion: an initial melodic voice that articulates a syncope on level 2 (2s), and a following voice that expresses a syncope or offbeat on level 1 (1s or 1t). Example 2.16b summarizes features of the syncopated passages in these three locations. Since I will be discussing melodic-​rhythmic closure in these locations, I first define what constitutes such closure. F-​F♯ and A♯/​B♭-​B have been established as primary pitch-​class pairs in earlier pieces of the Op. 19 set.33 Pairings of these pitch classes—​and in particular, directed motion within such pairs—​therefore tend to create a sense of melodic closure. Rhythmic closure occurs when syncopes or offbeats “resolve” to strong-​beat articulations. In Example 2.16b, the first two examples, at piano-​pianissimo dynamics, evade melodic and rhythmic closure. Mm. 4–​5 articulate an intermediate cadence: melodic motion stops on A♯, holds over the barline, and begins anew with B♮ in the next phrase. Mm. 6–​7 oscillate between F♯ and F♮ (overlaid with G), sustain over the barline, and trail off into a rubato-​like passage. (A♯–​B lies underneath, pianissimo.) The last two examples, at forte-​fortississimo dynamics, repeat, intensify, and eventually resolve the pitch motion and syncopes of the first two examples. In mm. 11–​12, F–​F♯ moves decisively to a downbeat G, and in mm. 12–​13, B♭ moves emphatically to a downbeat B♮. Thus both passages resolve their level 2 syncopes and their associated pitches clearly. As shown in Example 2.15, in phrases 1 and 2 the diamond offbeat chords and the boxed syncope patterns do not intersect. But by the end of the piece, level 1 in the boxes, previously the site of gentle syncopes, has been taken over by the increasingly brash diamond offbeat chords. The trajectory of these offbeat chords—​ ever louder, longer, and stronger in metric level—​concludes with the final motion to m. 13’s downbeat. Thus, both threads of syncopation—​the melodic syncopes and the punctuating offbeats, representing different textures, levels, and types of syncopation, and associated with characteristic pitch motives—​converge on the final fortississimo downbeat thrust.34 In both pitch and rhythm, then, phrase 3 recapitulates, condenses, and resolves materials and processes begun in phrases 1 and 2. For this reason, and recognizing the contrast between phrase 3 and phrases 1 and 2 (both on the surface and in the way phrase 3 treats prior materials), I view the piece as a synthesis of all three formal options presented at the opening: a two-​part form A~B a'b' (Example 2.9d) in which phrases 1 and 2 (A~B) link tightly, and phrase 3 (a'b')contrasts with and summarizes them.35 33 See, for example, James Baker’s discussion of Op. 19, No.1 (Baker 1990, 181, 187, 190). 34 Dörr’s (2001, 179)  graphic analysis also conveys the sense of convergence to a single point. I  thank Matthew Arndt for sharing this source with me. 35 I have used ~ to indicate the link between phrases 1 and 2, and an overhead bar (the symbol for complementation) to show the contrast between phrases 1 and 2 and phrase 3.

80  Performing Knowledge Example 2.15.  Offbeats (t) and syncopes (s).

The foregoing analysis raises several performance questions. The ambiguity of the boundary between phrases 1 and 2 affords multiple performance choices. One could make a sharp break between phrases 1 and 2, or let the pedal connect to the beginning of the B. After the poco rit. of phrase 1, one could begin a tempo immediately at the leicht soprano fragment, or use the fragment to ease into the a tempo, achieving it at m. 6. How should phrase 3 be shaped? The parallel rhythmic structure of mm. 11 and 12 suggests playing these measures (and by implication m. 13) as distinct units. But the downbeat resolutions of the syncopes and offbeats (with their associated pitches

Schoenberg’s Klavierstück, Op. 19, No. 4  81 Example 2.16.  Offbeats (t) and syncopes (s) outlined.

and ) imply driving over the barlines.36 One can expand this dynamic shaping to the entire phrase by hearing the F and F♯ beginning the 32nd-​ note flurries of m. 10 driving to the G of m. 12 (after being rearticulated in m. 11), and the preceding the rest in m. 10 answered unequivocally by the piece’s final .

36 The accent markings on the F♯ and G suggest linking them.

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The analysis also proceeds from certain choices. It focuses on pitch and rhythmic structure, taking three phrases as a starting point, and deriving a particular formal and processual understanding therefrom. These choices are interpretive: I could have focused on pitch contour, on other aspects of rhythmic structure, on the performer’s physical motions, on hermeneutics, among a host of other possibilities. The three phrases seemed to me self-​evident, but other approaches are possible. And my formal options are interpretive readings in themselves, built upon the preceding analytical decisions. My analysis takes Schoenberg’s score (this published edition of it) fairly literally, perhaps even more literally than is easily practicable: it is difficult to play the final fortississimo single note more loudly than the preceding chordal sforzandi.37 Even so, it is grounded in my experiences as a pianist learning, playing, and performing Schoenberg’s Op. 19, and on the aural and kinesthetic sense embedded from those experiences. And its interpretation of the piece’s dynamic trajectory and formal possibilities could easily inform a performance. Given my literal reading of the score’s symbols and the general straightforwardness of Schoenberg’s notation, one could say unproblematically that my analysis was afforded by the score, my creative insights as an analyst meeting the score’s features. The three recordings we will discuss, by Edward Steuermann, Maurizio Pollini, and Mitsuko Uchida, go beyond the score, contributing to and contradicting it in varying and distinct ways.

Recordings Our discussion will refer to five graphs of tempo and volume (Figures 2.1–​2.5. These may also be found in color online ). The graphs stack Steuermann (1949), Pollini (1974), and Uchida (2000) on top of one another for comparison.38 Measure numbers run across the bottom of each graph; vertical lines show phrases. The graphs display tempo between articulated quarter-​note beats (Figure 2.1), between all attack points (Figure 2.2), and between eighth-​note attacks in phrase 3 (Figure 2.3) (all measured in quarter notes per minute); volume at every attack point (Figure 2.4); and played durations and volume of the diamond offbeat chords (Figure 2.5). (For comparison, the top of Figure 2.5 shows the durations and volume of these chords as notated.) Note that tempo graphs do not show the tempo of the final note, on the m. 13 downbeat, because there is no following attack from which to calculate the tempo. (The Appendix to this chapter describes the methods used to obtain this data.)



37 One can compensate for this with timing, directness of attack, sound quality, and so on. 38 We refer to these recordings by year of recording, rather than by year of issue.

Figure 2.1.  Tempo by quarter note.

Figure 2.2.  Tempo by note. Measured in beats per minute (beat = quarter note).

Figure 2.3.  Tempo by eighth note, phrase 3. Measured in beats per minute (beat = quarter note).

Figure 2.4.  Volume (Db below maximum speaker volume).

Schoenberg’s Klavierstück, Op. 19, No. 4  87 Figure 2.5.1.  Diamonds as notated and played.

88  Performing Knowledge Figure 2.5.2.  Diamonds as played.

Example 2.17.  Steuermann (1949): phrase 3 compared to score. (a) Steuermann (1949)

(b) score

Steuermann (1949) (Audio 2.2  ) Example 2.17a provides our transcription of the last phrase of Steuermann’s 1949 recording. Compare to Example 2.17b and notice the pedal through the second half of m. 10 and on the sf chords (mm. 11, 12), the swap of F and G♯ at the m. 11 barline, the dynamics decreasing from f to meno f to mp, and (Figure 2.3) the speed through the

Schoenberg’s Klavierstück, Op. 19, No. 4  89

m. 10.25 triplet and rush to the downbeat of m. 12. In general, Steuermann’s recording treats the score fairly loosely: score details and larger-​scale shaping seem to be subsumed by local color and rubato, and even a little technical unsteadiness at the end of m. 10.39 Steuermann’s tempo overall is relatively quick (Figure 2.1, quarter = 78.9 bpm),40 and quite variable. A glance at Figure 2.2, showing the tempo of individual notes, demonstrates Steuermann’s rubato touches: in Phrase 1a, he lingers on the forte chord of m. 2; in phrase 2b, he stretches out the triplet, slims and overdots the dotted rhythm, and lingers on the staccato chord (much as he did in m. 2). He ends phrase 2, surprisingly, with a staccato on the final E. Steuermann’s diamond chords (Figure 2.5.1) do not follow the contours of their notated durations (increasing but for the lack of a staccato on the first chord) or dynamics (generally increasing). In fact, his later (1957) recording, in which the tempo is steadier, the dynamics more purposefully shaped, phrase 3 cleaner and without pedal, the played durations of Steuermann’s diamond chords (Figure 2.5.2) trace the opposite general trajectory of what is notated. Clearly, Steuermann does not intend his performance to be a sonic image of the score. Rather, his pedaling, rubato, and larger shaping produce a three-​ dimensional, textural, and somewhat romantic interpretation. Though surprising to the modern ear, Steuermann’s contradictions of the notated score should be considered in the context of his close relationship with the composer: he studied composition with Schoenberg, premiered many of Schoenberg’s works involving piano,41 made the first LP recordings of the Op. 19 set,42 and at Schoenberg’s request prepared vocal scores for Erwartung Op. 17 and Die Glückliche Hand Op. 18, and the two-​piano version of the Piano Concerto (Steinberg 2012; Leibowitz [1951]). In 1949 Schoenberg wrote that “thereafter [after Richard Buhlig’s premiere of Op. 11] came Eduard Steuermann, who since then has remained my ambassador of the piano.”43 We also know that Steuermann was dissatisfied with his recording of Schoenberg’s piano works. When in 1949, soon after Schoenberg’s seventy-​ fifth birthday, “Steuermann’s recording of all Schoenberg’s piano pieces arrived, he was worried about mistakes in the performance. Schoenberg reassured him: ‘There is no absolute purity in this world: pure water contains infusoria. But I am certain that you can play music so convincingly that it evokes the impression of purity, artistic purity, and after all that’s all that matters.’ ” In 1950 “difficulties about the recording of 39 Steuermann writes that in Schoenberg’s piano music “[color] is not an adornment of, but something that cannot be separated from the essential ‘thought’; it is something that develops and changes with the thought” (1937, 130–​31). 40 Overall tempo is measured as follows: Let t = overall tempo. Let d = the duration in minutes from the m. 1 downbeat to the m. 13 downbeat. 24 quarter notes occur in this span, so t (in quarter notes per minute) = 24/​d. 41 Including Pierrot Lunaire; Fünf Klavierstücke, Op. 23; Suite für Klavier, Op. 25; the Piano Concerto; and Ode to Napoleon (Stuckenschmidt 1978, 201–​2, 292–​93, 459, 463–​64, 468). 42 Walter Gieseking made the first recording, a piano roll, in 1925 (Meyer 2009, 23). 43 Unpublished program notes for Op. 11 (in English), meant to accompany Steuermann’s performance for Dial Records. It was Etta Werndorf who premiered Op. 11 in 1910; Schoenberg refers to Buhlig’s performance of the pieces in 1912 in the context of the scandal they provoked (Brinkmann 1975, XIV).

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Schoenberg’s piano music that Eduard Steuermann had begun” continued. “The all too self-​critical great pianist still had scruples. Schoenberg’s patience was exhausted. He wrote an angry letter, which bore no date beyond the year 1950. Steuermann must finally finish with it, or else he would never be able to. Perfection does not exist among human beings; he himself, Schoenberg, had had to do without it.”44 Contrast Schoenberg’s praise of “artistic purity” in Steuermann’s imperfect renditions with his qualified evaluation of Egon Petri’s technically proficient interpretation of Op. 19.45 After hearing Petri play through the pieces, Schoenberg wrote in his diary, “He will probably play the pieces very well. At least pianistically. In general he took everything too fast; or rather too hastily. I said to Webern: One must have time in my music. It is not for people who have other things to do. At any rate it is a great pleasure to hear one’s pieces played by someone who can master them perfectly from a technical point of view” (Stuckenschmidt 1978, 156).

