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An Improviser's OS Wayne Krantz
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Copyright 2004 by Wayne Krantz
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Published bv waynekrantz.com
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aj.a aj.
Production: Serrins Editing: Jerry Krantz Programming: Richard Huddleston Layout: Sunna Gunnlaugs / J)'Steam Creative
Thanks to my teachers and students, some of whom know who
.'... . .... "'1·
are
...r. [. I
If you like this book... PLEASE 00 NOT MAKE COPIES OF IT! The survival of the artist depends entirely upon your support. This book will always be avail able at a reasonable price directly from the artist's website, www.waynekrantz. com, where WK stuff has been distributed internationally since '99.
Or send $20 US + or US or Euro cash
check or money order to:
Wayne Krantz Prince Street Station PO Box 548 NY, NY 10012 USA
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Stand and Be Counted (All rights reserved. No part of this book may be reproduced in any manner whatsoever without written permission except in the case of brief quotations embodied in critical articles and reviews. Contact www.waynekrantz.com for information)
2
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To invent, the slate must be dean.
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Out goes the the design; not bv default.
the
the blues... to be added
if desired,
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• 1. ..i. i• •• i__
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•!
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Along with idiom, heroes are respectfully dismissed. Imitation of an artist is
contrary to what any artist stands for: innovation.
Tradition brought us here and that's enough. It need not occupy our thoughts
and actions anv more or less than our own birth.
Rhythm, melody, harmony and
derivative are expressions of the
and
••
Il-
aL_ at. __l_
4
.'_ 1
--~-
5
Some definitions for this book:
Melody - music played one note at a time Harmony Rhythm
music played two or more notes at a time the temporal placement of melody and harmony
Composition any preconceived music, including all licks, stylistic vocabulary, chord voicings, scale and arpeggio patterns, songs, pieces, tunes and chord progressions that one knows, or will learn Improvisation
6
any spontaneously created music
1
.- -,
&-. &-.
ONE-NOTE FORMULA
I b2 2 b3
I b2 4 b7
I 2 3 b6
I b2 2 3
1 b2 4 7
I 2 3 6
1 b2 2 4
1 b2 b5
5
1 2 3 b7
I b2 2 b5
I b2 b5 b6
I 2 3 7
I b2 2 5
I b2 b5
6
I 2 4 b5
~-:8
I b2 2 b6
I b2 b5 b7
I 2 4 5
I b2 2 6
I b2 b5
7
I 2 4 b6
tI--:8
I b2 2 b7
I b2
5 b6
I 2 4 6
I b2 2 7
1 b2
5 6
I 2 4 b7
I b2 b3
3
I b2
5 b7
I 2 4 7
I b2 b3
4
I b2
5 7
1 2 b5
a-. ti--.
TWO·NOTE FORMULAS
I b2 I 2 I b3
1 4
I 6
ti.-.a
. b5
I b7
ti--
I 5
I 7
.. -.a
. b6
I 3
a.-.a .. -.a
THREE-NOTE FORMULAS
::
1 b3
3
I 4 6
I b2 b3
I b3
4
I 4 b7
1 b2
I b3 b5
I 4 7
I b2 4
I b3
1 b5
I b2 b5 I b2 5
I b3
1 b2 b6
I b2
3
b2 6
8
I 2 b5 b6
I b2 b6 b7
1 2 b5
I b2 b6
1 2 b5 b7
I b3 b6
I b5 b6
tl,.--
I b2 b3 b6
6
I b5 6
~-.
I b2 b3
1 b3 b7
I b5 b7
I b3
I b5
7
I 5 b6
b2
7
1 3 b5
1 5 6
I 2 b3
1 3 5
I 5 b7
1 2 3
1 3 b6
I 5 7
1 2 4
1 3 6
I b6
I 2 b5
1 3 b7
1 b6 b7
1 2 5
1 3 7
I b6 7
1 2 b6
1 4 b5
I 6 b7
I 2 6
I 4 5
1 6 7
I
I 4 b6
I b7
Form1lla,
I b2 b6 6
I b2 b3
7
6
7
5
I b2 b3 b5
~.
I 3 4
:: 7
fi.--. tJ.- ~--.
5
5
1 b2 b7
2 b7
FOUR-NOTE FORMULAS
5
7
6
6
I b2 6 b7
I 2 b5
~-.,.
I b2 b3 b7
I b2 6 7
I 2 5 b6
tL--.
I b2 b3
7
1 b2 b7
7
I 2 5 6
L--· L--
I b2 3 4
1 2 b3
3
I
I b2 3 b5
I 2 b3
4
1 2 5 7
I b2
I 2 b3 b5
I 2 b6 6
I b2 3 b6
I 2 b3
5
1 2 b6 b7
I b2 3 6
1 2 b3 b6
1 2 b6 7
1 b2 3 b7
I 2 b3
6
1 2 6 b7
1 b2 3 7
1 2 b3 b7
I 2 6 7
1 b2 4 b5
1 2 b3
I 2 b7
I b2 4 5
1 2 3 4
I b3
3 4
1 b2 4 b6
I 2 3 b5
I b3
3 b5
I b2 4 6
I 2 3 5
1 b3
3 5
L--
L-· L-- L--- L· L· ~-
.. ..
~--. ~---. ~-
3 5
7
7
2 5 b7
7
~--.
~-.
~r"
Formulas
9
457
3 b6
3 4 b6
I b3
3
6
3
4
6
I
4 b6
I b3
3 b7
3
4 b7
1
4 b6 b7
1 b3
3
7
3
4
7
1
4 b6
b3
4
b5
3 b5
5
1
4
I b3
4
5
b3
I
1
6
6
7
b7
3 b5 b6
146 7 I
4 b7
7
b3
4 b6
3 b5
b3
4
3 b5 b7
I b5
5 b6
4 b7
3 b5
7
I b5
5 6
4
7
3
5 b6
b5
5 b7
b3 b5
5
356
I b5
5 7
I b3
b3
6
6
5 b7
I b5 b6
6
I b3 b5 b6
3
1 b3 b5
357
1 b5 b6 b7
1 b3 b5 b7
3 b6
I b5 b6
1 b3 b5
3 b6 b7
I b5
6 b7
5 b6
3 b6
I b5
6
7
5
3
b5 b7
7
5 b6
6
I b3
b3
6
7
6
6
7
6 b7
1 b3
5 b7
367
I b3
5
7
3 b7
7
I b3 b6
6
4 b5
5
1 b3 b6 b7
4 b5 b6
1 b3 b6
4 b5
7
6
I b3
6 b7
4 b5 b7
1 b3
6
7
4 b5
1 b3 b7
7
4
3 I
4 b5
345
5 b6 b7 I
5 b6
5 1
7
6 b7
567 5 b7
7
7
I b6
6 b7
5 b6
1 b6
6 7
456 4
I
7
5
b7
.-,.,-...
.. .-.-.. .. .. .,--" .--.. .-'" .-. .-'. .,-
FIVE-NOTE FORMULAS
b2
2 b3
3
I h2
2 5 b7
1 b2 b3
5 b7
1 b2
2 b3
4
I h2
2
1 b2 b3
5
7
I b2
2 b3 b5
I b2
2 b6 6
1 b2 b3 b6
6
1 b2
2 b3
5
I b2
2 b6 b7
1 b2 b3 b6 b7
1 b2
2 b3 b6
I b2
2 b6
I b2 b3 b6
1 b2
2 b3
6
I b2
2 6 b7
I b2 b3
6 b7
1 b2
2 b3 b7
I b2
2 6 7
1 b2 b3
6
7
I b2
2 b3
7
I b2
2 b7
b2 h3 b7
7
I b2
2
4
I b2 b3
3 4
b2
3
4 h5
1 b2
2 3 b5
b2 b3
3 b5
I b2
3
4
I b2
2
5
I b2 h3
5
b2
3
4 b6
I b2
2 3 b6
b2 b3
3 b6
h2
3
4
6
I b2
2 3 6
b2 b3
3 6
b2
3
4
h7
I b2
2 3 b7
b2 b3
3 b7
b2
3
4
7
~-~)
I b2
2 3 7
b2 b3
3 7
1 b2
3 h5
5
~,--")
-
.-::8 .-:.8 .~-
.-:a> •
:8)
•.-:a>
1
3
3
5
3
7
7
7
5
I b2
2 4 b5
I b2 b3
4 b5
b2
3 b5 b6
t:- _:8)
I b2
2 4 5
1 b2 b3
4
5
F~·f
b2
3 h5
I b2
2 4 b6
1
b2 b3
4 b6
b2
3 b5 b7
F--:tr
I b2
2 4
6
b2 b3
4 6
b2
3 b5
I b2
2 4 b7
b2 b3
4 b7
I b2
3
5 b6
I b2
2 4
7
1 b2 b3
4
7
1 b2
3
5
1 b2
2 b5
5
I b2 b3 b5
5
I b2
3 5 b7
I b2
2 b5 b6
I b2 b3 b5 b6
I b2
2 b5
1
F--~
F--' F-· F--~
f---- . . r
6
b2 b3 b5
I
b2
6
5
7
6
3 h6
I b2
3 b6 b7
7
1 b2
3 b6 3
t" (_1_.
I b2
2 b5 b7
1 b2 b3 b5 b7
6 b7
7
fT"
I b2
2 b5
1
(r-.
I b2
2 5 b6
1 b2 b3
5 b6
1 b2
fT·
I h2
2 5 6
b2 b3
5 6
1
b2 b3 b5
7
1 b2
7
7
3
6
6
I b6 b7
1
7
b2
7
6 b7
3 6 7
(f-~
u·
('}*,
10
Formulas
Formulas
11
.t .t .+ .- .-
.- .- .- .- .-
.--= .--=
.-. .--=
I
1 b2
3 b7
7
b2
5 6 b7
2 b3 b6
b2
4 b5
5
b2
5
6
7
2 b3 b6 b7
b2
4 b5 b6
b2
5 b7
7
2 b3 b6
4 b5
6
b2 b6
6 b7
2 b3
6 b7
b2
4 b5 b7
b2 b6
6 7
2 b3
6
7
b2
4 b5
b2 b6 b7
7
2 b3 b7
7
b2
4 5 b6
6 b7
7
2
3
4 b5
b2
4
6
2 b3
3
4
2
3
4
b2
4 5 b7
2 b3
3 b5
2
3
4 b6
b2
4
7
2 b3
3
5
2
3
4
b2
4 b6 6
2 b3
3 b6
2
3
4 b7
b2
4 b6 b7
2 b3
3
2
3
4
7
b2
4 b6
7
2 b3
3 b7
2 3 b5
5
b2
4 6 b7
2 b3
3
2 3 b5 b6
b2
4
6
7
2 b3
4 b5
2
b2
4 b7
7
2 b3
4
2 3 b5 b7
b2 b5
5 b6
2 b3
4 b6
2
3 b5
1 b2 b5
5 6
2 b3
4
6
2
3
5 b6
I b2 b5
5 b7
2 b3
4 b7
2
3
5
1 b2 b5
5 7
2 b3
4
7
2
3
5 b7
2 b3 b5
5
2
3
5
7
2 b3 b5 b6
2 3 b6
6
2 b3 b5
2 3 b6 b7
1 b2
5
5
1 b2 b5 b6
7
6
b2 b5 b6 b7 b2 b5 b6
12
7
b2
6
7
5
6
3 b5
6
7
5
6
6
7
6
b2 b5
6 b7
2 b3 b5 b7
2
3 b6
b2 b5
6 7
2 b3 b5
7
2
3
6 b7
3
7
b2 b5 b7
7
2 b3
5 b6
2
6
7
b2
5 b6
6
2 b3
5
6
2 3 b7
7
b2
5 b6 b7
2 b3
5 b7
2 4 b5
5
b2
5 b6
2 b3
5 7
2 4 b5 b6
Formulas
7
6
2 b6
6 b7
b3
4 b5
2 4 b5 b7
2 b6
6 7
b3
4
5 b6
2
.-a
.-a
.--=
a-· a-·
a--' a--'
.-. .-.
.--=
.--=
.-... ..
.....
.-_ ..
