Tao of Bass.Vol.1: The left hand [1, 1 ed.] 9780692808405

Double bass method for the double bass

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Table of contents :
Introduction
Chapter 1: Endurance, Coordination, Articulation
Permutations : Traditional Lower Positions
Chapter 2: Four Finger Technique/Pivot
Permutations: Four Finger Technique
Chapter 3: Thumb Position
Permutation: Thumb Position
About the Author
Recommend Papers

Tao of Bass.Vol.1: The left hand [1, 1 ed.]
 9780692808405

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Citation preview

Cn\~Qf1 . A\ejt1n dr o ~toS~ Me~o~ ~u .

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MACHADO

OF BASS

Volume 1, The Left Hand Volume JI, Scales, Arpeggios, Chromatic Exercises Volume III, The Right Hand Vol u me TV, Tao of Bass Applied



OFBAS 1 1

r

-

1

1 1 /

1

l J -.~

MARCOS

MACHADO

Volume 1, The Left Hand Volume II, Scales, Arpeggios, Chromatic Exercises Volume III, The Right Hand Volume TV, Tao of Bass Applied

...

Copyright © 2017 by Marcos Machado All rights reserved. This book or any portion thereof may not be reproduced or used in any manner whatsoever without the express written permi~sion of the author except for the use ofbrief quotations in a book review or scholarly joumal. \

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First U.S. Printing, November 2016. Second U.S. Printing, August 2017. ISBN 978-0-692-80840-5 www.TAOofBASS.com Ordering Information: Spedal discounts are available on quantity purchases by corporations, associations, ~ducators, and others. For details, contact the author at the above listed website address. Author: Marcos Machado Editor: Roberto Pineda Assistant editors: Jeffery Baugman Guilherme Oliveira Guilherme Zils Graphic Design: Eleonora Machado

Jo\1-

Table of Contents: Introduction ............... ~ .................................................................. 3 Chapter 1: Endurance, Coordination, Articulation ..................... 5 Permutations: Traditional Lower Positions ............................... 52 Chfllpter 2: Four Finger Technique!Pivot ................................... 71 Permutations: Four Finger Technique ..................................... 112 .. '/

Chapter 3: Thumb Position ...................................................... 131 Permutations: Thumb Position ................................................ 200 About the Author ..................................................................... 220

/

Teaching wonderful students at the University ofSouthern Mississippi is a constaht source of inspiration. Mj gratitude to all double bass students, alumni, faculty and USM administrators. It is my hope that yo u willfind in this book a pq_th that is appropriate for yo u and will help guide your technical development. Photo ofMarcos Machado with current bass students (Fall2016) L-R: Nathaniél De la Cruz, Santiago Zorrilla, Roberto Pineda, Vincent D'elia, Marcos Machado, Guilherme Oliveira, Gonzalo Kochi, Sergio Flores, Carlos Valdez, Javier Barreta, David Pellow. Not pictured: William Valencia.

Acknowledgements: After more than 20 years of writing, this book takes form thanks toa sabbaticalleave granted by the University of Southern Mississippi (USM) School of M usic and to the assistance of double bass students. 1 am deeply grateful to you all. The second volume ofthis work is forthcoming in 2017.

INTRODUCTION Because human beings share the same basic physiology, there should be no major differences when performing an activity, be it playing a sport or playing a musical instrument. However, individuals vary in such characteristics as height, arm and finger length, thickness of finger pads, and so on. It is therefore unrealistic to teach a single, unvarying system of playing the double bass. Adjustments can be made to suit students' varying physiological needs, as long as these small changes do not alter the basic governing principies of string playing. There are many schools of double bass (Czech, German, Italian, French, Bulgarian, Hungarian, Dutch, etc.), each with its own set of rules for fingerings, bow hold, etc. While each is important for its historical value, inany rely on now obsólete concepts. Sorne of the traditional methods were developed at times in which the double bass was strung with gut strings, or worse, with harsh, underdeveloped metal strings. The past few decades have witnessed a revolution in the development of the double bass technique and one should embrace these changes. Double bass playing is an art, andas such, there can be no single right or wrong approach. This is the danger of the narrow nationalistic appro~ch~ which ignores individuals' strengths and weaknesses in favor of perpetuating someone else's view of how one should play the double bass. The Tao ofBass rejects sorne of the rigid rules that have been present for years in sorne traditional double bass schools. For example, while traditional schools favor using only three fingers in the lower positions, the Tao of Bass suggests that double bassists should use all the left hand fingers equally, independently, in all positions. This will vary according to the shident's particular strengths and weaknesses; there can be no one-size-:fits-all in double bass playing. Each musician should identify his or her own fingering and bowing solutions. This book is intended to be used as a tool to train the left hand and elevate the skilllevel of the double bassist. The variety of exercises, including many permutations of patterns, will help students think logically and develop their analytical FÚmprehension of future left-hand challenges found in the repertoire. I advise students to choose, with the guidance of a teacher, the appropriate exercises to complement their main practice routine consisting of scales, etudes, solos, orchestra excerpts, etc.

0

In tro duction

1

Tao of B as s by Marcos Machado

1

To deliver a creative, inspiring performance, one cannot take technical shortcuts. At the same time, all the technique in the world will not make one an artist. Simply performing technical exercises mechanically is not sufficient; when working on these exercises the mind must be actively engaged. Even on the purely mechanical exercises students should focus on sound quality, intonation, flexipility of the hand, articulation, direction (grouping), etc. When all of these elements are o bserved, yo u will notice that even exercises that first appear dull will sound musical. Everything must be perfect, or you risk i.J;lgraining bad habits by practicing incorrect techniques day after day. The exercises in this book will help you master left-hand techniques in a manner that will eventually feel and look natural and relaxed, even when using extensions. Aim to transform the initially conscious movements into unconscious ones, enabling you to focus on the musical qualities described above. After you've discussed with your teacher your speci:fic lefthand needs, practice a small set of exercises for a short period of time daily to gradually in crease your enduran ce, stamina, and flexibility. Set specific goals before you pickup your instrument. Be aware of the areas in which you need to improve. Avoid working only on what feels good and that which you have already mastered. Carefully and systematically add new exercises so your fingers, hands, and arms can adapt to the new movements without injury. It takes time to acquire new patterns, as the neurophysiological events involved in this process begin to adjust the muscles to these new movements. Most of the exercises in this book should be practiced in different keys and various positions. Be inventive. Be aware that sorne exercises will not be right for you; when you encounter these, just ignore them. The guidance in this book represents a small but crucial stage oh your lifelong journey to develop asan artist. Don't worry that these technical exercises will transform you into an insensitive musician; on the contrary, they will help you learn to express yourself fully and become a better artist.

lt is my hope that you .will find in this book a path that is appropriate for you and will help guide your technical development.

tao ofb as s. com

page 3

Endurance, Coordination, Articu lation The exercises in this chapter are aimed at developing your reflexes, flexibility, and coordination to ultimately result in improved speed and clearer articulation.

/

The maxim, "No pain, no gain'' applies here, but by the same token, you must be careful to pay attention to your body. Increase the intensity of the exercises gradually so your fingers, hands, and arms can Jdapt to the new movement without risk of injury. As in sports, sorne discomfort and muscle soreness are to be expected, reflecting the unfamiliarity of the movement and the effectiveness of the training. Be sure to warm up befare beginning these exercises, using very basic light stretches to help avoid potential injury. Coordination is one of the most important assets in playing a musical instrument. Avoid muscle tension, which creates stiffness and results is loss of motion and flexibility, making you more susceptible to injury. Truly great performers display ease of movement, making even difficult passages appear effortless.

0

Chapter 1: Endurance, Coordination, Articulation

1

This takes time, as new patterns of neurophysiological. adjustment must be acquired gradually when leaning a new exercise (movement). With slow, methodical, and proper training, you will eventually acquire the skills necessary to perform with ease and without tension. Coordination relies on training your nervous system as well as your muscles. I always recommend singing the exercises in your head, anticipating the sound and motion of it, and also singing them out loud. Achieving a high level of endurance requires serious and consistent work, practicing until near exhaustion, and students are often unprepared for or unwilling to commit to this intense schedule. As in sports, endurance also requires high maintenance with consistent practice. In practicing each exercise avoid unnecessary movement of the fingers, as this consumes energy. Use only the necessary motion to perfectly execute the exercise. This can be a determining factor in improving your speed.

Tao of Bass by Marcos Machado

page 5

First position Technique Basics This chapter will feature exercises using the . traditional hand position, which encompasses a whole step between the first and fourth fingers. Below are the combinations that are possible when using this traditional technique combined with an open string.

Basic Fingering Combinations group O Oa

1

2

Oh Oc Od Oe

1

2 2 4 4

Of

'group 1 la

4 1

4 2 4

4 1 2

1 2 1

lb

o o

4

le

2

o

4 2 4

ld

4

4

o

le lf

4

o

2

4

2 ·O

group 4

group 2

4a

2a

4b

2b

4c .

2c

4d 4e

2d 2e

#

~

page 6

2

Chapter 1: Endurance, Coordination, Articulation

1

1 1

o o 4 4

o

4.

4 1

o 4

1

4 1

o

o

1

Tao of Bass by Marcos Machado0

....... ,....,_,__ 1

---

Applying the fingering combinations on two strings

~-,.··.•·• _o_ _ ._ _ . :

~

~---'_._ . •_ . o_ ._._._l___ . _._>

.

~---• 2 _ ._:4_ _ ._._ . _· .

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11

L

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~

11

e E r :;;j

11

11

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11

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y:¡ E

J!t r: 1

11

e

#¡ E 3

--'(111

11

r

#r

r tr

_j

0chapter 1: Endurance, Coordination, Articulation

1

Tao of Bass by Marcos Machado

page 7

Exercise 1.1 Warm-Up J=80 1

~J:I

4

V~

1"1~

r

r

F

~

1r

r

r

2=

r r r r r r r r

:1=

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3

3

3

1r

E

r

3

r r r r r 3

3

3

-~~~~

:r r r r r r r r r re r.r re r r 1r er r re r r re r r re r r 1 ~~~~

2=

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6

;:::::=:=~

6

6

~

6

6

~------

6

6

~~-----~--:~---

2= rcrrrcFFrrccrcccrrrrrrrrrrrrrrrrl rrccrcrcocccccrrccro:rrcrrccrorrll

p a ge 8

eh a p ter 1 : Enduran e e, e o o r di na ti o n, A r ti e u 1 a ti o n

J.

Tao o f B as s by Mar e os M a eh a do

0

. '\

Exercise 1.2 Daily Warm-Ups

a. o

o

1

1212

0101212

:1= II=~ID o o 1

o

4

42121

2121

o

242121010121

2

4

2

1

2

1

o

l.

o

1

2

1

12

421421

o

12

012421421012

ID r•rqr EJEt =111= r'r"r El? ID ID =111= &a•OO•tfJ t1]' =11 1

2

1

2

4

o

1

o

101212

1

2

1

2

2

4

2

1

2

4

2

42121

2

42121010121

2

1

1

2

1

2

1

·o

2

2,. 1

2

o

1

4

1

o

1

1

1

o

2

1

o

1

2

1

1

o

o

2

1

4

2

12

2

4

1

2

4

1

421

4

2

1

o

2

1

o

1

2

1

2

4'21012

Exercise 1.3 Hand Shape .J=S0-120

o

o

2

1

9= rbt:FELEfrErrctcrlr"GrrtrErtrtrtrtr =11 ........_..., ........_..., ........_..., "'---" ......_..... "'---" "'---" "'---" Rest the fingers not being used on the G string.

. - .........

Rest the fingers not being used on the D string.

~

,

1.

Exercise 1.4 Coordination .J=120-192 1

4

2~2

2=

b

b~

~

1t ~r r r Er FJ =111= (fr r Er1 r E =111= E~r r EEr r E =11

2= 11= E~r

page 10

~-~

-..;::::_..._

F EEr f E =111= E~r EEEr f E =111= E~r EEEr EE =11

Chapter 1: Endurance, Coordination, Articulation

1

Tao of Bass by Marcos Machado0

~--

Exercise 1.5 Coordination J=120-192 o

o

1

o

2

4

~x 1 r ~r r Er Er E =111= r t r Er Er E =111= r be r r r r r r =11 1

2

1

4

4

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E

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r Er Er EE =III:~F r EE Er EE =ll =bÉ E r Er r r E =11

2

1

r E C E C E =lll=~r bg

2

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4

r

E E E E f =III=~E bE

1

4

=ll =bE ~E E E E E E E =ll =bE

0chapter 1: Endurance, Coordination, Articulation

1

E f E E E f =11

2

~E

E E E E E E =11

Tao of Bass by Marcos Machado

page 11

·

Exercise 1. 6 Coordination

page 12

Chapter 1: Endurance, Coordination, Articulation

1

Tao of Bass by Marcos Machado0

Exercise 1. 7 Coordination and Independence Between Hands J=92-144 2

4

il~

~= tLE

V~

il~

V~

i1

~V

i1

y simile

r E E r E E E E E E 1CE E E.E r· r E E E E E =11

3

3

3

3

3

3

3

2= 11= E E E E E E E E E E E C ¡~e E E E E E E E E 3

:>= II=#E ' :

3

3

Er E E r

3

2

3

3

3

r E E E E E I#E . 3

3

3

3

3

r r E =11 3

E E E 3E·E E 3E E E 3E E =11

3

1

~= 11= E#E3 E E 3E E E 3E E E 3E E 1E#E3 E E 3E E E 3E E E 3E E =11 ~= li:CE 3 4

r EEr r 3

1

4

~~

/.

