CelloMind - Intonation and Technique 0692890297, 9780692890295

Citation preview

Ce oMind Hans Jrgen Jensen I Minna Rose Chung

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Ce oMind (

Hans J0rgen Jensen and Minna Rose Chung

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.

l Ovation

Fre"•

Chicago, IL 60647

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First Edition Managing editor: Colin Cronin {

Copy editor: Audra Gorgiev Publication design: John Funk Photography: Oleksander Myzyk (principal), Ian McCausland (1), Matthew Ryan Dueck (2),

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Charmaine Mallari (3) Photography captions: John-Henry Crawford (Front Cover), Hans J0rgen Jensen and Minna Rose Chung (vi), Saga De Leon and Hans J0rgen Jensen (x), John-Henry Crawford (xiv), Grant Zempolich (4), Nicolus Augustin Chappuy (11) and (13), John-Henry Crawford (24), Riana Anthony (30), David

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Liam Roberts1 (46), Henry Chen (59), Minna Rose Chung1 (64), Andre Micheletti1 (78), pianist Qiyun

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Dai, cellist Drake Driscoll (102), John-Henry Crawford (110), Hana Cohan (114), Emily Yoshimoto

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(138), Myrtil Mitanga (146), RianaAnthony (164), Emily Yoshimoto (173), Riana Anthony (183), from

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left to right: Wickliffe Simmons, Grant Zempolich, Drake Driscoll (191), Kevin Zaporski (194), Minna Rose Chung2 (197), John-Henry Crawford (206), Brannon Cho (212), Saga De Leon (224), JiHee Kim1 (228), SiHao He (238), Desiree Abbey1 (244), John-Henry Crawford (248), Hans J0rgen Jensen (Back

Cover), Minna Rose Chung3 (Back Cover)

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O

vation

Fress"

CelloMind: Intonation and Technique

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© 2017 by Hans Jingen Jensen and Minna Rose Chung Published by Ovation Press, Ltd., Chicago, IL 60647 http://ovationpress.com

All rights reserved. No part of this publication may be reproduced, distributed, or transmitted in any form or by any means, including photocopying, recording, or other electronic or mechanical methods, without the prior written permission of the publisher, except in the case of brief quotations embodied in critical reviews and certain other noncommercial uses permitted by copyright law.

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Printed in China

ISBN 978-0-692-89029-5

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Contents ..

...

111

Preface

vii

Part 2: Technique

How to Use This Book

xi

19

The Light Touch .

115

20

Velocity Studies

125

.l

21

Natural Harmonics Vibrato

.139

Part l: Intonation )

1

Introduction to Intonation

5

22

Finger Agility and Balance

147

()

2

The Harmonic Overtone Series

9

23

Introduction to Shifting .

165

3

Tonic Sympathetic Vibrations of the Open Strings

13

24

Organized Shifting into the Higher Positions

173

4

Cents Explained

19

25

Melodic Shifting Exercises with Vibrato

183

5 · Just Intonation and the Harmonic Series .

25

26 ·· Tartini Tones

191

6

Dissonant and Consonant Double Stops .

27

27 ·· Double Stop Studies in Thirds

195

7

Just Intonation System for Double Stops

31

28

Double Stop Studies in Sixths

207

8

Just Intonation System for Major Triads

37

29

Double Stop Studies in Octaves .

213

9

The Just Scales

47

30

Double Stop Studies in Tritones

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( ( 'l (

)

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.. ·· - ...

10

The Pythagorean Comma

55

31

Combination Double Stop Studies

(;

11

The 24 Enharmonic Pythagorean Pitches

59

32

Practical Shifting Examples from the Cello

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)

12

The Pythagorean Triads

65

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)

13

The Pythagorean Semitones

71

14

The Pythagorean Scales

79

15

The Syntonic Comma

87

Appendix

89

Glossary .

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/

16 ·Advanced Sympathetic Vibrations 17

Solo Cello Suites

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Intonation Performance Practice in the Bach

18

Intonation Performance Practice with Piano

93

33

225 229

Repertoire

239

Practical Application for Double Stops .

245 249

. . . . . . ...........

259

Exercise Index

263

Bibliography

268

103

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CelloMind: Intonation and Technique

v

Preface A note from Coauthor Hans J0rgen Jensen This book has been on my mind for a long time; certain

I remember another special lesson when cellist Allan

sections of the book were created many years ago. When

Steele (as a teenager) came to his lesson and told me with

Minna Chung, professor of cello at the University of

an incredibly excited expression in his eyes: "I have found

Manitoba, called me in the spring of 2013 to tell me that

theF!"

she was taking a sabbatical that fall and wanted to spend it in Chicago, I responded in an exuberant voice: I know what we should work on together. I have a book that has never been.finished, and.finishing this book together with you would indeed be exciting.

Little did I know at that time that the original book would never be finished. Instead, a new book, larger in scale,

(

would emerge from our collaboration. Since that first

(

sabbatical in Chicago, we have spent countless hours hard at work together, meticulously going over every detail in

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"What F?" I asked him. He replied, "The F that makes the 7th partial vibrate on the G string." Before that lesson, I had mostly shown Allan something called tonic sympathetic vibrations, but Allan had now taken it one step further and started to explore the entire fingerboard on his own. At the following lesson I asked Allan, "Why are your ears now suddenly so much better? Why are you able to really play in tune now?"

order to produce the highest-quality book possible. I am

Allan answered, "I have started to do what you asked

forever indebted to her willingness and patience; for her

me to do all the time, and by hearing and listening to the

drive to never quit until we both were happy with the final

sympathetic vibrations, I can now calibrate the pitch that I

result.

need and want."

Throughout my instructional career, I have spent a great

"What do you mean?" I responded.

(

(

deal of time and energy on teaching my students great intonation. I remember vividly the first time a student asked me, "Why do I have to play that note higher?" after I had asked for a certain pitch to be raised. (

(

From that lesson on, I rarely needed to talk about

lower."

intonation with Allan. I think he loved that there are

That incident inspired me to start searching for and

wanting a certain pitch to be raised or lowered.

l_.·

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L. 0 (..._,

it as a tonic, I place it higher than the 7th partial on the G

The students then replied, "I don't think so .. .I like it

intonation so that I would be able to explain the reason for

·--

measurement] lower than the piano pitch, so when using string."

reading all the material I could get my hands on about

I

that the 7th partial F is 31 cents [a unit of intervallic

My answer was simple: "Because it sounds better."