.-_ ....
a-·
.-_. .-~
.--~
.--
I
4 b5
7
7
2 b6 b7
7
b3
4
5
4
5 b6
2 6 b7
7
b3
4
5 b7
2
4
5
6
1 b3
3 4 b5
b3
4
5
7
2
4
5 b7
b3
3 4 5
b3
4 b6
6
3 4 b6
b3
4 b6 b7
3
6
b3
4 b6
4 6 b7
2
4 b5
2
6
245
7
b3
2 4 b6
6
1 b3
2 4 b6 b7
b3
3 4 b7
b3
2
4 b6
7
b3
3 4 7
1 b3
2
4
6 b7
b3
3 b5
2
4
6
7
b3
3 b5 b6
b3 b5
5 b6
2 4 b7
7
b3
3 b5
6
b3 b5
5 6
2 b5
5 b6
b3
3 b5 b7
b3 b5
5 b7
2 b5
5 6
b3
3 b5
2 b5
5 b7
b3
3 5 b6
b3 b5 b6
2 b5
5 7
b3
3 5 6
b3 b5 b6 b7
6
b3
3 5 b7
b3 b5 b6
2 b5 b6 b7
b3
3 5 7
b3 b5
6 b7
2 b5 b6
7
b3
3 b6
b3 b5
6 7
2 b5
6 b7
b3
3 b6 b7
b3 b5 b7
7
2 b5
6 7
b3
3 b6
7
b3
5 b6
6
2 b5 b6
4
5
7
6
b3
4
7
6
7
4 b7
7
1 b3 b5
5 7
6
7
2 b5 b7
7
b3
3 6 b7
b3
5 b6 b7
2 5 b6
6
b3
3
6
7
b3
5 b6
2 5 b6 b7
b3
3 b7
7
b3
5 6 b7
2
5 b6
7
b3
4 b5
5
b3
5
6
7
2
5
6 b7
b3
4 b5 b6
b3
5 b7
7
2
5
6
7
b3
4 b5
6
b3 b6
6 b7
2 5 b7
7
b3
4 b5 b7
b3 b6
6 7
7
Formulas
13
-t-t -'.
.'-,.
.-:=8)
I
1 b3 b6 b7 b3 I
I
7
1
3 b5
6 b7
4
3 b5
6
7
4 5 b(} 7
5 b6 b7
6 b7
7
3 4 b5
5
1
3 b5 b7
7
1
4
5
6 b7
3 4 b5 b6
1
3 5 b6
6
I
4
5
6
7
4 5 b7
7
3
4 b5
3
4 b5 b7
3 5 b6 b7
6
3
5 b6
7
1
4 b6
6 b7
1 b2
2 b3
4 b(}
1 b2
2 3 b5
7
I b2
2 b5
I b2
2 b3
4 ()
I b2
2 3 5 b6
I b2
2 b5 b6
I b2
2 b3
4 b7
1 b2
2
6
1 b2
2 b5 b6 b7
1 b2
2 b3
4 7
b2
2 3 5 b7
I b2
2 b5 b6
5
I b2
2 3 5 7
I b2
2 b5
6 b7
1 b2
2 b3 b5 b6
I b2
2
3 b6
6
I b2
2 h5
6 7
I b2
2 b3 b5
6
I b2
2 3 b6 b7
I b2
2 b5 b7
7
1 b2
2 b3 b5 b7
1 b2
2 3 b6
7
1 b2
2 5 b6
6
1 b2
2 b3 b5
7
I b2
2 3 6 b7
1 b2
2 5 b6 b7
I b2
2 b3
5 b6
I b2
2 3 6 7
I b2
2 5 b6
1 b2
2 b3
5 6
I b2
2 3 b7
7
I b2
2 5 6 b7
I b2
2 b3
5 b7
1 b2
2 4 b5
5
1 b2
2
6
7
1 b2
2 b3
5 7
I b2
2 4 b5 b6
I b2
2 5 b7
7
1 b2
2 b3 b6
6
I b2
2 4 b5
6
1 b2
2 b6
6 b7
1 b2
2 b3 b6 b7
1 b2
2 4 b5 b7
I b2
2 b6
6 7
1 b2
2 b3 b6
7
I b2
2
4 b5
7
1 b2
2 b6 b7
7
1 b2
2 b3
6 b7
b2
2 4 5 b6
1 b2
2 6 b7
7
.-!:i)
1 b2
2 b3
6 7
I b2
2 4 5 6
I b2 b3
3 4 h5
I b2
2 b3 b7
7
I b2
2 4 5 b7
b2 b3
3 4 5
.-l:i)
I b2
2 3 4 b5
1 b2
2
5
7
I b2 b3
3 4 b6
.--:it;
I b2
2 3 4 5
I b2
2 4 b6
6
1 b2 b3
3 4 6
2 4 b6 b7
I b2 b3
3 4 b7
2 4 b6
7
1 b2 b3
3 4 7
-ill' -ill' -ill'
e1 I
e~.
I
4 b5
3
7
1345b6
1
3
5
6 b7
I
4b6 67
3
5
6
1
4 b6 b7
7
7
e-c e-: I
I
3
4
5
I
3
4
5 b7
4
6 b7
7
6
3 b6
6 b7
1 b5
5 b6
3 b6
6 7
1 b5
5 b6 b7
3 4 b6
6
I
3 b6 b7
7
b5
4 b6 b7
I
3 6 b7
7
1 b5
5 6 b7
I
4 b5
5 b6
1 b5
5 6 7
4 b5
5
3
4
7
6 b7
()
b5
5 b6
5 b7
7
7
346
7
4 b5
5 b7
1 b5 b6
6 b7
3 4 b7
7
4 b5
5 7
1 b5 b6
6
7
1 b5 b6 b7
7
3 b5
5 b6
3 b5
5 6
4 b5 b6 b7
3 b5
5 b7
4 b5 b6
3 b5
5 7
4 b5
1
4 b5 b6
6
b5
6 b7
7
7
I
5 b6
6 b7
6 b7
1
5b6 67
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.-~=-) I
.-~)
.-,~)
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4
5
7
7
7
5 b6 b7
7
._~J
I b2
2 3 4 b6
b2
3 b5 b6 b7
4 b5 b7
7
5 () b7
7
.,-;:iI)
1 b2
2 3 4 6
I b2
3 b5 b6
4
5 b6
6
1 b2
2 3 4 b7
b2
2 4 6 b7
b2 b3
3 b5
1 b2
2 3 4
7
b2
2
3 b5 b6
1 b2
2 3 b5
5
1 b2 1 b2
2
1 b2
6
7
1 4 b5
1 b6
6 b7
7
SIX-NOIEFORMlIAS
14
._l~,
2 b3 b5
5
6
6
3 b5 b6
I
1
7
13 4b6
I
7
345
3
I
3 5 b7
6
b2
3
5 7
I b2
2 b3
3 4
1 b2
2 b3
3 b6
1 b2
2 b3
3 7
I b2
2 b3
3 b5
I b2
2 b3
3 6
1 b2
2 b3
4 b5
1 b2
2 b3
3 5
1 b2
2 b3
3 b7
I b2
2 b3
4 5
Formuills
•.. .-~
e a- e at'
.
5
6
7
b2 b3
I b2
2 4 b7
7
I b2 b3
3 b5
2 3 b5 b6
I b2
2 b5
5 b6
I b2 b3
3 b5 b7
3 b5
()
1 b2
2 b5
5 6
I b2 b3
3 b5
2 3 b5 b7
1 b2
2 b5
5 b7
I b2 b3
3 5 b6
4
()
7
Forllluills
15
3 5 6
b2 b3
3 5 b7
1 b2 b3 b5 b6
b2 b3
3 5 7
1 b2 b3 b5
6 b7
1 b2 b3
3 b6 6
1 b2 b3 b5
6
7
I
1 b2 b3
3 b6 b7
I
b2 h3 b5 h7 b2 b3
5 b6
1
1
b2 b3 3 b6 7
7
b2 3 b5
5 b6
b2 3 b5
5
b2
3 b5
5 b7
7
I b2
3 b5
5
6
I
b2 3 b5 b6 6
b2 b3
5 b6 b7
I
b2
I
b2 3 b5 b6 7
7
I
6
7
1 b2 b3
3 6 b7
b2 b3
3 6 7
I
b2 b3
5 b6 7
b2 b3
3 b7 7
I
b2 b3
5 6 b7
b2
3 b5
6 b7
b2 b3
4
I
b2 b3
5 6 7
I b2
3 b5
6 7
4 b5 b6
1 b2 b3
5 b7 7
1 b2
3 h5 b7
b2 b3
4 b5
1 b2 b3 h6
6 b7
I b2
3 5 b6 6
b2 b3
4
b2 b3 b6 6 7
I b2
3
b2 b3 b6 h7
I
1
1
1 b2 b3
1
b5
5 6
b5 b7
1
1 b2 b3
4 b5
I b2 h3
4
5 b6
b2 b3
4
5 6
1
h2 b3
4
b2 b3
4
b2 b3
4
1
I b2 b3
16
b2 3 4 b7
b2 b3 b5 b6 b7
1 b2 b3
7
7
7
5 b6 b7
b2 3 5 b6 7
1 b2
3
5
6 b7
I b2
3
5
6
7
4 b5 b6
b2 3 5 b7
7
3
4 b5
b2
h2
3
4 b5 b7
I
4 b6 b7
I b2
3
4 b5
I b2
b6 7
1 b2
3 4 5 b6
1
I b2
b2 b3
6 b7 7
b2
3
4
5 b7
I b2
3
5
7
I b2
b6 6
b5
5
6
7
1
b2 b3
4
I
b2 h3
4
6
b7
I b2
3
I b2 b3
4
6
7
1 b2
3 4
5 b7
b2 b3
4
b7
7
I b2
3
5
4
4
5
6
b2 b3 b5
5 b6
1 b2
3 4 b6 6
I
b2 b3 b5
5 6
b2
3 4 b6 b7
h2 b3 b5
5 b7
1 b2
b2 b3 b5
5 7
I b2 b3 b5 b6 6
I
3 b6 6 b7
b2 3 b6 6 7 3 b6 b7
7
b2 3 6 b7
7
4 b5
5 b6
b2 4 b5
5 6
b2 4 b5
5 b7
b2 4 b5
5 7
b2 4 b5 b6 6
7
1 b2
4 b5 b6 b7
I
b2 3 4 6 b7
1 b2
4 b5 b6
1
b2 3 4 6 7
1 b2 4 b5
3
4 b6
I
7
I
Forlllillas
3 b5 b6 b7
7
6 b7
.-.
a-·
a-::a a-::a
I b2
4 b5
6
7
2 b3
3 4 b6
1 2 b3
I b2
4 b5 b7
7
2 b3
3
4
6
1
2 b3
4 b6
I b2
4
5 b6
6
2 b3
3
4 b7
1
2 b3
4
6 b7
1 b2
4
5 b6 b7
2 b3
3 4 7
1
2 b3
4
6
7
1 b2
4
5 b6
2 b3
3 b5
I
2 b3
4 b7
7
1 b2
4
5
6 b7
2 b3
3 b5 b6
1 b2
4
5
6
7
2 b3
3 b5
1 b2
4
5 b7
7
2 b3
b2
4
a-· a a-
.-.
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.-= a-
.~=-
1
b2 4 b6 b7
I
1 b2
._*J
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1
a-itt)
6
b7
4
6 b7
7
b2 b5
5 b6 6
I b2 b5
5 b6 b7
1 b2 b5
5 b6
I b2 b5
5 6 b7
1 b2 b5
5
1 b2 h5
5 b7 7
1
b2 b5 b6
1 b2 b5 b6
6
6
7
7
6 7 7
.. .