Pollini (1974) (Audio 2.3  ) Pollini, in contrast to Steuermann, does follow the score closely. Figure 2.1 shows that he begins much more slowly than does Steuermann or Uchida, and is therefore able to better maintain this tempo over the course of the piece (overall tempo quarter = 71.7). In rhythmic detail (Figure 2.2) he is also the most accurate: in m. 1, for example (boxed in the figure), all three performers lengthen the thirty-​second notes and shorten the double-​dotted eighth notes, but Pollini does so the least. Pollini’s formal shaping is cleaner-​cut and larger-​scale than that of the others. His timing delineates whole phrases: (Figure 2.2) he begins each phrase with a note (circled) that is slightly faster than what follows, (Figure 2.1) he knits subphrases 1a and 1b together by speeding up slightly in m. 2.5, and he keeps basically the same tempo within each of phrases 1 and 2 prior to their ritardandi. His phrases overall decline in tempo. Pollini’s dynamics (Figure 2.4) are rather angular. Local dynamic peaks tend to fall on downbeats (mm. 1, 2, 3, 6), suggesting a “metrical” interpretation.46 (In other cases they emphasize pitch peaks [m. 3.75] and unit onsets [m. 7.25, phrase 2b].) Phrase 3 expresses intensifying dynamics, growing over m. 10, then swooping upward in parallel fashion in measures 11 and 12. Pollini’s third phrase is the most directed of the three performances. The tempo (Figure 2.3) slows from measure to measure:  m. 10, at a quick but overall steady eighth-​note tempo, leads into m. 11; m. 11, at an overall slower tempo, accelerates through its three events, leading into m. 12; m. 12 as a whole slows very slightly into m. 13, with a tiny push from m. 12.5 leading to the downbeat of m. 13. The overall slowing across the phrase combines with the parallel dynamic shapes and overall 44 Stuckenschmidt (1974, 461, 468). The translation is Leong’s revision of Searle’s (Stuckenschmidt 1978, 507, 514). These remarks refer to Steuermann’s 1957 recording of Schoenberg’s complete piano music. 45 Petri was to have premiered the pieces, but was replaced by Louis Closson due to a scheduling conflict (Stuckenschmidt 1978, 157). 46 The actual local peak at m. 2.875 is the accented forte diamond chord within the phrase’s piano dynamic.

Schoenberg’s Klavierstück, Op. 19, No. 4  91

volume intensification of mm. 11, 12, and 13 to lead quite clearly to the final downbeat. In both played duration and volume, Pollini’s diamond offbeat chords (Figure 2.5.1) represent the score most closely (it is difficult to play the final single note as loudly as the preceding chords), thus reinforcing the piece’s drive toward the final note. Pollini, who is known for “the analytical strictness of his interpretations” (Rattalino 1980, 49), comes closest of our three recordings to providing an interpretation afforded by the literal meaning of the score’s symbols. In his notes to Pollini’s recording—​a recording made in 1974 when, for the Schoenberg centenary, Pollini performed the complete Schoenberg works for piano internationally—​Gregor Willmes (2001, 7) quotes critic Joachim Kaiser: “Pollini doesn’t bring something special to the works—​he brings it out of them.” Adhering closely to the score is in itself an interpretive choice. This stance can present the performer with further choices when the score makes contradictory demands. In this case, Pollini plays Op. 19, No. 4 moderato rather than Schoenberg’s indicated rasch aber leicht (quick but light), presumably in order to present the score’s notes and rhythms accurately at a consistent tempo.

Uchida (2000) (Audio 2.4 ) Uchida’s 2000 recording is definitely “rasch, aber leicht.” Her clear, transparent touch, mercurial tempo, and gestural shaping give the impression of quicksilver tracings. Her overall tempo (Figure 2.1, quarter = 74.7) is not especially fast, but she begins quickly in phrase 1a and moves even more quickly in phrase 1b. Her playing traces arch shapes in both tempo and volume.47 All of her (sub)phrases 1a, 1b, 2a, 2b, and 3 articulate the same temporal shape (Figure 2.2): an acceleration toward the middle and deceleration toward the end, with a slight pause before the final event. (Please listen to Audio 2.4 .) Paired subphrases 1a and 1b, and 2a and 2b, as well as the two halves of m. 10, display similar temporal profiles.48 Uchida’s final phrase (Figure 2.3) begins quickly, but slows quite smoothly through mm. 11–​13. (The deceleration suggests a parsing of phrase 3b into the parallel units of mm. 11, 12, and 13, rather than a drive to the downbeats of mm. 12 and 13.) Her diamond chord durations through mm. 11–​13 (Figure 2.5.1) support the wedge shaping of her gestures: her final B (m. 13) is much shorter than expected, particularly when scaled to her slow closing tempo. Uchida’s dynamics (Figure 2.4) also support a gestural interpretation. Arch shapes again articulate (sub)phrases 1a, 1b, 2a, 2b, and 3, as shown by the figure, which fits quadratic curves to each subphrase. (The curves for Uchida’s subphrases are not only more curved but also better fitted to the data than those for Steuermann and Pollini, not shown.49) Notice the relative quietness of the m. 2 offbeat chord; the mf dynamic 47 See Cook (2013, 176–​223), for a wide-​ranging discussion of “phrase arching.” 48 Uchida’s evening out of the long and short notes of mm. 1–​2.5 (the long notes become increasingly short and short notes increasingly long) also supports her arch shaping of the subphrase. 49 Based on the x2 coefficient and the r2 value, respectively.

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allows the chord to remain within the general dynamic arch of phrase 1a. Notice, too, the smooth increase in volume over m. 10a (up to the rest), then the curve upward through m. 11, followed by decreasing dynamics on the punctuating diamond chords (mm. 11.5, 12.5, 13), shaping the phrase’s gesture. (The offbeat chord of m. 11.5 forms the loudest point of Uchida’s performance.) All of Uchida’s (sub)phrases except for 2b end louder than they began; subphrase 2b ends softer than it began. Uchida’s tempo and volume arches are not afforded by the score in any literal sense; they even contradict Schoenberg’s express indications in certain places. For instance, the loudest note in phrase 2b is not the A of m. 7 as indicated by Schoenberg, but the immediately following G♯, which swings the subphrase’s center of gravity considerably toward m. 8, where Uchida’s quickest phrase 2 tempo occurs (she speeds up slightly over the triplet, contrary to Schoenberg’s poco rit.). Her recording of the piece is a creative response to Schoenberg’s score. Mitsuko Uchida is known for performing works by Vienna-​ associated composers, particularly Mozart, Schubert, and Schoenberg. Her acclaimed recording of the Schoenberg Piano Concerto with Pierre Boulez and the Cleveland Orchestra in 2000 includes the Op. 19 recording discussed here. Also lauded for her 1990 recording of the Debussy Etudes, Uchida brings an impressionistic sensibility to her interpretation of Schoenberg’s Op. 19, No. 4. We were surprised to find that the three recordings discussed here can be understood as articulating three of the formal views outlined earlier (Example 2.18). Due to its distinct dynamic, rate of activity, and articulation, the third phrase necessarily distinguishes itself from the first two. An interpretation’s formal deciding factor, therefore, is how the first two phrases relate to one another and to the whole. Steuermann takes a large breath (silence) between phrases 1 and 2, and begins phrase 2 with a new color (and more softly). Tempo shaping also differentiates Steuermann’s first and second phrases:  clearly shaped subphrases 1a and 1b resemble one another, in distinction to the lack of clear tempo patterning in following (sub)phrases. Steuermann’s second phrase thus stands out as a separate unit, creating a three-​part form for the piece (Example 2.18a). Example 2.18.  Form and recordings.

Schoenberg’s Klavierstück, Op. 19, No. 4  93

Of the three recordings, Pollini presents first and second phrases most homogeneous in tempo, volume, and tone color. He does make a small break between the two phrases, and begins the second phrase with a clean a tempo, but the overall similarity of his two phrases sets them in sharp distinction to his third phrase. The result is a two-​part form (Example 2.18b). Uchida’s second phrase is much slower than her first, and also louder, especially at the downbeat of m. 6. Of the three recordings, she makes the biggest deceleration at the end of phrase 1, and, at the end of phrase 2, the least shortening of the notated duration from the final E to the first attack of phrase 3. These factors set the second phrase apart. However, Uchida links phrases 1 and 2 by connecting them smoothly in volume, tempo, and articulation (her pedal blurs slightly into the B beginning phrase 2). Her phrases 1 and 2, while distinct units, nevertheless shade into one another at their boundaries. As a result Uchida articulates a hybrid two-​part form (Example 2.18d). These commonalities between the recordings and the analysis come about not because of the score’s affordances alone, as all four interpretations make independent creative choices—​selecting from, elaborating upon, adhering to, or conflicting with the score. They come about through intersections among creative choices. Nos. 1–​5 of Op. 19 were written in a single day (Stuckenschmidt 1978, 136). There is therefore a spontaneous aspect to their composition, and one wonders if the almost improvisatory quality of the set bears any implication for its performance. Yet the score of each fleeting vignette also affords multiply determined structures, giving rise to creative responses both rigorous and free. Detailed and abundant expressive markings further highlight both the precision and flexible nuance of the set. Steuermann neither follows the score closely nor creates consistent temporal/​dynamic shapes. Rather, he tinges the piece with shades of a Romantic intermezzo, articulating small rubatos, and blurring the martellato line of the last phrase with pedal. Uchida combines a light and transparent touch, gestural shaping in time and volume, and overall tempo variation to lend the piece the aura of an impressionistic miniature. Pollini delivers the performance with the most drive, directed toward the last note. While closest to the notated score, his interpretation finds Schoenberg’s “rasch, aber leicht” directive elusive. Leong focuses on pitch and rhythmic elements of the score, and derives a particular understanding of formal balance, phrasal connections, and dynamic trajectory therefrom. As a reading expressed in words and diagrams, her analysis makes no specific decisions regarding aspects—​tempo, timing, touch, pedaling—​integral to physical performances. Each interpretation brings something new to the work: Ayrey argues that “interpretation must produce, must be itself, a new sign [in Pierce’s infinity of interpretants]. Interpretation itself, therefore, must be creative; it must match the challenge of the artwork” (1996, 4–​5). Bloom says, “the meaning of a poem can only be a poem, but another poem—​a poem not itself.” This poem may be “the precursor

94  Performing Knowledge

poem or poems. The poem we write as our reading. A rival poem, son or grandson of the same precursor. A  poem that never got written—​that is—​the poem that should have been written by the poet in question. A composite poem, made up of these in some combination” (1997, 70, 94–​96). Following Lewin (following Bloom), analyses and performances are “other poems”—​creative responses to a composer’s work (1986, 381–​82).50 As “other poems,” analysis and performances create their own affordances; they themselves meet creative responses that hear, see, sense, and enact intelligible relationships among their invariant features, understanding them to create, among other things, musical structure.

Recordings Cited Schoenberg, Sechs Kleine Klavierstücke, Op. 19 Pollini, Maurizio. Recorded 1974. 2001. Deutsche Grammophon 471 361-​2. Reissue of 1975 Deutsche Grammophon 2530 531 stereo LP. Steuermann, Edward. Recorded 1949. [1951.] Dial Records 14 [mono LP]. Steuermann, Edward. [1957.] Schoenberg:  Complete Piano Music. Columbia Masterworks ML5216. Uchida, Mitsuko. Recorded 2000. 2001. Philips 289 468 033-​2.