--

I.____,

Then, Allan explained how he was able to do it: "I know

The science behind intonation can be explained in ways that are much easier to understand than your average

scientific theories behind intonation. Ultimately, it inspired Allan to take decisions about intonation into his own hands. People with great intonation are intuitively sensitive to sympathetic vibrations. However, this is also a skill that almost anyone can develop with organized practice.

high-school science class. However, because scientists are

At its core, intonation is very personal, subjective, and

usually not performing musicians, there has always been

intuitive. However, understanding the science behind

a large gap between the science of intonation and practical

intonation and integrating it with our natural instinct can

application.

open up a whole new world of possibilities. One of the end goals of our practice is to reach that autonomous stage where all movements become almost automatic. CelloMind: Intonation and Technique

Preface

vii

f'.

When performing-when engaging your CelloMind-you

feel the physical sensations of a particular technique, and to

must be free to focus on the musical and expressive

engage your CelloMind.

aspects of the music. Yet, we must also remember that no matter how advanced we become, it is always important to continue seeking opportunities to grow and improve. This book is a resource to help us all do exactly that.

Our collaboration has led to a novel approach in finding a direct way to communicate important concepts. The final result is gratifying because our knowledge and resources continue to help many students realize that intonation is a profound and sophislicated skill sel for lefl-hand lechnique. It is our hope that cellists worldwide will use this book to

A note from Coauthor Minna Rose Chung

enlighten their CelloMinds.

A revolution is happening ...that's what I began to think

Acknowledgments

after listening to Hans J 0rgen Jensen, professor of cello at Northwestern University, speak ferociously about one of his favorite subjects: string intonation. When he invited me to contribute to a left-hand technique book, the concept seemed simple: present contemporary approaches

This book has been a joint venture involving far more than simply the two of us authoring a book. We are greatly indebted to the following people for all their help and support over the years.

to fundamental cello techniques. What we didn't know at

Russell Roland, cellist with the Spektral Quartet, had a

the time was that we would end up explaining how great

profound influence on the practical application of just

musicians intuitively play with exceptional intonation.

intonation in this book. The Spektral Quartet are firm

After months of expounding original examples that would

believers of performing the classical repertory with a very

best clarify Jensen's teaching methods, the idea of "how to

strong influence from just intonation, and Russell's very

play in tune" became impossible to ignore.

deep knowledge and practical advice on this topic was

When I first began my studies with Professor Jensen, I

Dr. Paul Stark, an esteemed radiologist and a terrific

improved my left-hand technique and intonation in

cellist, helped to review the book and provided a keen eye

preparation for my orchestra debut with the Haydn C Major

to ensure all of our information was precise.

higher sharps and lower fiats for my rapid scale passages, but I was just excited that this incremental adjustment made my sound brilliant! Since those early years, Professor Jensen has advanced his pedagogical theories on how to teach intonation. I have also learned from these ideas and

Dr. Michael Kimber was gracious enough to allow us to use his illustration of the "Schism a" in Appendix V. He to refine our definitions and explanations of theoretical concepts in the book. A few more cellists deserve special mention due to their

perception of pitch and its surrounding tonal reference.

keen interest in the topic of intonation: Allan Steele, Mira

particular the mathematical and scientific information set forth in the intonation chapters. We recommend that you study and absorb the information with patience and

Luxion, Nicholas Heinzmann, Nicky Swett, Henry Myers, Christopher Bennett, and Leandro Saltarelli. All of these musicians provided their own unique ideas, which will have a lasting influence on this book.

consistency. Our original exercises and those borrowed

The vibrato and shifting exercises in Chapter 25 of this

from history were selected to improve your intonation

book were written by cellist James Czyzewski as his final

ability and left-hand technique, incorporating both the

paper in his pedagogy class at Northwestern University.

mental and physical awareness into proper practicing skills.

A number of these exercises were given to James (by

It is important to play through all the exercises within each

Professor Jens en) for personal use during his studies.

chapter in order to train your inner and outer hearing, to

viii

CelloMind: Intonation and Technique

Preface

(

was also an excellent subject-matter expert, helping us

continue to develop my own "inner and outer" hearing: the

At times you may find the material quite challenging, in

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vital.

remember his creative and fun techniques that quickly

Cello Concerto. I did not fully understand why I needed

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He expanded the exercises, adding a few more and giving them all his personal touch. We extend our sincere appreciation to theory and piano professor Charles Horton at the University of Manitoba Desautels Faculty of Music for his editorial advice and invaluable analysis of Popper Etude No. 34. We would also like to express our gratitude to engraver Roman Turowski for his patience and terrific work on this

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'.11 very special and heartfelt thank you

goes to my wife, FumikoJ for her incredible

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help, understandingJ and patience with

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me while working on this book. I also must

CJ

thank all my wonderful students over the

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years at the Chicago Music institute, the

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Robert McDuffie Center for Stringy the

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Meadow mount School ofMusicJ and the

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Bienen School ofMusic at Northwestern

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for sharing your precious timeJ wisdomJ and stories with me and so many legions of

and students around the worlcl thank you

from each of us:

(__-)

to lend me invaluable advice. Thank you

In addition, this book could not have come together

Finally, we would like to close with a short personal note

c)

immense collaboration andfor continuing

students. To my family, circle ofcolleagues,

Colin Cronin, editor and project director of this book.

( -)

J0rgen Jensenfor inviting me aboard this

project.

without the multifaceted aid and organizational skills of

()

'.11 tremedous thank you to Professor Hans

for your endless supply ofhumor_, insightJ and support. Lastly, my contribution to this book wouldn't have been made possible without the collegial supportfrom the extraordinary administration, faculty, and student body at the University ofManitoba Desautels Faculty ofMusicJ Canada.J) - Minna Rose Chung

University.,, - Hans J0rgen Jensen

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CelloMind: Intonation and Technique

I Preface

ix

How to Use This Book This book is separated into two parts:

(

.

I.

Intonation

II.

Left-Hand Technique

One of the most important aspects of practicing a musical instrument is to use healthy, efficient biomechanical

Part I on intonation should be studied in the order the

movement patterns when practicing and playing. The "no

chapters are presented (unless you are already familiar

pain, no gain" philosophy can be very dangerous; it should

with the material) as the concepts in each chapter

not be part of our vocabulary.

build on one another. In contrast, the chapters in Part ,-

Healthy Practicing

II on technique are mostly composed of separate and independent studies ofleft-hand cello techniques. As such, it is perfectly fine to study them in any order (with the exception of the shifting studies in Chapters 23-25), depending on your skill level. As a general rule, we recommend practicing a minimum of 20 minutes per day on a section of one chapter, with a smaller percentage of the allocated time to study the other sections. For a more intensive practice session, dedicate

Remember to perform proper warm-ups and cool-downs before and after practicing. Give yourself adequate time for taking breaks. Also, switching back and forth between different repertory and technique studies can help with concentration and fatigue. Over-practicing one kind of technique can lead to injury or other issues, even when done the right way. Treat your body and mind with the utmost intelligence and respect, and know when enough is enough.