I b2 b5
7
a- aa-· a-
.-
1
6 b7
1
I
1
5
2 b3 b5
5 b6
2 b3 b5
5
3 b5 b7
2 b3 b5
5 b7
2 b3
3 b5
2 b3 b5
5
7
2 b3
3 5 b6
2 b3 b5 b6
6
2 b3
3 5 6
2 b3 b5 h6 b7
2 b3
3 5 b7
1
2 b3 b5 b6 7
2 b3
3 5 7
I
2 b3 b5
6 b7
2 b3
3 b6 6
1
2 b3 b5
6 7
2 b3
3 b6 b7
2 b3
3 h6
2 b3
3
6
I
7
6
2 b3 b5 b7
7 6
1
2 b3
5 b6
6 b7
1
2 b3
5 b6 b7
2 b3
3 6 7
1
2 b3
5 b6 7
2 b3
3 b7
7
2 b3
5
6 b7
I
2 b3
4 b5
5
I
2 b3
5
6
1
2 b3
4 b5 b6
1
2 b3
5 b7 7
2 b3
4 b5
6
2 b3 b6 6 b7 2 b3 b6 6 7
1
I
b2 5 b6 6 b7
I
2 b3
4 b5 b7
I
b2
5 b6 6 7
I
2 b3
4 b5
I
b2
5 b6 b7 7
I
2 b3
7
7
1
2 b3 b6 b7 7
4
5 b6
I
2 b3
6 b7
7 5
6 b7
7
2 b3
4
5
6
2
3
4 b5
b2 b6 6 b7
7
2 b3
4
5 b7
2
3
4 b5 b6
3
4 b5
1 b2 1
7
7
b7
I b2 b5 b6 b7
& &
1
7
& ___J
._1tIJ
I
b2 4 b6 6 7
a-· a-ltI'> a- a·)
a 18) a J ·)
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b6
7
I
4 b6 b7
5
I
2 b3
3 4 b5
I
2 b3
4
5
7
I
2
6
I
2 b3
3 4 5
1
2 b3
4 b6
6
I
2 3 4 b5 b7
Formulas
17
.-~.)~
2
3
4 b5
123 4
2 b5 b6 b7
7 7
3
4
5
6
2 4 b5
5 b6
2 b5
2
3
4
5 b7
2 4 b5
5 6
2
5 b6
6 b7
2
345
7
2
4 b5
5 b7
2
5b6
6
2
3
4 b6
6
2
4 b5
5 7
2
5 b6 b7 7
2 3 4 b6 b7
2
4 b5 b6
2
5 6 b7 7
I
I
2 4 b5 b6 b7
4
6 b7
I
2
4 b5 b6
4
6
7
2
4 b5
6 b7
2 3 4 b7
7
2 4 b5
6 7
3
2
3
2 3 b5
5 b6
2 3 b5
5 6
2 3 b5
5 b7
2 3 b5
5 7
I
I
I
6
7
I 2
7
2 b6
7
6 b7 7
4 b6
6 b7
b3
3 b5 6 7
1 b3
4 b6
6
7
1
3
.-~
1
b3
3 b5 b7
b3 4 b6 b7
7
1
3 4
5 b6
1
b3
3 5 b6 6
I b3
3
5
.-.~
1 b3
3 5 b6 b7
I b3 b5
5 b6 6
.-:a'
1 b3
3 5 b6
I
b3 b5
•
I
.-~
.-"1f
.-...
;;.8'
6
1
4
5 b6
b3
2
4
5 b6 b7
I b3
2
4
5 b6
1
b3
3
4
b5
7
3 4 5 b6 3
4
5 6
I b3
3 4 5 b7
2 3 b5 b6 b7
2
5
I b3
3 4
2 3 b5 b6 7
2 4 5 b7 7
1
b3
3
4
2 3 b5
6 b7
2 4 b6 6 b7
1
b3
3
4 b6
6
7
2
2 3 b5 b7
7
2 4 b6 b7
5b6 6
2 4 6 b7
5 7 b6 6
3 5 b7
1 b3 b5
5 6 7
3
4 b6 b7
7
5 b7
3 4 6 b7 7
b3
1
b3 b5
b3
3 b6 6 7
I
b3 b5 b6 6 b7
3 b5
5 b6
b3
3 b6 b7
7
1
b3 b5 b6 6 7
3 b5
5 b6 b7
1
b3
3 6 b7
7
I
b3 b5 b6 b7 7
3 b5
5 b6 7
I
b3
4
b5
5 b6
1
b3 b5
3 b5
5 6 b7
I b3
4 b5
5 6
I b3
5 b6
6 b7
3 b5
5 6 7
1 b3
4 b5
5 b7
1 b3
5 b6
6
7
3 b5
5 b7
I b3
4 b5
5 7
I b3
5 b6 b7
7
3 b5 b6 6 b7
.~)
1 b3
4 b5 b6
1 b3
5
7
3 b5 b6
~)
1 b3
4 b5 b6 b7
-~)
a-}:e) .-~)
&-;;e) &-;4) .,~)
&-~) a-~)
1 b3 I
3 b6
4 b5 b6
7
1 b3
3 4
a~i
1 b3
4 b5
2b5
5b6 6
1 b3
3 4 b7
I b3
4 b5
7
2 b5
5 b6 b7
1
b3
3 b5
5 b6
a-~ al.ilJ ,
1 b3
4 b5 b7
I b3
4
1 b3
4
3
5 b6
2
3
5
6 b7
2 b5
5 b6 7
1 b3
3 b5
5 6
2
3
5
6
7
2 b5
5 6 b7
1 b3
3 b5
5 b7
a7t'
2 3 5 b7
7
2 b5
5 6 7
1
b3
3 b5
5 7
5 b7
....
7
b3
3 b5 b6 6
2
3 b6
6 7
2 b5 b6 6 b7
b3
3 b5 b6 b7
7
a:~
a-;e ~
a. a· -...- &-.
b3
6
1 b3 b6
6 b7
6 b7
7
6 b7
6 b7
2
Formulas
7
1 b3
2 b5
7
6
Il.~)
6 b7
3 4 5 b7 4 b6
3 4 6 b7
3 b6
5 b6 b7
3
1 b3
2
7
5 6 b7
7
7
6
1 b3 b5
•..
2 3 5 b6 b7
134 5
6 b7
3 5 6 7
3 4 b6 7 6 7
4
7
3 4 b6
I b3
4b6 6 7
b7
7
4 5 b6 b7
5 b6 7
3 4 b5 b7
•.
6 b7
5b6 6
1 b3 b5
3 4 b5
.-~)
7
4
34
7
3 5 6 b7
1 b3
6
7
7
b3
1
A··
18
1
.-tal
5 6 b7
23
1 b3
3 b5
3 4 b5 b6
3 4 b5
2 4
3 b5
6 b7
b3
1 b3
2
7
4
1 b3
I b3
6
1 b3
3 b5 b6
5 b7
I 3 4 b5 b7
7
b3
I
.-:::8)
b3
7
4
.'-t!
.-l~
5
I
2 4 b5 b7
7
6 b7
2 3 b5 b6 6
2
I
I
2
4 b6
I
2 b5 b6 6 7
2 3 b6 b7 7 2 3 6 b7 7
3
I
I
5 b6
2
I
7
7
6 b7 7
6
7
6
7
3 b5 b6 b7
7 7
4 b5
5 b6
3 b5 6 b7
6 b7
3 4 b5
5 6
3
6 7
3
4 b5
5 b7
3 5b6 6 7
3
4 b5
5
7
3 5 b6 b7 7
5 b6 6
3
4 b5 b6
6
3
5 b6 b7
3
4
3
4 b5 b6
7
7
4 5 b6 7
3
b5 b6 b7
I b3
4
5 6 b7
3 4 b5
1 b3
4
5
3
6
7
4 b5
7
5 b6
6 b7
5
6 b7
7
3 b6
6 b7
7
4 b5
5 b6
6
6 b7
4
b5
5 b6 b7
6
4
b5
5 b6 7
7
Formulas
19
1
4 b5
5 6 b7
4 b5
5 6 7
4 b5
5 b7
1
7
1
4 b5
7
I b5
5 b6
6 b7
4 5 b6
6 b7
b5
5 b6
6 7
5 b6
6 7
I b5
5 b6 b7
7
5 6 b7
7
4
6 b7
4 b5 b6 6 b7
4 5 b6 b7
7
I b5
4 b5 b6
4 5 6 b7
7
I b5 b6
6 b7
7
4 b6
7
1 5 b6
6 b7
7
6 7
4 b5 b6 b7
7
6 b7
SEVEN-NOTE FORMULAS I b2
2 b3
3 4 b5
1 b2
2 b3
4 b5
1 b2
2 b3
3 4 5
I b2
2 b3
4 b5 b6
I b2
2 b3
3 4 b6
1 b2
2 b3
4 b5
1 b2
2 b3
3 4 6
1 b2
2 b3
4 b5 b7
1 b2
2 b3
3
4 b7
1 b2
2 b3
4 b5
b2 2 b3
3 4 7
1 b2
2 b3
4
5 b6
b2
2 b3
3 b5
5
I b2
2 b3
4
5
I b2
2 b3
3 b5 b6
I b2
2 b3
4
5 b7
b2 2 b3
3 b5
6
I b2
2 b3
4
5 7
b2
2 b3
3 b5 b7
I b2
2 b3
4 b6
I b2
2 b3
3 b5
7
b2
2 b3
4 b6 b7
1 b2
2 b3
3 5 b6
b2
2 b3
4 b6
b2
2 b3
3 5 6
I b2
2 b3
4
6 b7
I b2
2 b3
3 5 b7
1 b2
2 b3
4
6 7
I b2
2 b3
3
4 b7
b2 2 b3
20
5
6
7
6
6
7
5
7
1 b2
2 b3
3 b6
6
I b2
2 b3 b5
5 b6
7
1 b2
2 b3
3 b6 b7
I b2
2 b3 b5
5 6
b2
2 b3
3 b6
7
1 b2
2 b3 b5
5 b7
1 b2
2 b3
3 6 b7
b2
2 b3 b5
5 7
b2
2 b3
3 6 7
b2
2 b3 b5 b6
b2
2 b3
3 b7
Formulas
7
1 b2
6
2 b3 b5 b6 b7
.-. -i- .. .- .. .-. ... .-.-... .-- .-- .-. .- a-. .-. .~
.--8
&-:a>
•• .--=-) .-:tI •• a--:iI>
a-.
.-. •• •••• a-. a-. a--:tIJ
a-· ~-.
......-_::& -_. rt-_-::A
~- :it .-~) l
7
I b2
2 3 b5
5 b6
2 b3 b5
6 b7
1 b2
2 3 b5
5 6
b2 2 b3 b5
6 7
1 b2
2 3 b5
5 b7 5 7
I b2
2 b3 b5 b6
I b2
1 b2
2 b3 b5 b7
7
1 b2
2 3 b5
1 b2
2 b3
5 b6
6
I b2
2 3 b5 b6 6
I b2
2 b3
5 b6 b7
1
b2
2 3 b5 b6 b7
1 b2
2 b3
5 b6
7
1 b2
2 3 b5 b6
I b2
2 b3
5
6 b7
1 b2
2 3 b5
6 b7
1 b2
2 b3
5 6 7
1 b2
2 3 b5
6 7
I b2
2 b3
5 b7
7
1 b2
2 3 b5 b7
7
6 b7
1 b2
2 3 5 b6
6
6 7
1 b2
2 3 5 b6 b7
1
b2 2 b3 b6
7
I b2
2 b3 b6
1 b2
2 b3 b6 b7
7
I b2
2 3 5 b6
1 b2
2 b3
6 b7
7
1 b2
2
I b2
2 3 4 b5
5
1 b2
2 3 5 6 7
I b2
2 3 4 b5 b6
1
I b2
2 3 4 b5
6
1 b2
2 3 b6 6 b7
1 b2
2
3
4 b5 b7
1 b2
2 3 b6
I b2
2
3 4 b5
I b2
2
3
4
5 b6
1 b2
2
3
4
5
6
b2
2 4 b5
5 b6
b2
2
3
4
5 b7
b2
2 4 b5
5 6
1 b2
2
3
4
5
7
I b2
2 4 b5
5 b7
b2 2 3 4 b6 6
1 b2
2
b2
2 3 4 b6 b7
I b2
2 4 b5 b6 6
b2
2
7
1 b2
2
b2 2 3 4 6 b7
1 b2
2 4 b5 b6
3
4 b6
7
b2
3
5
7
6 b7
2 3 5 b7
7
6 7
b2
2 3 b6 b7
7
I b2
2 3 6 b7
7
1
4 b5
5
7
4 b5 b6 b7
7
1 b2
2 3 4 6 7
b2 2 4 b5
6 b7
1 b2
2 3 4 b7
b2
6 7
7
2 4 b5
Formulas
.._l..