Editions Schönberg, Arnold. 1968. Sämtliche Werke: Werke für Klavier. Edited by Eduard Steuermann and Reinhold Brinkmann. Vienna: Universal Edition. Schönberg, Arnold. 1975. Sämtliche Werke:  Werke für Klavier:  Kritischer Bericht—​Skizzen—​ Fragmente. Edited by Reinhold Brinkmann. Vienna: Universal Edition. Schönberg, Arnold. 2009. Sechs kleine Klavierstücke op. 19: Facsimile. Vienna: Arnold Schönberg Center. [contains holograph fair copy and first written copy, commentary by Christian Meyer]

50 My point is not that analysis and performance are equivalent, but that both are creative. Analyses can be creative in diverse ways, of course; analyses that might be considered explicitly compositional and performative are those that create new “pieces” built upon the piece being analyzed. An example is harpsichordist Robert Hill’s practice of creating playing reductions for works of J. S. Bach. (Please see Video 2.1 for a brief demonstration from the Praeludium of the Partita in B♭ major, BWV 825. I am grateful to Robert Hill for the permission to include this video clip.)

Schoenberg’s Klavierstück, Op. 19, No. 4  95

Appendix: Data Acquisition and Analysis Data Acquisition Attacks Attacks were calculated using Sonic Visualiser’s “Note Onset Detector:  Onset Detection Function.” The settings that proved most successful were “complex domain” function type, 1024 window size, 16 window increment, and Hann window shape. This analysis produces a graph that reaches a local maximum at the onset of a new frequency. (The method was appropriate to our analysis since the piano attacks are sharp and notes are not repeated, trilled, or tremoloed.) Results were confirmed with a visual change in waveform and a color change in the chromagram, a two-​dimensional graph of pitch (y axis) and loudness (coloration) over time (x axis). They were then fine-​tuned by ear, using an additional “Time Instants Layer” and its associated “click” sounds. All three recordings were analyzed in stereo. To find the true note onset time, the left and right channels were analyzed separately, and the earlier of the two onsets chosen.

Releases Releases were determined using Sonogram’s Fast Fourier Transform operation (FFT). The FFT graphs volume versus frequency. It separates the frequencies, allowing us to examine the volume envelope of a specific note rather than a group of notes. To find releases, we located the timepoint at which volume of the note’s fundamental frequency begins to decrease quickly. With the piano, a held note experiences a gradual decay, but a released note produces a sharp decay. The timepoint at which the decay rate changes from gradual to sharp is recorded as the raw release value of that note. Because of FFT’s “window” of 4096 samples on each side of the test point, each release point appears to be 4096 samples too early. To correct for this, we added 4096 samples to the release point.

Dynamics Dynamics were measured using Sonic Visualiser’s “Amplitude Follower” from its software developer kit. This program finds the maximum amplitude over short timespans. The settings chosen were 1024 audio frames per block, 16 window increment, and 0.01 second attack and release times.

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Data Analysis Local Tempi Figure 2.5 features a bar graph that scales the played durations of “diamond” notes to local tempi. The local tempi were determined as follows: m. 2 diamond m. 8 diamond m. 11 diamond m. 12 diamond m. 13 diamond

average tempo of mm. 1.0–​2.5 average tempo of mm. 8.0–​8.75 average tempo of mm. 11.0–​11.5 average tempo of mm. 12.0–​12.5 average tempo of mm. 12.5–​13.0

3 Understanding of Structure

Performed Rhythm at the Center of Bartók’s Fifth String Quartet Daphne Leong with the Takács Quartet

Structural understanding is not culturally neutral. In an early presentation of this chapter’s material, an argument arose with a well-​known theorist about the structural interpretation of the (3 + 2 + 2 + 3)/​8 meter. At the time I could not explain why I disagreed with his interpretation. I now understand that, while theoretically plausible, his interpretation was incongruent with an understanding of the Hungarian source material. This chapter explores evidence beyond the notation itself—​commercial recordings, Bartók’s writings, and primary source materials—​to provide a cultural backdrop for interpreting the asymmetrical meters in the trio section of the Fifth Quartet’s scherzo movement. It concludes with a practical performers’ guide. We begin by asking the reader to listen to two recordings of a passage from the middle of Bartók’s Fifth String Quartet:  Audio 3.1 and Audio 3.2 . One is struck by distinct interpretive differences, particularly in rhythm, articulation, and accentuation. The first performance is rhythmically more angular and accentuated, the second more flowing in its rhythms and lyrical in its legato. Well-​known string quartets differ remarkably in the manner in which they perform the rhythms of this passage. What are these differences in rhythmic interpretation, and what explains them? Perhaps Hungarian quartets play the rhythms differently from other ensembles. This chapter explores this hypothesis, examining ten recordings by noted Bartók interpreters and investigating the cultural context for the passage. Two additional hypotheses emerge from this exploration; all three hypotheses are analyzed statistically.

I thank all members of the Takács Quartet—​(at the time of writing) Edward Dusinberre, András Fejér, Károly Schranz, and Geraldine Walther—​for discussing questions of performance interpretation with me. András and Károly gave valuable feedback on cultural context, and András in particular assisted with important aspects of this chapter, not the least of which was the video interview. I am also grateful to Katalin Boros for assistance with Hungarian translation. Daphne Leong with the Takács Quartet, Understanding of Structure In: Performing Knowledge. Edited by: Daphne Leong, Oxford University Press (2019). © Oxford University Press. DOI: 10.1093/oso/9780190653545.003.0005

98  Performing Knowledge Example 3.1.  Bartók, Fifth String Quartet: Arch form (Bartók 1935, 414).

Example 3.2.  Bartók, Fifth String Quartet: Formal symmetry (after Bartók 1935, 414–​415).

Structure in Cultural Context To set the passage in cultural context, we describe its structure in relation to Bartók’s writings on folk music: his analysis of Hungarian folk music, Bulgarian meters, and folk rhythmic transformations. (Leong 2014 explores this question in detail; here we summarize the relevant aspects of those findings.) The quartet is strikingly laid out in a five-​movement “arch” form, a plan in which the outer movements relate symmetrically by thematic content, “tonality,” textures, or tempos around the central scherzo, as summarized in Example 3.1 by Bartók’s diagram.1 Each individual movement of the quartet  also displays symmetry. As outlined in Example 3.2, the first movement, in sonata form, contains a recapitulation that presents the first theme, transitional section, and second theme of the exposition in reverse order and loosely inverted. The fifth movement, in rondo form, can be parsed as A B C B' A' Coda. The second and fourth movements are cast 1 This aspect of the Fifth Quartet’s form is well documented by Bartók himself (1935, 414), as well as by many others.

Bartók’s Fifth String Quartet  99

in ABA' form. The third movement takes the form of a scherzo and trio, with the scherzo itself in ABA' form. The trio section lies at the center of the entire quartet. Example 3.3 provides the score of the trio; please refer to it throughout the remainder of this chapter. In form, the trio consists of (a) an introduction (mm. 1–​8) that accelerates to (b) the main tempo and the section’s main body (mm. 9–​52), marked by the entrance of the melody in rilievo, and (c) an “outtro” (mm. 53–​65) that bridges to the return of the scherzo. In texture, the trio features a melodic voice (the viola or cello) in rilievo against an almost constant ostinato and droned pitches, con sordino.2 The trio’s main melodic material occurs first in the viola, at m. 9, and then in the cello, at m.  17. This material strongly resembles Hungarian folk song, although it translates the standard rhythmic patterns of Hungarian folk song into 3:2 proportions, resembling Bulgarian meters. The trio’s meter signature is notated as (3 + 2+ 2 + 3)/​8 and marked, in Bartók’s footnote under the score, “also (2 + 3 + 2 + 3)/​8, and (2 + 3 + 3 + 2)/​8.” The viola’s melody in mm. 9–​16 links clearly to “old-​style Hungarian folk song,” as characterized by Bartók (2002, 13–​24). As summarized in Example 3.4, its rhythmic structure resembles that of a common category of this repertoire: eight-​ syllable isometric melodies in variable tempo giusto. Example 3.4a diagrams Bartók’s linkage of poetic units to metric-​rhythmic ones in this type of folk song. The basic unit, the line, articulates two measures, with each line displaying the prototypical pattern of metric stresses 3

. The lines combine into line pairs, which themselves pair to form strophes.4 The trio’s viola melody (mm. 9–​16) displays the same 1-​m., 2-​m., 4-​m., and 8-​m. hypermetric levels and grouping structure as shown in Example 3.4a. Bartók categorizes the old-​style tunes based on the number of text syllables per line, the most common category being that of eight syllables per isometric line (2002, 13). The viola melody of our trio also expresses eight notes in each two-​measure unit or “line,”5 in a line structure based on the aforementioned 4/​4 pattern, although the rhythmic values involved are not pure quarter notes. Rather, the trio’s basic rhythmic patterns are shown in Example 3.4b’s first column, and can be represented as the duration-​segments in the second column: X1 = , X2 = , and X3 =  (1= ).6 These are the 2 Bartók used in rilievo to indicate the main voice. (See Somfai 1996b for his discussion of the notation for strings in Bartók’s chamber music, focusing on articulation and critiquing recordings.) 3 Bartók (2002, 16). Although Bartók describes this pattern as a rhythmic pattern, his discussion shows that he conceives of it as a metric-​rhythmic pattern. 4 “The tune-​strophe consists of four isometric lines.” “The most important final note is that of the second line, the chief caesura, which divides the tune into two equivalent parts complementing one another: into question and answer, so to speak” (Bartók 2002, 13, 17). 5 The last “line” (mm. 15–​16) features a cadential change to five syllables from the usual eight. 6 A duration-​segment (seg) is defined as an ordered set of durations, and notated between angle brackets < > (Leong 2000, 71).

100  Performing Knowledge Example 3.3.  Bartók, Fifth String Quartet, III Trio.

three duration-​segs that correspond to the notated meter and Bartók’s footnote to this meter, and essentially the only three duration-​segs (but for a one-​measure exception) expressed by the trio’s melodic voices. More generally, as shown in the third column of Example 3.4b, these duration-​segs can be abstractly expressed

Bartók’s Fifth String Quartet  101 Example 3.3  (cont.).

in terms of long (L) and short (S) durations, where L = and S = : , , and . Viewed this way, the trio’s rhythmic patterns fall (in principle) into Bartók’s subcategory of eight-​ syllable isometric melodies, “variable” or “adjustable tempo giusto.” In this subcategory, the quarter-​ note pairs of the pattern adjust to or   , or remain as  ,

102  Performing Knowledge Example 3.3 (cont.).

depending upon the length of the text syllables.7 Bartók lists eight possible variable tempo giusto patterns for the first measure of the two-​measure line, the most common of which are ,  , and  , or, where S =  and L = , < S, L, L, S >, 7 Bartók (2002, 27). Although variable tempo giusto is of vocal origin, it also occurs in instrumental music (Bartók 1943, 384–​89).

Bartók’s Fifth String Quartet  103 Example 3.3 (cont.).

< L, S, S, L >, and < S, L, S, L >. As shown in Example 3.4b, these are the same three long/​short patterns as found in the trio. In general, rhythmic patterns in variable tempo giusto change from line to line in conformity to text stresses. The actual proportions of the dotted rhythm (or its reverse) vary according to the tempo and the performer’s inclinations; they

104  Performing Knowledge Example 3.4.  Viola melody (mm. 9–​16): Rhythmic similarities to old-​style Hungarian folk song (8-​syllable isometric melodies in variable tempo giusto).

can approach in quick tempi and or even in slow tempi, according to Bartók (2002, 28). In the trio they conform to the 3:2 proportions characteristic of Bulgarian meters—​non-​isochronous meters that Bartók found in Romanian, Hungarian, Slovakian, and Turkish music, as well as in Bulgarian music.8 Although the proportions of Bulgarian meters are fixed, Bartók’s conception of them resembles the variable tempo giusto model, in that he views the unequal durations as rhythmic alterations of even ones. For instance, he explains the Bulgarian “Ruchenitza” meter (2 + 2 + 3)/​16 as lengthening the last beat of a 3/​8 bar: “My feeling is that this extension of the note value is no other than the translation of a dynamic stress into terms of duration. For it is as a stress, or a substitute for a stress, that the note that is lengthened by a sixteenth value is experienced.”9

8 Bartók (1938). Leong (2014, 118) describes an intriguing link between variable tempo giusto and 3:2 proportions. 9 Bartók (1938, 47–​ 48). The “Ruchenitza” is a common Bulgarian folk dance (also transliterated “rachenitsa”). See Buchanan (2001, 578); also Rice (2000, 198). According to Rice, Bartók errs in certain details of his theory of Bulgarian rhythm. First, isochronous and non-​isochronous meters should be placed on equal footing; neither should be viewed as more normative. Second, transformations do occur in actual practice between 6/​16 and 7/​16. However, the transformation is from 3+3 (and not 2+2+2, as Bartók postulates) to 2+2+3, or vice versa. Finally, Rice adds that transformations of meter occasionally result from changes of tempo.