15-20 minutes per day on each of the three core subjects:

intonation, left-hand technique, and double stops. If you have any additional time, explore the practical repertory examples. However, we recommend to not exceed an hour

Routine and GoalSetting Strategies

per day of study on this material.

"Many people fail in life, notfor lack of ability or brains or even courage but simply because they have never organized their energies around a goal.,, - Elbert G. Hubbard Goal setting is a powerful tool for building both longterm vision and short-term motivation. High-performing achievers use it in almost all fields, including music and sports.

' ----'

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CelloMind: Intonation and Technique

I How to Use This Book

xi

I .

Hierarchy of Goals

Cello Practice Example

--7

Short-term-weekly and daily practice schedules

The following example illustrates how you might create a

--7

Mid-term-one to two months

study plan for improving your intonation, your ability to

--7

Long-term-one year

play fast, and your vibrato.

It is important to have a daily routine where a set amount

Select exercises from the following chapters:

of time is dedicated to specific exercises. In particular, technique is often practiced without a long-term goal in

--7

--7

mind. It should be practiced the same way as your concert

a specific goal over the course of several weeks, months, or years.

--7

PartII

practicing scales: --7

--7

--7

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(

--7

Velocity Studies (Chapter 20)

(

--7

Natural Harmonics Vibrato (Chapter 21)

(

and Melodic Shifting Exercises with Vibrato

(

Identify the aspects of your playing that need attention and improvement. Here are some specific ideas for

Intonation (Chapters 1-18; studied in chapter order)

repertoire, and mastered to the best of your ability. Conversely, scales, for example, should be practiced with

Part!

(Chapter 25) Intonation

(

For the chapters on intonation, start from the beginning

Short-term goal-master a four-octave scale at a slow

and spend at least one or two weeks working consecutively

speed with a beautiful warm legato sound, applying

through each chapter (trying to absorb the information

different intonation systems appropriately.

too quickly can lead to confusion). Take the necessary

(

Medium-term goal-play all major and minor scales

time to read, comprehend, and implement all the

(

in three or four octaves at a slow speed with solid

information and exercises before proceeding to the next

(.

intonation and a beautiful warm legato sound.

chapter.

Long-term goal-perform all major and minor scales in three or four octaves (without stopping) in sixteen notes with detache, spiccato, or legato bowing and with solid intonation (fast tempo: ~ = 160).

\

Mastering the intonation section of this book and making it a natural part of your musical mind can take a few months to perhaps one or two years, depending on your interest and knowledge.

Setting such specific goals provides focus to your practice and is of the utmost importance for long-term

Velocity Studies

(

development.

In Chapter 20 on velocity studies, it is most beneficial

(

to select a few different exercises (velocity and scale

l

exercises, or scale and Cossmann exercises) to work on

(

simultaneously. Practice the exercises systematically and

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ffLet me tell you the secret that has led me to my goal: my strength lies solely in my tenacity.))

consistently, with a diligent review of the previous day's exercises.

Louis p, steu

(_ (_

Vibrato." For further vibrato development, practice

L L L L

the exercises in Chapter 25, focusing on evenness and

L

different vibrato speeds for each exercise.

L

Vibrato Chapters

If you have tension or fundamental problems with your

basic vibrato, start at Chapter 21, "Natural Harmonics

L L L

xii

CelloMind: Intonation and Technique

How to Use This Book

L L L

,Your Slight Edge Consistency is one of the most powerful tools for longterm development. Maximizing the use of small amounts of time will make your practice more productive, effective, and efficient. People often want to see results immediately, r-'

!

not realizing what they can achieve when building up a skill over a number of days, weeks, months, and years. The Slight Edge1 is a philosophy promoted by personal development coach Jeff Olson that focuses on leveraging small, daily disciplines to create substantial results and

,--, i

)

success over the long term. Consider the following:

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1 minute each day becomes 6 hours in one year

~

10 minutes each day becomes 60 hours in one year

~

30 minutes each day becomes 180 hours in one year

(

( -)

Select which skills you want to focus on, and spend a short amount of time on those skills each day. Be disciplined and

(

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creative in the way you spend your practice time-even for just a few minutes. As you improve in a particular skill, your method of practicing that skill should change.

( (

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('-- )

()

We have designed this book to be a custom-made source of information for intonation and left-hand technique, It is our hope that each person using this book will select a topic and chapter they need to explore further, and then take the necessary time to master that chapter or chapters before moving on to the next topic.

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Jeff Olson, The Slight Edge: Secret to a Successful Life. (Momentum Media, division ofVideoPlus, L.P., 2005).

CelloMind: Intonation and Technique

I How to Use This Book

xiii

Part l: Intonation Intonation, at the highest accuracy level, is an intuitive skill that requires a very sophisticated inner and outer hearing. For those with extremely sharp listening skills, theoretical knowledge about intonation is not a necessity in order to master it. However, if your listening abilities are not quite at that level, understanding the theories about intonation can be a great help in refining your ear and making it a more intuitive part of your playing. It is quite possible to spend a considerable amount of

time working on the intonation sections of this bookperhaps as long as one to two years! Trying to absorb the information too quickly can lead to confusion, which is why we recommend short and focused practice sessions over longer periods of time. In our experience, when students spend the necessary time and begin to assimilate the applied information to their own playing, an incredible change in their ability to play in tune takes place. Over the years, we have seen numerous players with less than perfect ears develop intonation control at the highest level. Each chapter in Part I is intended to be studied in the order they are presented, as the concepts that are introduced build on previous concepts. The following is a brief overview of what to expect from each chapter.

CHAPTER 1 - INTRODUCTION TO INTONATION This brief overview provides an introduction to the three primary intonation systems in use today: equal temperament, just intonation, and Pythagorean tuning.

CHAPTER 2 - THE HARMONIC OVERTONE SERIES The harmonic overtone series (or harmonic series) is one of the most basic aspects of intonation and the scientific backbone for just intonation. Thoroughly understanding the harmonic series and committing it to memory is essential to developing a more refined sense of intonation.

CelloMind: Intonation and Technique

1

CHAPTC:R 3 ~ TONIC SYMPATHETIC VIBRATIONS OF THE OPEN STRINGS

CHAPTER 8 - JUST INTONATION SYSTEM FOR MAJOR TRIADS

Sympathetic vibrations play a very important role in

Just intonation is not a fixed-note tuning system but a

sound production and intonation on string instruments.

relational system where each pitch must always relate

The most resonant sympathetic vibrations of the cello are

to its corresponding dominant pitch. In the arpeggio

known as the tonic sympathetic vibrations.

exercises for this chapter, the keys are organized with

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the open string as the dominant pitch. Practicing the

CHAPTER 1l

·~

CENTS EXPLAH'1Ei:J

Cents are used in this book to compare and measure

arpeggios with just intonation will provide a better foundation for understanding the just intonation system and how to use it in practical applications.