b2
2 4 b5 b7
7
1 b2 b3
1 b2
2 4 5 b6
6
b2 b3
I b2
2 4 5 b6 b7
I b2 b3
3 4 5 b6
2 4 5 b6
1 b2 b3
3 4 5 6
I
I
7
3 4 b5
7
1 b2
2 4
5 6 b7
I
b2 b3
3 4 5 b7
1 b2
2 4
5 6 7
I
b2 b3
3 4 5 7
I b2
2 4 5 b7
7
b2 b3
3 4 b6 6
I b2
2 4 b6 6 b7
b2 b3
3 4 b6 b7
1 b2
2 4 b6 6 7
I b2 b3
3
4 b6
7
b2
2 4 b6 b7
7
b2 b3
3 4 6 b7
1 b2
2 4 6 b7
7
b2 b3
3
1 b2
2 b5
5 b6 6
I
b2 b3
3 4 b7 7
I
b2
2 b5
5 b6 b7
1 b2 b3
3 b5
5 b6
1
b2
2 b5
5 b6
7
I
b2 b3
3 b5
5 6
I
b2
2 b5
5 6 b7
1
b2 b3
3 b5
5 b7
1
b2
2 b5
5 6 7
1
b2 b3
3 b5
5 7
1
b2
2 b5
5 b7
7
I
b2 b3
3 b5 b6 6
I
b2
2 b5 b6 6 b7
I
b2 b3
3 b5 b6 b7
I
b2
2 b5 b6 6 7
I
b2 b3
3 b5 b6 7
I
22
b2
3 4 b5 b7
4
6
7
1 b2
2 b5 b6 b7
7
b2 b3
3 b5 6 b7
1 b2
2 b5
7
b2 b3
3 b5
b2 b3
3 b5 b7
6 b7
6 7
I
b2
2 5 b6 6 b7
1
1
b2
2 5 b6
I b2 b3
3 5 b6 6
I
b2
2 5 b6 b7
7
I
b2 b3
3 5 b6 b7
1
b2
2 5 6 b7
7
l
b2 b3
3 5 b6
I
b2
2 b6
6 b7
7
1 b2 b3
3 5 6 b7
5
1 b2 b3
3
6 7
1 b2 bJ
J
4 b5
I b2 bJ
J
4 b5 b6
I
I b2 b3
J
4 b5
I b2 b3
Formulas
6
b2 b3
5
7
7
6
7
3 5 b7
7
3 b6 6 b7
a-r;, .,.-.. .,-:..8' ~-~'
1 b2 b3
3 b6 6 7
b2 b3 b5 b6 6 b7 b2 b3 b5 b6 6 7
I
b2 b3
3 b6 b7
7
1
b2 b3
3 6 b7
7
1 b2 b3 b5 b6 b7
b2 b3 b5
6 b7
7 7
1 b2 b3
4 b5
5 b6
1
1 b2 b3
4 b5
5 6
1 b2 b3
I b2 b3
4 b5
5 b7
I
b2 b3
5 b6 6 7
I b2 b3
4 b5
5 7
I
b2 b3
5 b6 b7
7
I b2 b3
4 b5 b6
1
b2 b3
5 6 b7
7
1 b2 b3
4 b5 b6 b7
1 b2 b3 b6
,,-~,
1 b2 b3
4 b5 b6
7
1 b2
3 4 b5
5 b6
. ..
I b2 b3
4 b5
6 b7
1 b2
3 4 b5
5 6
b2
3 4 b5
5 b7
b2
3 4 b5
5 7
~-::a\
..-=-' .,.-:.:8'\ I;-:a'\
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1
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6
11r--~) 1 b2 b3 4 b5 6 7 1 b2 b3 4 b5 b7 7 -~) I b2 b3 4 5 b6 6 ~-:a)
IfE --.:8) I'r --;:8) &.:e) ~)
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.. _-:11) &.-=-J
&.-= &--= &-= &-.-= &-.....
e-.." e--.1
..--= __ -.1 ..--=
..-.
I
1 b2
3
5 b6
6 b7
6 b7
4 b5 b6
7
6
I b2 b3
4
5 b6 b7
1 b2
3 4 b5 b6 b7
I b2 b3
4
5 b6
1 b2
3 4 b5 b6
I b2 b3
4
5 6 b7
1 b2
3 4 b5
I b2 b3
4
5 6 7
1 b2
3
1 b2 b3
4
5 b7
I b2 b3
4 b6
I b2 b3
4 b6
I b2 b3
4 b6 b7
1 b2 b3
4
4 b5
7
6 b7 6
7
b2
3 4 b5 b7 7
6 b7
1 b2
3 4 5 b6 6
6 7
I b2
3 4
5 b6 b7
1 b2
3
4
5 b6
6 b7 7
1 b2
3
4
5
6 b7
5 b6 6
1 b2
3
4
5
6
7
b2 b3 b5
5 b6 b7
I b2
3 4 5 b7
7
b2 b3 b5
5 b6 7
1 b2
3 4 b6
b2 b3 b5
5 6 b7
1 b2
3
b2 b3 b5
5 6 7
1
b2 b3 b5
5 b7
I b2
1 b2 b3 b5 I
7
7
7
7
4 b6
6 b7 6
b2 3 4 b6 b7 3
4
7
6 b7
7
7
7
Formulas
23
&-~ I b2
3 b5
5 b6
1 b2
3 b5
5 b6 b7
1 b2 b5
5 b6
6 b7
I b2
3 b5
5 b6
7
I b2 b5
5 b6
6 7
1 b2
3 b5
5 6 b7
1 b2 b5
5 b6 b7
7
I b2
3 b5
5 6 7
I b2 b5
5 6 b7
7
1 b2
3 b5
5 b7
[ b2 b5 b6 6 b7
7
1 b2
3 b5 b6 6 b7
1 b2
6 b7
7
1 b2
3 b5 b6
I
2 b3
3 4 b5
5
1 b2
3 b5 b6 b7
7
I
2 b3
3 4 b5 b6
I b2
3 b5
7
2 b3
3 4 b5
2 b3
3 4 b5 b7
b2
24
6
7
6 7
6 b7
3 5 b6 6 b7
1 b2
I
4 b6
5 b6
6 b7
7
6
&- ... &- . . &- . . &--. . &--. . &-:8 &-:8 &-:8
&-. &-. &-.
6
7
2 b3
3
1 b2
3 5 b6 b7
7
2 b3
3 4 5 b6
1 b2
3 5 6 b7
7
2 b3
3
4
5
6
~-1II
I b2
3 b6 6 b7
7
2 b3
3
4
5 b7
&-}8
b2
4 b5
5 b6
6
2 b3
3 4 5 7
1 b2
4 b5
5 b6 b7
I
2 b3
3 4 b6
1 b2
4 b5
5 b6
7
I
2 b3
3 4 b6 b7
1 b2
4 b5
5 6 b7
I
2 b3
3 4 b6
1 b2
4 b5
5 6 7
2 b3
3 4 6 b7
I b2
4 b5
5 b7
7
2 b3
3 4 6 7
1 b2
4 b5 b6
6 b7
1 2 b3
1 b2
4 b5 b6
6 7
I
2 b3
3 b5
5 b6
I b2
4 b5 b6 b7
7
I
2 b3
3 b5
5 6
b2
4 b5 6 b7
7
2 b3
3 b5
5 b7
b2 4 5 b6 6 b7
2 b3
3 b5
5 7
2 b3
3 b5 b6
3 4 b7
6
7
7
1 b2
4
I b2
4 5 b6 b7
7
2 b3
3 b5 b6 b7
I b2
4 5 6 b7
7
2 b3
3 b5 b6
Formulas
5 b6 6 7
I
7
1
6
7
6 b7
2 b3
4 b6
2 b3
3 b5
6
7
2 b3
4 b6 6 7
2 b3
3 b5 b7
7
2 b3
4 b6 b7
7
2 b3
3 5 b6
6
2 b3
4
6 b7
7
2 b3
3 5 b6 b7
2 b3 b5
5 b6
6
2 b3
3
5 b6
2 b3 b5
5 b6 b7
2 b3
3 5 6 b7
2 b3 b5
5 b6
2 b3
3 5 6 7
2 b3 b5
5 6 b7
2 b3
3 5 b7
2 b3
3 b6
2 b3
3 b6 6 7
2 b3
3 b6 b7
7
1
2 b3
3 6 b7
7
I
2 b3
4 b5
5 b6
2 b3
4 b5
5 6
2 b3
4 b5
5 b7
2 b3
4 b5
5 7
1
I
I
&-.
3
4 b5
3 b5
&-.
1 b2
5 b6
2 b3
~-.
&-5
&,-.
&L
a;}tI &i_ W L
a; a;
I
7 I
6 b7
7
7
1
2 b3 b5
5 6 7
6 b7
I
2 b3 b5
5 b7
7
2 b3 b5 b6 6 b7
1
1
2 b3 b5 b6
6 7
2 b3 b5 b6 b7
7
2 b3 b5
7
6 b7
2 b3
5 b6
6 b7
I
2 b3
5 b6
6
I
2 b3
5 b6 b7
7
6
1
2
b3
5 6 b7
7
2 b3
4 b5 b6 b7
I
2 b3 b6 6 b7
7
2 b3
4 b5 b6 7
2 3 4 b5
5 b6
2 b3
4 b5
6 b7
2 3 4 b5
5 6
1 2 b3
4 b5
6 7
2 3
b5
5 b7
2 3 4 b5
5 7
I
1 2 b3 1
I
&; &; &;
4 b5 b6
2 b3
4 b5 b7
2 b3
4
5 b6
2 b3
4
5 b6 b7
2 b3
4 5 b6 7
1
7 6
I
2
3
4
4 b5 b6
7
6
2 3 4 b5 b6 b7 2 3 4 b5 b6
7
&-;
I
2 b3
4
5
6 b7
1
2
3
4 b5
6 b7
&; &; &; &; &;
I
2 b3
4
5
6
7
I
2
3
4 b5
6 7
4 5 b7
7
I 2 b3
2 3 4 b5 b7
7
Formulas
25
2 3 4 5 b6 6
2
4 b5
5
6
7
2
4 b5
5 b7
7
2
3
4
5 b6 b7
2
3
4
5 b6
2
3
4
5
7
I
2
4 bS b6
6 b7
6 b7
I
2
4 bS b6
6
7
:. J:
.. ..
I b3
3
1
I b3
4 b5 b6
6 b7
-~
1 b3
3 4 5 6 b7
I b3
4 b5 b6
6
7
-~
1 b3
3
4 b5 b6 b7
7
&-''''
I b3
3 4
7
26
345
6
7
5 b7
2
4 bS b6 b7
7
I b3
3 4 b6
7
2
4 b5
7
2
3
4
2
3
4 b6
6 b7
2
4
5 b6
6 b7
23
4b6
6
7
2
4
5 b6
6
7
2
3 4 b6 b7
7
2
4
5 b6 b7
7
2
3 4 6 b7
7
2
4
5
6 b7
7
2
3 bS
5 b6
6
2
4 b6
6 b7
7
2
3 b5
5 b6 b7
I
2 b5
5 b6 6 b7
2
3 bS
5 b6
I
2 b5
5 b6
2
3 bS
5 6 b7
2 b5
5 b6 b7
7
2
3 bS
5
6
7
2 b5
5 6 b7
7
2
3 b5
5 b7
7
2 b5 b6
6 b7
7
2
3 bS b6
5 b6
6 b7
7
7
6 b7
2
3 bS b6
2
3 b5 b6 b7
2
3 bS
2
3
23
I
I
6 7
2
6 b7
I b3
3
6 7
b3
3 4 b5
5 b6
7
I b3
3 4 b5
5 6
7
b3
3 4 b5
5 b7
5 b6
6 b7
1 b3
3 4 b5
5
7
Sb6
6
7
1 b3
3 4 b5 b6
6
2
3 5 b6 b7
7
b3
3 4 b5 b6 b7
2
3 5 6 b7
7
1 b3
3 4 bS b6 7
2
3 b6 6 b7
7
I b3
3 4 b5
2
4 b5
5 b6
6
I b3
3
2
4 b5
5 b6 b7
1
2
4 bS
5 b6
7
I b3
3 4
2
4 bS
5
6 b7
I b3
3 4 5 b6 b7
For11lulas
6 b7
b3
4 b5
6 b7 6
7
3 4 b5 b7
7
5 b6 6
5 h6
6
7
b3
5 b7
7
I b3
4 b5
6 b7
I b3
4
5 b6 6 b7
6
7
I b3
4
5 b6
6
7
I b3
3 4 b6 b7
7
1
b3
4
5 b6 b7
7
I b3
3 4 6 b7
7
b3
4 5 6 b7
7
-~
I b3
3 b5
5 b6 6
I b3
4 b6
7
&-. &-=8
I b3
3 b5
5 b6 b7
b3 b5
5 b6 6 b7
b3
3 b5
5 b6
7
b3 b5
5 b6
b3
3 b5
5
6 b7
b3 b5
5 b6 b7
7
I b3
3 b5
5 6 7
I b3 b5
5 6 b7
7
I b3
3 b5
5 b7
I b3 b5 b6
6 b7
7
I b3
6 b7
7
'
2
4
;
&-'" &--=8 &-'" &-=
...