Bartók’s Fifth String Quartet  105

Our trio is located in the middle of the Fifth Quartet’s scherzo, which is labeled alla bulgarese and notated in a time signature of (4 + 2 + 3)/​8. The trio itself employs what Bartók (1943, 45–​46) calls “hyper-​Bulgarian” meter:  a type of Bulgarian meter found in Romanian folk music that features very fast subdivisions, at MM 500 or even 600. Our trio’s main tempo (m. 9), at  = 120, or  = 600, falls in the “hyper-​Bulgarian”  range. In addition to similarities to old-​style Hungarian folk song and Bulgarian meter in rhythm, the viola melody of mm. 9–​16 and the cello melody of mm. 17–​24 also display characteristics of Hungarian folk song in pitch and form. The viola melody resembles old-​style Hungarian folk song as described by Bartók (2002, 16–​20), in its pentatonic collection, melodic formulae, caesura pattern, descending melodic shape, and line formal pattern. The cello melody displays loose resemblances to new-​style Hungarian folk song as described by Bartók (2002, 20–​21) and Kárpáti (1994, 379), in overall pitch contour and formal structure. Thus the trio’s primary melodic material links strongly to Hungarian folk song and Bulgarian meter as described by Bartók, drawing upon the grouping and metric structure of eight-​syllable isometric melodies, featuring characteristic variable tempo giusto patterns altered to the proportions of Bulgarian meters, and displaying pitch features of old-​and new-​style Hungarian folk song. In addition, in the trio Bartók develops this material with rhythmic techniques that resemble folk-​rhythm transformations (rhythmic-​ metric transformations, segmental manipulations, and “shifted rhythms”) that he described (Leong 2014). These similarities to folk materials and processes present performance implications for our trio.

Ten Recordings The recordings that we surveyed, by noted interpreters of the Bartók quartets (see discography), display great differences in the performance of these rhythms. This chapter examines ten of these recordings. Following the sequence of the actual investigation, it surveys the evidence informally, assessing our initial hypothesis (that Hungarian quartets perform these rhythms differently from other quartets), then tests this and two emergent hypotheses statistically. We begin by summarizing our ensembles’ connections to the Bartók string quartets, and to one another. Example 3.5 displays these connections. The boxes represent the ensembles at the times of our recordings; shaded boxes show the three premieres. Example 3.5c displays the Kolisch’s world premiere in Washington, DC, followed a few months later by the Pro Arte’s performance in Marseille; the New Hungarian Quartet (Example 3.5b) gave the Hungarian premiere in Budapest several months after that. Ovals indicate Bartók’s direct influence, where present. Lines indicate coaching; arrows show lineage (personnel in common). The Juilliard Quartet (Example 3.5a) was the first American quartet to perform the complete cycle of Bartók quartets, in 1948, and the ensemble has since performed the

Example 3.5.  Selected string-​quartet connections: Lineages and coachings.

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cycle numerous times.10 The Tokyo Quartet was formed at the Juilliard School, and studied with the Juilliard Quartet, which at that time included two of the members—​ Robert Mann and Raphael Hillyer—​from the Juilliard recording discussed here. Tokyo’s violist Kazuhide Isomura cites the Juilliard Quartet, and particularly Mann and Hillyer, as strong influences, saying “we especially loved their Bartók and the new Viennese music” (Eisler 2000, 46). The Emerson Quartet was also founded at Juilliard; it became closely associated with Bartók’s quartets, first performing all six in a single evening in 1981. Its recording of the Bartók quartets received two Grammy Awards and a Gramophone Award, along with two major European awards (Eisler 2000, 11). The New Hungarian Quartet (Example  3.5b) gave Bartók’s Fifth Quartet its Hungarian premiere in March 1936, after rehearsing it with Bartók. Consisting of Sándor Végh, László Halmos, Dénes Koromzay, and Vilmos Palotai, this quartet provided the ancestry for the Végh Quartet and Hungarian Quartet of the recordings discussed here. Sándor Végh formed the Végh Quartet after leaving the New Hungarian Quartet. The New Hungarian Quartet dropped the “New” from its name, and became the Hungarian Quartet; by the time of the recording discussed here, Zoltán Székely was the first violinist and Dénes Koromzay the only remaining original member.11 Székely had been Bartók’s close friend, sonata partner, and trusted interpreter of his music, as well as the dedicatee of the Second Violin Concerto.12 The Takács Quartet of our recording worked on Bartók’s compositions under Székely and Koromzay.13 The Keller Quartet was coached by Sándor Végh on Bartók’s works (Végh 1995, 7); their recording of the Bartók quartets won a Deutsche Schallplattenpreis. The Tátrai Quartet won the Budapest International Bartók String Quartet Competition in 1948 and the Kossuth Prize in 1958, and premiered many works by Hungarian composers.

10 We have not listed a date for the Juilliard Quartet in Example 3.5a since this box represents the ensemble at various points: in 1950 during the recording we discuss, and later during the quartet’s associations with the Tokyo and Emerson Quartets. 11 There is no recording of the Fifth String Quartet by the New Hungarian Quartet, the only quartet that coached the work with Bartók. Nor are there recordings by the Kolisch Quartet with the same personnel as played the world premiere in Washington, DC, in April 1935 (Bartók had sent them a letter with detailed instructions [Kenneson 1994, 459]), or by the (Belgian) Pro Arte Quartet with the personnel who played it in December 1935, although the 1945 Pro Arte recording features Rudolf Kolisch of the Kolisch Quartet as first violinist and Germain Prévost of the Belgian Pro Arte Quartet as violist. For the history of the (New) Hungarian Quartet, and the story of the Fifth Quartet’s Austrian and Hungarian premieres, see Kenneson (1994, 167–​76), and Glyde (1997, 288). We are thankful to Judith Glyde for sharing her transcripts of Dénes Koromzay’s taped memoirs with us. Further documentation of early performances of Bartók’s Fifth Quartet and information on the New Hungarian Quartet is found in Kárpáti (1994, 365–​67), Somfai (2006, 8–​10), and Potter (2003a, 67). Note that the original New Hungarian Quartet is a different ensemble from the New Hungarian Quartet later formed by Dénes Koromzay and Andor Toth after the Hungarian Quartet disbanded. 12 Székely contributed significantly to revisions of the concerto. (See Somfai 1996b, 46–​49, and Kenneson 1994, 185–​86, 191–​93, 204–​7.) 13 The 1998 recording of the Bartók cycle by a later Takács Quartet, with the same second violinist and cellist but two new members (Edward Dusinberre as first violinist and Roger Tapping as violist), received a Gramophone Award. The quartet was also awarded the Order of Merit of the Knight’s Cross of the Republic of Hungary in 2001. The current Takács Quartet, with Geraldine Walther as violist, continues to program the complete Bartók cycle, and to collaborate in their Bartók performances with Muzsikás and Márta Sebestyén, a Hungarian ensemble and singer dedicated to reproducing Hungarian folk performance practices.

Bartók’s Fifth String Quartet  109

The Kolisch Quartet (Example 3.5c) gave Bartók’s Fifth Quartet its world premiere in April 1935; although he did not coach these performers, Bartók wrote them a letter with detailed instructions on certain passages (Kenneson 1994, 459). The (Belgian) Pro Arte Quartet played the work a few months later in December 1935. (Bartók had written the work in August–​September 1934 in response to a commission by Elizabeth Sprague-​Coolidge, made on the recommendation of the Pro Arte Quartet.) In 1940 a new formation of the Kolisch Quartet made a recording of the Fifth Quartet (which we have not been able to obtain). In 1941 this same formation premiered Bartók’s Sixth Quartet, after being coached by Bartók on it. After the Kolisch Quartet disbanded in 1944, first violinist Rudolf Kolisch, who was Viennese, joined the American Pro Arte Quartet (so called because of its residence at the University of Wisconsin) (Somfai 2006, 8–​10; Potter 2003b, 16). In 1945, this group, which included the Belgian violist Germain Prévost of the original Pro Arte group, recorded Bartók’s Fifth Quartet. The Hagen Quartet is of Austrian and German background; three of its members studied at the Salzburg Mozarteum, and its second violinist, Rainer Schmidt, studied in Hannover and at the Cincinnati Conservatory. The quartet worked on Bartók’s quartets with György Kurtág in 1995 (Markl 2000, 12); it received the 2000 Prix Caecilia for its recording of the cycle. Thus our ten recordings feature three ensembles of American origin or training (Juilliard, Tokyo, Emerson), five of Hungarian origin (Tátrai, Végh, Hungarian, Takács, Keller), and two of Western European (and American) background and training (Hagen, Pro Arte). We now examine empirical data from these ten recordings.

Data: Informal Survey The reader is invited to listen to the ten recordings that we discuss (Audio 3.3–​ 3.12 ). We examine only mm. 9–​24—​the “expository” portion of the trio, which presents primary rhythmic-​melodic material prior to hypermetric and grouping manipulations and eventual rhythmic-​metric dissolution. Our analysis focuses on performed rhythm in the melodic line, particularly with regard to duration-​ segs X1, X3, and X2, which occur in that order and are marked in the score. It will refer to the four melodic notes of each measure as beats 1, 2, 3, and 4. First we orient the reader to the functions of the three duration-​segs X1, X2, and X3. X1 expresses the trio’s primary melodic material, forming the basis for the crucial opening melodic statement in the viola (m. 9), and for the cello’s second phrase (m. 21) and the echo in the viola (m. 31). X3 has a “cadential” function within the eight-​ measure prototype, occurring at timepoint class 6 within the passage’s hypermetric scheme.14 X2 plays a responding and intensifying role, defining the cello’s m.  17 14 The eight-​measure hypermetric scheme and its manipulations are labeled with timepoint classes 0–​7 under the score; for further discussion see Leong (2014, 122–​24).