(

similar intervals in different tuning systems. It is a great tool for sensitizing the ear and refining the mind to hear and visualize very small distances between the same intervals that may be tuned in a variety of ways.

CHAPTER 9

~

THE JUST SCALES

While particularly applicable to performers specializing in early Classical and Baroque performance practice,

CHAPTER 5 ·, JUST INTONATION

learning to play the just major and minor scales is very

!\ND THE HARMONIC SERIES

beneficial for any musician striving to develop a more

Just intonation is based on the harmonic series and is used

highlight how overtones affect sympathetic vibrations,

for tuning double stops and chords. This chapter teaches

which will help refine your ear and mind for intonation.

sophisticated sense of intonation. The scale exercises

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how the first eight partials compare to and deviate from equal temperament.

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CHAPTER 10 - THE PYTHAGOREAN COMMA

(

The Pythagorean comma is the 24-cent difference

(

between 12 stacked perfect fifths and seven stacked

l

Dissonant and consonant double stops are very important

octaves. It is also the interval difference between all

(_

aspects of harmony and have a tremendous influence

enharmonic keys and enharmonic Pythagorean pitches.

on intonation. This chapter teaches you how to hear the

By understanding how the Pythagorean comma works,

(

beating (or absence of beating) in double stops. Training

you will understand why, for example, C sharp major is

your ear and mind to hear the difference between

slightly sharper than D flat major, and how this guides

l

dissonant and consonant intervals is a great way to learn

musicians in expressive playing.

CHAPTER 6 - DISSONANT AND CONSONANT DOUBLE STOPS

l

·.

l

how to play double stops in tune.

CHAPTER 7 - JUST INT NATION SYSTEM FOR DOUBLE STOPS

CHAPTER 11 - THE 24 ENHARMONIC PYTHAGOREAN PITCHES Pythagorean tuning is a very sophisticated and beautiful

Developing the ability to visualize and imagine the

system. Most people use it intuitively; however, learning

sound of the just intervals in your mind is one of the most

how it works will make a tremendous difference in

important aspects of intonation to master. In this chapter,

developing a more comprehensive understanding and

you will explore listening to the vibrations (or absence of

control of intonation.

vibrations) of chords and double stops when tuning them.

2

CelloMind: Intonation and Technique

l

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CHAPTER 12 - THE PYTHAGOREAN TRIADS

0

Practicing all the major and minor triads using

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CHAPTER 17 - INTONATION PERFORMANCE PRACTICE IN THE BACH SOLO CELLO SUITES

Pythagorean tuning is an excellent way to become familiar

Just intonation plays a major role in the J. S. Bach solo

with all the keys that use the Pythagorean pitches.

cello suites due to the frequent use of double stops, chords, and the vertical harmonic aspects within the composition.

CHAPTER 13 - THE PYTHAGOREAN SEMITONES (

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Today, however, many cellists use a combination of just and Pythagorean intonation for maximum expressive effect. The selected samples in this chapter will help you

The Pythagorean chromatic scale is a vital element in

understand how these systems can be used to accentuate

adding color and expression to music. In this chapter, you

different aspects of the Bach suites.

will learn about the two different kinds of semitones in the scale. Additionally, the concept of the Pythagorean halfstep attraction is applied to the standard cello repertory.

(

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CHAPTER 18 - INTONATION PERFORMANCE PRACTICE WITH PIANO Playing together with a keyboard tuned using equal

CHAPTER 14 - THE PYTHAGOREAN SCALES

temperament presents a different set of challenges. The

The Pythagorean major and minor scales are the basis

equal temperament is introduced, and samples from

of playing scales and music with an expressive, melodic

the repertory are used in order to show how to adjust

quality. When Casals talked about "expressive intonation,"

intonation when playing together with the keyboard.

concept of compatibility between Pythagorean and

in reality, he was advocating for Pythagorean intonation.

(

APPENDIX CHAPTER 15 - THE SYNTONIC COMMA The Syntonic comma is 22 cents, and is the difference

()

between the Pythagorean major third (408 cents) and the

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just major third (386 cents). It is used regularly to switch

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from vertical just tuning to horizontal Pythagorean melodic tuning.

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CHAPTER 16 - ADVANCED SYMPATHETIC VIBRATIONS

The appendix explore a number of topics related to intonation in greater detail: I.

The Helmholtz Intonation Chart

II.

The Just Diatonic Semitone Divided in Two, Four, and Eight Parts

III.

Harmonic Series in Scientifically Accurate Cents

IV.

Just Intonation in Consonant Double Stops

V.

The Schisma

The charts in this chapter illustrate the most important harmonics of the open strings that can be activated by sympathetic vibrations. Practicing the exercises in this chapter will sharpen the way you perceive pitches, as well as how you navigate the entire fingerboard.

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CelloMind: Intonation and Technique

3

Chapter l:

Introduction to Intonation

,

Developing a sophisticated understanding of intonation is a critical component of musical expression and a

Cents

continuous challenge for any string player. Unfortunately,

The cent is a logarithmic unit of measure used for musical

the theories behind how intonation works are often

intervals, and is a fundamental concept in building a more

complicated and introduced with little practical

sophisticated sense of intonation. One octave contains

application. In other words, they are not particularly

1200 cents. Typically, cents are used to measure extremely

useful for musicians. Through the intonation studies in

small, finite intervals, or used to compare the sizes of

this book, we aim to present these theories in clear and

similar intervals in different tuning systems.

understandable terms that will improve your ability to play in tune.

It is difficult to establish how many cents are perceptible

to the human ear because it varies from one person to

For string musicians, intonation is a particularly sensitive

the next. However, most professional musicians can

and dynamic process where each pitch must adjust to its

distinguish differences in pitches from five to six cents and

musical function, be it melodic or harmonic. Throughout

above.

history, musicians have used many different intonation systems. Today, we use a combination of three main systems, depending on the context. For example, when playing with the piano, string players are influenced by the piano's equal temperament tuning. On the other hand, many musicians who specialize in authentic Baroque and Classical performance practice use just intonation-a system based on the harmonic series (also called the

Intonation Systems Today There are three primary intonation systems in use today: 1. Equal temperament-a system that divides the

octave into 12 equal semitones 2. Just intonation-a relational pitch system based on

harmonic overtone series). Furthermore, when playing melodically, we are strongly affected by the balance of, and gravitational pull toward, perfect intervals (i.e., perfect

the natural harmonic overtone series 3. Pythagorean tuning-a system based on stacked pure perfect fifths

fourths, perfect fifths, unisons, and octaves). This melodic expression is called Pythagorean tuning, which is based on pure perfect fifths.