... -. •• ...... -. -:a .. --:a
a.-.
• .,:8 • .:8 a...:8
a. . :8
..... •• a·· a,·
a-. a· a-·· a.'. a'· a-··
4
5
4 b6
7
b3
3 b5 b6
6 b7
b3
3 b5 b6
6 7
5 b6
6 b7
6 b7
6 7
3 4 b5
5 b6 6
3 4 b5
5 b6 b7
1 b3
3 b5 b6 b7
7
I b3
3 b5
7
I
3
b3
3 5 b6 6 b7
I
3 4 b5
5 6 b7
b3
3
6
7
I
3 4 b5
5 6 7
b3
3 5 b6 b7
7
3 4 b5
5 b7
b3
3 5 6 b7
7
3 4 b5 b6
I b3
3 b6 6 b7
7
I b3
4 b5
5 b6
6
I b3
4 b5
5 b6 b7
I b3
4 b5
5 b6
I b3
4 b5
5 6 b7
I b3
4 b5
5 6 7
4 b5
5 b7
.-.
.- ..
I b3
6 b7
5 b6
I
I
7
7
3
4 b5
5 b6
4 b5 b6
7
7
6 b7 6
7
3 4 b5 b6 b7
7
3 4 b5
7
6 b7
3 4 5 b6 6 b7 3 I
4
5 b6
6
7
5 b6 b7
7
3 4 5 6 b7
7
3 4
Formulas
27
3 4 b6
6 b7
7
I
4 b5
5 b6
6 b7
3 b5
5 b6
6 b7
4 b5
5 b6
6
7
I
3 b5
5 b6
6
7
4 b5
5 b6 b7
7
I
3 b5
5 b6 b7
7
I
4 b5
5 6 b7
7
3 b5
5 6 b7
7
I
4 b5 b6
6 b7
7
4 5 b6
6 b7
7
6 b7
7
I
3 b5 b6
6 b7
7
3 5 b6
6 b7
7
1
b5
5 b6
EIGHT·NOTE FORMULAS I b2
2 b3
3 4 b5
5
b2
2 b3
3 b5 b6 b7
I b2
2 b3
3 4 b5 b6
I b2
2 b3
3 b5 b6
b2
2 b3
3 4 b5
6
I b2
2 b3
3 b5
6 b7
I b2
2 b3
3 4 b5 b7
I b2
2 b3
3 b5
6 7
7
b2
2 b3
3 b5 b7
7
6
b2 2 b3
28
3 4 b5
7
I b2
2 b3
3 4 5 b6
I b2
2 b3
3 5 b6
1 b2
2 b3
3
6
I b2
2 b3
3 5 b6 b7
I b2
2 b3
3 4 5 b7
I b2
2 b3
3 5 b6
1 b2
2 b3
3
5
7
b2
2 b3
3 5 6 b7
I b2
2 b3
3 4 b6
6
I b2
2 b3
3 5 6 7
b2
2 b3
3 4 b6 b7
I b2
2 b3
3 5 b7
I b2
2 b3
3 4 b6
7
I b2
2 b3
3 b6
6 b7
b2
2 b3
3 4 6 b7
b2
2 b3
3 b6
6 7
I b2
2 b3
3
6
7
I b2
2 b3
3 b6 b7
7
b2
2 b3
3 4 b7
7
b2
2 b3
3 6 b7
7
4
4
4
5
7
7
.-.. ..- .- .-. .-.-.-...... .-.
.. .-
.-.. .-.. .--. .,.--. .,--. .-'-. .~
.,,:11 .,-:11 17,-::8 17--::8
17-· 17· 17"·
17·
3 b5
5 b6
I b2
2 b3
4 b5
5 b6
17'·
b2 2 b3
3 b5
5 6
b2
2 b3
4 b5
5 6
IT--"
IT'·
2 b3
3 b5
5 b7
I b2
2 b3
4 b5
5 b7
I b2
2 b3
3 b5
5 7
b2
2 b3
4 b5
5 7
I b2
2 b3
3 b5 b6
I b2
2 b3
4 b5 b6
6
6
4 b5 b6 b7
I b2
2 b3 b6
I b2
2 b3
4 b5 b6
7
I b2
2 3 4 b5
I b2
2 b3
4 b5
6 b7
b2
I b2
2 b3
4 b5
6 7
I b2
2 3 4 b5
5 b7
I b2
2 b3
4 b5 b7
7
I b2
2 3 4 b5
5 7
I b2
2 b3
4
5 b6
6
I
I b2
2 b3
4
5 b6 b7
1 b2
2 3 4 b5 b6 b7
I b2
2 b3
4
5 b6
7
I b2
2
I b2
2 b3
4
5 6 b7
I b2
2 3 4 b5
6 b7
I b2
2 b3
4
5
6
7
b2
2 3 4 b5
6 7
b2
2 b3
4
5 b7
7
I b2
2 3 4 b5 b7
7
I b2
2 b3
4 b6
6 b7
b2
2 3 4 5 b6
6
I b2
2 b3
4 b6
6 7
~--.
I
b2
2
3
6 b7
4 b5
5 b6
5
2 3 4 b5 b6
3
7
4 b5 b6
6
6
7
b2 2 3 4 5 b6 b7
5 b6
b3
4
b6 b7
7
b2
2
I b2
2 b3
4
6 b7
7
b2
2 3 4 5 6 b7
I b2
2 b3 b5
5 b6 6
I b2
2 b3 b5
5 b6 b7
I b2
2 b3 b5
5 b6
b2
b2
2
3
4
7
b2 2 3 4 5 6 7
b2
2 3 4 5 b7
7
b2
2 3 4 b6 6 b7
2 b3 b5
5 6 b7
I b2
2 3 4 b6
I b2
2 b3 b5
5 6 7
1 b2
2 3 4 b6 b7
7
I b2
2 b3 b5
5 b7
7
b2
2 3 4 6 b7
7
I b2
2 b3 b5 b6
6 b7
b2
2 3 b5
5 b6
6
I b2
2 b3 b5 b6
6 7
I b2
2 3 b5
5 b6 b7
b2
I
7
6 7
2 b3 b5 b6 b7
7
b2
2 3 b5
5 b6
I b2
2 b3 b5
7
I b2
2 3 b5
5 6 b7
I b2
2 b3
6 b7
I b2
2 3 b5
5 6 7
5 b6 6 7
I b2
2
b2 2 b3
.. ..
.-.
~r_"
6 b7
5 b6
3 b5
5 b7
7
7
I b2
2 b3
5 b6 b7
7
b2
2 3 b5 b6
6 b7
I b2
2 b3
5 6 b7
7
I b2
2 3 b5 b6
6 7
~-~-
FOrl/llllns
2 b3
.-:tI I
b2 2 b3
I b2
I b2
I
29
1 b2
2 3 b5 b6 b7
7
b2 b3
3 4 b5
5 6
b2
2 3 b5
7
1 b2 b3
3 4 b5
5 b7
b2
2 3 5 b6
6 b7
b2 b3
3 4 b5
5 7
b2
2 3 5 b6
6 7
1 b2 b3
b2
2 3 5 b6 b7
7
b2 b3
3 4 b5 b6 b7
b2
2 3 5 6 b7
7
b2 b3
3 4 b5 b6
1 b2
2 3 b6
6 b7
7
b2 b3
3 4 b5
6 b7
1 b2
2 4 b5
5 b6
6
b2 b3
3 4 b5
6 7
b2
2 4 b5
5 b6 b7
1 b2 b3
3 4 b5 b7
7
b2
2 4 b5
5 b6
7
b2 b3
3 4 5 b6
6
b2
2 4 b5
5 6 b7
b2 b3
3 4 5 b6 b7
1 b2
2 4 b5
5 6 7
b2 b3
3 4 5 b6
1 b2
2 4 b5
5 b7
7
b2 b3
3 4 5 6 b7
1 b2
2 4 b5 b6
6 b7
b2 b3
3 4 5 6 7
1 b2
2 4 b5 b6
6 7
b2 b3
3 4 5 b7
6 b7
3 4 b5 b6
6
7
7
7
b2
2 4 b5 b6 b7
7
b2 b3
3 4 b6
6 b7
b2
2 4 b5
7
b2 b3
3 4 b6
6 7
b2
2 4 5 b6
6 b7
b2 b3
3 4 b6 b7
7
b2
2 4 5 b6
6 7
b2 b3
3 4 6 b7
7
b2
2 4 5 b6 b7
7
b2 b3
3 b5
5 b6
6
b2
2 4 5 6 b7
7
b2 b3
3 b5
5 b6 b7
b2
2 4 b6
7
b2 b3
3 b5
5 b6
b2
2 b5
5 b6
6 b7
b2 b3
3 b5
5 6 b7
b2
2 b5
5 b6
6 7
b2 b3
3 b5
5 6 7
b2
2 b5
5 b6 b7
7
b2 b3
3 b5
5 b7
b2
2 b5
5 6 b7
7
b2 b3
3 b5 b6
b2
2 b5 b6
6 b7
7
b2 b3
3 b5 b6
b2
2 5 b6
6 b7
7
b2 b3
3 b5 b6 b7
7
5 b6
b2 b3
3 b5
7
b2 b3
6 b7
6 b7
3 4 b5
-1. -t-t -t·
-t-t .f .-
b2 b3
3 5 b6
6 b7
b2
3 4 b5
5 6 b7
b2 b3
3 5 b6
6 7
b2
3 4 b5
5 6 7
b2 b3
3 5 b6 b7
7
b2
3 4 b5
5 b7
b2 b3
3 5 6 b7
7
b2
3 4 b5 b6
6 b7
b2 b3
3 b6
6 b7
7
b2
3 4 b5 b6
6 7
b2 b3
4 b5
5 b6
6
b2
3 4 b5 b6 b7
7
b2 b3
4 b5
5 b6 b7
b2
3 4 b5
7
b2 b3
4 b5
5 b6
7
b2
3 4 5 b6
6 b7
b2 b3
4 b5
5 6 b7
b2
3 4 5 b6
6 7
b2 b3
4 b5
5 6 7
b2
3 4 5 b6 b7
7
a-a
b2 b3
4 b5
5 b7
7
b2
3 4 5 6 b7
7
.-=8 .-=8
b2 b3
4 b5 b6
6 b7
b2
3 4 b6
7
.--.
a:8
b2 b3
4 b5 b6
6 7
b2
3 b5
5 b6
6 b7
b2 b3
4 b5 b6 b7
7
b2
3 b5
5 b6
6 7
b2 b3
4 b5
7
b2
3 b5
5 b6 b7
7
.-:8
b2 b3
4
5 b6
6 b7
b2
3 b5
5 6 b7
7
b2 b3
4 5 b6
6 7
b2
3 b5 b6
6 b7
7
&--.
b2 b3
4 5 b6 b7
7
b2
3 5 b6
6 b7
7
&--:8
b2 b3
4 5 6 b7
7
b2
4 b5
5 b6
6 b7
b2 b3
4 b6
7
b2
4 b5
5 b6
6 7
a-a
.-.
a~a
&~-:a
.
&-~
&--:8
Fom/Illas
6 b7
6 b7
b2 b3 b5
5 b6
6 b7
b2
4 b5
5 b6 b7
7
&--:8 &---
b2 b3 b5
5 b6
6 7
b2
4 b5
5 6 b7
7
b2 b3 b5
5 b6 b7
7
b2
4 b5 b6
6 b7
7
b2 b3 b5
5 6 b7
7
b2
4 5 b6
6 b7
7
&-~
b2 b3 b5 b6
6 b7
7
b2 b5
6 b7
7
6 b7
&
b2 b3
5 b6
6 b7
7
2 b3
3 4 b5
5 b6
6 7
&-
b2
3 4 b5
5 b6
6
2 b3
3 4 b5
5 6
~--
b2
3 4 b5
5 b6 b7
2 b3
3 4 b5
5 b7
&-:.
b2
3 4 b5
5 b6
2 b3
3 4 b5
5 7
6 b7
7
7
-~
.,....
.;-
~-:.