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answer to the viola, projecting three-​measure extensions at mm. 24, 28, and 34, and expressing the related material that makes up the accelerando (m. 40 ff.). Here we examine the data informally in an initial assessment of our hypothesis that Hungarian quartets’ performance of the trio’s rhythms differ from that of other quartets. Example 3.6 shows our ten recordings’ tempi by measure, of mm. 9-​24, with the non-​Hungarian quartets on the left and the Hungarian quartets on the right.15 We call the Hungarian quartets Group H (for “Hungarian”) and the others Group G. The average tempo for each excerpt is shown in a rectangle on the right of its graph. At first glance there seem to be no clear-​cut distinctions between the tempi of Groups G and H, although the faster tempi tend to occur in Group G, and the slower tempi in Group H. The span from slowest to fastest tempo for each excerpt is shown in an oval on the right of its graph (and bracketed on the graph itself). The largest tempo spans occur in Group H and the smallest in Group G. Example 3.7 shows the relative inter-​onset durations for sample X1, X2, and X3 measures. The durations are shown as percentages of their measure duration. The top of the page shows the durations exactly as represented by the score; such durations would comprise 20% and 30% of the measure for the quarter note and dotted-​quarter note, respectively. 20% falls at the bottom of the grey band, and 30% at the top of the grey band. Juilliard’s m. 10, for example, begins with a disproportionately long beat 1, moves to beats 2 and 3 at approximately 20% of the measure, and ends with beat 4 considerably shorter than the notated 30% of the measure. Note that the graphs represent durations as proportions of the measure; they do not show how these durations would be perceived in a dynamic hearing. In Juilliard’s m. 10, the second beat appears quite close to the “desired” 20% mark, but sounds short because of the length of the first beat. Furthermore, a listener’s impression of the performed durations is colored not only by the durations themselves, but also by factors such as articulation, dynamics, vibrato, and so on. A comparison of Example 3.7a (Group G) with Example 3.7b (Group H) reveals certain distinctions. First, with some exceptions, the quartets of Group G show a much wider variation in durations within the measure than do those of Group H (Group H profiles are flatter), and this is particularly true of mm. 10 and 17, the measures that function more melodically. The three exceptions to this tendency are Hagen and Pro Arte in the G group, and Tátrai in the H group. Second, the Group H quartets show much greater variety in the durational contours of these measures than do the Group G quartets; several of the Group H measures depart quite radically from the relative proportions specified by the notated durations. For example, m. 15 should express ; Hungarian Quartet’s m. 15 articulates . The three exceptions to the two groups’ tendencies are, again, Hagen (m. 17), Pro Arte (m. 17 and m. 15), and Tátrai. Third, in Group G, the three “American” quartets (Juilliard, Tokyo, and Emerson) show a high degree of similarity, and this is perhaps to be expected given Tokyo and Emerson’s connections to the Juilliard Quartet.



15 Our methodology for the empirical measurements in this chapter is described in the chapter’s Appendix.

Bartók’s Fifth String Quartet  111 Example 3.6.  Bartók, Fifth Quartet, III Trio:  Tempi by measure (mm. 9–​24), at 

.

112  Performing Knowledge Example 3.7.  Bartók, Fifth String Quartet, III Trio: Melodic durations as percentage of measure.

Bartók’s Fifth String Quartet  113 Example 3.7 (cont.).

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Example 3.8 sums up the factors that we examined for the ten recordings. Example  3.8a shows the average tempo by measure across the passage. For a rough visual guide, white boxes indicate faster tempi and grey boxes slower tempi. Example  3.8b displays the span between maximum and minimum tempi:  white boxes show smaller spans and grey boxes larger spans. Example 3.8c lists the spans between longest and shortest durations (measured as a percentage of the entire measure) in mm. 10 and 17, the melodic measures. White boxes show larger spans, grey boxes smaller spans. Example 3.8d provides a rough description of accentual and articulative qualities; white boxes indicate more accented and less legato qualities, grey boxes smoother qualities. Example 3.8e lists the contours of the durations of mm. 10, 15, and 17 (X1, X3, and X2 representatives); 0 indicates the shortest duration within the measure, progressively increasing to 3, the longest duration within the measure.16 In the example, the rows for each measure are ordered as follows: (1) conform to S-​L, multiple: contours that present the short notes (quarter notes) as the two shortest    durations 0 and 1, and the long notes (dotted-​quarter notes) as the two longest durations 2 and 3,   and that appear in more than one recording For example, for m. 10, where notated durations are , appears in Juilliard’s, Tokyo’s, Tátrai’s, and Végh’s performances; also appears in multiple recordings. (2) conform to S-​L, single: contours that conform to the relative shorts and longs, and that appear in only one recording For example, for m. 10, appears only in Pro Arte’s interpretation; only in Keller’s. (3) violate S-​L (in grey): contours that violate the relative short-​long criterion For example, for m. 10, the Takács Quartet’s has its two shortest durations 0 and 1 not in the middle of the measure but at the end. Some observations about the duration contours: Juilliard and Tokyo are equivalent in mm. 10, 15, and 17 contours. Much greater flexibility occurs in the European (Western European and Hungarian) performances than the American ones, with all of the grey non-​conformist contours appearing in the European group.

16 In some cases (e.g., Végh m. 17), actual durational distinctions are slight.

This conception of duration space was defined by Elizabeth West Marvin (1991, 65–​66).

Example 3.8.  Bartók, Fifth String Quartet, III Trio: Overview of melodic lines (mm. 9–​24), American and European ensembles.

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This informal view of the data, with the preponderance of grey in the European performances, and conversely, the balance of white in the American interpretations, suggests a second hypothesis:  that the stylistic divide occurs between American and European performance traditions rather than between Hungarian and non-​Hungarian  ones. Motivated by the passage’s clear resemblances to folk melodies, we also considered a third hypothesis (Example 3.9). Two of the “grey” characteristics—​small duration span (Example 3.9c), and legato articulation (Example 3.9d)—​are the most distinctive features of a vocal conception of the viola and cello melodies, and both are essential to a folk-​song-​like performance of these melodies. Example 3.9 regroups our ten recordings into ensembles that include both small duration spans and legato articulation (Group B), and those that lack one or both of these features (Group A). Group A contains the American ensembles Juilliard, Tokyo, and Emerson along with Western European Hagen and Hungarian Tátrai. Despite Hagen’s “grey” features—​its larger tempo span, smaller duration spans, and rogue m. 17 contour—​its overall quick tempo, and especially its dry and accented sound, place it with the American quartets, to my ear. The Tátrai Quartet, despite its slow tempo (the slowest among those surveyed), somewhat large tempo span, and legato interpretation, distinguishes its short and long durations quite strongly, as do the American quartets.17 Group B includes all of the Hungarian quartets except Tátrai, and the Pro Arte Quartet as well. The Pro Arte Quartet, despite a quick tempo, does evidence both small duration spans and legato articulation, along with “greynesss” in all other aspects. In Example 3.9, the preponderance of grey occurs in Group B. Group B is characterized generally by greater variability in tempo, smoother (more equal) rendition of the long and short durations, more legato and less accented lines, and greater freedom in the interpretation of the longs and shorts, even to the point of violating the basic notated contour. Group A, on the other hand, shows less variability in tempo, tends to exaggerate the distinction between longs and shorts, plays with a more articulated and accented sound, and keeps the relative durations in line with the notation. Group B’s characteristics, including but not limited to the two (small duration span and legato articulation) that we have taken as definitive, together produce an approach that is more vocal in nature, and that more closely resembles the Hungarian folk-​song tradition to which the trio’s melodies are related. To my ear, this A and B grouping of the recordings demonstrates a clearer stylistic divide than does our initial G and H grouping, or even our subsequent American and European categories. That Groups A and B—distinguished by the absence or presence of folk-​song-​like interpretation—provide the most meaningful clustering of the ten ensembles, was our third hypothesis.

17 Károly Schranz of the Takács Quartet reports hearing a program ca. 1970 on Hungarian National Radio in which Robert Mann was quoted as saying that the Tátrai Quartet’s sound influenced the Juilliard Quartet, but we have not been able to substantiate this.

Example 3.9.  Bartók, Fifth String Quartet, III Trio: Overview of melodic lines (mm. 9–​24), Group A and B ensembles.

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Data: Statistical Analysis To more objectively assess the three binary groupings hypothesized in the foregoing, we now present statistical results. Prior to undertaking statistical analysis, we clarified the rough “accent/​articulation” rating by separating it into two items—​“similarity in dynamic level from attack to attack” and “continuity of sound from note to note”—​ and by having three doctoral string students independently rate the two attributes on a scale of 1 to 5 (Example 3.10). Assumptions for no significant outliers and normal distribution were checked and met. Inter-​rater reliability, as determined by separate single measure intraclass correlation coefficient tests, was .71 for continuity and .45 for dynamic similarity. Subsequent Pearson r product-​moment correlations revealed Judge 2 and Judge 3 to have moderate levels of agreement, r = .65 and r = .64 for dynamic similarity and sound continuity, respectively; other judge combinations yielded inconsistent results, so scores from these two judges were averaged and used in subsequent analyses, and scores from Judge 1 were omitted. The following discussion first examines correlations among the performed variables. It then analyzes differences in these performed variables among our various groupings: it investigates differences among the three basic groups (American, Western European, and Hungarian), followed by those between the binary groupings (G versus H, American versus European, and A versus B). We referenced six variables: average tempo, tempo span, the mean of the duration spans of mm. 10 and 17 (henceforth duration span mean), dynamic similarity rating, sound continuity rating, and number (0–​3) of duration contour violations. Each of these six variables was normally distributed and the assumption of linearity was not violated, so a series of Pearson product-​moment correlations was conducted to examine the relationships among the variables. Example 3.11 shows that three of the ten pairs of variables were significantly correlated. Duration contour violations were positively correlated with tempo span, r(8) = .68, p = .03, and negatively correlated with duration span mean, r(8) = –​.76, p = .01. These correlations suggest that as numbers of duration contour violations increased, tempo spans widened, and durations became more similar. Duration span mean had a moderate negative correlation with dynamic similarity, r(8) = –​.61, p = .06; the more differentiated the durations, the more differentiated the dynamics from note to note tended to be. Due to the small sample size (N = 10 recordings), separate Kruskal-​Wallis H tests were conducted to compare the three basic groups (American, Western European, Hungarian) and the six dependent variables (average tempo, tempo span, duration span mean, dynamic similarity, sound continuity, and duration contour violations). Example 3.12 displays mean ranks for these variables and the three basic groups. Since this investigation is interested in marginal differences, an alpha level of .10 was chosen (Barlett, Kotrlik, & Higgins 2001, 43). Kruskal-​Wallis H tests revealed significant differences among the basic groups in tempo span, χ2 (2) = 4.73, p = .09, sound continuity, χ2 (2) = 5.02, p = .08, and duration contour violations, χ2 (2) = 5.34, p = .07; there were no significant differences in average tempo (χ2 (2) = 2.55, p = .28), duration span mean (χ2 (2) = 2.98, p = .23), or dynamic similarity (χ2 (2) = 2.96, p = .23).

Example 3.10.  Ratings of dynamic similarity and sound continuity.

Example 3.11.  Intercorrelations, means, and standard deviations for the six dependent variables (N = 10).

Example 3.12.  Mean ranks for the three basic groups.

122  Performing Knowledge Example 3.13.  Mean ranks for Group G and Group H comparisons.

Subsequent post hoc Mann-​Whitney U tests with a Bonferroni corrected p value of .011 indicated no statistically significant differences between the groups pairwise, that is, between the American and Western European quartets, the American and Hungarian quartets, or the Western European and Hungarian quartets. It was hypothesized a priori that Hungarian quartets (Group H) might differ in their playing styles from other ensembles (Group G). To test this hypothesis, a series of Mann-​Whitney U tests was carried out. Example 3.13 shows mean ranks, U scores, and p values for the six dependent variables and Groups G and H. Dynamic similarity and sound continuity ratings for Group G (mean rank 3.90 and 3.50, respectively) were significantly different than for Group H (mean rank 7.10 and 7.50, respectively), U = 4.50, p = .095; and U = 2.50, p = .03. There were no statistically significant differences for average tempo, tempo span, duration span mean, or duration contour violations. It was further hypothesized post hoc that the performances of American ensembles differed from those of European ones. To explore this hypothesis, a series of Mann-​Whitney U tests was conducted. Example 3.14 displays mean ranks, U scores, and p values for the dependent variables and American and European ensembles. Results indicated that American quartets differed significantly from European ones in tempo span (mean ranks 2.33 and 6.86, respectively; U = 1.00, p = .03) and in duration contour violations (mean ranks 2.50 and 6.79, respectively; U = 1.50, p = .03). There were no significant differences for average tempo, duration span mean, dynamic similarity, or sound continuity. Finally, a third grouping (Group A versus Group B), based on musical characteristics and not geographic association, was hypothesized. This grouping categorized ensembles based on the presence of the features considered most necessary for a song-​like rendition of the melodies: small duration span and legato articulation. Those ensembles featuring both smaller duration spans and legato articulation were placed in Group B, while those that lacked one or both of these two

Bartók’s Fifth String Quartet  123 Example 3.14.  Mean ranks for American and European comparisons.