~

E r E E r !LE

3

~

3

3

~

r E E r E E E E E E =11 3

3

3

~

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3

3

3

0chapter 1: Endurance, Coordination, Articulation

3

1

3

3

Tao of Bass by Marcos Machado

3

page 13

Exercise 1.8 Limbering Exercise

---··--~·

--·-----.-

......... -.:.... ... -··-·\

Exercise 1.9 Limbering exercise

page 14

Chapter 1: Endurance, Coordination, Articulation

1

Tao of Bass by Marcos Machado0

Exercise 1.1 O Coordination

Exercise 1.11 Bridge 00

'.

a.

~

2=112 f

2 1

4 1

qf

~f

2 1

gf

bf

f

f

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2=~f

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r

m

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f

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0chapter 1: Endurance, Coordination, Articulation

f

f 1

qr q~

Tao of Bass by Marcos Machado

f r f

~

11

page 15

~24

E=:!)12

~14

tx 1'r ~[ Eqr 'r [ Eqr 1'E ~[ qE r 'E [ qE 1

1

b.

~

1

1

~

2.

r 1'E ~[ r r E [ E r 1

1

2

1

~

4

14

2= ~[ 'E Eqr [ 'E Eqr 1~[ 'E qE F [ 'E qE f 1~[ bE E f [ E r F 11 1

1

1

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1

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1

11

12

2

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2= ~

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1

2

4

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1

11

12

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1

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4

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1

12

1

4

41

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1

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11

21

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21

11

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2

41

11

2

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11

Bridge or barred fingering is the technique of pressing down two strings with the same finger (notes inside the box).

Double-stop exarnple

~= ''~f bf ~f f page 16

2

14

1

4l

L

q~

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tJ

4

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What is the Bridge? rn

14

12

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11

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~ Melodic exarnple

~= ' r ~E ' E F ' E· ~E ' E qr

Chapter 1: Endurance, Coordination, Articulation

11

1

Tao of Bass by Marcos Machado0

~--

Exercise 1.12 Bridge Exercises

11

b.

2=

t

ll

t f

e' kt

L=:!J

c.

2=

f r kt f

4

j

f t

kr r

j

r r j Ef

4

j

t Ej

kc

kr E

11

f j EEj EEr E

E 1Err kc

11

Exercise 1.13 Fork Exercises

Exercise 1.14 Fourths (Fork and Bridge) ~E}]~~ ~ ~ ~ ~

2= 2 1

~:

ti:] E}j[C]

~

E]

2

2

IC]

!

F1t1F'rf(IF1t1ftE 1F1f1f'rf(¡F1ftCtE 1 4 3

2 1

3 2

3 2

2 1

4 3

2 1

1 1

4 4

1 1

2 2

2 2

1 1

4 4

1 1

f ~ f ~ 1~ f ~ f lf ~ f ~ 1~ f ~ f JVhat is the Fork?

11

Fork is a technique which allows you to perform fourths between two strings smoothly and without breaking the line.

0chapter 1: Endurance, Coordination, Articulation

1

Tao of Bass by Marcos Machado

page 17

Exercise 1.15 Three-Note Patterns a. :J= c.

~1

~2

r

j

b4

r

~r

b4

:>=~E

~2

b4

g.

b4

1

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1

1

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.

t.

1

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~2

1

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~E

E 4

~

r

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b4

r

2

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~2

E

~

1

f

2

~r

r

~

1

~

1

11

t>=~E

11

f. :>=~E h ..

11

r

~1

r

b4

1

2

~2

r

11

r

11

r r

11

4

~

E E 4

b4

F

E

~2

4

E E

b4

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~

1

~

2

4

1

1

~2

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.

11

j

b4

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4

2

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1

4

r

1

t>=~E d.

2

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11

4

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b.

4

b4

1

r

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2

4

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11

r 1

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1

k.

1

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m.

2

:>=t o.

2

b4

~

~

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~

·4

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~

1

E

E

page 18

q~

r

f

E

b4

11

r

2

b4

4

~2

E r

~

11

~

2

~

11

Chapter 1: Endurance, Coordination, Articulation

4

r

b4

1

2

E

~1

r

b4

1

r 1

1

11

4

E E E E E

11

r.

E

1

:>=~E n.

4

r E E 1

E

l.

2

4

1

~1

~

~1

r

4

11

~

E r 1

11

4

E

11

Tao of Bass by Marcos Machado0

..... -

s. 2 :J= qr

b4

u. 2 :J= r

b4

w. 2 tJ= qr

b4

y.

b 4

r

:>= a a.

:J= l>é cc.b 4

r

tJ= e e.

:J= l>E gg.

:J= l>E

..

tt.

tJ=

k4

r

r

~

r

~

r

~1

1

~E

~

~

1

E 1

E

q2

1

1

E

r

1

r

q2

~

1

E E 4

1

r

r q2

.2 qr

~

1

E q2

E E E 2

bf

E E ~

ijf ~

1

~1

~

r r 1

1

q2

E E E E 2

E

~

1

~

q2

~

1

r 4

r

11

4

2 br

r

11

11

11·

11

tJ=

11

r

:J= l>é :J= l>r tJ=

r

hh.

4

11

:J= l>E

..

~2

~1

E f

4

r

1

JJ· k4

q2

E E

11

Practice each of these patterns chromatically and on all strings

tJ=

r

~

~1

ff.b 4 11

r

~

r

b 4

tJ=

r

~

b4

dd.

4

E E ~

b4

bb.

2

r

v. 2 tJ= qr

z.

4

b~

b4

x. 2

4

r

t. 2 :J= r

r

1

r

1

r

1

r q2

E F

~

2

r

q2 r

r

~

q2

~

4

r

4

4

q2

2

~1

r

2

r

2

E

b~

2

~1

4

1

E E

r

q2

q2

~1

4

~

1

E F

4

r

r

r 4

~1

q2

11

11

11

~1

q2

E E E ~ 2

r

E f 4

11

1

r 4

r

~1

E

r

~1

11

1

E F

E qF 1

2 qr

r

1

r

E

11

11

11

~1

E· E

11

Exercise 1.16 Endurance

1

n-.

1

n-

1

n-

1

n-

_...-·-~-·

- - . - .. -.;•·•·e-- - 1

continues

page 20

Chapter 1: Endurance, Coordination, Articulation

1

Tao of Bass by Marcos Machado0

:>=qfritfifrf~¡t~f~¡ .

t.

t. ~·~ ::1= rttt r rtk r Vrt r &#f f r~ r €r r r €r r r €r r r 1 1

· 2=

#i

i

·~~

f:_

f:_

D~

dr r ErE r ErE eErE eE 1 f##rtfr~tfdrtfrtt 1

2= t r~r Et Eb r t

f:.

r b Et Eb E1t f r f tE r EtE j EtE j E1 )

:>= r~r r r LEr r Lr r r Lr r r 1Pr ~r qt nr~r qt nj ~r qt nj ~r qt 1 q~~~~

:>=~f~tEEFIEEt ~~~re~

1

:>=f~f~ ~~~BEUfTEt1 ~r~L~L~1F~F~1

continues

0chapter 1: Endurance, Coordination, Articulation

1

Tao of Bass by Marcos Machado

page 21

page 22

Chapter 1: Endurance, Coordination, Articulation

1

Tao of Bass by Marcos Machado0

Exercise 1.17 Hand Shape 4

tJ= 11=1

1

4

1

1

4

e E ~ Er ~ ~ r ~ r r F 1~ r ~ r r r E r E E' j 3

3

:>=

4

4

·1

1

1

1

1

4

Er EE r E E r FE r

r 1~

m

11

3

3

3

m

IV

3 m

11

4

1

3 m

11

1

4

4

1

4

3

3 m

11

4

1

4

3'

11

4

4

4

1

r

4

1

~ Er 3

3

m

4

1

m

11

1

1

1

3

4

3rv m

m 1

1

f ~ r ~ Er ~ 4

1

1

1

1

F'

4

:11

3

3

11

11

Keep the fingers close to the string. Only move the fingers that are needed.

Exercise 1.18 Shifting 1~1

1~~2

~=~1)

1

3

~

f

~

1

1

1

~

3

3

~=~!)

~=~1)

~fu

~

1

1

0

n

1

f

. S 2



e e

S2

~/



S2

~ $;f 3

f S2 gtS·

~~

t?F ~ey 1

1

• S 2

~ 3

~=~!)

ter

~ 1

:>=~!)

1

~ 3

2:~¡,

1

S2

~

-~

~

m

~

1

3

~



2

1

s;mik

.

fu ~=~1) ~

2

-----~ ¡r~ ~ ~-----~ ~~ r

a. tJ=~I' ~-------~ 3

1~4

1~3

ey • S 2

3

3

3

~

f

~

1

3

1

~

~~ 3

3

~

~~

1

4

4

f

~

111-

~

2

1

2

·~

AA=

1

4

~ fi ¡rter ~~ ¡r4 3

4

1

4

ter ~ fi ¡Fn ~ ~ fi ¡rn 1

3

1

2

4

1

3

3

*

m ~m 1

3

~ 3

3

3

1

~ 3

~

4

4

2

4

1

m 1

N

#1

Chapter 1: Endurance, Coordination, Articulation

1

4

,~

1

4

~

#1 ¡r 4

~

f

~

3

4

~

~ 4

~

€ 4

~



f

~

2

2

3

~~

2

4

~~

4

3

4

4

2

4

e e

~

~~

n n 2

2

3

. S 2

$;f

4

ey • S 2

3

ter

~

• S 2

2

3

~ 4

Tao of Bass by Marcos Machado

~~ ~

~

m ~n ~m 2

4

~

~



2

~

~ 4

3

f

• S 2

4

~

~

f

~ •

~

2

~

• S 2

4

2

S2



3

4

~ 2

~ 4

~

fi

m .

4

ey .

4

4

#1 page 23

t)=~l)

r~ r'gf r~ rfl 1

1

3

1

:J=~I, r~

1

1

3

4

1

2

2

~ ¡L



2

rfl

2

3

F~

4

2

r5]

~· 'gf ~ rfl r~ r.fl r r rfl ¡C= 3

3

3

4

1

4

4



2

4

3

4

4

.

-·-~·~--·

-- ··-··

...,..~ ...-· 1

1~1

b.

t>=~l)

2:~¡,

k

3

1

r%l

t)=~l)

~=~1)

1

3

f

s.2

3

S 2 giS·

1

3

r 1

f

3

page 24

3

~

. S 2

~

r

r r

~

3

r

1

2

3

4

4

4

2

1

4

• S 2

3

~

~

1

r~r 3

~

4

~

r

~

4

1

~ 1

3

2

.

4

~clCr ~Mr

• S 2

4

r

3

4



4

p·c1?f ~fJC F ,

mr r r r r r m E~ r r 1

~ 1

2

fJ?

r

3

~-

2.

~~ ~a ~fJC ¡C=t ~m= Pe flC

r

~

1~

qr ~r~r s&n¡~rtSr ~e

~r

r~ E~ 1

.

~

~

E t Pe qr

glisS· •

1

1~

;~2

~

2

4

~

Chapter 1: Endurance, Coordination, Articulation



2

~

r

s 2 giS·



3

2

4

3

4

~

~

~

1

~



4

~

4

~

Tao of Bass by Marcos Machado0

.. --

~:~¡,

~ :J= ~'' 2=~1)

:J=~I'

!)=~!)

rs

2

rs

2

r~ rft r~~

cm r~ rm

1

1

2

1

1



r~ r 3

j2=~1)

ex

g~·

m ¡F~ rm ¡E~

1

1

1

.

3

S2

rs

gtS •

1

3

3

3

4

4

1

1

2

2

cm 4

g~·

3

~ ~ 4

3

rm 2

.

4

4

4

2

4

~

S 2

2

3

S2

1



S2

3

3

r~ ¡EfSr e r r~ r51-.