30
6 b7
6 b7
7
.-
7
5 b6
Forlllulas
31
tt-:" 3 4 b5 b6
6
2 b3
3 5 6 b7
7
2 b3
3 4 b5 b6 b7
2 b3
3 b6
6 b7
7
2 b3
3 4 b5 b6
I
2 b3
4 b5
5 b6 6
I
2 b3
4 b5
5 b6 b7
2 b3
4 b5
5 b6
2 b3
4 b5
5 6 b7
2 b3
4 b5
5 6 7 5 b7
7
2 b3
3 4 b5
6 b7
2 b3
3 4 b5
6 7
2 b3
3 4 b5 b7
7
I
2 b3
3
4
5 b6
6
I
2 b3
3
4
5 b6 b7
2 b3
4 b5
2 b3
3
4
5 b6
7
2 b3
4 b5 b6
6 b7
2 b3
3
4
5
6 b7
2 b3
4 b5 b6
6 7
2 b3
3 4
5 6
7
2 b3
4 b5 b6 b7
7
2 b3
3 4 5 b7
7
2 b3
4 b5
7
2 b3
3 4 b6
6 b7
2 b3
4 5 b6
6 b7
2 b3
3 4 b6
6 7
2 b3
4
5 b6
6 7
I
2 b3
3 4 b6 b7
7
2 b3
4 5 b6 b7
7
I
2 b3
3 4 6 b7
7
2 b3
4
5 6 b7
7
2 b3
3 b5
5 b6
6
2 b3
4 b6
2 b3
3 b5
5 b6 b7
2 b3 b5
5 b6 6 b7
2 b3
3 b5
5 b6
7
2 b3 b5
5 b6
2 b3
3 b5
5 6 b7
2 b3 b5
5 b6 b7
7
2 b3
3 b5
5 6 7
2 b3 b5
5 6 b7
7
2 b3
3 b5
5 b7
2 b3 b5 b6 6 b7
7
2 b3
3 b5 b6
6 b7
2 b3
5 b6
6 b7
7
I
2 b3
3 b5 b6
6 7
2 3 4 b5
5 b6
6
I
2 b3
3 b5 b6 b7
7
2
3 4 b5
5 b6 b7
2 b3
3 b5
7
2
3 4 b5
5 b6
2 b3
3 5 b6 6 b7
2
3 4 b5
5 6 b7
2 b3
3 5 b6
2 3 4 b5
5 6 7
2 b3
3 5 b6 b7
2 3 4 b5
5 b7 7
I
I
I
I
I
I
I
32
2 b3
FOrll II tins
6 b7
7
6 7 7
I
6 b7
6 b7
7
7
7
6 7
7
&- . .
a-. a ..
,,- ... &-. ,,-. &- . .
ti.-" ti.-" &--
.-.. .-. .-.. .-. &-. a-:8
.-:8 .,-:tI,
11.-:8 .-:11 .-:tI
.- .-- .-. .,. .--r- .-. .-. .-,. .--:tI
a--
ai a'. .~
..
I
2
3 4 b5 b6 6 b7
b3
3 4 b5 b6
6 7
I
2
3 4 b5 b6 6 7
b3
3 4 b5 b6 b7
7
I
2
3 4 b5 b6 b7
7
2
3
4 b5
2
3
4
I
2
3
4
I
2
I
7
I b3
3 4 b5
7
I b3
3 4 5 b6 6 b7
5 b6
6 b7
I b3
3 4
5 b6
5 b6
6
7
b3
3 4
5 b6 b7
7
3 4
5 b6 b7
7
b3
3 4 5 6 b7
7
2
3 4
5 6 b7
7
b3
3 4 b6
7
I
2
3 4 b6
7
b3
3 b5
5 b6
I
2
3 b5
5 b6
6 b7
I b3
3 b5
5 b6 6
7
I
2
3 h5
5 b6
6 7
I b3
3 b5
5 b6 b7
7
I
2
3 b5
5 b6 b7
7
I b3
3 b5
5 6 b7
7
I
2
3 b5
5 6 b7
7
I b3
3 b5 b6
I
2
3 b5 b6 6 b7
7
b3
I
2
3 5 b6
7
I b3
4 b5
5 b6
6 b7
2
4 h5
5 b6
6 b7
b3
4 b5
5 b6
6 7
2
4 b5
5 b6
6 7
b3
4 b5
5 b6 b7
7
2
4 b5
5 b6 h7
7
I b3
4 b5
5 6 b7
7
I
2
4 h5
5 6 b7
7
I b3
4 b5 b6
I
2
4 b5 b6
6 b7
7
b3
2
4
5 b6
6 h7
7
b3 b5
2 b5
5 b6
6 b7
7
3 4 b5
5 b6
6 b7
I b3
3 4 b5
5 b6
6
3 4 b5
5 b6
6 7
I b3
3 4 b5
5 b6 b7
3 4 b5
5 b6 b7
7
b3
3 4 b5
5 b6
3 4 b5
5 6 b7
7
b3
3 4 b5
5 6 b7
3 4 b5 b6
6 b7
7
I b3
3 4 b5
5 6 7
3
4
5 b6
6 b7
7
I b3
3 4 b5
5 b7
7
3 b5
5 b6
6 b7
7
I b3
3
6 b7
4 b5
5 b6 6 b7
7
I
I
6 b7
6 b7
6 b7
4 b5 b6
7
6 b7
6 7
6 b7
6 b7
6 b7
7
3 5 b6 6 b7
7
6 b7
7
4 5 b6 6 b7
7
5 b6 6 b7
7
Formulas
33
NINE-NOTE FORMULAS
34
tal-. ~-. til.-.a
1 b2
2 3 4 b5
5 b6
6
I b2 b3
3 4 b5
5 b6 b7
I b2
2 3 4 b5
5 b6 b7
b2 b3
3 4 b5
5 b6
1 b2
2 3 4 b5
5 b6
7
1 b2 b3
3 4 b5
5 6 b7
b2
2 3 4 b5
5 6 b7
b2 b3
3 4 b5
5 6 7
1 b2
2 3 4 b5
5 6 7
I b2 b3
3 4 b5
5 b7
5 b7
7
I b2 b3
3 4 b5 b6
6 b7
6 b7
1 b2 b3
3 4 b5 b6
6 7
7
I b2
2 b3
3 4 b5
5 b6
I b2
2 b3
3 b5 b6 b7
7
I b2
2 b3
3 4 b5
5 6
I b2
2 b3
3 b5
7
I b2
2 b3
3 4 b5
5 b7
I b2
2 b3
3 5 b6
6 b7
1 b2
2 b3
3 4 b5
5 7
I b2
2 b3
3 5 b6
6 7
I b2
2 b3
3 4 b5 b6
1 b2
2 b3
3 5 b6 b7
7
£-:8
1
1 b2
2 b3
3 4 b5 b6 b7
1
b2
2 b3
3 5 6 b7
7
1 b2
2 3 4 b5 b6
I b2
2 b3
3 4 b5 b6
7
1 b2
2 b3
3 b6 6 b7
7
~-.
1 b2
2
6
7
I b2 b3
3 4 b5 b6 b7
7
1 b2
2 b3
3 4 b5
6 b7
I b2
2 b3
4 b5
5 b6 6
1 b2
2 3 4 b5 b6 b7
7
1 b2 b3
3 4 b5
7
I b2
2 b3
3 4 b5
6 7
1 b2
2 b3
4 b5
5 b6 b7
t:.-'.
b2
2 3 4 b5
7
I b2 b3
3 4 5 b6
6 b7
1 b2
2 b3
3 4 b5 b7
7
1 b2
2 b3
4 b5
5 b6
b2
2 3 4 5 b6 6 b7
I b2 b3
3 4
6 7
I b2
2 b3
3 4
6
1
b2
2 b3
4
b5
5 6 b7
t:.-:8 t.-:8
1 b2
2 3 4
5 b6
1 b2 b3
3 4 5 b6 b7
7
I b2
2 b3
3 4 5 b6 b7
I b2
2 b3
4 b5
5 6 7
t.-".
I b2
2 3 4
5 b6 b7
7
b2 b3
3 4
5 6 b7
7
1 b2
2 b3
3 4 5 b6
b2
2 b3
4 b5
5 b7
t.-:tI
I b2
2 3 4 5 6 b7
7
b2 b3
3 4 b6 6 b7
7
1 b2
2 3 4 b6 6 b7
7
1 b2 b3
3 b5
5 b6
6 b7 6 7
5 b6
6
6 b7
7
..
te-.a ~-.a
~-
(1;-.
t:.-.a k-.a
1 b2 2 b3
3 4 b6 b7
7
1 b2
2 b3
4
1 b2 2 b3
3 4 6 b7
7
1 b2
2 b3
4 5 b6 b7
7
. t..
t.-.
..•
.•
1 b2
2 b3
3 b5
5 b6 6
1 b2
2 b3
4 5 6 b7
b2
2 b3
3 b5
5 b6 b7
b2
2 b3
4 b6 6 b7
b2
2 b3
3 b5
5 b6
7
1 b2
2 b3 b5
5 b6 6 b7
b2
2 b3
3 b5
5 6 b7
b2
2 b3 b5
5 b6 6 7
1 b2 2 b3
3 b5
5 6 7
1 b2
2 b3 b5
5 b6 b7
7
1 b2
3 b5
5 b7
7
I b2
2 b3 b5
5 6 b7
7
7
7
I b2
2 b3
3 4
5 6 b7
b2
2 b3
4 b5 b6 6 b7
I b2
2 b3
3 4
5 6 7
b2
2 b3
4 b5 b6
I b2
2 b3
3 4
5 b7
7
I b2
2 b3
4 b5 b6 b7
7
I b2
2 b3
3 4 b6 6 b7
I b2
2 b3
4 b5
7
I b2
2 b3
3 4 b6
1 b2
2 b3
4
5 b6
6 b7
5 b6
6 7
2 b3
6 7
6 7
6 b7
4 b5 b6
6 b7
6 7
1
6 b7
5 b6
b2
2 3 b5
5 b6 6 b7
1 b2 b3
3 b5
5 b6
1 b2
2 3 b5
5 b6
1 b2 b3
3 b5
5 b6 b7
7
1 b2
2 3 b5
5 b6 b7
7
b2 b3
3 b5
5 6 b7
7
b2
2 3 b5
5 6 b7
7
b2 b3
3 b5 b6
6 b7
7
5 b6
6 b7
7
1
1
6 7
2 3 b5 b6
6 b7
7
1 b2 b3
1 b2
2 3 5 b6 6 b7
7
b2 b3
4 b5
5 b6
7
~:-.
..,!II
1 b2
2 4 b5
5 b6 6 b7
b2 b3
4 b5
5 b6 6 7
7
4k:..• l:.'.
I b2
2 4 b5
5 b6 6 7
I b2 b3
4 b5
5 b6 b7
7
I b2
2 4 b5
5 b6 b7
7
1 b2 b3
4 b5
5 6 b7
7
1 b2
2 4 b5
5 6 b7
7
1 b2 b3
4 b5 b6
6 b7
7
1 b2
2 4 b5 b6
6 b7
7
b2 b3
4 5 b6
6 b7
7
I b2
2 4 5 b6
6 b7
7
b2 b3 b5
6 b7
7
5 b6 6 b7
7
b2
3 4 b5
5 b6
6 b7
6
I b2
3 4 b5
5 b6
6 7
6 b7
I b2
2 b3 b5 b6 6 b7
7
1 b2
3 b5 b6 6 7
1 b2
2 b3
7
Formulas
~
3
I b2
3 b5 b6
5 b6 6 b7
4t:.-= 4t:..ltI
1
b2 2 3 4 b5
7
~'
1 b2 2 b3 2 b3
~'
1
1:.,_
1:.-.
l:.~_
I:.r1tl
I b2 2 b5
a..~.
I b2 b3
a..,~1.tt
a;-I &.r
3 4 b5
5 b6
3
5 b6
6 b7
Formulas
35
---;1 • b2
3
4 b5
5 b6 b7
7
2 b3
3
b2
3
4 b5
5
6 b7
7
2 b3
4 b5
5 b6
6 b7
b2
3
4 b5 b6
6 b7
7
2 b3
4 b5
5 b6
6
7
b2
3
4
5 b6
6 b7
7
2 b3
4 b5
5 b6 b7
7
b2
3 b5
5 b6
6 b7
7
2 b3
4 b5
5
6 b7
7
b2
4 b5
5 b6
6 b7
7
2 b3
4 b5 b6
6 b7
7
4 b5
5 b6
6
2 b3
4
6 b7
7
2 b3
3
5 b6
5 b6
6 b7
7
-t -t- -t-
.'- .r .} .1' .-
.-
.- ..-- -
.T- .--
.-.