Example 3.15.  Mean ranks for Group A and Group B comparisons.

features were placed in Group A. To compare the groups, a series of Mann-​Whitney U tests was conducted. Results are reported in Example 3.15. Statistically significant differences are as follows. Group B had higher mean ranks than Group A for tempo span (U = 3.00, p = .06), dynamic similarity (U = 3.00, p = .06), and duration contour violations (U = 1.50, p = .01). Group A had a higher mean rank than Group B for duration span mean (U = 3.00, p = .06). Groups A and B did not show statistically significant differences in average tempo or in sound continuity. Example 3.16 summarizes the results for the three binary groupings (G versus H, American versus European, A versus B), showing the variables that displayed statistically significant differences for each pair. For these variables, the table lists the group with the higher mean rank. G differed from H in dynamic similarity and

124  Performing Knowledge Example 3.16.  Statistically significant differences within the three binary groupings. Entries indicate the group with the higher mean rank.

sound continuity; that is, H ensembles were generally smoother in the similarity of their dynamics and continuity of their sound. American and European quartets differed in tempo span and numbers of duration contour violations, European ensembles showing larger tempo spans and more duration contour violations. Groups A and B differed in tempo span, duration span mean, dynamic similarity, and numbers of duration contour violations; Group B displayed larger tempo spans, smaller duration spans, more similar dynamics, and more duration contour violations than Group A. Thus of our three binary groupings, Groups A and B differed significantly in the greatest number of variables—​four of six—​tested.

Bartók’s Influence After arriving at the A and B grouping, we undertook the investigation of quartet backgrounds described earlier (Example  3.5), and discovered that all of the performances in Group B were influenced directly, or with one degree of separation, by Bartók’s coaching. As far as we can ascertain, this is not true of any of the performances in Group A. Thus Bartók-​influenced quartets tend to play these melodies like the folk songs described earlier. We then obtained a copy of the letter that Bartók wrote to Rudolf Kolisch about the Fifth Quartet.18 Dated October 23 [1934],19 this four-​page handwritten letter accompanied the score that Bartók sent to the Kolisch Quartet for the premiere performance. It provides performance directions on specific details of notation, rhythm, meter, grouping, tempo, articulation, character, and technically unusual or difficult spots. It addresses the first, second, third, and fifth movements in particular, with the third movement occupying the most space, 1⅓ pages.

18 A black-​and-​white photocopy of the letter is held in the Bartók Archive in Budapest, obtained from Jonathan Khuner (son of Felix Khuner of the Kolisch Quartet) through David Schneider (Schneider, email message to Leong, June 7, 2015). We thank László Vikárius for providing us with a copy of the letter. 19 No year is given, but since the Fifth Quartet was completed in September 1934 (as indicated by Bartók’s notation at the end of the score) and premiered by the Kolisch Quartet in April 1935, the year must be 1934.

Bartók’s Fifth String Quartet  125

About the third movement, Bartók writes: Here I tried to use two of the so-​called “Bulgarian” rhythms, to some degree also imitatively-​contrapuntally. “Bulgarian” rhythms arise when very fast metric units (M.M. 300–​400 or even faster) are combined into asymmetrical groups such as e.g. here 4+2+3 (and not 3+3+3!). I do not know if you are already familiar with such rhythms. If not, . . . [Bartók provides simple exercises for internalizing the 4+2+3 rhythm]. With the main part of the Scherzo there will likely be no special difficulty; in the Trio however the metric units are yet faster: M.M. 560. So one can conceive of things, as if one had nearly equal values to play:  , only the indicated notes (shown in the Quartet with ) should be barely noticeably longer. Actually this rhythm should be understood as an overhasty , in which the quarter notes become somewhat too short. The difference between , and is of course important. This type of rhythm must be called “Bulgarian” because it is extremely common in Bulgarian folk music—​approximately 2/​3 of the melodies are of this kind (there are approximately 100 variations, e.g. [sic], or [sic] etc.) But it is found also among the Romanians, moreover traces occur among the Székely.20

One sees from these instructions that Bartók wanted the quarter and dotted-​quarter notes of the trio’s notated meter signatures to be almost equal, the dotted-​quarter notes “barely” longer than the quarter notes. One also notices resonances with Bartók’s descriptions of variable tempo giusto (discussed earlier): he conceives of “actually” as an “overhasty” variation of the variable tempo giusto pattern  ; it seems that the faster tempo changes the proportions of the note values, shortening the quarter notes within the variable tempo giusto pattern.21 Despite this evening-​out of the rhythms, Bartók does want the distinction among the three

20 Hier versuchte ich zweie der sogenannten “bulgarischen” Rhythmen anzuwenden, teilweise auch imitatorisch-​kontrapunktisch. “Bulgarischer” Rhythmus entsteht, wenn sehr rasche Zähl-​Einheiten (M.M. 300–​400 oder noch mehr) zu asymmetrischen Gruppen vereinigt werden also wie zum B. hier 4+2+3 (und nicht 3+3+3!). Ich weiss nicht, ob Ihnen derartiger Rhythmus schon geläufig ist. Wenn nicht, . . . Mit dem Hauptteil des Scherzo’s werden wohl keine besonderen Schwierigkeit sein; im Trio jedoch sind die Zähleinheiten noch rascher: M.M. 560. Da kann man sich die Sache so vorstellen, als ob man fast gleiche Werte zu spielen hätte: , nur sollen die mit-​bezeichneten (im Quartett mit bezeichneten) Noten kaum merklich länger sein. Eigentlich ist dieser Rhythmus wie ein überhastetes zu betrachten, in welchem die Viertel etwas zu kurzgeraten sind. Der Unterschied zwischen , und ist natürlich wichtig. “Bulgarisch” muss diese Rhythmusart gennant werden, weil sie in der bulgarischen Volksmusik ungemein häufig sind—​etwa 2/​3 der Melodien sind in dieser Art (es gibt etwa 100 Variazionen, z.B. , oder usw.). Kommt aber auch bei den Rumänen vor, ja sogar finden sich Spuren bei den Szeklern. Translated by Leong. Thanks to Lisa de Alwis for assistance with deciphering parts of Bartók’s letter and with the translation. 21 Leong (2014, 118) provides an example of Bartók revising the note values of a transcription from 2:1 proportions (triplet quarter and eighth notes) to 3:2 proportions (dotted-​quarter and quarter notes).

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(X1, X2, and X3) patterns to be maintained—​a distinction not always adhered to by our Group B quartets.22 Finally, further evidence for fluidity in the performance of Bulgarian rhythms in Bartók’s music, particularly when melodically treated, comes from Bartók’s own recorded performances: the Sonata for Two Pianos and Percussion (first movement’s second theme), the Six Dances in Bulgarian Rhythm from Mikrokosmos (Nos. 148, 150, and 153),23 and Contrasts (third movement’s trio). In general, where mixed quarter and dotted-​quarter notes articulate melodic or primary lines, and where hocket-​like textures do not govern, Bartók plays with rhythmic flexibility, at times slightly offsetting the primary line from the steady eighth-​note accompaniment. A good example of such fluidity occurs in Bartók’s 1940 Columbia recording of Contrasts with József Szigeti and Benny Goodman. The third movement contains a middle section notated in (8 + 5) /​8, comprised of the subdivisions 3 + 2 + 3 + 2 + 3. Example 3.17a (Audio 3.13 ) shows the section’s opening two measures, where the piano plays alone before the entrance of the other two instruments. Example  3.17b graphs inter-​ onset durations in the two measures, using the eighth note as the unit. The top graph shows the durations exactly as represented by the score; the durations are 3 and 2 eighth notes in length for the dotted-​ quarter note and quarter note, respectively. Dotted-​ quarter-​ note durations fall at the top of the grey band, and quarter-​note durations at the bottom of the grey band. The lower graph uses Bartók’s performed durations from downbeat to downbeat as the bases for measurement: positing eighth-​note durations as 1/​13 of their performed measure, the graph’s points show durations of the dotted-​quarter and quarter notes as performed, measured in these eighth notes.24 Since m. 132 introduces the section, and the performer is settling into the pattern, we look at m. 133. Notice the agogic accent on the downbeat, and in the remainder of the measure, the lengthening of the quarter notes and shortening of the dotted-​quarter notes, creating a sense of swinging motion. The third note of the measure is significantly shortened, leading to the mid-​measure “downbeat” (after the dotted barline), and causing the two large parts of the measure (8 + 5) to come very close to the notated proportions. Bartók’s performance of the measure can be summed up as a lengthening of the downbeat note, and a smoothing-​out of the following / pairs, with a particular shortening of the dotted-​quarter note that falls

22 Bartók does not address the relationship of first violin, which plays constant eighth notes, to the flexible rhythms of the melodic line in viola and cello. An aural survey of the Group B quartets reveals a range of approaches: first violin and viola or cello can play essentially together, their eighth-​note subpulses aligning; they can play roughly together, prioritizing downbeats and two-​bar hypermeter; or they can relate quite loosely, not even lining up precisely at many downbeats. 23 See also Somfai (1996a, 288) on tempi and tempo variations in Bartók’s performances. 24 Bartók does not play right and left hands exactly together. The “performed” graph in Example 3.17b shows the data for the left hand; that for the right hand follows the same contour.

Bartók’s Fifth String Quartet  127 Example 3.17. Bartók, Contrasts, III, mm. 132–​33.

before the dotted barline and in between the two quarter notes. Similar tendencies can be seen in the first measure, m. 132, although here, at the beginning of the section, the opening note is quite a bit longer, causing the remainder of the notes to be “too short” relative to the measure as a whole.

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Conclusion Bartók’s coaching influence seems to explain a folk-​song-​like interpretation of the rhythms at the center of his Fifth String Quartet. Evidence that converges on this explanation includes (a) the strong resemblance of the trio’s melodic material to Hungarian folk song and Bulgarian meters, as described by Bartók, (b) the close relation between Bartók’s techniques in developing the trio’s melodic material and the folk-​rhythm transformations that he discussed, (c)  flexibility in folk performance of variable tempo giusto rhythms, a flexibility noted in Bartók’s writings and transcriptions, (d)  fluid rhythmic performance of the trio by Bartók-​influenced string quartets, (e)  fluidity in Bartók’s own performances of similar rhythmic structures, and finally and most concretely, (f) Bartók’s explicit instructions to the Kolisch Quartet to even out the notated rhythms. This explanation evokes a particular “enactive landscape” for this trio’s notation—​ a set of affordances activated for performers from a Bartók-​influenced interpretive tradition.25 These affordances include flexible interpretation of the notated rhythms and singing articulation of the melodic line. Other performers tend to read the score’s rhythms more literally, since Bartók gives no written indication to do otherwise. Cultural situatedness, then, gives rise to different notational affordances in the case of our trio—​affordances that result in wide variances in performed interpretation.

Playing the Melodies of the Trio Section:  A Bartók-​Influenced Guide



• Be aware of the basic rhythmic-​metric structure of the melodies, whose units are the half measure (pairs of notes),26 the measure, two-​ measure “lines,” four-​measure “line pairs,” and the eight-​measure “strophe.” • Understand that these rhythms come from a folk-​song tradition of variable proportions; the fast tempo here motivates an evening-​out of the quarter and dotted-​quarter values. Read Bartók’s instructions, provided earlier in this chapter.