1



S2

1

3

1

4

rm

g~·

3

3

3

4

~

3

~

3

1

1

1

r~

r r~ r r r~ r51 r~

3

1

3

F~

2

4



1

r~ e r~

1

~ r

~~

3

2

3

rs

2

cEJ r~ F51 r~



2

4

¡E~

rfi 3



1

4

er S2

3

4

4

2

2

3

2

4

S2

4

3

4

4

1

4

~

2

1

2

g~·

4

1

4



¡E~



~ F~ F. 4

4

¡F~

r5Cf



~

rs

cEJ r~ r5Cf r51 F~ F5Cf

•'

1 .

~

:Ji r 3 •

~

2:~1, E 1

1

E 1

1



S2

1

3

3



S2

3

3

E r51 r~ 1

1

4

~ 2 •

1

2



2

2

3

2

4

3

4

4 •

1

4



S2

4

3

4

4

2

1

2



S2

2

3

2 ' •

4

4

1

4



S 2

4

3

4

4

rm 1E E r51 r~ rm rm ¡F E r51 ~~ r5Cf

r=r r~ rq 1



S2

1

3

1

tJ=~I'

F~

:J=~''

r~ r=r r:~ rq 3

0

1

3



S2

3

3

3

.

~

~

4

¡E~ F:S. r~

4

Chapter 1: Enduran ce, Coordination, Articulation

¡E=~

1

rfl r~

Tao of Bass by Marcos

Macha~o

rq q ·F

page 25

1 •

~

1

tf~l, r f 3 •

~

thl' E t>=pl'

1

f

. S 2

1

rfl 3

n ;¡;· S

1

3

1

:l= l1'' F~

3

1

rq

4

F~

2 .

1

¡L~e 4 •

1

2

. S 2

4

. S 2

rfl

2

3

3

F~

3

rq

4

¡L~

¡E~ Fq

F

F~ Fq 1

1

1



2

1

3

1

4

3

.

2

3

3

3

4

r~ F:1 ey q ~ r F F

2

1

4

1

r:S 2

.

2

·:r

¡E~ F

2

3

rq

4

3

rrr

e~ e~

2

4



4

4

ey F~ F 2

3

2

4

4

3

.4 .

4

F~

rN

2

page 26

Chapter 1: Endurance, Coordination, Articulation

1

Tao of Bass by Marcos Machado0

r r r r----r r

4 gtiss. 1

1

~

r

2:~¡,

c.

4 gtiss. 1

~

r r

~ ~: ~!z

~

4

4~1

~

1

L 1 $Éss. 4

~~ p~

~~

tisS· 1

Simü·

4

SimU.

~

1~4

[

Simü·

[

- .:r•

'- 1 ~z.fs.4

pt

4 tisS· 1

q p

1 gliss. 4 ~

4

~r

1[

r~r-

fL

gh.rs.

4

r: r r~ r: r

1

ghss. 4

1

glis_

~

4

~r 1

4 g\iSS· 1

gh.rs.

!etc.

4

r r r~ r r ~

l.G!_z.fs. 4

4 gtiss. 1

1

tisS-1

f?r4r r4fj

tiss.1

L ¡L

[ q[

4 trgltiissp.;.1

4

[ ¡[~r:

~4

r~

~

[ t 9(l

ghtiss~~.~

1

4~1

gliss. 4

~

1~4

4~1

4

r-r ~

1~4

r~

4 gtiss. 1

d. !J=~Iz

gliss.

~

4

~

& •

1

~

1 ~z.fs. 4

fL

~

- 1-':J='-f: -1"- ~!z- +- C-L....____._L--~--C--~--E__._L___._E-t--=--+1-+--=___._L___.__L-+--C---tC-===:E__.____.__L---~E--~¡ etc. ---

~ss._

gliss.

~ingerings (for c. and d.)

~=~ll

-r r ?

4 4 4 4 4 3 3 3 3 3 2 2 2 2 2

1

0

::.:--::::::::

2 3 4

r~ 2 3 4

+

+

1 2

1 2

3

3

4

4

+

+ 1 2

2 3 4

3

+

+

1 2

1 2

3

3

4

4

4

+

+

Chapter 1: Endurance, Coordination, Articulation

~

~

~~

4 4 4 4 4

4 4 4 4 4

3 3 3 3 3 2 2 2 2 2

3 3 3 3 3 2 2 2 2 2

1 1

2 3 4

1

r 1 2 3 4

+

+

1 2

1 2

3

3

4

4

+

+

1 2

1 2

3

3

4

4

+

+

1 2 3

1 1

~S.

2 3

4

4

+

+

Tao of Bass by Marcos

4 4 4 4 4 3 3 3 3 3 2 2 2 2 2

Simt1e

!etc.

Exercise 1.19 Shifting Exercise to Connect Two Positions l

J

4

tf?:t

\

l

11

Exercise 1.20 Shifting Exercise 1~2

'§l

121212

121212121

¡1

121212121212

= =\,_.;= a,_y.=+ w\,_.;a a""-'w J~ ::± a J w a a w w '-----"' ~ 11

11

oawwoJr·r~, ~

3:=+ a=+ w

~~ ~

~

Exercise 1.21 Finger Substitution 4

2

1

2

4

!]=~ F F F F F r E E E E F F F F F1 t e. f t F r r r r r 1 1

1

1

e ¿Emi ¿ f et ee r r r r r rr i i i .;:_ ·i . ;. i t>=~ r r r: r: r: r: r: r: r: r r r r r r r r r r r r r r E)=~ ¿ i i i i i ¿ i i f f f i f f f f f i f f t>=~ t t r t

1

1

1

1

1

2

3

4

3

E E E E

2

1

4

3

2

E1

1

2

3

2

3

4

3

1

4

1

1

1

page 28

2

1

Chapter 1: Endurance, Coordination, Articulation

1

1

Tao of Bass by Marcos Machado

0

1 11

Exercise 1.22 lntonation

~=~~~~~~

1

4

1

2

(One octave scales on one string) 2

1

4

1

(3)

att crtt1ttrr1étr; 1 ~~# ;ttt Efff1ttrr1trcr 1 . 1

1

:~=~~~ att 1ttEf 1ITEf1ttr:r 1 1##~~ att1Utft 1tfU 1ttr:r 1 ¿ F DI Dgl EJ Bl JJJ) 11~1'1,~~ JJfPI !JalE! iJ¡ ~~ 1

¿ü~ ntJI na1 u81 nn 11~1'1, nDigctl ElEJI nn 1

¿ü~ n1DI g 1tFI er tr14i0n 11~

n JJ¡ aa1 u a18 n 1

&ü~#~~# nn1 a·a¡ Eiul nn 11ü DEfl gct¡ E! al un 1 ¿~~~~~~ na1 ar:t¡r:ra¡ a ®¡¡ü~#

na1 ar:t¡r:r a¡ a811

ce 1gft¡ ME! 1El EJII &a a 1att, ttu, a a·,,~~~~~~ ce ce 1rttf¡litr¡ u a 1 &~1' Ef U 1gft¡ tE E! 1L1 EJIIü~#~# Ef

.'Ü# tF cr 1u:0

u 1ff u 1LJ E! 11

Chapter 1: Enduran ce, Coordination, Articulation

1

Use always the same fingerings.

Tao of Bass by Marcos Machado

page 29

Exercise 1.23

17

&~#~~ DDI ctEF 11~ ac;1 JJn 11~#~~#~ nn1 u a 11ü t1cr:1

&~lv fiu1

crn 1

ua= 11ü~~ tra1aJJ 11~'' uctl r:rtt 11ü~~~~ LEen rtcr 1

11

&qc:r c:r 1trrf 11~'''h €ftr1 cr rr 1 1# el c1 1r:tff1f 11. --. ·-- -- · - . ,. .~...:, --- ;¡

page 30

Chapter 1: Endurance, Coordination, Articulation

1

Tao of Bass by Marcos Machado

0

Exercise 1.24 lntonation and Coordination

21

4jjJ ¡~ tlf J. j 1

1

1

31

4## ;;J a a:r 1m 1

1

:J. jJ 11~ '1,~~ fj 31 ¡J]J 1 E1f 1 ilJ 1 J3!.3 1

1

J. jJ

~~~~~~,

na c;ff r1r ca w. JJ 1

1

1

1

41

0chapter 1: Endurance, Coordination, Articulation

1

Tao of Bass by Marcos Machado

page 31

11

11

J '1

'l

&#~#~~# J. ~ n

page 32

1 e:-

;; e:- ;;

11#

r- ;

e- ;

u

1

Chapter 1: Endurance, Coordination, Articulation

1

J.

~ 11~1'1,~

n

t ;; ~-~,

Tao of Bass by Marcos Machado0

d

,;:

Exercise 1.26 Trill Exercise J=60

1 4

11

11

TII

Play the same pattern two!thrr;:e octaves

0chapter 1: Endurance, Coordination, Articulation

1

Tao of Bass by Marcos Machado

page 33

Exercise 1.27 Finger Substitution;, Coordination

~

Exercise 1.28 Finger Substitution

p1 ~2 e 1ft :f f f 3

2

\p;,age. 34

2

,¡.¡.3

¡..1

,¡.¡.2

~er

1

t 3

,¡.¡. 2 ""1 ,¡.¡. 3 ""2 ttlt~f 3

1

f1ef2p1f 4

Chaptc;:r 1: Endurance, Coordination, Articulation

1

~.4D2 1

'

.

f Er Er r1

4

2p1

1

Tao of Bass by Marcos Machado0

Exercise 1.30 Intonation:J Finger Substitution;, Endurance

2= 1 sf#E f E[#E r~rkct r~r cqr r 1rgc#r rqr E#r rrOr E rOr E1 o

2

1

2

1

4

2

4

1

4

2

4

1

~1

4

4

4~

2

1

¡¡~2¡¡3

1

~

¡¡

~4

2

4¡_1

¡_

41_2

¡_

¡_4

2

4

1

:r!!cf!!f f fit!!f ff f tf fi tf trtff t fff ff t f~L & f~L

:.r qt~tqt r t~t!- r~t t t~t Ct t~r ¡qÉ t frlt fqj ftqéktgt t gkrt E 4

0

2

4

1

1

eh a p ter 1 : Enduran e e, e o o r di na ti o n, A r ti e u la ti o n

1

1

Tao o f B a S S by Mar e o srwMN~~;;,;il.PA;:::-D-~~ ®

BIBLIOTECA

Exercise 1.31 lntonation:J Coordination) Endurance 21

o

1

4212

4212

4212

::rt E#rt#E E rqE#EkE EEEOEEElqtürqrür Erqrür EEr CE EEC1

eE r Eer r rrt#r EeErE1f C~ EEr: fE f1ci~c~r f tc~r 1 2: er#t Eer r E~ fl r er fl r E ftfl ~et ~ fll~E *= p4

2

1

2

¡.¡4

2

1

2

p

4

2

1

2

q

4

1-t

,¡.¡.2 ¡.¡1 ,¡.¡.2

,¡.¡.

:>=

4

2

1

2

p

4

2

1

2

~

q

3

1-t

,¡.¡.2 ¡.¡1 ,¡.¡.2

,¡.¡.

~

1

p 4 q2

:>=

Er:~ EEr: rE ef#r EGf r E 1ett EGErEEtür: rEEr r1

page 36

1

2

4

2

1

2

p4

2

1

2

Chapter 1: Endurance, Coordination, Articulation

4

1

2

1

•,2

Tao of Bass by Marcos Machado0

Exercise 1.32

Intonation~ Coordination~

1201

·

sz1nile

2= E~nr Et~E

rr Emr1kct r rkc 9cr r1rEkr Eqr Ekc t 1

2414

2= ~~rqr r r~rqr r r 1rkf#g

Endurance 2414

2414

~

~

~

~

~

r E1~r cqr r~ cr r r f"r rtEr f EEr t EEr r ·

1

1

te

epE e~ epE e e1w r~#e Ee rt f#e tqe r t#t#e rqt#E er

:E 2

1

1

1

1

-

: 2

#eqtqfl f#f Eqfl t f#fl Efqf#fl Ef EqflpE tqf flpf t (EqE nrtqrn r

2:

r1t r e er r 1~r er r~, eqr n Et r r qf ~E r r

1

Exercise 1.33

0

1

1

1

Intonation~ Whole

Step Shifts with the S ame finger

Chapter 1: Endurance, Coordination, Articulation

1

Tao of Bass by Marcos Machado ,

page 37

1

Exercise 1.34 Finger Substitution ~~~~~~.~ 1

:>=•¡

4

.

2

4

4

f r r 1 r r r=r 1r e r=t r nr r 1r E er fe E f 1

1

4

2

4

4

~

~

3

1~

{±E e F ex E1 1r r r r E r E E e r r e r r r r T :>=## r ¿ f r j E j E 1Wr Wc 1ttrr 1FfFF r 111## 1 ot>= # 2

---

1

:::::;¡: . --

1-------

1

3

cta

3

~~

1.

1

4

1 3 ~

"1 #

o

1

1

4

1

2

1

4

:>·=# 1 3~~~~ J 3 J J j J j 1J J 3J J j J j

1

1

4

:@ J

tJ 4 j f9 1

3

=•#

:r:r:r:r¡ EEEEEEErl rrrrErFrl rtErEf:E~ 1EEE!EEEF 1r J

6

1

6

& EEIF Er r r E~

6

6

.

11

6

m

11

11

(Play the quá'rter notes on the open G string with left hand pizz.) 2

3

4

12

+ + +

3

+ + +

2

3

4

+ + +

~

13

4

+ + +

~

a. :>=•#1~!. J J J ¡l J J J 1.. J J J ¡Ro J J J 1¡· F F E 1f E E E 1 arco

1

4

m ~~

1

:>=•#

1 11

.

1

2

.

3

4

'

+ + +

4

1

2

3

1

f E F E 1- J E E F 1f E F F 1t E E·E 1f E E F 1 + 2

+ 3

1

~

~·~:~~~e

+

+ 4

3

+

+1

4

+

J J J

+3

2

~ 1 i 1

+

+4

+ 2

3

+

+3

4

1

J J J

cJi·apter 1: Enduran ce, Coordina ti o n, A rticulatio n

+ 4

+

+

1

2

0

+ + +

2

t 4 111

1

+1

2

+

+ ;z

+3

3

+

J J J

+2

2

+

3

+

+3

+ 4

4

+

~~~~ J J J

Tao of B as s by M arcos M a eh a do

11

p age 49

r 1 Exercise 1.41 Daily Exercises for Intonation 2

1

a.