.--.
.--:8t
..--
--.
.--=
.-. •
t~
_t.a
I
36
2 b3
3
4 b5
5 b6 b7
2 b3 b5
2 b3
3
4 b5
5 b6
7
2
3
4 b5
5 b6
6 b7
2 b3
3
4 b5
5
6 b7
2
3
4 b5
5 b6
6
7
2 b3
3
4 b5
5
6
7
2
3
4 b5
5 b6 b7
7
2 b3
3
4 b5
5 b7
7
2
3
4 b5
5
6 b7
7
2 b3
3
4 b5 b6
6 b7
2
3
4 b5 b6
6 b7
7
2 b3
3
4 b5 b6
6
7
2
3
4
5 b6
6 b7
7
2 b3
3
4 b5 b6 b7
7
2
3 b5
5 b6
6 b7
7
2 b3
3
4 b5
7
2
4 b5
5 b6
6 b7
7
6 b7
5 b6
6 b7
7
2 b3
3
4
5 b6
6 b7
b3
3
4 b5
5 b6
6 b7
2 b3
3
4
5 b6
6
7
b3
3
4 b5
5 b6
6
7
2 b3
3
4
5 b6 b7
7
b3
3
4 b5
5 b6 b7
7
2 b3
3
4
5
6 b7
7
b3
3
4 b5
5
6 b7
7
2 b3
3
4 b6
6 b7
7
b3
3
4 b5 b6
6 b7
7
2 b3
3 b5
5 b6
6 b7
b3
3
4
5 b6
6 b7
7
2 b3
3 b5
5 b6
6
7
b3
3 b5
5 b6
6 b7
7
2 b3
3 b5
5 b6 b7
7
b3
4 b5
5 b6
6 b7
7
2 b3
3 b5
5
6 b7
7
3
4 b5
5 b6
6 b7
7
2 b3
3 b5 b6
6 b7
7
Formulas
lB'J-N01E FORMUlAS
.-~
.~.
.---
.J..
.---
.--
.-~-
1 b2
2 b3
3
4 b5
5 b6
6
1 b2
2
3
4 b5
5 b6
6 b7
1 b2
2 b3
3
4 b5
5 b6 b7
1 b2
2
3
4 b5
5 b6
6
7
1 b2
2 b3
3
4 b5
5 b6
7
1 b2
2
3
4 b5
5 b6 b7
7
1 b2
2 b3
3
4 b5
5
6 b7
1 b2
2
3
4 b5
5
6 b7
7
1 b2
2 b3
3
4 b5
5
6
7
1 b2
2
3
4 b5 b6
6 b7
7
1 b2
2 b3
3
4 b5
5 b7
7
1 b2
2
3
4
5 b6
6 b7
7
1 b2
2 b3
3
4 b5 b6
6 b7
1 b2
2
3 b5
5 b6
6 b7
7
1 b2
2 b3
3
4 b5 b6
6
7
1 b2
2
4 b5
5 b6
6 b7
7
1 b2
2 b3
3
4 b5 b6 b7
7
1 b2 b3
3
4 b5
5 b6
6 b7
1 b2
2 b3
3
4 b5
7
1 b2 b3
3
4 b5
5 b6
6
1 b2
2 b3
3
4
5 b6
6 b7
1 b2 b3
3
4 b5
5 b6 b7
7
1 b2
2 b3
3
4
5 b6
6
7
1 b2 b3
3
4 b5
5
6 b7
7
1 b2
2 b3
3
4
5 b6 b7
7
1 b2 b3
3
4 b5 b6
6 b7
7
1 b2
2 b3
3
4
5
6 b7
7
1 b2 b3
3
4
5 b6
6 b7
7
1 b2
2 b3
3
4 b6
6 b7
7
1 b2 b3
3 b5
5 b6
6 b7
7
1 b2 2 b3
I
7
3 b5
5 b6
6 b7
1 b2 b3
4 b5
5 b6
6 b7
7
4 b5
5 b6
6 b7
7
1 b2
2 b3
3 b5
5 b6
6
7
1 b2
1 b2
2 b3
3 b5
5 b6 b7
7
1
2 b3
3
4 b5
5 b6
6 b7
1 b2
2 b3
3 b5
5
6 b7
7
1
2 b3
3
4 b5
5 b6
6
7
1 b2
2 b3
3 b5 b6
6 b7
7
1
2 b3
3
4 b5
5 b6 b7
7
1 b2
2 b3
3
6 b7
7
1
2 b3
3
4 b5
5
6 b7
7
1 b2
2 b3
4 b5
5 b6
6 b7
1
2 b3
3
4 b5 b6
6 b7
7
1 b2
2 b3
4 b5
5 b6
6
7
1
2 b3
3
4
5 b6
6 b7
7
1 b2
2 b3
4 b5
5 b6 b7
7
1
2 b3
3 b5
5 b6
6 b7
7
1 b2
2 b3
4 b5
5
6 b7
7
1
2 b3
4 b5
5 b6
6 b7
7
1 b2
2 b3
4 b5 b6
6 b7
7
1
2
3
4 b5
5 b6
6 b7
7
1 b2
2 b3
4
5 b6
6 b7
7
1 b3
3
4 b5
5 b6
6 b7
7
1 b2
2 b3 b5
5 b6
6 b7
7
.--.;_.
.-
.-1..
6 b7
5 b6
3
Forlt/ulas
37
.·-..... .-. .-.-... .-..-.-.. .-. .-. .-= .--. .--=-.
ELEVEN·NOTE FORMULAS
b2
2 b3
3 4 b5
5 b6 6 b7
1 b2
2 b3
3 4 b5
5 b6
1 b2
2 b3
3 4 b5
5 b6 b7
7
1 b2
2 b3
3 4 b5
5 6 b7
7
1 b2
2 b3
3 4 b5 116 6 b7
7
1 b2
2 b3
3 4 5 b6
6 b7
7
1 b2
2 b3
3 b5
5 b6
6 b7
7
I b2
2 b3
4 b5
5 b6
6 b7
7
1 b2
2 3 4 b5
5 b6 6 b7
7
6 7
b2 b3
3 4 b5
5 b6 6 b7
7
1 2 b3
3 4 b5
5 b6 6 b7
7
.~.
•
.--=
TWELVE-NOTE FORMULA
1 b2
2 b3
3 4 b5
5 b6
6 b7
7
.---= .--:11
.---.
• . -jIf
•.•..-JII--.--. .-JII .. .... • . -jIf
-
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-if
• . -if .--if
38
Formulas
. - -iI .--iI
formulas
39
AN IMPROVISER'S OS FAQ, PART 1
Each sequence of numbers describes a unique tonality.
"7onality" ? Yes - a consistent sonic combination of one or more specific tones. A context for music to exist within; a stage setting that relies on actors, in this case melody and harmony, to flesh it out. All two thousand, forty-eight tonalities available within the chromatic are listed here, from the most commonly used triads and blues scales to never used, nameless, faceless combinations.
.1. .1. .1.
.1. .1. .1. .1.
The body of formulas includes all known scales, but
much further than
All known and unknown chords are included in the formulas, too. But the words "scale" and "chord" are mostly irrelevant here; formulas do the iob of both. The of formula unifies melody and h"'TIT>{m A
a-. a-:--.
It's iust semantics. amfwau .. ."what's ill a name", for the artist if it answers more
Huh? Formulas are pure, untouched. They have no connotation, no melodic or har monic obligation. They rely on no particular groove, make no ethnic reference, have no stylistic allegiance. They have no history. They are abstractions, until they are touched by the musician. In human hands they become tonal filters, through which musical energy can be channeled and subsequently shaped and shaded, melodically and harmonically.
one note at a time is
.1__ A formula played two or more notes at a time is harmony. a~-.
Redefining basic elements can provide a cleaner slate to work from. The word "scale" implies an orderly sequence of notes learned by rote; a known quantity with little potential for reinvention. "Formula" suggests a blend, a concoction; something open-ended and without a tendency toward any particular order - though they are usually written step-wise from the root for convenience.
A name or a word can become a tions than it asks.
entirety; a realization that is constantly rejuvenated by the improviser, as the techniques of utilizing formulas have little to do with the memorization of pat terns and the habitual reiteration of those patterns.
• 1. What about chords?
a].
Why?
FAQ ParI 1
.l•
• 1.
then.
They're called "formulas".
40
• 1. Then what about scales?
• 1. that: it's tonally all-inclusive. It maps out the chromatic world, realizing it in its
What is this
so these are
.: .
Depending on which formula is used, this can create the sound of any known scale or chord, as well as a vast number of other melodic and harmonic possi bilities, arcing out in subtle gradations from familiar to unfamiliar, beautiful to ugly, consonant to dissonant and back again. An unrestricted exploration of tonality.
.-
.--
.-
a-
•• . .
•• ... .-.
.-
.--. .--.
.- ..
Uh ...yeah, right. Listen why are the formulas listed m.; 11llmbers, instead of Ilotes? And how come there are flats, but no sharps or naturals? A formula is equally useful in all keys; the numbers allow its unique sound to be more easily transposed. Each numeral describes a chromatic loca called a function, within the octave of a given key. The natural numbers " 7 to the note locations of the mula 1234567. The other five and natural signs from formulas standardizes their notation and makes them easier to read. Once spelled out in a key, their acciden tals are listed conventionally.
So for example,Jormula 1b35b7 in Eb would be Eb, Gb, Bb, Db? And in B, it's B, D, F#,A?
Yes. If one can spell a major scale in any key, the other functions can be refer enced from those 7 notes. Take 1b35b7 in Eb, for example:
~-.
a--:a
.-_:a
Eb major: Eb, F, G, Ab, Bb,
D
l-AQ Pari 1
41
.-~
.-~ AN IMPROVISER'S OS FAQ, PART 2 .-r:.
1 is Eb, the root and the key
b3 is Gb, half step below of Eb major
5 is Bb, like 5 of Eb major
b7 is Db, half step below 7(D) of Eb major
Ultimately, the ability to spell any chromatic function in any key allows the uickest transposition of formulas.
How do I learn to do that? Sounds hard. And boring. Key signatures are useful because they signify which accidentals are needed to make a major scale in any key. They offer a shortcut to the process of figuring it out by calculating the interval sequence of 2 whole steps, 1 half step and 3 whole steps that creates the major scale formula 1234567. Memorizing a dozen or so key signatures is a process made less boring by understanding the creative relevance of the information. In this case, it will im mediately be put to use in the playing of formulas as music. Once the key signatures are memorized, practice spelling chromatic functions in twelve keys, on and away from the instrument. Gradually, the realization that b3 in F# is A, 6 in G is 4 in Eb is Ab, and so on, will become instantaneous.
.-~ .-~ .-~ .-~ .,-~
.,-;a
..
convenience", but how come they Why can't
It can, when music is being made with it. At that point, it's up to the musician which tones played when, or if they get plaved at all.
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fi-:tf)
G-:tf) I; .:tIl
Without a "1", there is no "3" or any other function. Any tonality that exists within the chromatic scale can be described with a formula that begins with "1".
17-1>
.,.:tIl 6~
G--.J fj-.
Good. Wondering is what got us this far. Keep it up.
G- iti E--~ ~--~
E- 1Ai 42
IAQ Pari 1
Is this a guitar book? The exercises are guitar-specific, but the ideology isn't. With a little creative thinking, most of the content can be applied to any instrument.
Is all this theory really necessary?
No. One look at Prince, Sly Stone, the Beatles, Jimi Hendrix - all of whom have played and composed without extensive knowledge of theory, it is said - makes it plain that theory is not a necessary component of musical excellence. Alternatively, the music of Igor Stravinsky, Duke Ellington, John Coltrane and Bela Bartok establishes that theoretical knowledge doesn't preclude greatness, either. Both lists could continue indefinitely.
The root has a unique role among the functions; it determines the key of the formula and is the center of the formula's tonality. The distinctive sound of that tonality is defined by the functional relationships between the root and the other tones.
I wonder...
Chiefly, a way to practice that can significantly inform one's playing.
.,.
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You said before that formulas start with the root all contain "1"? None of the other functions seem start with "3", with no 'T?