25 De Souza (2017, 52 ff.) borrows David Kirsh’s (2013) term “enactive landscape” to discuss the affordances of a diatonic harmonica in folk music, blues, and jazz; these three practices offer different possibilities and opportunities for use of the instrument. See Clarke and Doffman (2017, 5) for description of a musical culture as “a field of possibilities” or “a set of (musical) ecological conditions.” With regard to implicit and culturally situated understandings of notated rhythm, consider notes inégales and the swung rhythms of jazz. Bayley (2017, 102) describes a notational situation similar to ours, in Mariana Sadovska’s collaboration with the Kronos quartet. About her composition inspired by Ukrainian folk songs, Sadovska says, “For me, it’s easier sometimes really to sing it, so that they [Kronos] can hear what I mean, than to notate it. Because it’s so much based [on] vocal music.” 26 See Leong (2014, 119)  for explanation and support of the half measure as an essential unit in these melodies.

Bartók’s Fifth String Quartet  129





• Keep in mind that the performance style of such melodies originates in a vocal (folk-​song) tradition. • One may wish to listen to: • recordings of the movement made by string quartets influenced by Bartók directly or indirectly. Of the ensembles studied here, these include Vegh (1972), Hungarian (n.d.), ProArte (1945), Takács (1984), and Keller (1995) (Audio 3.8–​3.12  ). • recordings of the type of folk song that inspired these melodies. Examples  3.18 and 3.19 provide three samples, transcribed by Bartók, with links to audio files of the field recordings that he used.27 • Example 3.18 shows old-​style Hungarian folk song with four isometric lines: eight-​syllable lines in Example 3.18a and seven-​ syllable lines in Example  3.18b. Both tunes display variable tempo giusto, adjusting the prototypical (or ) pairs to the text structure. • Example 3.19 shows Bartók’s revised transcription of a Gypsy violinist’s performance of the Hungarian melody “Árvátfalvi kesergő” [Árvátfalva Lament].28 Bartók notates the melody in 10/​16 meter and 2:3 rhythmic proportions, similar to the 10/​8 meter and Bulgarian proportions of our melodies.29 • Watch Videos 3.1 and 3.2 in which András Fejér, cellist of the Takács Quartet, discusses working on Bartók’s string quartets with Székely and Koromzay, explores the rhythms of the trio section (along with ensemble considerations), provides practical tips, and considers interpretation in this scherzo movement.

27 These audio files are found in Bartók-​system, the online database of the Hungarian Academy of Sciences Institute for Musicology. 28 The violinist was János Balog; the melody was recorded by Béla Vikár, and a vocal version by László Lajtha. For more information on Bartók’s transcription, see Somfai (1981). Example 3.19, a facsimile of the revised fair copy, is reproduced from Bartók-​system by the kind permission of Pál Richter. http://​db.zti.hu/​nza/​ br_​search_​en.asp, inventory number 12957_​01. The facsimile appears in color online. 29 Bartók originally notated this melody in triplet and even eighth notes, and borrowed it for his Violin Rhapsody No. 1 (see Somfai 1981). Leong (2014, 118) discusses Bartók’s notational revision and its relation to the rhythm of our trio melodies.

Example 3.18.  Old-​style Hungarian folk song, transcribed by Bartók (Bartók 2002 [1924], 8; Bartók 1923, 118).

Example 3.19.  “Árvátfalvi kesergő”: Bartók’s revised transcription (Hungarian Institute for Musicology RCH HAS inv. no. ZTI_​BR_​12957).

Bartók’s Fifth String Quartet  131

Discography Bartók String Quartets All are recordings of the complete Bartók quartets, except for Pro Arte (1945) and Kolisch [1940], which include only Bartók’s Fifth Quartet. * indicates recordings to which we did not have access. Emerson String Quartet (Eugene Drucker, Philip Setzer, Lawrence Dutton, David Finckel). 1988. Deutsche Grammophon 423 657-​2. Hagen Quartett (Lukas Hagen, Rainer Schmidt, Veronika Hagen, Clemens Hagen). 2000. Deutsche Grammophon 463 576-​2. * Hungarian Quartet (Zoltán Székely, Alexandre Moskowsky, Dénes Koromzay, Vilmos Palotai). 1946. HMV C.3511-​4. Remastered 2007 Pristine Audio PACM052. Hungarian Quartet (Zoltán Székely, Michael Kuttner, Dénes Koromzay, Gabriel Magyar). n.d. [1960s]. Deutsche Grammophon 138 650/​52. The Juilliard String Quartet (Robert Mann, Isidore Cohen, Raphael Hillyer, Claus Adam). n.d. Columbia Masterworks D3L 317 /​D3S 717. The Juilliard String Quartet (Robert Mann, Robert Koff, Raphael Hillyer, Arthur Winograd). 1950. Columbia ML 4280. Keller Quartet (András Keller, János Pilz, Zoltán Gál, Ottó Kertész). 1995. Erato 4509-​98538-​2. * Kolisch Quartet (Rudolf Kolisch, Felix Khuner, Jascha Veissi, Stefan Auber). [1940.] Columbia. New Hungarian Quartet (Andor Toth, Richard Young, Dénes Koromzay, Andor Toth Jr.). 1994. Vox SVBX 593. Pro Arte Quartet (Rudolf Kolisch, Albert Rahier, Germain Prévost, Ernst Friedlander). 1945. In Honor of Rudolf Kolisch. Music & Arts CD 1056 (issued 2003). Takács Quartet (Gábor Takács-​Nagy, Károly Schranz, Gábor Ormai, András Fejér). 1984. Hungaroton SLPD 12502-​04. Takács Quartet (Edward Dusinberre, Károly Schranz, Roger Tapping, András Fejér). 1998. Decca 289 455 297-​2. Tátrai Quartet (Vilmos Tátrai, Mihály Szűcs, György Konrád, Ede Banda). 1967. Hungaroton LPX 1294-​96. Reissued 2000 on Hungaroton HCD 31895-​97. Tokyo String Quartet. (Koichiro Harada, Kikuei Ikeda, Kazuhide Isomura, Sadao Harada). 1981. Deutsche Grammophon 2740 235. * Végh Quartet (Sándor Végh, Sándor Zöldy, Georges Janzer, Paul Szabo). n.d. Angel 35240. Végh Quartet (Sándor Végh, Sándor Zöldy, Georges Janzer, Paul Szabo). 1972. Astrée AS 69.

Bartók’s Own Playing (Sonata for Two Pianos and Percussion, 6 Dances in Bulgarian Rhythm, Contrasts) Bartók at the Piano. 1991. Edited by László Somfai and Zoltán Kocsis. Hungaroton HCD 12326-​ 28 and 12329-​31.

Field Recordings Listed by media reference number, title/​incipit, performer, place, date of recording (where provided), collector, Bartók-​system inventory number. Muz. F. 471e, “Cigány vagyok,” Ignác Péter, Felsőboldogfalva (Udvarhely), Béla Vikár, 04121. F. 184b, “Kerek ucca szëgelet,” Antalné Lőrinc, Istensegits (Bukovina), 1914, Zoltán Kodály, 03831. MF 99 IIa, “Árvátfalvi kesergő,” János Balog, Medesér (Udvarhely), Béla Vikár, 12957.

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Appendix: Methodology Temporal data for this chapter were collected using Sonic Visualiser 1.4. Audio files were imported as AIFF files and viewed as waveforms. To obtain tempi, markers (“time instants”) were manually inserted at the onsets of the melodic notes occurring at the downbeats of mm. 9–​24, and were checked and aligned more precisely through audio playback, with the markers sounding as clicks. To obtain melodic durations in mm. 10, 15, and 17, markers were inserted at the onsets of each of the melodic notes in these measures and the downbeat of the following measure, and were aligned more precisely through slowed-​down audio playback. Two splices are audible in Tátrai (1967), in m. 16 and at the downbeat of m. 17; at the m. 17 downbeat, the cello’s attack is heard twice. No adjustment was made for the splice in m. 16; in m. 17 the cello’s second attack was used for all measurements. Tempo by measure was calculated as follows:

bpm =

2 ∗ 60 , ( y − x)

where bpm is beats per minute, the beat is the half measure (as Bartók indicates), x is the timepoint for the measure’s downbeat, and y is the timepoint for the following measure’s downbeat.

4 Story in Structure

Schnittke’s Piano Quartet and “the attempt to remember” Daphne Leong and Judith Glyde

Schnittke’s Piano Quartet is based on a Mahler fragment. Informed by the structure created from this fragment, we tell four stories: compositional, performative, aesthesic, and analytical. We had performed Schnittke’s Piano Quartet together some years earlier. (That live performance can be heard on Audio 4.1 .1) Later, after writing this chapter, we gave an interactive presentation accompanying a performance of the quartet at the Music in the Mountains summer festival.2 Since this performance involved Judith Glyde and three different ensemble members, we had opportunity to discuss interpretive issues anew, as well as to interact with the audience. We present thoughts from these interactions as a “Fragment” at the end of this chapter. Schnittke’s aim in his one-​movement Piano Quartet (1988) was to complete a 27-​measure scherzo-​movement fragment abandoned by the teenage Mahler:3 I thought for a long time how I  could continue the composition of this work. I tried for years to find a continuation of these measures composed by Mahler. And then I imagined it not as a continuation but rather music that would approach Mahler’s music—​as a reminder that the end will come, and that was the solution. At first the attempt to remember and then remembrance itself. (Borchardt 2002, 29; emphasis ours)

1 Judith Ingolfsson, Erika Eckert, Judith Glyde, and Daphne Leong, Schnittke Piano Quartet, Pendulum New Music Series, University of Colorado, Boulder, April 11, 2007. 2 Music in the Mountains Chamber Music Workshop Faculty Quartet (Jacob Murphy, John Dexter, Judith Glyde, Kuang-​Hao Huang) with Leong, closing concert, Rocky Ridge Music Center, Estes Park, Colorado, August 21, 2015. We thank Jacob, John, and Kuang-​Hao for discussing questions of interpretation with us. 3 Written perhaps in 1876–​78, Mahler’s Piano Quartet (a first movement and associated fragment) is his earliest extant work (Franklin 2012, works list), although two song fragments are probably earlier (Hefling 2010, 281). Daphne Leong and Judith Glyde, Story in Structure In: Performing Knowledge. Edited by: Daphne Leong, Oxford University Press (2019). © Oxford University Press. DOI: 10.1093/oso/9780190653545.003.0006

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The Quartet begins with a confused heterophonic and heterometric murmuring (Example 4.4) that builds in register and density. The flux settles into a clear meter at m. 18 but remains melodically and harmonically opaque. Melodies and motives surface, only to be submerged in an increasing cacophony of dense polyphony, swirling chromaticism, and rhythmic dissonance. Disturbance, distortion, and despair build to a point of no return—​a fortississimo screech of tritone glissandi resounding over an abyss. Out of these hanging shards, Mahler’s fragment emerges. What story is being told? For Schnittke it is the story of the journey to Mahler’s fragment. He “attempts to remember” Mahler’s fragment, much as we try to recall an idea half forgotten. We retrace our steps over and over; we remember partially, hazily, incorrectly; we are interrupted by associated memories. As we keep trying but cannot remember clearly, we become frustrated and distraught. Schnittke makes four passes through Mahler’s fragment as he tries to recall it. Each time he remembers the fragment, but incompletely, in self-​similar shards, obscured by the noise of related memories. Pressure builds and increasingly distorts the remembered material, until the attempt reaches a breaking point. Only then is the Mahler theme remembered. What story do performers tell? How is the scene set? Do we give guidance through the thick textures? Is the sound to be beautiful and lyrical, or unpleasant and ugly? Do we point the listener to the fragment to come? What story do listeners hear? The Quartet’s opening is ambiguous, vaguely dissonant. Lines emerge, only to be immediately obscured. We hear increasing derangement, strange shifts of mood. We hear the undercurrent of consonance and wonder whether clarification will come. And what stories might analysts discover or create? In this chapter we tell four stories about and through this Quartet. We trace the attempt to recall Mahler’s fragment through the structure of the Quartet, examining, first, Mahler’s fragment and Schnittke’s literal use of it at the end of the work, and, second, the Quartet’s rotational form (four passes through the Mahler fragment in “the attempt to remember,” followed by “remembrance itself ”). We then tell a performers’ story. We present our reading of the piece and practical techniques for its communication. We also tell a broader story about the creative roles of memory, the tensions of past and present, the manipulation of temporality, and the irony inherent in Schnittke’s treatment of Mahler’s fragment. We suggest that these themes resonate in a listener’s experience of Schnittke’s Quartet, that their echoes evoke the “recollection of a piece that never came into being” (Schnittke in Borchardt 2002, 32). And finally, we tell one analyst’s story about how Schnittke tells his story, about temporal techniques that Schnittke uses to foil time’s directedness. * * *