Equal Temperament The 12-tone equal temperament system divides the octave

Knowing when and how to use these different intonation

into 12 equal-sized semitones, each one consisting of

systems is a major challenge for musicians today. By

100 cents. Keyboard instruments (such as the piano) are

understanding these theories of intonation and learning

tuned using equal temperament. This system enables

how to apply them, you will cultivate a more refined and

these instruments to play in all keys with minimal flaws in

comprehensive ability of how to play in tune.

intonation. In equal temperament, however, perfect fifths and

I

.

perfect fourths are not completely in tune-they are two cents smaller or larger, respectively, than their just and

I'-

l_

Pythagorean counterparts. In addition, major intervals are slightly larger in equal temperament compared to just intonation, and minor intervals are slightly smaller.

L

CelloMind: Intonation and Technique

I Chapter 1: Introduction to Intonation

5

Just Intonation

Comparing the Three

Based on the natural harmonic overtone series, just

Intonation Systems

intonation is required to tune double stops and chords so that the instrument rings with all the overtones of the double stops, lined up according to the overtone series.

String players tend to use all three systems in order to play in tune. Since most musicians do this intuitively, how and when to switch between the systems is not always

Developing a thorough understanding of just intonation

understood. In this book, we will provide the tools and

and the overtone series will greatly help to refine your

exercises to explore the melodic value of the Pythagorean

inner and outer hearing. Just intonation is a purely

system and the basis for harmonic tuning in the just

relational system where the pitches constantly adjust to

system.

(

Additionally, adjustments must be made when playing

(

with the piano to account for the equal temperament

(

different tonal centers. In double stops and chords, it is important to know what note is the key center and then let the other pitches adjust to the dominating pitch.

tuning of the keyboard.

Just intonation can be used both melodically and harmonically for Baroque and early Classical music. It is also used for tuning chord-like structures vertically in chamber music ensembles.

Comparing Pythagorean and Just Tuning In the following three samples, you will sec how to switch between the two systems; the fourth exercise illustrates a practical example.

Pythagorean Tuning Pythagorean tuning (named after the Greek philosopher and mathematician Pythagoras) is the scientific

The Trouble with Pythagorean

explanation for our preference for lower minor thirds/

Tuning and Double Stops

sixths, higher major thirds/sixths, and leading tones in melodic playing. Expressive intonation has its roots in

1. Keep in mind that Pythagorean tuning only works

the Pythagorean system, which is built upon the stacking

for pure double stops (unison, octave, perfect fourths

of perfect fifths. The legendary cellist Pablo Casals

and fifths) but not for major or minor double stops.

(

(

introduced the term expressive intonation to musicians

2. Play the three-note pattern with a high F sharp that

on a mass scale, saying, "Each note is like a link in a chain,

leads up to the G. When that same F sharp is played

l .

important in itself and also as a connection between what

together with the open A, it sounds out of tune.

(

has been and what will be."

1

third out of tune high F sharp

All scales have an expressive, melodic quality. The notes on the first degree (tonic), the fourth degree

0

3

0

4

(subdominant), and the fifth degree (dominant) are the pivotal balance points upon which the other notes in the scale rest. In a major scale, the major third has a gravitational pull up toward the fourth, while the major seventh-as the leading tone-has a gravitational pull up toward the tonic. In a minor scale, the minor third has a gravitational pull down toward the second scale degree, and the major seventh-again, as the leading tone-has an upward pull toward the tonic.

1

Blum, Casals and the Art ofInterpretation, (Berkeley: University of California Press, 1980), 19.

6

CelloMind: Intonation and Technique

Chapter 1: Introduction to Intonation

match

3

Combining Expressive Pythagorean Tuning with Just Vertical Tuning

Exercise 1. 3 Just Tuning Used Vertically and Melodically

1. Play the three-note pattern with an expressive F

sharp that leads up to the G.

1. Play the lower F sharp in the three-note passage

and keep the same F sharp for the double stop. The

2. When playing the double stop, lower the F sharp to

double stop is now in tune with the same F sharp. This is an example of pure just intonation.

tune with the A string.

2. Used melodically, the lower F sharp might sound third in tune

high F sharp

low, but it has a beautiful, soft, and round tone quality. This method of tuning is often used by players specializing in Baroque and Early Classical

lower F sharp

performance practice. low just F sharp

third in tune

match

• Casals' Cadenza from Haydn D Major Concerto, Hob. Vllb/2, Op. l 01 The two F sharps: 1. In the first measure, use the low F sharp for the double stop in order to play the D major chord in tune.

2. In the second and third measures, use the higher and expressive F sharps in order to make the scales sound more expressive.

v ~

Pablo Casals (1876-1973) high C#

2

low F#

3

low F#

t

high F#

high F#

high F#

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'-·-'

CelloMind: Int onation and Technique

Chapter 1: Introduction t o Intonation

7

Using Equal Temperament to Match Unison Passages with the Piano When playing in unison with the piano, it is important to listen to and match its equal temperament pitches. In the next exercise (taken from the D major unison passage of the Beethoven A Major Sonata), the tricky notes are the F sharp (the major third) and the C sharp (the leading tone). The just F sharp and the just C sharp will sound too low. The higher, melodic Pythagorean pitches will sound better (but will still be slightly higher).

Excerpt from Beethoven A Major Sonata, Op. 69

To best match the unison passage with the piano: 1. Tune the cello to the piano A. Match the other strings with pure fifths.

2. Match the A and D to the open strings and slightly lower the melodic Pythagorean F sharp, C sharp, and D sharp for the unison passage to sound perfectly in tune with the piano.

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CelloMind: Intonation and Technique

Chapter 1: Introduction to Intonation

l;

11 1

believe that from the earth emerges a musical

poetry, which is by the nature of its sources tonal.

I

believe that these sources cause to exist a phonology of music, which evolves from the universal known as the harmonic series

11

- Leonard Bernstein 1

Chapter 2·

The Harmonic Overtone Series The harmonic overtone series or harmonic series is the basis of all tonal music and the foundation of our understanding of Western music. It is also present in nature and through man-made sounds, from chirping birds to blasting fire sirens. To better understand the

Standing Wave The way a string vibrates is called a standing wave and is composed of the fundamental (the lowest standing wave frequency) and several other smaller standing waves.

harmonic series, let's first define a few basic concepts.

Partials Fundamental Tone

A partial is the portion of a wave that vibrates. A string

The fundamental tone or fundamental is the main note heard when playing any note on any string. It is the lowest standing wave frequency, where all parts of the string vibrate together. When playing an open A string, the note heard (A) is the fundamental tone. It can also be referred to as the first harmonic/ partial.

vibrates in many parts; theoretically, standing wave patterns can divide the string into an infinite number of partials. In this book, we will focus on the first eight partials.

Nodes Harmonic nodes refer to the points between the partials where the overtones are located. These nodes do not vibrate.

L

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u

Leonard Bernstein, The Unanswered Question: Six Talks at Harvard. (Cambridge: Harvard University Press, 1976), 424.