9:•¡

4 13 1~

14

1~

14

~

1

12 13 .......----..,::

~

~

1

14

~

4

~

12

14

Cfritr: rfrtEr rrrrer ftfrfr tftrEr rfFffr ~~~~~~,~ 1

1

3

3

6

3

3

6

1

1

3

3

3

3

1

3

3

6

.3

3

7

:J: ¡,J 3#J q~ ~~ ~ J j ~~ q~ ~j ~ J 3~J qJ ~J fj J 3#J qJ ~J 3 J 4

page 50

4

2112

Chapter 1: Endurance, Coordination, Articulation

4

1

4

!etc.

21212

Tao of Bass by Marcos Machado®

l 1

Exercise 1.42 Shifting/Intonation 1

r

D=##~l

r ¡F r ¡L r ¡f

·4

1

1

F ¡f

4

2

4

4

1

4

1

r 4

¡f

f

1

(All on one string)

r r ¡f r ¡L r ¡L r·

:D=I#~

4

1

1

1

4

1

r r

:J=~I~

1

4

1

2

liT

~

2

1

r ¡L r

IF

1

4

2

1

4

1

liT

-

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Permutations Human beings are designed to respond to changing stimuli, and the finger permutations will thus help stimulate and motívate students. Sorne of these exercises are difficult and will demand the student's full attention. Be creative, practicing these permutations in different positions, and modulating diatonically or chromatically. Remember that shorter, more frequent practice sessions are the most effective. Do not try to play all the permutations in the same day or even the same week. The body needs time to adjust the new movements. New patterns require subtle finger rearranging and rethinking. These permutations will also help you learn new correlations, allowing you to change fingerings without discomfort.

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Chapter 1: Endurance, Coordination, Articulation

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Chapter 1: Endurance, Coordination, Articulation

1

Tao of Bass by Marcos Machado

4 4

page 53

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Chapter 1: Endurance, Coordination, Articulation

1

Tao of Bass by Marcos Machado0

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0chapter 1: Endurance, Coordination, Articulation

1

Tao of Bass by Marcos Machado

page 55

page 56

Chapter 1: Endurance, Coordination, Articulation

1

Tao of Bass by Marcos Machado0

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Chapter 1: Endurance, Coordination, Articulation

1

Tao of Bass by Marcos Machado

1

page 57

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Chapter 1: Endurance, Coordination, Articulation

1

Tao of Bass by Marcos Machado

1

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Chapter 1: Endurance, Coordination, Articulation

1

Tao of Bass by Marcos Machado

page 59

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Chapter 1: Endurance, Coordination, Articulation

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_1

Tao of Bass by Marcos Machado

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page 61

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Chapter 1: Endurance, Coordination, Articulation

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0chapter 1: Endurance, Coordination, Articulation

1

Tao of Bass by Marcos Machado

page 63

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Chapter 1: Endurance, Coordination, Articulation

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Tao of Bass by Marcos Machado0



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Tao of Bass by

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Chapter 1: Endurance, Coordination, Articulation

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Chapter 1: Endurance, Coordination, Articulation

1

Tao of Bass by Marcos Machado

page 67

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eh a p ter 1 : En d u r a n e e, e o o r di na ti o n, A r ti e u la ti o n

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Tao o f B as s by Mar e o s M a e ha d o

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1

Tao of Bass by Marcos Machado

page 69

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4-fingerTechnique/Pivot This chapter focuses on the four-finger technique. The most important concept is that pivot should be applied at all times, with the exception of a few exercises involving bridge and double-stops.

The four-finger technique is a useful approach that allows double bassists to group passages, similar to violinists, violists or cellists. It vastly improves articulation when performing more intricate passages, including many orchestra excerpts.

Without proper training and correct motions, however, years of applying this technique incorrectly can cause injuries. Consult the many artides and books that discuss the pivot technique to fully comprehend the technique befare commencing the exercises.

din

0

Chapter 2: 4-finger Technique

1

Tao of Bass by Marcos Machado

page 71

T

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PivotTechnique Basics

1

Pivot refers to the rotation of the forearm around the thumb. lt allows you to reach more notes without shifting, reducing the motion of the left hand. The pivot technique is particularly useful in reducing left-hand shifts in fast passages. Start the basic fingering combinatións, described below, with half-steps between adjoining fingers. This position encompassesa minar third between the first and fourth fingers.

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4

2

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4

2

3

4

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2

2e 2f

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4d 4e

4f

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1 3 1 2 3 2

1 1 3 3

l

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1

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3 1

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1

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page 72

Chapter 2: 4-finger Technique 1 Tao of Bass by Marcos Machado0

1

Applying the basic fingering combinations in two strings

1

1 .

G-Q). f!iJ'~ ...../ /. ,,.,.;:: ..

t>=

0

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Chapter 2: 4-finger Technique

1

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r f t f t f r f r f r t t Et t 1

1

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1

Exercise 2.9 ·1 1 3

3

3

3

3

3

3

3

1

1 3

3

3

3

3

3

3

3

Exercise 2.13

-~------~--------~--------~-----

~~~~~~

t>=tqti5tftftftftfti5tf 1ti5tfti5tfti5ttti5tf =11 page 80

Chapter 2: 4-finger Technique

1

Tao of Bass by Marcos Machado0

J J

Exercise 2.14 J= 144

~2 ~4

q3 ~ 4

q4

rE r r rE r: r rE r r rE r r r f r r rE r

1

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2

1

4

2

2

1

3

1

4

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1

2

2

1

4

2

2

11

1

Exercise 2.16

Exercise 2.15

1

3

4?'"

1

2

1

3

~

e~~~ r r f r er

2:1 _e Exercise 2.17 3

11

Exercise 2.18

2

4

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2

4

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2:1

t f Ef t f Ef

11

Exercise 2.19 4

r r t 3

2 '

4

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f

11

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1

4

1

3

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1

4

3

1

2

4

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1

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n

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Tao of Bass by Marcos Machado

m

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page 81

1

í Exercise 2.21 Patterns

1 1

1

1

1

1 1

. \l ·~-

··- ¡ J

1

J

(

1

)

) ] !

page 82

Chapter 2: 4-finger Technique

1

Tao of Bass by Marcos Machado0

Exercise 2.22 Exercise on Three Diatonic Positions

:tJ:

,___~~ ~2~ ~·~ ~~ F C E C 1r-E -E E EEL 1 ~E EEEEEF1r FEEEEEE 11

r

r

0chapter 2: 4-finger Technique 1 Tao of Bass by Marcos Machado

page 83

page 84

Chapter 2: 4-finger Technique

1

Tao of Bass by Marcos Machado

0

Exercise 2.24 Pivots Applied on Four Strings

3

4

4~

2\i@?JE (=?ffil UZ 2

4

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Tao of Bass by Marcos Machado

3

1

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page 85

1

1 Exercise 2.25 Dexterity .1

~=100-168 3

4

3

1~1~~~~

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:J:I EEEErE U EEEEEE(f 1Frf EFE EEFEEEEEU 1 11

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1

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~=100

4

2

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r

r

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gg 2

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rm 2

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page 86

Chapter 2: 4-finger Technique

1

Tao of Bass by Marcos Machado

0

Exercise 2.27 Daily "Clarke" Exercise 2

2

4

412

~x·~~ r: t

1

2

4

1

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412

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2

4

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0chapter 2: 4-finger Technique

1

Tao of _Bass by Marcos Machado

1

2

12

IL

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1

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page 87

T Bridge Exercises

Exercise 2.28

Exercise 2.29 J=IOO 3 1

2:

3 2

3 4

3 2

,--.....

,--.....

,--.....

1 3

,--.....

2

4 3

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f ~e f E fPf Lf f f f f 1f Ef E t f Bf t Ef f 1

1

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1

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.

rn

2

a.

9:

f ~; f f f

rn

3

1f

f

1

rn

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ff

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rn

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page 88

Chapter 2: 4-finger Technique

1

Tao of Bass by Marcos Machado0

Exercise 2.31 "Fork" Exercise 14~1414([31414([3

rE 6fr f rfe E6Fe [6 [1 ,r r;r [ j r f fr f rFe f 11~1v~

tJ=i

143

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Chapter 2: 4-finger Technique

414~141

Tao of Bass by Marcos Machado

11

page 89

l Exercise 2.32 Major Scales 1

..!=100-192 ~

4

tl=l r:r rr c:r Lkl rr a cr 2

4

m

1

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Exercise 2.33 Minor Scales ..!=100-192

..,_€ 2=~'' a a tC r:t1 cE lt Cr E! 11~~~~# 134124

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t tt t 2= r r r F r E r F 1r r r 214

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2=

r é r r e r rr r e e r r r r r r r r t r É rÉ 1

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page 90

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11

1

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Tao of Bass by Marcos Machado0

Exercise 2.37 f

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page 91

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page 92

1

3

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1

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1

Chapter 2: 4-finger Technique

1

3

1

3

4

1

3

1

11

Tao of Bass by Marcos Machado0

Exercise 2.45 Triads J=80

1

k2

4

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2

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2

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1

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· Exercise 2.46 1

1

2

4

4

4

2

4

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f

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~= 0

4

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1

Tao of Bass by Marcos Machado

11

page 93

Exercise 2.48 Endurance J=IOO

tl

eWr ew tW tW ,rm trtr tM teir,

:1=

i~

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4

3

1

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page 94

Chapter 2: 4-finger Technique

1

1 ;J

Tao of Bass by Marcos Machado0 \

ill

Articulation Exercise 2.49 ~= 100

1

4

2

4

.

1

4

3

4

1

2

4

2

1

3

1

11

4

3

~~~~

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1

1

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24

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11

11

11

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4

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rr

2

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1

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3

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1

11

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4

4

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4

11

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m

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Chapter 2: 4-finger Technique

11

1

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1

111

Tao of Bass by Marcos Machado

11

1

m

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11

page 95

Exercise 2.52 3

1

.;=7o

Sir 1

2

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1

3

4

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Chapter 2: 4-finger Technique

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n

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Tao of Bass by Marcos Mac4,ado

0

Exercise 2.56 .J=S0-132

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m

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1

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; Er

1

III

11

I

11

.

11 11

I

II1

11

1

11

III

11

11

III

11

I

Exercise 2.56 1~··

1_60

~-

~. . .