Schnittke’s Piano Quartet  135

Mahler’s Fragment Example 4.1 displays the ending of the Quartet, which quotes Mahler’s fragment in toto. The fragment can be divided into four sections, numbered on the example. The first opens with an undulating accompanimental sixteenth-​note figure, followed a measure later by the theme. Note that the of the accompaniment figure foreshadows the of the theme on both surface and slightly deeper levels. The theme itself, presented in the violin, consists essentially of nine measures, of which the closing motive (mm. 187–​88) occurs in successive imitation in viola, piano, and cello. The imitation in the cello elides into the fragment’s second section, in which the thematic incipit occurs twice. In the third section, the theme occurs alone in the piano, in simple octaves, breaking off after its seventh measure. The fragment itself breaks off here; three sketch measures follow and are shown in the fourth section. These measures echo the last measure of the third section, in sequence. Harmonically, the first section begins in G minor, moves at m. 187 to A major, and then shifts in m. 189 to A minor.4 The second section continues in A minor, with the thematic incipit in this key, returning to G minor for the third section and the piano’s broken-​off thematic statement. The fourth section remains potentially within the orbit of G minor until the penultimate chord, V56 of F♯, which moves inconclusively to A or perhaps to an implied F♯ minor. Schnittke found Mahler’s theme enigmatic: “Much contained therein was and remains a problem for me. I would not be able to find a single explanation, but rather two if I undertook a harmonic analysis—​and it could be interpreted this way or that” (Borchardt 2002, 29). And: “The theme is simply ingenious. It is unmistakable Mahler, recognizable from the very first measure. . . . And it is not comparable to anything else. The modulation from G minor to A major and then to A minor—​it is so unusual!”5 Mahler’s fragment can be found in two published editions. Sikorski published Mahler’s Piano Quartet, which consists of a first movement in A minor and the scherzo fragment, in 1973.6 Universal published Mahler’s first movement along with the scherzo fragment in facsimile and diplomatic transcription in 1997, in the Mahler Gesamtausgabe.7 This Gesamtausgabe transcription differs from the Sikorski edition in certain details of pitch and rhythm. From the dates (Schnittke wrote his Quartet in 1988) and from evidence to be presented next, it is clear that Schnittke worked from the Sikorski edition of the fragment. The ending of Schnittke’s Quartet (Example 4.1) presents the Sikorski edition of Mahler’s fragment almost verbatim, down to page layout. (Sikorski also happened to be Schnittke’s publisher.) There are only two changes (compare Example  4.1, 4 In the facsimile of Mahler’s fragment and its diplomatic transcription (Mahler 1997), the shift to A minor occurs in the second half of this measure. 5   .  .  .  das Thema ist einfach genial. Das ist unverwechselbar Mahler, den man bereits am ersten Takt erkennt . . . Und es ist mit nichts vergleichbar. Die Modulation von g-​Moll nach A-​Dur und anschließend nach a-​Moll—​das ist dermaßen ungewöhnlich!” (Schnittke 1998, 242, translation by Leong) 6 See Ruzicka’s editorial remarks in Mahler (1973, 31). 7 In his preface to the fragment, Kubik questions whether the fragment belongs with the A-​minor movement (Mahler 1997, 27).

136  Performing Knowledge Example 4.1.  Schnittke, Piano Quartet: the Mahler fragment as quoted by Schnittke.

m. 195 ff. with Example 4.2, the end of the Mahler fragment as given in the Sikorski edition). Schnittke’s m. 199 (compare to the fragment’s m. 21) has the strings take the sixteenth notes that appear in the fragment’s piano staves. More strikingly, Schnittke’s final chord (compare to the final chord of the fragment) adds an A-​C

Schnittke’s Piano Quartet  137 Example 4.1 (cont.).

cluster in the piano left hand and in the strings (as well as lengthening the original dotted-​quarter note to a full measure plus fermata). Apart from these two changes, all the details of the Sikorski edition of Mahler’s fragment appear in Schnittke’s quote. Even the fragment’s final squiggle, an editorial addition representing nine illegible sketch measures, occurs in Schnittke’s version as the string notation usually

138  Performing Knowledge Example 4.2.  Mahler fragment, Sikorski edition: m.17 ff.

interpreted as wide vibrato.8 The dotted double bar near the end of the Mahler fragment, an editor’s notation indicating the beginning of sketch material, is represented in Schnittke’s Quartet by a fermata. As well as providing source material, Mahler’s fragment displays two principles basic to Schnittke’s Quartet (and characteristic of Schnittke’s writing in general):  self-​similarity and circularity. Self-​similarity is articulated by the replication of the motive on multiple levels, and by the successive imitation of the theme’s concluding motive. Circularity is implied by the reappearance of the theme near the end of the fragment. Although Mahler’s fragment breaks off this thematic restatement prematurely, Schnittke’s quotations often complete the broken-​off  theme.

8 Penderecki’s Threnody (1960), which set important precedents in string notation, uses such a squiggle to mean “very slow vibrato with a ¼ tone frequency difference produced by sliding the finger” (score preface). In Schnittke’s orchestration of the Piano Quartet as the second movement of his Concerto Grosso No. 4–​ Symphony No. 5, he notates the squiggle more irregularly and adds the explanatory note “vibrato lento, quasi glissando.”

Schnittke’s Piano Quartet  139

Rotational Form The Quartet takes four large passes through Mahler’s material, “attempting to remember,” before finally arriving at the unadorned fragment, or “remembrance itself.” Example 4.3 summarizes these sections. Each pass moves through material from the Mahler fragment (MF), concluding with related material; the third and fourth passes are each followed by statements of two new themes, the “Strauss” and “perfect 4th” themes. In the following discussion of these passes, “Mahler’s fragment” will be abbreviated MF; references to it will use the measure numbers of the fragment as it appears at the end of Schnittke’s Piano Quartet.

The Attempt to Remember

First Pass The Quartet’s first attempt to remember (Example 4.4, mm. 1–​24) traverses Mahler’s entire fragment (except the three sketch measures) in exact order, accumulating its texture gradually. Compare Example  4.4 to Example  4.1. Grey material in Example 4.4 comes from the Mahler fragment. The traversal begins (Example 4.4a) with the MF’s undulating sixteenth notes and bass. The melodic line and harmony are added at Example 4.4b (the point at which the fragment moves to A minor); the entire texture appears at Example 4.4c (the passage in which the dominant of A shifts to the dominant of G).9 The fragment’s presentation of the theme alone in G minor occurs at Example 4.4d. Overlaid on this increasingly present fragment are textural elements refracted from the fragment itself. As shown by the arrows in the example, the piano’s opening consists of augmented imitations of the string undulations, at pitch (or, in m. 9, at the octave). This material stacks cumulatively (see mm. 1, 4, 6, 8, 9) until it evolves into the piano chords accelerating through mm. 11–​15; the acceleration culminates in the piano taking up its part in the full MF texture (mm. 16–​17). At Example 4.4d, where the MF consists of only a melodic line, expressed here in the cello, the violin reflects the cello in exact pitch inversional symmetry around F4/E4; the piano’s two 10 The sechands, likewise at IF4 E4 to one another, counterpoint the mirrored theme. tion concludes (Example 4.4e ff.) by completing the cut-​off thematic statement of Example 4.4d with material that would have followed it (in light grey), realizing the original material’s implication of circularity. Thus, the first “attempt to remember” produces an increasingly present MF that remains submerged in its own refractions (augmented imitation, inversional symmetry, circular repetition, and building density and registral range).

9 A few accidentals in the piano in m. 17 differ from those in Mahler’s fragment. 10 We use Lewin’s (1987, 51) labeling system for inversion, applied to pitch. In TnI nomenclature the pitch-​ class inversion is T9I. Throughout the Quartet, Schnittke chooses odd indices of inversion and highlights their semitonal axes of symmetry; in this passage the B/​B♭ and F/​E pairs are emphasized.

Example 4.3.  Schnittke, Piano Quartet: Form.

Schnittke’s Piano Quartet  141

Second Pass Similar elements characterize the second pass (Example 4.5). The theme is presented in canon twice, the first presentation (Example 4.5a) in four voices, at the interval of an eighth note, and at T-​1. The second presentation (Example 4.5b) occurs at the same durational interval, with the pitch interval expanded by an octave to T-​13. Once again strict pitch inversional symmetry characterizes accompanying material, in the piano.11 Here, for the first time, we hear the entire nine measures of the theme, in the first canon, and then, in the second canon, six measures of the theme, which could almost represent the MF’s broken-​off (seven-​measure) thematic statement. But the simple melody continues to be hidden by the close four-​voice canon and inversionally symmetric accompanying material. Third Pass The third pass (Example 4.6) moves through the complete MF (without the initial accompaniment measure, and again without the three sketch measures); the MF’s sections are marked on this example. The pass begins (section 1) with the MF theme, first in C♯ minor, and then (section 2) in D♯ minor, paralleling the original theme’s move up a major second from G to A minor. Voices in canon again counterpoint and obscure this MF presentation. Section 2 concludes (mm. 89–​90) with a partial presentation of the appropriate harmonic material at pitch, concluding, as the original does, with V7 of G minor. At section 3, the G-​minor theme follows, as it does in the MF, here in three-​voice canon at the eighth note and unison. Though the MF proper breaks off at the equivalent of m. 97, Schnittke continues it with the material that would have followed it, here still in three-​voice canon, but now at T-​13. In this third pass, two new themes enter. Though they contrast strongly with the Mahler material, they arise by association with that material. They grow from its elements and potentially associate with Mahler in other ways as well. We call the first of the new themes the “Strauss” theme because of its similarity to a melody from Richard Strauss’ Alpensinfonie (to be discussed shortly). The Strauss theme is shown at the bottom of Example 4.6. The core elements that it shares with the Mahler theme are labeled in the third section of Example 4.6, first in the Mahler theme in the violin, and second in the Strauss theme in the piano. They are the perfect 4th, the scalar [013], the semitonal neighbor,12 and a distinctive tritone figure X combining the perfect 4th and semitone.

A A 2 11 The symmetry occurs at IG 2 from m. 39 to m. 41 (except for the A-​G♯ in m. 40), and at IG  from m. 42 to m. 53. We do not label pitch axes of inversion in the second case because they switch between E♭3/​D3 and A3/​G♯3 (mm. 42–​49), and then between E♭4/​D4 and A4/​G♯4 (mm. 49–​53). Schnittke appears to have made a A and A mistake in m. 40: A2/​G♯2 occurs rather than A♭2/​G2, foreshadowing the A/​G♯ axis to come. IG IG correspond to T3I and T5I respectively. 12 On a certain level, the B♭ of m. 92 serves as neighbor to the A that follows.

142  Performing Knowledge Example 4.4.  Schnittke, Piano Quartet: Pass 1.

The Strauss theme occurs thrice. The first statement (a)  articulates lower and upper semitonal neighbors, followed by the {GD} perfect-​4th leap familiar from the MF; the intervening material (mm. 93–​94) uses the X figure in overlapping sequence. The second statement (b) alters the main motive to express [013] rather than [012], eventually spanning the perfect 4th (