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CelloMind: Intonation and Technique

I

Chapter 2: The Harmonic Overtone Series

9

Wave Representation of Partial Series

Overtones Located at the harmonic nodes, overtones refer to any partial except for the lowest-the

-

fundamental tone. These overtones ring

Fundamental 1st Partial

---

- -

along with the fundamental note, to which 2nd Partial

they are mathematically related. In some ways, we can describe overtones

3rd Partial

in comparison with light. For example, we understand that light is the total spectrum of all colors, but not all colors can always be

4th Partial

seen individually. The same principle applies with the overtones. These "over" tones

(

resonate as part of the total sound, but they

5th Partial

are not always distinguished individually. (

The greater the number of overtones 6th Partial

activated, the more full-bodied and brilliant

( (

the sound.

I

Natural harmonics are overtones found on

the string and are produced by touching the strings lightly at the harmonic nodes.

~/~~-~-~

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8th Partial

Partial

e

= Nodes I Overtones

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Relationship between

Port1ol

Ports of S ring

Vlbr

Partials and Overtones Partials and overtones both have a great influence on sound quality and intonation.

Pitch Produced

Overtone

1nq

1st

Whole string

Fundamental tone

2nd

Two parts

Octave above fund

1st

3rd

Three parts

Octave + fifth above

2nd

While they are very similar, it is important

t

fund

to be able to distinguish between the two. Remember that an overtone is defined as any

4th

Four parts

Two octaves above fund

3rd

partial except the lowest (fundamental) and

5th

Five parts

Two octaves +major

4th

third above fund

that they are located at the harmonic nodes between the partials (where there are no

6th

Six parts

vibrations). 7th

Seven parts

is the fundamental pitch. The second partial

8th

Eight parts

is counted as the first overtone (one octave above the fundamental).

~

Two octaves + minor

6th

seventh above fund

differently due to the fact that the first partial

CelloMind: Intonation and Technique

5th

above fund

Partials and overtones are counted

10

Two octaves + fifth

Chapter 2: The Harmonic Overtone Series

Three octaves above fund

7th

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Harmonic Series

r.

First eight partials on the open strings:

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1. Practice the eight partials on one string with a variety of fingerings.

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2. Locate and play the first eight harmonics on the indicated strings.

I' I'

3. Study and memorize the harmonic series and the overtone chart. 4. Know the names and numbers of the eight partials on all four strings.

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( C Major

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12

CelloMind: Intonation and Technique

Chapter 2: The Harmonic Overtone Series

Chapter 3-

Tonic y p th t· c Vibr ,t· on ft e p Stri gs The phenomenon of sympathetic vibrations on the cello occurs when a plucked or bowed pitch causes one or more harmonics on another string(s) to resonate in sympathy.

Hearing the Open String Sympathetic Vibrations

The sympathetic vibrations share a harmonic likeness with the original pitch. Physicist Hermann von Helmholtz proposed that the "sound-movement of a string can leave

Th ory

its originally narrow and fixed home and diffuse itself in

Playing the open string tones in different registers on

the air," and that this sound can "put another string into

other strings creates the most obvious and vibrant

sympathetic vibration."

sympathetic vibrations on the cello.

1

An example of sympathetic vibration (or resonance) is a window rattling when a bus or a big truck drives by. The window rattles at the same or higher harmonic frequency of the sound made by the bus or truck. Another classic example is the bursting of a wine glass from the powerful voice of a soprano.

How to Practic In Exercise 3.1, the lower staff line indicates the actual note to be played. The higher staff line indicates the sympathetic vibrations that are activated on the open strings. Play the solid notes in the center of the pitch to

Sympathetic vibrations play a central role in sound

activate the most resonant sympathetic vibrations on the

production and intonation. The most resonant

other strings.

sympathetic vibrations of the open strings take place when playing the solid notes C, G, D, and A in different registers.

L A lecture by Hermann van Helmholtz, as detailed by Shelley Trower, Senses of Vibration: A History of the Pleasure and Pain ofSound. (London: A & C Black, 2012), 39.

CelloMind: Intonation and Technique

Chapter 3: Tonic Sympathe tic Vibrations of the Open Strings

13

I

rr r· r

Tonic Sympathetic Vibrations of the Open Strings

('

Here are some helpful ways to hear the sympathetic vibrations:

( 1. Play the solid note forte with a fast up bow while traveling toward the frog. Lift the bow off the string and stop it from

vibrating with one of the fingers of the bow hand. Listen for the sympathetic vibrations.

r (.

2. When you place the left-hand finger right in the center of the note, it activates the sympathetic vibrations to a greater extent, resulting in a richer and more resonant sound. 3. To help hear the perfect placement of the left hand, experiment with placing the pitch near the center of the note. Notice how more vibrant the sympathetic vibrations are when the finger is placed right in the center of the note.

('

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Open A, the whole string vibrates ----------- ---- - - - ----- --- -- --- __________ 2nd partial on I

=Sympathetic Vibrations

SV

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lj@fi(JJ§C·J Creating a Pythagorean Whole Tone and Minor Third Pythagorean

Pythagorean

Whole Tone:

Minor Third:

2 Perfect One Fifths Octave 1404

1404cents

498cents

- 1200cents

- 204cents

204cents

294cents

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Pythagorean Whole Tone

1200

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204 ?

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Pythagorean Minor Third 294

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Just E

Pythagorean E

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Pythagorean Third 408 cents C>

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Match

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Recall in Chapter 12, "The Pythagorean Triads," that we discussed how the Pythagorean major triads are brighter/more brilliant and the Pythagorean minor triads are darke1/more expressive when compared to their just major and minor counterparts. The exact difference between them is the

(.)

syntoniccomma, 22 cents.

u

CelloM ind: Intonation and Technique

I Chapter 15: The Syntonic Comma

87

lj@ijfij~fj Pythagorean Melodic Tuned Scale vs. Just Tuned Third Professional string players constantly switch back and forth between Pythagorean and just intonation using the syntonic comma. This exercise illustrates how the syntonic comma is used to switch from melodic tuning to just tuning. (

Pythagorean E

(

I

. . • • • •t -----------E 22 cents Syntonic Comma

22 cents lower

(

To properly tune the E used in the double stop with the open G string, the E needs to be lowered 22 cents from the Pythagorean E.

(

The tuning of the two Es (as shown above) can be illustrated in a different way. The E that tunes with the A string is higher than the E that tunes with the G string. The difference is 22 cents.

( (

Pythagorean E Match ~~

Perfect Fourth

Match

Match

Just Major Sixth

Syntonic Comma

(

22cents

/'>,

(

~

Match

(

Just E

Deciding which F to use-the F that tunes with the A string or the F that tunes with the C string-can often create confusion. Again, the difference between the two Fs is the 22-cent syntonic comma. In this exercise, the Pythagorean F is tuned to the C string as a perfect fifth. However, using this F will be out of tune when played against theA string as a just major third. In order to tune that F with the A string, it must be raised by 22 cents.