2=

-

,,

1

3

1

3

1~

4

~

. ---.:

~.4L

-

'

1

3

1

4

3

~4

----._4

-

1

III

11

1

;

f [ f ~e r F r=f f Er F f Ef E~r E f [ f E r F •

3

1

3

4

11

I

1

3

11

1

3

III

4

11

III

11

1

3

1

4

I

11

3

1

3

1

II

III

4

3

1

II

~~~4~4

2=

Tf E

E

1

3

1

II

3

r E Ef EE r E 1f EE~f r f f EFbe f 1 III

II

4

1

3

1

II

III

3

4

II

I

1

11

m

4

3

1

3

I

11

.

1

3

1

11

III

4

3

II

~~3~4~4

2= ~r

f E~e •r E E EEE r E 1t EEr ijr 8 E EEOr r 1 II

m

II

3

1

3

II

0

III

U

II

III

II

11

III

1~

1~

-::-

-::-

11

f Ef o E 8 EEf E E 8 1f r EE•r Ef r EEr E 11 1

4

q~

t]=

11

m

II

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3

1

3

4

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I

Chapter 2: 4-finger Technique

II

1

III

o4L

---..._4

-

11

Tao of Bass by Marcos Machado

II

III

11

I

o4L

---..._4

-

II

I1I

ii

, page 97

Exercise 2.59 Bridge J= 100

a.

4

3

II::J]

4

3

II::J]

4

3

1 . 2

4

3

1

2

4

3

1

3 .4

3

1

3

4. 3

1

~

. 3

1

4

~ll fff; fftr 1ffrtr ffr; 1ffr~ ffú 1[ffrffrr :11

.

·¡

1



d.

~ ~

2:

tt t et t t et#t t et r t ~~c t#t t~r ert 1- . 1

2=•C

1

1

2

3

4

~ ~

1

2

3

4

E f #f f E f f

4

3

t

3

I~L

41212

3

212

4

3

g

~

4

212

3

4

1

2

1

4

3

41212

41

4

1

2

4

2

1

2

lql t #f t L t f t =11

3

41212

E r E r E r E p 1f ff ~ •r "r •r [ 1f#f t

e. 2=

2=

12

t #f t ~L t f t ~

1

4

2

12

:.--

4·3

4



-------1

r E•r E F 1· 1

2

1

2

~E e f r ~E r Et tE ~e f k qE ~r E#t 1f f f t PE e E t

page 98

Chapter 2: 4-finger Technique

1

11

Tao of Bass by Marcos Machado0

J=I00-132

t .,

2

f.

:J=i

1

2

r

4

[9 ~r

r •r

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-~ 4

2

J

g.

h.

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b

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4

2

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4

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1

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11

4

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r E qt t r E f E II==:Il

II==:Il

1

f E t E r E t r .11

#

t r

1

E

r

r 41

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2

2

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2

4

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1

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11

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t f

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f

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2

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~ 1

r.

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2

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r E" f r 4

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4

Chapter 2: 4-finger Technique

1

q. :J=

f

3

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11

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~:

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Tao of Bass by Marcos Machado

3

# #

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11

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4

1

#

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2

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11

11

page 99

Exercise 2. 60 Fork This is a useful technique to facilitate the execution of complex passages involving the interval of a fourth.

J=l00-132 3~1

3

2

3~1

3

2

#

3~1

3

4

3~1

3

4

371

~x 1ttbr ftf:r 1 cttr crt; 11 1

11

11 1

1

11

3

3~1

2

3

3~1

2

3

3~1

4

3

4

f cft ftf:r #r#rr ~ crnt 11

11 1

1

11 1

\

1

11

Exercise 2. 61 M odes The left thumb should be in a higher position than usual to improve the pivot range.

~:~

E

2

4

j

~

m

3

~:

~ m

r 2

tJ=

E

p!"

4

¡,~

~:

e

m

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¡,e

4

r r

4

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f 1

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k1

~

r ¡E ke1 3

3

E 2

~

k1

r r

p4

4

r

2

4

~

~

~

3

4

3

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e:

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k1

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r 4

r

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~

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k1

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r

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r

m

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r

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li

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m

i

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11 1 1

1

\ page 100

Chapter 2: 4-finger

Te~hnique

1

Tao of Bass by Marcos Machado

0

¡,'

Pivots on Major Thitd Interval Between First and Fourth Fingers

Exercise 2. 62 ..J=120-192

:x t t t t: t:t ñ ri t r r 1t t t t t t t r; ñ E1

11

11

11

Exercise 2. 63 ..!=130-192

:r r

m

11.

t r et t t t t t t 1r rt r r t t t t t t- t 11 11

Exercise 2.64 ..!=120-192

2=

~

=t;- e r 1 2

1

4

2

1

11

€r !ª r r e 1-ttt r E; 2

1

4

2

1

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2

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e E! 4

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Exercise 2.65 ..!=120-192 2

:J=

r

r 1

4

E

r

11

2

E

4

~

r

r r 4

2

E

1

2

E

4

~

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11

Exercise 2. 66 )=100 1

2:f

r 2

,¡.¡. 3

r

2

r

2

f

11

0

r

11

r

11

1

~r

Chapter 2: 4-finger Technique

1

Tao of Bass by Marcos Machado

2

r

page 101

Exercise 2.67 J=120-192

rt :--~~ctrrrJ~~~ r: r~ ~ i a a e r 1 •e r; r -1

~:

2

4

1

2

4

1

2

4

4

4

2

1

214

2

4

2

4

2

1

m

IV

~: i j j

u

E Élj L m

IV

m

II

1

fj t f f f r 2

1

1 ~

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2

r r• •r r .,

4

r:

1

2

4

4

3

J j

j

m

11

II

IV

J

1

IV

Exercise 2.68 J=180 2

4

tJ=

lm r 3

tJ=

l: ' E m

2

E II

4

1

E



1

f

J

2

4

f r r

11

rf

r 1

2

1

''r E ~~ f E E

lm

m

3

4



J

m

II

1

r rEE • 1

2

qr #E

l:

1

J

II

3

1

4

3

4

3

E J• II

1

m

11

4

Q

q4

1

2

3

11

j

II

m

II

Exercise 2. 69 Anticipation: Only move the finger after preceding finger is secured on its place Useful technique to achieve a smooth legato. Similar to the "crab" technique explained on chapter 3 (p.l38)

J=120-192 1

a.

tJ= t:

b.

r

~:

page 102

1

~2

~

L 3 !}~

+=

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t

r r r

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1

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r 1

Chapter 2: 4-finger Technique

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g2

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r r 1

Tao of Bass by Marcos Machado

11

0

1

c.

~

~:

d.

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g.

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-::;:L:.:J~=~==1==~:!=:t===::t:r====±g====#~==r=1:1 . -------LBII 1

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k. 2=!

z.

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0chapter 2: 4-finger Technique

1

Tao of Bass by Marcos Machado

page 103

4

o.

:.>=

2

1

f

r

4

1

r

f

f

r

2

f

f

q. t)=

r •r r 2

11

r.

~

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g4 11

s.

r •r r

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4

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f

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p. t)=

4

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page 104

Chapter 2: 4-finger Technique

1

Tao of Bass by Marcos Machado

0

Dexterity

Exercise 2. 70

Exercise 2. 71

0chapter 2: 4-finger Technique

1

Tao of Bass by Marcos Machado

page 105

Exercise 2. 72 '1

\

2 .·

fl

3

1

2

1

~

2

1

3

4

3

~1 .

1

1~3

r: frqtr: trqt 1r: tr~ff ft

fll .

1

3

1

2

2

1 ..

3

4

1

1~1

c~r ct c~r cqr 1 c~r cqrrr~c; 1

n

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m

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1

3

1

3

2. 1

1

2

·¡

1

3 .. 1

2

1

3 ... l

2

1

3

4

3

2

1

1

w

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1

.l

page 106

Chapter 2: 4-finger Technique

1

Tao of Bass by Marcos Machado

0

Exercise 2. 73 4

3

~

4

:J=

4

1

~:~ ~ ~ ~ ~. ~ ~ 2

t ~ 1~ ~ t ~

1

~

:>=

~2

et

1

4

Et

1

4

4

4

~ ~ 2

t ~

q 3

11

1

1

Exercise 2. 75

~

11

~2

q3

f E~

11

Exercise 2. 76

r er er er 1

:>=

4

q3

4

3

Exercise 2. 77 3

~

:>=

~2

4

1

~2

'4

~2

q3

4

4

f

11

1

f f t f Ef t

11

Exercise2. 78 4

:>= E 11

4

3

q~

1

r E ee r E r 1E#r E r r e r §t! 1

4121

:>= E#r E F IV

1

3

3

111

4

3

2

1

1

3

4

3

1

11

4

IV

0chapter 2: 4-finger Technique

111

2

e r ry

14



21

j :J J J 111

1

4

4

214

r Er f IV

111

Tao of Bass by Marcos Machado

2

1 .

2

4

4

11

111

2

1

1E r E e e r r J 21412

1

1

413

E E r E E E. E ; IV

111

=11

ll

page 107 .

Exercise 2. 79 4

;>= i l

4

4

~€

r ; t r t r f r =f t e r ;- e r J• 3

3

4

1

1

3

3

1

1

1

m 3

3

1

3

4

1

3

3

3

n

4

11

m

3

3 n

'

'•'

Exercise 2.80

---~2 t----

r r 5 E F~t r E1f:Ct r flr r f Hl J tJ 2

;>= ¡

.

1

4

~

2

1

2

4

..----;-~

2

1

4,.,.2

.

2

1

4

2

2

j ]!#

m

11

j

Exercise 2.81 ~2

4

2

;>=¡e r e ki lE r UF 1

1

n

2

3

b4

¡t~t

1

r r

1

3

J•

1 '•

11

1

n

m

1

1'

l

n

m

·n

1

m

n

1

m

m

n

1

1

n

m

l. e t

l

Exercise 2.83

1

4

;>=e

3

r #r m

4

2

b2

1

_, E ~ r d f F 11

11

1

tJ=j ~

1

~r

11

m

3

1

4

2

Fr F

j

11

m

11

1

4

r !ip

2

~

r

11 . l

l

Exercise 2.84 2

4

2

1

~

r

b2

q4

er

q3

1

#

2

~ 31L

~

r- tt r r 3

2

q 1

4

3

4

2

E~

11

r

r

J 11

Exercise 2.85

page 108

Chapter 2: 4-finger Technique

1

Tao of Bass by Marcos Machado0

Exercise 2.86 2

4

1

2

2

4

1

'r #r

2

4~1

2

1

1

2

~

4

11

r

111

• J 11

lm

4

2

1

~

4

r

1•c #g m

11

4

1

3

4

1

11

4

2

3

4

1

11

2

1

1

!#t

m

11

11

1

tf

e

2

4

~

4

1

EJ E m

11

1

4

1

3

2

1

4

4

2

• J

2

1

r rr

e: ~

• j

3

=11

m

11

2

11

3

4

E E E E#E !t

2

111

J

4~1#

1

3

11

1

1

4

4

r+trrttrrqct 11

1

11

1

1

11

er r 4

2

4

1

m

#.,¡. -!t.

1

1

4

• j

r:rc rfüc rrc rr 2

1

11

3

4

• j #e:

11

4

4

11

3

1

4

r E m

11

2

m

11

9= l

~J=E

.4

E F r L r ; E r f 1rr r

:>= 1 L•r ft m

1

1

4

t #e

E'

m

11

1

4



:J

11

m

11

11

2

L Exercise 2.87 Fork

a.

4

b.

3

~4

1

3

~J: f f f r f E f E 1f ~j f 4

2:

1

3

2

E

1

frf r

2

1

11

4 3

2 1

~

f

0chap~er

4

2

3

c.

2

~f

2: 4-finger Technique

11

1

Tao of Bass by Marcos Machado

page 109

Exercise 2.88 Endurance 2

1

1

~-2

0

:>=•ana=~ IVm·

TI

m

IV

.··.·¡

}2=s±:D

~

m

TI

m

2142142143121414

l@j9l21Jtf6=&1

IV

miVm

TimTI

m

&11 @ 6fEt f?i} 1819 (f7t FJfft ~ f ~ E

:>=~1'1,~

1

IVm

TI

m

IV

m

TI

m

IV

miVm

TimTI

m

¡

m TI

TI

m

m

TI

TI

TI

a11 Eitr (ff1 Q

:>=·~~

IV

m 2

m

TI

m

ITI

TI

TI

1

4

4

2

IV

4

1

1

TI

4.

4

4

2

m 4

1

2

1

m

TI

IV

m

TI

m

J

IV

819 EfE1f= EW ~ E~ E 1

IV

m

IV

TI

m

TI

mTI

m

m

TI

IV m

m

1

4

4

2

4

1

4

2

1

4

2

1

4

2

m 4

42

TI 4

m

1 ..

TI

IV

m

IV

~2 1~4

1

4

2d-::1

m

TI

E

miVm

·~·

1

TimTI

2

mTI m

TI

m

4

IV

m

IV

m

4

1

2

--

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1

TI

m

IV m

tflí E7fF) 4ldJ tfft eE f Ef E~ 2

~~~~~ ;--:::--~~ m TI

m

1

m

TI

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TI

TI

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m

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1

2

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m

IV

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m

m

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page 110

Chapter 2: 4-finger Technique 1· Tao of Bass by Marcos Machado

0

mn

n

n

m

n

m

n

mn m

IVm

IV

w; :sz:t: :x au=~ e~~lf[F1 EW r r rfg~rr 2

~

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2

n

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tt~ m

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11

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4

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1

4

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4

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1

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m

11

n

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1

2

4

1

2

4

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1

11

mn m

IVIII

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IV

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0

1

11

m

n

Chapter 2: 4-finger Technique

1

1

n

m

1

1

1

n

1

m

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4

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11

Tao of Bass by Marcos Machado

mnm

IVm

11

IV

page 111

Permutations Human beings are designed to respond to changing stimuli, and the finger permutations will thus help stimulate and motivate students. Sorne of these exercises are difficult and will demand the student's full attention. Be creative, practicing these permutations in different positions, and modulating diatonically or chromatically. Remember that shorter, more frequent practice sessions are the most effective. · Do not try to play all the permutations in the same day or even the same week. The body needs time to · adjust the new movements. New patterns require subtle finger rearranging and rethinking. These permutations will also help you learn new correlations, allowing you to change fingerings without discomfort.

group 1 & 1 group 1 & 1 groupl &2 group 1 &3 group 1 &4 group2&2 group2&2 group2& 1 group2&3 group2&4 group3 &3 group3 &3 group3&1 group3 &2 group3 &4

1

! group4&4

I l

group4&4, group4&1 group4&2 group4&3

page 112

Chapter 2: 4-finger Technique

1 1

1

Tao of Bass by Marcos Machado

0

group 1 &2

group 1 &3

group 1 &4

group2 & 1

group2 &3

group2 &4

1

group3 & 1 2

1

4

2

4

3

1

2

4

1

4

2

4

2

1

4

1

2

group4 & 1

0

C ha p ter 2: 4- finge r Te eh ni que

1

2

group3 &2

group3 &4

group4&2

group4,&3

Tao o f ·B as s by Mar e os M a eh a do

page 113

la&~group

1

lb & group·l

'fJ

2

3

4

2

3

4

2

4

3

2

4

3

3 3

2 4

4 2

3 3

2 4

4 2

4

2

3

4

2

3

4

3

2

4

3

2

ld & group 1

le & group 1 2

3

4~

2

4

3

3

2

4

3

4

2

4

2

3

4

2

3

4

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2

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,.

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J

2

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4

2

3

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2

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3

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2

4

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2

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4

2

3

4

2

3

4

2

3

4

3

2

4 4

4 2

2 3 2

3

1

l ~~, 1

page 114

Chapter 2: 4-finger Technique

1

Tao of Bass by Marcos Machado0

··~

la & group 4

lb & group 4 2

3

2

1 2 1 2 3

3 3

1 1

1 3 1 2 3 2

le & group 4

3

2

1 1

1 2 1 2 3

3 3

1 3 1 2 3 2

ld &group4 2

3

J

2

3

2

1 2 1 2 3

3

2

1 2 3 2

3

1 1

1 2 1 2 3

2

3

2

1 2 1 2 3

3 3 1

1

le & group 4

3

1 3 1 2 3 2

lf&group4 2 2 3 3

1 1

0chapter 2: 4-finger Technique

2

1

3

1 2 1 2 3

1 3 1 2 3 2

Tao of Bass by Marcos Machado

3 3 1

1

1 3 1 2 3 2

page 117

1

2a & group 1

2b & group 1 2

3

4

2

3

4

2

4

3

2

4

3

3

2

4

3

2

4

3

4

2

3

4

2

4

2

3

4

2

3

4

3

2

4

3

2

2d & group 1

2c& group 1 3

4

4

3

.'¡ 1

l

3

4

2

3'

4

3

2

1

1

2f&group1

2e & group 1 2

3

4

2

3

4

2

4

3

3

2

4

3

2

4

3

4

2

3

4

2

3

4

2

4

2

3

4

2

3

4

3

2

4

3

2

r I

l page 118

Chapter 2: 4-finger Technique

1

Tao of Bass by Marcos Machado0

2a &group2

2b &group2 1

3

4

4

1

4

3

1

3 4

3 4

3

4

1

1

4

1

3

3

4

3

1

1

2c&group2

2d &group2 4

1

3

4

1

3 4

3

1

4

3

3

1

4

3

1

4

3

4

1

3

4

1

4

1

3

4

1

3

4

3

1

4

3

1

4

1

2e&group2

0chapter 2: 4-finger Technique

2f&group2

1

1

3

4

1

1

4

3

1

3 4

3

1

4

3

1

3 4

3

4

1

4

1

4

1

3

3 4

1

4

3

1

4

3

3 1

Tao of Bass by Marcos Machado

page 119

2b & group3

2a&group3 2

1

4

2

1

4

2

1

2

4

1

1

4 2

1

4

1

2 4

4

1

4 2

4

2

1

4

2

1

4

1

2

4

1

2

2

1

1

1

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1 -¡

l.

4 1

2

4

4

2

2

1

1

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r

2f&group3

2e&group3

page 120

1

2

1

4

2

1

4

2

4

1

2

4

1

1

2

4

1

2

4

1

4

2

1

2

4

2

1

4

4 2

4

1

2

4

1

2

Chapter 2: 4-finger Technique

1

1

Tao of Bass by Marcos Machado0

1

2a &group4

2b & group4 2

3

1

2

3

1

2

1

3

2

3

3

2

1

3

1 2

·3 1

1

2

3

1

2

2

3

1

2

3

1

3

2

1

3

2

2c&group4

2d & group4 2

3

1

2

3

1

2

1

3

2

1

3

3

2

1

3

2

1

3

1

2

3

1

2

1

2

3

1

2

3

1

3

2

1

3 ·2

2e&group4

0chapter 2: 4-finger Technique

1

2f&group4

1

2

3

1

2

3

1

2

1

3

2

3

3

2

1

3

1 2

3

1

2

3

1

2

1

2

3

1

2

3

1

3

2

1

3

2

Tao of Bass by Marcos Machado

1

page 121

j'

l

l

\, 1

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3a & group 1

3b & group 1 2

3

4

2

3

4

2

4

3

2

4

3

3

2

4

3

2

4

3

4

2

3

4

2

4

2

3

4

2

3

4

3.

2

4

3

2

4

2

2

3

4

3

2

2

3

4

3

2

4

3

4

2

3

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2

4

2

3

4

3

2

3c & group 1

3d & group1 2

3

4

2

4

3

3

2

4

3 4

4 2

2 3

4

3

2

3e & group 1

page 122

l.

3f&group1

4

2

.4

3

2

Chapter 2: 4-finger

Techniq~e

1

Tao of Bass by Marcos Machado

0

3a &group2

3b &group2 1

3

4

1

4 1 4 1

3

4 1

3

3

3

1

4 4

3 3

4 4

1

3c&group2

3

3

4

4 1 4 1

3

4 1

3

1

3

3d &group2

l

1

3

4

1

3

4

1

4 1 4 1

3

1

3

4 1

3

4 1 4 1

3

3

1

3

1

3

'f

3

4 4

.3

4 4

3

4 1

3f&group2

3e&group2

0chapter 2: 4-finger Technique

1 '1

1

1

3

4

1

3

4

1

4

3

1

3

3

1

4

3

3

4

1

3

4 1

4

1

3

4

3

1

4 4

4 1 4 1 3

1

Tao of Bass by Marcos Machado

3

page 123

1

l

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l 3b &group3

3a &group3 2

1

4

2

1

4

2

4

1

4

1

1

2

4

4

2

2 4

4

1

2 1 1

4

2

1

4

4

1

2

4

2 1

2 1

2

3d & group3

3c&group3 2

1

4

2

4

1

1

2

4

1

4

2

4

2

1

4

2

1

4

1

2

4

1

2

1

1

,.

3f&group3

3e&group3 2 2 1 1 4

1 4 2 4 2

4 1 4 2 1

4

1

2

1

1 page 124

Chapter 2: 4-finger Technique

1

Tao of Bass by Marcos Machado0

l

l

3a &group4

3b & group4 2

3

1

2

3

1

2

1

3

2

1

3

3 3

2

3

2

1

1

1 2

3

1

2

1

2

3

1

2

1

3

2

1

3

3 2

2 2

3

1

1

3

3c&group4

3d & group4 2

3

1

2

1

3

3

2

3

2

1

3

3

3

1

1 2

2

1

1 2

1 2

1

3

2

1

3

2

3e&group4

3f&group4 1

2

3

1

2 3

3 1

3

2

1

3

2

1

3

2

1

3

1

2

1

2

1

2

3

3 1

1

3

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1

2 3

3 2

2

0chapt~r

2: 4-finger Technique

3

1

Tao of Bass by Marcos Machado

page 125

.

1 1

1

f

4b & group 1

4a &group 1

l 1

2

3

4

2

4

3

3

2

4

3

4

2

4

2

3

4

3

2

4d & group1

4c & group 1 ·2

3

4

2

4

3

3

2

4

3

4

2

4

2

3

4

3

2

4

l.

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4

3

1 1.

2 1

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4e & group 1 2

3

4

2

3

4

2

4

3

3

2

4

3

2

4

3

4

2

3

2

3

4

2

4

4 2

3

4

2

3

4

3

2

4

3

2

l 1

page 126

Chapter 2: 4-finger Tech.nique

1

Tao of Bass by Marcos Machado

0

4a & group2

4b & group2 1

3

4

1

3

4

1

4

1

4

3

3

1

3 4

3

4

3

4

1

3

1 4

4

1

3

4

1

4

3

1

4

3

3 1

4c&group2

4d &group2 4

1

3

4

1

3 4

3

1

4

3

3

1

4

3

1

4

3

4

1

4

1

4

1

3

3 4

1

3

4

3

1

4

3

1

4

1

3

4

1

4

3

3

1

4

1

4e&group2

4f&group2 1

0chapter 2: 4-finger Technique

1

1

1

3 4

3

1

3 4

3

4

1

3

4

1

4

1

3

4

1

4

3

1

4

3

3 1

Tao of Bass by Marcos Machado

page 127

4b & group3

4a &group3 2

1

4

2

1

4

2

1

2

4

1

1

4 2

1

2

4

1

4

4 2

1

4

2

4

2

4

2

1

4

1

1 2

4

1

2

4d & group3

4c&group3

4 1 1

2

4

1 4

4 2

2

4 2

1

1

4

1

2

2

2

1

4

4

2

4

1

1

1

2

4

4

1

4

2

2

.4

2

1

1

4

1

2

2

Chapter 2: 4-finger Technique

1

Tao ·of Bass by Marcos Machado

1 1

!

4f&group3

4e&group3

page 128

;:

0

4a & group4

4b & group4 2

3

1

2

3

1

2

1

3

2

1

3

3

2

1

3

2

1

3

1

2

3

1

2

1

2

3

1

2

3

1

3

2

1

3

2

3

1

1

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4c&group4

4d & group4 2

3

1

2

1

3

2 2

3

2

1

3

2

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3

1

2

3

1

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1

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2

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1

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0chapter 2: 4-finger Technique

4f&group4

1

2

3

1

2

3

1

2

1

3

2

1

3

3

2

1

3

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1

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2

Tao of Bass by Marcos Machado

UNIVIERSil'lf)AD

-

p age

BIBLIOTECA

1

.1

CHAPTER 3: Thumb position The Tao of Bass presents a systematic and gradual approach to learning the thumb position technique. Most methods list three or four basic thumb positions. I have expanded the technique to 18 basic positions to help students master the thumb position technique in a more comprehensive manner. The "Crab'' and the "Fan"* are techniques that many players have unconsciously used throughout the years. The "Crab" and the "Fan" will be integrated with the "thumb position;' not treated as distinct techniques. Introducing these techniques organically and simultaneously will help demystify them.

*These terms were coined by my teacher Fram;:ois Rabbath, who was the first to codify the technique in his double bass method, "Nouvelle Technique de la Contrebasse."

din

0chapter 3: Thumb position

1

Tao of Bass by Marcos Machado

page 131

Thumb position Technique Basics When performing using thumb position, the wrist should be as flat as possible. Use the fleshy (pads) part of your fingers. Fingers should be slightly curved, with natural springiness on them. When working on the basic fingering combinations, start with the easiest positions, such as the chromatic, semi-chrorriatic/ etc.