Perteet Fifth

Pythagorean Third

Match

~~ +

: ,

,

Just Major Third 1n Tune

s

II

F moves up 22 cents lor Just Tuning Just Major Third

•

•

•

Pythagorean Melodic Minor Third

•

• Up 22cents

The above scale also illustrates how the syntonic comma is used during a Pythagorean melodic minor scale to tune a just third in a double stop. The Fused in the double stop is raised by 22 cents from the starting Pythagorean Fin the melodically tuned scale.

88

CelloMind: Intonation and Technique

Chapter 15: The Syn tonic Comma

11

Sensitizing your ears to the sympathetic vibrations will sharpen the way you perceive pitches." - Hans J0rgen Jensen

Chapter 16:

Advanced Sympathetic Vibrations Earlier in this book, we introduced the basics of

Activation of Partials

sympathetic vibrations. Now, let's look at more advanced examples beyond the tonic. The charts in this chapter

Knowing which partial should be activated is the key to

illustrate the most important harmonics of the open strings

navigating the placement of the solid tone. The 5th partials

that can be activated by sympathetic vibrations.

are 14 cents lower and the 7th partials are 31 cents lower when compared to equal temperament. When placing

Being able to visualize the sound and placement of all

solid notes that activate those partials, the solid pitch must

fundamental pitches on the cello that fully activate the

be placed lower. In the following example, you will be able

overtones is an invaluable skill to have. Developing this

to hear and experience how three different placements of

refined inner hearing will sharpen the way you perceive

the F natural in first position on the D string will activate

pitches and how you navigate the entire fingerboard.

three different overtones.

[email protected] The Three F Naturals on the D String 4th

The F natural on the D string can activate three different partials, depending on the placement of the F.

Partial Ac tivated

t.l

( -7

The F that t unes with the A string is a just major third and is 386 cents.

-7

Play on Ostring

difference between the two Fs is 22 cents, the syntonic comma.

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The F that tunes with the G string is

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--

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431

408

386

-

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431 cents under the open A string. The F tunes with A

difference between this and the equal-

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A

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The F that tunes with the C string is the Pythagorean F and is 408 cents. The

-7

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7th

8th

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--

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--

--

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-

-

--

F tunes wilh G

F tu nes with C

tempered major third is 31 cents. 1 -7

This F needs to be lowered almost a quarter tone compared to the first F that tunes with the A string.

l.1 L,

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Look in Appendix III for exact cent amounts for the 7th partials on the cello.

G

u

CelloMind: Intonation and Technique I Chapter 16: Advanced Sympathetic Vibrations

89

Advanced Sympathetic Vibration Charts The following points apply to the four advanced

How to Practice

sympathetic vibration charts (Exercises 16.2-16.5):

1. Center the notes so that they line up perfectly with

the overtones (see the previous section, "Activation

1. The lower staff line indicates the notes to play.

of Partials"). (

2. The higher staff line indicates the overtones that

2. Before playing each note, visualize in your mind's

are activated. -?

ear the sound of:

The Roman numerals listed above and below

a. the fundamental note

the sympathetic harmonics indicate which

b. the sympathetic vibrations

string each harmonic is located on.

c. the placement of the left hand on the fingerboard

3. The ordinal numbers below the bottom staffshow

3. In the beginning, take time before and after each

which partials share the common overtone relative

(

note to visualize and anticipate the next note.

to the solid pitch that is being played. Remember that the numbers are the same for harmonics and partials. -?

(

4. When searching for the best location of the fundamental pitch, place your finger a little flat and

As an example, "2nd" appears under the first

then a little sharp. Slowly work up and down toward

measure because the sympathetic partial is the

the exact center position of the pitch.

2nd partial of the open A string.

(

.

5. It may also be helpful to search for a particular string

4. The ordinal numbers above the top staffshow which

partial by stopping the other vibrating strings.

partials share the common overtone relative to the string(s) that contain the sympathetic overtones. -?

As an example, the first measure of Exercise 16.2 indicates that the harmonic A on the D

(

string is the 3rd partial of the D string.

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4 3 1

3 2

4

2 3

4

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CelloMind: Intonation and Technique I Chapter 20: Velocity Studies

129

The Five-Stage Impulse Patterns: C Major, Three-Octave Scale Follow the five stages outlined below in order to properly practice and learn the impulse patterns. This exercise will help promote facility in all scales and passage work. "' Stage 1: Stop between each string crossing and position change.

(

"' Stage 2: Isolate and practice each position shift.

(

.

.

"' Stage 3: Play four notes very fast and stop between each group. "' Stage 4: Play eight notes very fast and stop between each group. "' Stage 5: Play the whole scale at a fast tempo, from

J=100 to J=180.

(

Play through each of the five stages with legato bowings and separate bow strokes, both on and off the strings. ( (

When first learning a new technical passage,

v

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it can be very helpful to organize the passage in your mind by stopping and before each string

simile

crossing.

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between each position

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the bow at the

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beginning of each

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impulse group

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2. Feel each group as one impulse, but make sure that each note is played and articulated with great clarity. 3. Practice at various tempi, from

.

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J= 60 to J= 100, alternating between slow and fast.

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4. Use fingertip impulses supported by a wrist-forearm rotation.

(

5. Use less bow when increasing the tempo. The faster you play, the smaller and more efficient the motion.

l t L

6. Use Pythagorean intonation. In fast playing, use the higher thirds as well as the higher 6th- and 7th-step leading tones to make the sound more brilliant.

L L

l 1. Practice the following shifts

in different tempi, and use forearm rotation with a very

4

1

,,.-...

9: u r f

4

1

,,.-...

414

1 simile

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light left arm, releasing the

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shift.

4

1

4

1

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130

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CelloMind: Intonation and Technique I Chapter 20: Velocity Studies

l. D_

1

II

l.,

l.. L L{

Stage 3: Impulse Units Organized by Four- Note Rhythmic Patterns 1. Practice this four-note impulse unit the same way as described in Stage 1(Exercise20.4).

>

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v

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Stage 4: Impulse Units Organized by Eight- Note Rhythmic Patterns 1. Practice these eight-note

impulse units the same l'I

way as described in Stage 1 (Exercise 20.4).

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Stage 5: Playing the Complete Three- Octave Scale (Final Goal) 1. Practice the complete three-octave

scale using a four- or eight-note impulse pattern. 2. Eventually, you should be able to play the scale with a single impulse for the low C and the highest C.