Basic Fingering Combinations group + +a

1

2

+b

1

+e

2

+d

2

3 1 3 1

+e

+f

3 3

2

group 1 la

3 2 3 1

2

3

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le

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ld

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+ 3

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+

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1

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+

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3b

1

+

2

2b

1

3e 3d 3e 3f

2

1

+

2e

2

+

1

2d

+ +

+ +

1

2

'----- 2e

2

1

2f

page 132

Chapter 3: Thumb position

1

3

+ 3

+

1

3

3

1

3

1

+

3

+

1

Tao of Bass by Marcos Machado0

Applying the basic fingering combinations on two strings

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page 133

page 134

Chapter 3: Thumb position

1

Tao of Bass by Marcos Machado0

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0chapter 3: Thumb position 1 Tao of Bass by Marcos Machado

1

2

3

11

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page 135

Exercise 3.2 Daily lfizrm-Up a.

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page 136

Chapter 3: Thumb position

1

Tao of Bass by Marcos Machado0

Exercise 3.3 The Pan f

In the jan techn,ique there are no shzfts. Rather~ slide the finger to the new posltion. Thumb remains stationary throughout the exercise.

-J.

b.

+

1

2

1

2

+

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1

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0chapter 3: Thumb position 1 Tao of Bass by Marcos Machado

page 137

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FrEE EFE Ir EEEE t r F1j J J J J 3J J 1 What is the Crab?

page 138

2

r r rE EEEf 1t Er f F EFE1r Er E[ t Ff 1

~ tEr[ r ~ ll +

213

+

2

2

0

o

11

Crab:~ term coined by great pedagogue and double bass guru Francois Rabbath:~ is an antiá'pation technique whereas the circled note remains stationary until the following note is placed into position.

2

+

J F J F 1F J F J 11

Chapter 3: Thumb position

1

Tao of Bass by Marcos Machado0

1

Exercise 3.5 Finger Substitution On this exercise., the hand moves in blocks. Careful with intonation when executing the finger substitution (1 - +). The pitch should match perfectly.

..J=56 ~

finger substitution +

2

1

3

2

+

1

2

+

1

1

2

1

213

2

3

2

+

2

1

+

2

1

3

2

+

2

+

21

2

+

1

2

1

3

+

2

2

1

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~

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1t2

+

21

+

+

21

+

213

+

213

2

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rE L ;ErE F1r F EEFr FE le EEFEEEE1r EE EEr EE1

r

~ # ; EE f E Er Ér FE~ É r Jj j J j j j j 1;

0chapter 3: Thumb position 1 Tao of Bass by Marcos Machado

1

1o

11

page 139

Crab

Exercise 3.6

11

.

n

1 1

~

+

1

1

®

2

+

~~ '¡, :J J J 3 '~

+

1

2

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1

2

i J

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3

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3

2

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1

+

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1

+

2

!

3

33 J ~

)

11 J

1 +

1

2

3

3

10

2

3

+

1

2

+

+

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2!

3; J J J I;J J J 3 J j J J lj 3 3 J

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1'

1

11 n

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2

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page 140

~

n

1

+

n

+

(

1

2

3

3

2

1

e .,

r r r Ir r r J

3

2

+

1

J j J

J

+

1

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r

1

11

'1

J

1

+

2

l 1

3

JJ~

11

n

1

Chapter 3: Thumb position

1

Tao of Bass by Marcos Machado0

Exercise 3. 7 J=82

-J_

+

1

®

2

+.

1

2

3

3

2

1

e

3



1

2

1

+

+

1

®

2

+

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2

3

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+

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+

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2

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3

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2

e

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3

21

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2

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e

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2

3

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j

21

1

1

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3

3

j

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e

21

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2

1

+

3 3 ;J 3 J J 1

12

®.

12

3

r r re r r; 21

e

r r F !ErE!

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3

12

3

1

21.

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12

3

r E E r; Ir: E Ef L r E r 1

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1

12

r EJ l

3

r r F r EEf

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12

2

+

2

~ Et ~

3

r

0chapter 3: Thumb position 1 Tao of Bass by Marcos Machado

11

page 141

Exercise 3.8 J=IOO +

12

+

1

2®+

12

3(!)+

12

+

12

312

+

12

3

n1

n

1: 1

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1

1

·

·

CD

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1

2

+

1

2

®

+

1

2

3

+

1

2

+

1

2

+

1

2

+

1

2

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1

2

3

CD . +

1

2

+

1

2

+

1

n

2

3

E Er J J 2 J 1·+·

1

#

3

1

2

3

1

n

1

2

+

n

1

2

+

1

n

1

2

3

n

1 ·

+

1

2

+

1

2

®

+

1

2

3

CD

+

1

2

+

1

2

3

1

1

2

3

,~# J J J J J J j J j 3 J J J J J J J J j j 3 J J J 1

1

n

m n

+

1

2

+

1

2

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2

3

CD

+

1

2

+

1

2

3

1

2

+

1:

'

.

+

12

+

1

~### J J J J j n

page 142

2®+

12

3®+

12

mn

+

12

312

+

2 ·

1

Chapter 3: Thumb position

m

1

n

11

m

l

1 1

{ \

11

3

1:

.

11

m

J J J j J j J J J J J j 3J JJ 3J J 1

1

3

1: mn

12

J

~

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11

n

m

1

l

n

,~# J J J J EEEr 1E EEr J J J J 1E r Er d J J 31 ·+· 1

11

11

-n-- -·· m

Tao. of Bass by Marcos Machado0

.l

Exercise 3.9 CrabJ Articulation and Dexterity J=120

+

1

}L!!_ -}!:. 1

2

1

+

1

~

+

1

jL

2

2

3

1

2

1

+

1

a:>

1

2

3

2

1

3

2

1

1

a:>

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+

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~

2

3

2

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+

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a:>

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Chapter 3: Thumb position

1

1

+

1

~

2

~~ ;j-

3

2

E Ej

Tao of Bass by Marcos Machado

3 ~

2

1

~ Ej ~ ~

1

+-~

2

~

3

i:l

1

11

page 143

Crab Exercise 3.10

&

+

+

2

..!.=120 12

31

®

+

12

3

~g f±lCJLr 1tU 1

3

®

1

+

1

f

2

2

+

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12

®

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+

12

3

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lf_J 1(fJ (LF 1ClfJ lLJ 1 +

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1

3

2

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+

2

1

~

2

~-

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1

1



1

1 1

1

1

1 11

1

l Exercise 3.11 +

+

1

+

2

®

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&EF F r Ef +

1

+

2

+

+

@

1

1

+

1

+

+

1

®

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2

+

1

+

2

+

~

+

2

®

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1

+

2

+

®

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+

@

+

1

+

r F E E r E1Er r EE;

+

+

~

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[J F C± 1

1

1

11

1 1 page 144

Chapter 3: Thumb position

1

Tao of Bass by Marcos Machado0

Exercise 3.12

2

n

m

n

m

+

1

1

2

2 ® e) +

J#J]jJJ#fiJ n

+

&''E qry 1

,~3

m

1

2

¡,J qj

+

~J ;~:J

1

+

Eijf 1 ~J J q] n

1

&qc

1

+

2

1

+

1

2

+

2

n

m

2

n

+

2

n

+

1

n

1

+

l''t rJt

2

+

2

3

m

11

+

2

2

2

3

1

J

n

2

1

i~:J m

~2

+

1

+

n

1

+

+

L F r 1E EJ ~J J 3 i J J ijr #r !r 2

i qJ

1

¡,J j

2

1

1

1

2

m

+

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0

2

1

n

3 1

+

11 1

0

n

m

Chapter 3: Thumb position

11

1

1

11

Tao of Bass by Marcos Ma,chado

m

n

1

page 145

Exercise 3.13

'1 til3 J JJ

J=l20

3

+

12

3121

J

j

212

1

+

12

m

2

3

+

12

3121

212

+

1

2®+

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~~m Simile

11

+

1

1

11

11

11

1

m

11

1

m

11

11

1

1

11

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+

12

11

3

+

12

11

3121

m

3121

m

212

+

11

212

12

+

2

3

+

1111

+

12

1

11

11

+

12

3121

m

11

2

3

+

1

12

3121

m

11

212

+

11

212

1

2@+

1

+

1

2@+

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1

) 1

,11

m

1

11

11

1

m

11

11

t r"Pr J J J J1JJpJ 3r r r F1Er Pr J J J·J1JJpJ J r Ff#r 1

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+

12

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11

m

11

m

212

+

12

+

2

3

+

12

3121

212

11

1

11

1

11

m

11

11

1

11

1

11

m

11

+

1

2@+

11

page 146

Chapter 3: Thumb position

1

Tao of Bass by Marcos Machado0

Exercise 3.14 .J=120

t~

+

1

2

~ a:J :J J

j

2

®

3

+

err r

+

1

1

2

3

2

3

®

+

LE arE Er

+

1

1

2

3

2

3

®

+

+

1

2

3

2

3

®

+

rJ r; ErE EtraE EEr 1

1

11

Exercise 3.15 Pan

r r r rr r r_; cr r r =re r eert =e r r

~

'+

112

3

21

+

+

11

2~2

1

+

+

1

2

11

~

2

2

-e-

1

1

1

-

11

Exercise 3.16 Articulation .J=l32

-J.

+

1

1

2

2

3

1

2

1

® .

+

1

1

2

2

3

1

2

1

®

®&dJ 4M2 f1FF ftt2t fQ2 ERE FJW EfFF

-J.

1

+~

2 1,.....----...._

3

2~

1M'\

1~1.b

1

+,.....----...._

2

1~

3

1

21

2~

1~®

¡rcrErFrErrrrrrrclrFrrrrrrrrrrrrrrl +

1

1~ 2~ 1~® +~ 1~ 2~ 1~2 ~

' (fr'r rrrrrcrtrf'rr

1

rrr:rrtrtrrrrrcrr

0chapter 3: Thumb position 1 Tao of Bass by Marcos Machado

1

-

11

page 147

+1

12

2

3

12

+

1

12

2

3

12

~ &1JJJJJJJJrrrrJJJJ¡JJJJrrrrrrrrrrcrl '

+

1

.

1

2

2

3

1

+

2

1

1

2~3

2

1

2

eEEFrE bFE EEEbE bF1bE bfree Et=E bFE eeE

1

'+,

12

2

3

,

+,

2

,

2

l

E'

2t

'1

2

Exercise 3.17 Articulation:J crab J=68 '

o

+

+

1



2

+

~rtj J j J J J:J

=111=

+

1

2

+@

3J ~ ~ J J

=11

Crab

Exercise 3.18 J=68 '

J J 3J

~#l 3 j +

3

®

1

+

2

~ 1

2

3

11

1 Exercise 3.19

a.

-J.J=92 ® ® ® 1 ¡~#2 ¡:rs JJ J¡:rs 11~ '1, D J 3wJ LJJ ll~##n D J 3J J D J 11 ~

b.

l

+

1

2

+

12

+

2

+

1

+

21

1

+

+

1@

+

1

2

+

12

+

2

1

21

+

1

+

+

®

1

+

1

2

+

2

12

+

21

1

+

+

1

1@

3~#2 i :J J JJ ~ i:J J 1iJ J 3j J iJ J 1i:J J j J J i:J J 11

page 148

Chapter 3: Thumb position

1

Tao of Bass by Marcos Machado0

Exercises on 2 Strings. Practice each exercise diatonically and chromatically.

Exercise 3.20 +

'

2

:J

Exercise 3.21

+

2

~

:J J

+

1 J!"M7

~ ~ ~

~-

&j J

~

2

11

11

11

&j

1

+

2

2

J

~

11

+

3

3J

J

3

11

n

1

3J

' J ' J

+

2

~

2

J

~

3

3J

11

Exercise 3.24

11

11

Exercise 3.25 2

3

1

~ J ~ j

+

J

2

+

1

~ ~

11

11

2

1

~ ~

+

2

J

11

Exercise 3.26 +

+

2

~ J

'

2

--r=

11

11

&j

~

J

2

Exercise 3.23

~ ~ ~

2

~ ~

+

11

Exercise 3.22 2

+

1

2

~

+ '

J jJ J J

~

11

2

j

~ J

+

J

1

~

2

1

'=

J

~

J

11

1

J ~

2

3

+

11

2

J 3 ~

11

11

Exercise 3.27

&0 11

+

2

J

~

+

2

J ~ J

~

J

J

2

1

J ~

+

J

2

~

3

2

J ~

11

1

J

11

Exercise 3.28 +

'

~ 11

2

J

~

+

J

~

0chapter 3: Thumb position

1

2

3

~

J

J

2

+

~

J

Tao of Bass by Marcos Machado

+

j

+

2

J ~ 11

j

2

J 3

11

11

page 149

Exercise 3.29 Bridge a.

+

n

1

1

2

3

1

+

2

1

E]

~ .3.

2

+

1

&1 tJ 9O:J J J JJ) J JJ ~ ~ ~ 11 n

1

+

&n 3an uaJwJ J1-] ~ 1 +

b.