II >

CclloMind: Intonation and Technique

Chapter 20: Velocity Studies

131

Continuous Velocity Exercises in the 12 Major Scales Have you ever played through all the major and minor scales without stopping? This ability is a good example of a long-term goal and an important technical skill that requires careful practice over a long period of time. Begin with one scale and gradually add more to your practice. As you become more proficient, consider playing through all the major and minor scales

(

every day as a mindful warm-up activity.

Equal-Tempered Chromatic Preparatory Exercise Before we begin with the continuous scales, we'll first examine the following chromatic exercise. Practicing this drill will

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help you to play the equal-tempered chromatic tonics that should be used for the 12 continuous scales.

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1. Practice this exercise in two ways:

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a. Practice with the lower fingerings, the standard fingering for chromatic scales. b. Practice using all first fingers for the chromatic scale.

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2. Always use equal temperament tuning for the tonic pitches.

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simile fingering

1 ~-----------------------------

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Practice Instructions for the C( ·· - v~1odty Ex"'f' ·

1. Same fingerings in all keys: In the beginning, it

1. Apply the same method as described in the above

may be easier to use the same fingering for each key (listed below). To maintain consistency, do not use

chromatic exercise. 2. Use equal-tempered tuning for the tonics and Pythagorean tuning for the scales with high thirds and high leading tones. This will make the scales sound brighter and more brilliant in faster tempi. 3. Begin playing through the scales without stopping in a slow tempo, using very efficient movements for both arms and hands. 4. Gradually build up to a fast tempo, from J= 120 to

J= 180. The faster you play, the more efficient your movement must be. 5. Practice the scales with the following variations: a. Practice with separate bowings on and off the strings. b. Play the scales with four- and eight-note slurred legato bowings. Also practice in the fast tempo with 16- and 24-note slurred bowings. c. Practice in various dynamics, ranging from soft

any open strings (except for the first note of C majo1'.). a. To begin, play the fingering in groups of three notes. b. In C and C sharp: i.

CelloMind: Intonation and Technique

Chapter 20: Velocity Studies

l

l (

L

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The second octave ends with the fourth

d. In A, B flat, and B: The second octave ends with the third finger on theAstring. e. For all keys, the third octave uses the fingering 1- 2- 1-2-1-2-3. 2. Standard fingerings: As you become more proficient, experiment with using the standard uses the open strings whenever possible.

132

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fingerings as marked in the exercises. This fingering

to loud.

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finger on the D string.

finger on the A string. i.

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CelloMind: Intonation and Technique

Chapter 20: Velocity Studies

133

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CclloMind: Intonation and Technique

Chapter 20: Velocity Studies

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Cossmann Studies with Extensions

'4@Htff1 iil Preparatory Practice Varia tions 1

1. First, play through these preparatory practice variations before proceeding to the extended Cossmann exercise that

follows.

8-Note Impulse Pattern

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IV ---- - - ---------- --------------- -------------------CelloMind: Intonation and Technique I Chapter 21: Natural Harmonics Vibrato

143

l@ijij§J(I Three Vibrato Variations Apply the following four steps to the three variations, using any combination of fingerings. Use relaxed, fluid vibrato movements, and connect the notes with slow glissandos. 1. Inside the string: Allow your fingers to hang on the inside (the right side) of the string without touching the

fingerboard. With your arm, pull the fingers slightly to the left. 2. Inside the string, touching the fingerboard: Relax the weight of your arm into the fingerboard without depressing the string. Place your finger in between the two strings. Keep the side of the finger on the inside of the string. 3. Solid and harmonic alternating: Beginning with a solid note, release the arm weight from the back into the string and fingerboard, and then repeat the same note as a harmonic. Continue by alternating between solid notes and harmonics. 4. Solid: Release the weight of your arm into the string, lightly touching the fingerboard. During the shifts, release the

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arm weight from the back. Variation One (repeat on all strings)

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L LL 144

CelloMind: Intonation and Technique I Chapter 21: Natural Harmonics Vibrato

l,.. l

h@@§Jfj Low to High Positions f-'

1. Allow the vibrato to flow from one note to the next, from the low to the high positions.

2. Remember that only the playing finger touches the string. Keep all fingers relaxed. 3. In the high position, experiment with placing your thumb under the fingerboard. 4 . When using the thumb to vibrate, experiment with placing the first finger on top of the thumb for better support.

5. Experiment with the dynamics and the speed of the vibrato. 6. Practice using any finger combination.

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1. For the follow ing exercise, vibrate on the solid notes; stay on one string.

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CelloMind: Intonation and Technique

I Chapter 21: Natural Harmonics Vibrato

145

Chapter 22:

Finger Agility and Balance This chapter is divided into three sections that focus on

Lett-Hand Pizzicato

developing greater articulation, more clarity, and better balance and agility in the left hand.

Notice the different notations for the left hand:

1. Left-hand pizzicato: an excellent study for

....,. (+) - Use forearm rotation to support the striking

developing the habit of using forearm rotation to

action of the finger to sound the note:

support the lifting and dropping motion of the

a finger strike.

fingers.

._,. + - Use forearm rotation to lift the previous left-

2. Cossmann studies: this daily exercise promotes

hand finger to pluck the sounding note:

balance and agility in the left hand in the lower

a left-hand pizzicato.

positions. 3. Klengel thumb position exercises: a classic study for developing left-hand thumb position agility in the higher registers.

h@@ftfjl Left-Hand Pizzicato Exercise 1. For a louder pizzicato, lift your finger higher and

3. Release your arm weight and experiment with using

drop it quickly in a downward flicking motion.

vibrato after each pizzicato.

2. Firmly set the note to be plucked on the string and fingerboard.

2 3 4

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continued -7

L l.. l.,, l_,

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CelloMind: Intonation and Technique I Chapter 22: Finger Agility and Balance

147

2 1 3 2 43

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21

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+

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=II (+) +

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148

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CelloMind: Intonation and Technique

{+) +

IV

I Chapter 22: Finger Agility and Balance

C+l +

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CelloMind: Intonation and Technique

Chapter 22: Finger Agility and Balance

L-

Cossmann Studies These Cossmann exercises are great to include in your daily warm-up. Practice them in a systematic way-start out slowly by playing a few lines, and gradually increase your speed as you add more lines.

i#@ij§jjl Cossmann Preparatory Exercises 1. Play the following preparatory exercise with harmonics to apply a "light touch."

2. Keep your hand relaxed by playing the harmonics with a free and easy vibrato. 3. First, try playing with the bow on one string while the left-hand plays on both strings. 4. When you feel more comfortable, play the complete exercise with the left-hand and bow as written.

3

3

4

2

3

4

3

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IN:

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CelloMind: Intonation and Technique

I Chapter 22: Finger Agility and Balance

151

h@H(fffjl Cossmann Exercises 1. Use your arm weight to allow the fingers to lightly touch the fingerboard.

2. Start slowly and practice with shorter legato slurs. Begin with one beat per slur, then two beats per slur, and so forth . 3

4

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