2

1

®

2

+

1

( 2)

3

2

n

n

2

3

1

3

2

+

1

11

n

1

(lli)

Thumb Position Patterns

Exercise 3.30 1

2

+

+

2

2

'#~ ;J J J J J J ~

j

+F

no

n

1

+

2

J

+

2

~ j J j J J

J

n

1

,#1 J J

+

2

n

2

+

+

1

11

n

Exercise 3.31 +

2

~ J j J ~

2

1

2

~

¡J

j

+

~

1

2

J J

n

(3)

j

n

2

J ~--n

11

Exercise 3.32

,#1 ~ +

2

j

.1 1

J

+

2

+

1

~ j ~

JJ

n

11

2

11

11

Exercise 3.33 +

+

2

&~~ J J n

~ J

2

1

+

j J ~ n

2

1

~

¡J

+

2

~

j

1

2

J J n

1

+

(3)

2

j

~

1

11

J

11

(11)

Exercise 3.34 +

,.

2

&~t ;J J J 11

+

j

1

~

2

j

1

+

~ ~

2

+

1

¡j ~

~

n

+

~

2

J n

+

(3)

j 1

2

J ~

11

n

(ll)

page 150

Chapter 3: Thumb position

1

Tao of Bass by Marcos Machado0

Exercise 3.35

&~~!

+

2

+f

J 11

J J

1

J

]

+

1

2

+

2

J ~ j

j

+

1

~ J ~

1

+

2

J

2

J ~

j

11

11

11

11

Exercise 3.36 +

+

2

&~~~ ~ ~

&~'' ~

1

~

1

+

~

+

2

~

~

+

2

2

1

1

1

~

11

11

~ ~

~

1

j ~ 1~ ~ ~ ~ ~ ~

1

2

+

2

~ ~ ~ j

~

11

2

+

2

+

2

~

~

11

~

11

+

2

~

~

+

~

11

2

~

11

~ ~

11

3

Exercise 3.37

&~''¡,

+

~ 11

J

2

+

~

j

1

2

~ j

1

~

+

~

2

1

+

1

+

2

+

~ ~ ~ ~ ~

j

+

+

11

11

2

11

Exercise 3.38 •. 1

2

+

&~~,, ~ ~ j 11

2

+

1

2

~ ~ ~ ~ ~

1

2

+

2

1

2

~ ~ j ~ ~ ~ ~ ~ 11

11

11

1

11

11

Exercise 3.39 1

&~''¡, ~ 11

+

j 1

2

2

1

+

+

2

~ ~ ~ ~ ~ ~

1

11

11

2

~

~

1

2

1

+

2

1

~ ~ ~

~

+

1

11

+

2

~ ~

11

11

Exercise 3.40 1

&~''¡, ~ 11

+

+

2

j

~ ~ 11

0chapter 3: Thumb position

1

J

1

~

+

2

~ ~ 11

1

~

Tao of Bass by Marcos Machado

~

1

2

~ ~ ~ ~ 11

+

·~

2

~

11

11

page 151

Exercise 3.41 1

+

2

¿~''¡,j J

+

2

2

]

33

fA

J

+

2

]

33

~

11

11

+

2

]

3J

J

1

1

2

~

2

]

3J

J

11

1

2

{"'

11

11

Exercise 3.42 +

2

1

¿~~ ;J

J

]

ll

~

+

~~

~

1

1

;F3J

]

l#c:

qo

3

2

3

r

.

~

2

+

+

2

11

J

2

+

::J

11

f

11

f

11

Exercise 3.43 +

¿~~ ;J

ll

1

2

+

]

J

]

1

2

3

2

;-=J l#c:

11

2

1

+

J

::J

2

r C2J1'

IJ

::J

11

J

Exercise 3.44 2

¿~~ ~

3~ ~ 3~ ~ 3~ ~ 3 ~

~

1

11

1

11

1

1

3

3

2

~

~ ~ 1

~ ~

~

~ ~ ·~

-~

~

11 --

Exercise 3.45

¿~~ j

j 6 J J J i- j

1

11

1

1

n

1

1

11

J J

j J 1j

j 3 ;J J J ;J J J ;J J J

1

1

n

n

;J

JJ

1

1

1

n

1

1

n

11

1

Exercise 3.46

'~ j j J J J J j j j 1

page 152

n

1

1

n

11

1

Chapter 3: Thumb position

1

Tao of Bass by Marcos Machado0

la &group2

lb & group 2 1 1 3 3 4 4

3

4 1 4 1 3

4 3 4 1 3 1

le & group2

\

:

3

4 1 4 1 3

4 3 4 1 3 1

le & group 2

4

4 1 4 1 3

3

4 1 3

1

3

1 3 3

4 4

4 1 4 1 3

4 3 4 1 3 1

lf&group2 1 1 3 3 4 4

Chapter 2: 4-finger Technique

3

ld & group2 1 1 3 3 4 4

0

1 1 3 3 4 4

1

3

4 1 4 1 3

4 3 4 1 3 1

Tao of Bass by Marcos Machado

1 1 3 3 4 4

3

4 1 4 1 3

4 3 4 1 3 1

pagel15

l :¡

l

1

lb & group 3

la&group3 2

1

2 1

4 2

1

1

4

2

1

4

\

1

2

4

1

1

1

2

4

4

4 2

1

4

2

4

2

1

4

2

1

4

1

2

4

1

2

\

1

l 1

ld & group3

le & group 3

1 1

1

2

4

1

4

2

4

2

1

4

1

2

1 1

J

lf&group3

le & group 3

1

page 116

2

1

4

2

1

4

2

4

1

2

4

1

1

2

4

1

2

4

1

4

2

1

4

2

4

2

1

4

2

1

4

1

2

4

1

2

Chapter 2: 4-finger Technique

1

Tao of Bass by Marcos Machado

l

]· .~

l 0

Exercise 3.47 '

1

2

3

2

~~ ;fj :;¡ ;

JJ ¡ J:;¡ j JJ 1



1

2

3

2

1

3

11

Exercise 3.48

'1

+

1

2

1

3

~ ~ ~ ~

2

3

E

~

E ;j-

2

2

~

11

Exercise 3.49

'+

1

1

2

3

11

Exercise 3.50

'1

+

~

1

2

1

~ ~~ ~¡~

3

2

3

~

~E

~

+

~

1

1

2

1

~ ~~

~

~

+

2

3

3

2

3

~

~E

~

~

11

Exercise 3.51

'~#~

2

3

2

E ~

illl!

2

J

;t=

3

2

~ ~ ~

11

11

Exercise 3.52

'2 0

+

J

2

1

~ ~

3

2

~

E ~ E r lj #J

11

Chapter 3: Thumb position

1

11

1

Tao of Bass by Marcos Machado

~

~

~

~

~

1

J

11

11

page 153

Thumb Flexibility

Exercise 3.53 a.

#j j 1~

&t {fj +

b.

+

+

&tqJ J d J

.+

"2

J 2

J

+

¡J

JJJ

2

n

JJ

+

+

~

J

¡J

JJJ

11

n

n

JJ J

+

2

J ~~

~

J

+

JJ J

11

n

Exercise 3.54

&~tw

tJJ

+

1

,,J

J

~

,~J

+

d

3

~

+

3

+

+

2

2

j

3

I¡,J

J +

J lz~ J ~j J

3

I¡,J

+

+

3

J

d J +

d

+

3

~

J

+

2

~J 2

~~

J +

3

J 1

+

J +

J j2~-- J

Exercise 3.55

page 154

Chapter 3: Thumb position

1

Tao of Bass by Marcos Machado0

r ---

b.

c.

~

+

212'

2

1@+

212'

2

1@

+

212'

2

1

2

1@+

212

'2



er EFr r•5J cJ EEr rlij5Ef:F EEEr•5J r1 EEEr =11

a.ll= b E ~

+

11=

2

1

2

'2

1

®

+

2

1

2'

2

1

®

+

2

'2

1

®

+

2

1

2

,·2

1

®

;~E r f Er EF•b EV EEEFlijcrf rt Er EF#g; EG! EEEF =11

0chapter 3: Thumb position 1 Tao of Bass by Marcos Machado

page 155

Exercise 3.56 Diatonic intonation J=62 3

'

~2

3

~2

IL! L +-¡j; r; IL; L/~ !C? L r IF F ltt•r E1 1

3

1

2

2

1

3

1

3

.1

1

3

1

2

1

3

1

1

'

3

2

1

' ,,J:== =J

=

3

1

U r;

3

1

qJ

1;

3

Effl

1

1

2

2

3

2

~

1

&

1

1

3

J3

E!f 1

2

1

1

Et 3

~

;

2

J J 1

1

2

11

Exercise 3.57 Agility and chromatic intonation J=IOO 1

+

1

2

1

2

3

2

3

2

1

2

3

2

3

2

1

2

'1~»4±@ t¡Ji_J ~ezg ~rEr FTF ~6t1r 1

3~3

Gr

2~2

F1Et •r

1

l

1

page 156

Chapter 3: Thumb position

1

Tao of Bass by Marcos Machado0

Exercise 3.58 Dexterity J=IOO

-J. @14@J~$J.J~Jq8@2 Fi3F I~Bc e 3

2

1

2

3

2

1

2

3

2

1

2

3

2

1

2

3

2

1

rrWr 2

3

2

1

2

3~.?

2

1 '[

1

3~2

1

EEFlF 'E j 1

r

1

11

0chapter 3: Thumb position

1

Tao of Bass by Marcos Machado

page 157

'i

Exercise 3.60 Dexterity J=92 1

.! 1

.1 1

1

1

1

1

1

1· ~

+

3

2

3

1

3

+

3

2

3

1

3

+

3

2

.3

1

3

+

3

2

3

1

3

+

11

page 158

Chapter 3: Thumb position

1

Tao of Bass by Marcos Machado0

Exercise 3.61 Articulation and Limbering of Second and Third Fingers

(

J=IOO ~

\ \ )

t.J JijJ w.w JaJ J J~w.a; J; J ; 1~JijJ Jw~JaJ J ; r: r~r rijr: r~, r1 2

3132

313

2313

2313

23132

31323132

313

i )

~

21 3

1

3

2

3

1

3

0chapter 3: Thumb position

2

3

1

1

3

2

3

1

3

2

3

Tao of Bass by M.arcos Machado

1

3

2

3

1

3

2

3

1

3

2

3

1

3

page 159

Exercise 3.62 Fingering Substitution and 2-3 Articulation

i 2-i f-i~-5-Ri-'i:t~F ~ .~ E~rt 1t4 u ú a ~ !tl1 ' JB,]L d Jbéfi 1jJ ~L i JDiP 1í8 qJ 1,3 J J@&Q 1i

11

Flexibility

Exercise 3.63 +

+

1

+

1

+

1

+

1

+

1

+

1

1

' i J¡,J 1J qJ 1J ~F 1J ~F 1J F 1J~F 1J F .

'

1

2

1

2

2

3

F 1F ~E

F #F 1F

2

3

lqE

f

~3

2

1E

q3

2

t

t

1E

'

~

. 2

1

2

1

2

2

1

1F 'F 1F qE 1F F 1 ~~

2

é

2

= 1E = 1F

1E

1

~

1

Exercise 3. 64 J=lOO

-J_

2 ® 3~2

®

CD

~#~~~

ij 1 J~J JqJ a~ J2J33J 33J 3gt)' =111= r ~ ~ 3

2

2

+

1

+ +

1

2

1

+

2

+

1

¡'---.-/'

3~2

tJ= 11=

1

page 160

+

+

CD

+

+

1

2

1

+

2

1

+

3

=111=

2

CD

+

~

+

1

2

+

1

~

2

··.

®

2

+

1

~

r C#E CRr ErE r Ere r 1

11

E~r Et•rTr[t EfE? FITF m

EL

1

1

+

CD

.

+

+

1

2

1

+

2

1

+

FfFiF~J•3 3~3 8]] d2 J ~11 ~

IV

Chapter 3: Thumb position

1

~

Tao of Bass by Marcos Machado0

Exercise 3.65 Dexterity ~=100

-::J.

+

1

3

+

3

+

1

3

1

3

+

1

+

1

3

1

@1 ¡;t-JJ iJ ;p ;J.JJ dJ :J J m

-::J.

+

1

2

n mn

+

2

+

1

3

1

3

+

1

+

1

3

1

3

3

1

1

+

3

+

3

1

+

1

+

3

1

3

1

+

1

n.w;a nao n#J:ZJJJJ n 1 n

1

+

2

+

2

n 1

n

+2

+

1

1

m

+

1

+

2

1

2

1

+

1

1

+

131

~ fJq) j 10 j ~j [:J 1J ] j J :J J 11ª0 qJ ~ -J J J O ; ! J J J J J J 1 m

u mn

3131

n1

+

1

+

12

m

1313

+

J) JAJ 31&