Are formulas a way to play, or a way to
E-~
5- 1iV
There is no obligation on the part of a musician to investigate music theory. But a certain kind of curiosity will make it almost inevitable. At its most relevant, theory is the head introducing new sounds to the ear in a process that expands both. Necessary? No. Inspiring? Potentially.
All ri!{ht...so what do you do with these formulas, Above all, they're a study of tonality. They describe an immense palette of available tonal color with subtle gradation and wide range. Each formula pres ents an opportunity for the head to offer a unique tonal shade to the ear, via the available melody and harmony within that formula's tonal boundaries, with the heart and soul on hand to organize those available notes as music. A given formula's limitations whether from the number of its functions or the intervals it contains - are relative, because quality in music is not determined by which notes or intervals are used, but by how musicians use them. Con sequently all formulas, regardless of size or content, are of potential musical value. But for the ear to recognize and accept the tonality of a formula, that formula
must be expressed clearly, much as a word must be spoken clearly to be under
stood. Formulas are distinct entities; each function is exact and indispensable
to the formula's identity, so the musician must be able to precisely articulate it
FAQ Pari 2
43
on the instrument. Otherwise the tonal message of the formula will be com promised.
Does that sound bad? Not necessarily; it might sound great - but it won't be the intended formula any more. And though accidents can sometimes be high points in music, the basis of this concept of formulas is that the control of tonality on the instru ment is desirable, and the practice of that control is a valuable discipline. In other words: in terms of this book, a good improviser would be able to nail any tonality, in any key, melodically and harmonically, limitlessly, anywhere on the instrument, and sound good at it.
1'd like that. Hmo do I start? Like this.
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.
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For piano and wind players that's not such a big deal, but for guitarists it can be. The layout of the guitar neck is confusing and many great players know only a small fraction of its note names. That doesn't prevent them from playing well, but to use formulas, note knowledge of the neck is essential.
th th
Why?
.,_
Patterns are shortcuts that rely on mechanical memory rather than the underly ing theory to access specific sounds. They indicate where to put the hands to get a desired sound and as such they work fine .
.,-re .,...,
., e,
Because in contrast to how chords and scales are usually taught and learned, formulas are not played as patterns.
., .•
The problem with relying on patterns is that one can't play significantly more than what one knows.lf the goal is free access to all 2048 available formulas in all keys, anywhere on the instrument, then - considering the limitations of human memory and the amount of time we have left on the planet - it may be necessary to look for alternative means of access.
4F.,
tI7
•••
.I= •.~ 5·
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Additionally, as far as this book is concerned, playing patterns generally falls under the category of compositional playing; a category that includes any preconceived music such as scale or modal patterns, arpeggio patterns, chord forms, licks, habitual hand moves, tunes, pieces, songs or riffs - in other words, anything previously learned . Improvisational playing, by contrast, includes any spontaneously created music.
.~
Hm. So, by these definitions, most of the solos I hear are they compositiollal or impro visational?
5··~
Some are largely compositional, many are largely compositional ideas that are organized in improvisational order, some are largely improvisational.
.. I:e ~.(t'J
FAQ Pari 2
If one can spell any formula in any key - in other words, if one can determine the names of specific desired notes then any formula can be played on the in strument. A couple of things will make that possible; one is knowing the names of the notes on the instrument itself.
..,-1=8
.
44
AN IMPROVISER'S OS FAQ, PART 3
G-·~ G"·~ £" :iii i..... i
t;-:. -::wI
Generally speaking, the faster soloing gets the less improvisational it tends to
FAQ p(frt 3
45
..-.
-. .-.
a- •
be - at least today, in 2004. That will ues to evolve.
if the art of improvisation contin
There is no ultimate value judgement to be made in comparing compositional and improvisational playing. Both are equally valid and encompass all music that exists. But it's important for the musician to make the distinction between them, in order to better decide how to practice and develop both disciplines; each with its own laws, dynamics and, maybe, This book focuses on developing improvisational skills within the context of defined tonalities. Accordingly, it moves away from the more compositionally related pattern as a means of tonal access. So: "note name" is one essential method of finding a formula that doesn't rely on pattern. If one can spell a given formula in a given key and knows the names of the notes on the instrument, the formula can be played.
Any advice on/zow to learn the notes on the
One way is by reading music. Start as simply as is appropriate, 20 minutes a - every day, or it won't work - and progress to reading the beautiful stuff. Almost anything written by J5. Bach, for example. Not much rhythm, but lots of note names. As with the practicing of most things, it's important to begin at a level of speed and complexity that is comfortable, no matter how modest, and to build from there. Incremental improvement beats discouragement any day. Another idea: memorize the names of the open strings / twelfth fret, then the fifth fret / seventeenth fret, then the tenth fret / twenty-second fret. That's only 3 series of 6 pitches to memorize, making any note on the neck within a whole step of an identified note and easily referenced. Eventually, as note names find
are consistently encountered and identified, more and more way into memory.
Okay. Next? A second essential method of finding formulas is by "function". To use this requires two pieces of knowledge, one being the intervallic distances between all 12 functions within a given octave. For example: from function 1 up to function 2 is a whole step from 2 up to 4 is a minor third from 5 down to 1 is a perfect fifth 46
FAQ Part 3
from b5 up to b6 is a whole step from b5 up to 1 is a tritone
a-. a-. a-. a-. a-.
from b6 up to 7 is a minor third
from 7 down to b6 is a minor third, etc.
Remember, an interval is the distance between two notes. A function is the
specific chromatic location of a note within the octave.
Hmo do Iteam these
a.
a.
a-.
On the instrument. Choose a key, then figure out the intervals between each function of the major scale. Then add the "flat" functions. It's a little tedious, but it won't take too 10n2:. Write it all down and memorize it.
a-. other requirement is knowing how to play those intervals, namely major a-. The and minor seconds, maj/min thirds, perfect and augmented fourths, fifths, a- maj/min sixths and maj/min sevenths, all over the instrument. These can all be learned as patterns, since there aren't that many to memorize.
a"1.
a-:8 a·:8
I thought you said patterns weren't used?
a-.
a--
•.
a·-'
•• - •• •• •• •••• ••• ••••
This case is the exception. The idea is this: if J 35 is the desired formula and function 3 is being played, then, if one knows that the interval from 3 up to 5 is a minor third and from 3 down to 1 is a major third, then either of those two interval patterns can be plugged in appropriately to find right notes. Another example: in looking for 13b5b6b7, the function b5 has been located. If the intervals within the chromatic scale are known, it's clear that a move up or down a whole step will still be within the formula (to b6 above, to 3 below) . But one must know how to playa whole step to do that. Using the shortcut of an interval pattern at that point is practical and sacrifices nothing. After the intervals and their patterns have been learned, the following exercise can be used to practice playing functions: any note that's low on the high "E" string and call it function 1 OK, if that's I, go down to function 5 on the next string (no, don't play the in
terval of a fifth; go from function 1 down to function 5. That's a perfect fourth.)
a-. OK, that's 5, go up to 6 on the same string (yes; up a whole step) aT. OK, if that's 6, go down to b6 on the next string (yes; a half step) a·. OK, if that's 1 (yes, we're changing it up), go up to 4 on the next string (a perif
a.-.•
a-·
a-·
FAQ Part 3
47
It-=-'
fect fourth) OK, if that's 4, go up to 6 on the next string (yes, a major third)
OK, if that's 2 (changed up again), go down to 1 on the next string (a whole step) OK, if that's I, go down to 7 on the next
(a half step)
OK, if that's I, go up to #9 on the same (a minor third. Yes, #9 is notated in formulas as b3, but #9 is a common function and one should get comfort able with translating it to/from b3. Likewise b9/b2, #4/b5, #11 Ib5, #5/b6 and around like this to and from all randomly changing the functions and using intervals to find them. With this kind of movement note names are irrelevant; the search is purely by function. And a very useful search method it is.
head is exvlodill'? What do Tneed to know to liseformulns, again? 1. To spell any formula in any key 2. The names of the notes on the instrument 3. The intervals between all functions within the chromatic scale 4. How to play all intervals within one octave on the instrument: same-string,
adjacent strings and skipped strings where applicable
Do 1l1eed to master these requirements before 1 can start using formulas?
No. But working to improve these four skills makes it easier to use formulas. It's a relatively small bit of required memorization, considering the immensity of the potential creative return.
We'll sec.
Yes.
.-. .,-. .,-. .,-.,-...
AN IMPROVISER'S OS FAQ, PART 4
fr-·
fr-· fr-· fr-· ~-. fr-· ~-. fr --=tI) .-:8) • -:11) .-:8) .-:8 1
..... 8-.-" 8--,,1 8- ..-'.
......-.-. ...-.
,,_~l
How
I initiallu armroach this
the guitar?
Much practicing of formulas can be done by using a basic exercise "4-fret".lt up the guitar neck into 4-fret zones, arranged out across the neck like a deck of cards or a pile of The lowest zone on the guitar starts on F and includes frets 1,2,3 and 4; the next starts on F# and includes frets 2,3,4 and 5; the next, so on, a]] the way up to the highest end of the neck. group of 4 frets is a zone.
Why 4 frets? Why not
or 7 or 1?
Any number of frets is worth experimenting with as a defined area to search in; ultimately all the zones blend together to make one big zone that includes the entire neck, like the aforementioned snapshots fitting together to make a panorama. Using 4 frets is limiting enough to make many common-scale formulas, such as major and minor scales and their modes and arpeggios, impossible to play in their usual order, which often requires 5 frets to do. So, some familiar old patterns are left behind and a conscious awareness of note choice is intensified . Also, using 4 frets allows access to enough notes of the formula to establish its tonality to the ear. Four fingers, four frets.
What do 1 do with them?
Pick a zone; it doesn't matter which one. Let's say the one and 10. Now choose any
frets 7,8,9
say Ib235b7.
.-:if
Now any
.-"it
.-. .-~
First: what are the Db.
.... .-.
searching by note name and/or function: where are those notes in that 4 fret zone? Consider onlv the fretted notes within the zone; this exercise doesn't include open strings.
.-.".'
say Eb. notes? In
the formula
E is
..-1
48
FAQ Port 4
.---t.
FAQ Part 4
49
.-~
a-I=-
Why not? tend to fill in available notes of formulas that, if left out, create interesting intervals. This exercise deals only with the notes on the neck. A related exercise with open strings can be created later. For now, play available notes in fret one of the zone with the first finger, avail able notes in fret two with the second finger, fret three with the third, fret four with the'
If that's 5, go down to 3 on the next string (a minor If that's 3, go down to b2 on the same string (a minor third) Is a move down to 1 available within the zone? No. So go from b2 down to b7 (a minor third)
·-r~
-1·
·-r~~
Now, up from that E (b2) on the G
8- l - 8-8--
Go from b2 up to 3 on the next string (a minor third)
1
Is a move up to 5 available within the zone? No. So go from 3 up to b7 on the next string (a tritone/ augmented fourth)
.'=
1
When playing formulas harmonically (two or more notes at a time) it's not a issue, but with melodic playing (one note at a time), it's good practice to keep one finger to each fret because it keeps the zone clearer visually as one looks down at the neck to find notes. It also ends up strengthening all four fingers equally.
I thought
didn't have to look at their hands.
Some look, some don't. Some players close their eyes for various reasons: con centration, fear, inspiration, habit. But when using theory to search the guitar for something new that isn't pattern based, the eyes - although not essential - can really help. Use them. So, Ib235b7 in Eb, frets 7,8,9 and 10: E string: Db
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..1.
.1.
.i. .i.
.. •. "t~
~
.-:e
So a flexible combination of these two methods is the most practical way to -~ proceed with looking for formulas on the instrument. In a given moment of .:e. improvisation one method will work better than the other. .t~
E string: Db
finger)
To find them by note name, look for those notes by name on the neck in the
defined zone.
To find them
function / interval:
Locate any desired note of the formula by name, say E (b2 on the G string)
If that's b2, go down to 1 on the same string (a half step)
Is a move down to b7 available within the zone? No. So go from 1 down to 5 on
the next string (a perfect fourth)
When searching by function - which relies on interval knowledge - as long as a note of the formula can be identified to start with, one is not dependent on calculating the other note names to find them. That can make it easier to play in keys with lots of accidentals, to play through changes, and to play harmonically.
.-=1'
D string: Bb (second finger) A strin2': E, G (first, fourth finger)
"nate-name" or "function "?
When searching by note name, one is not dependent on interval patterns to find the right notes. That can make it easier to skip strings and play unknown intervals within the zone, and ultimately to play bigger intervals horizontally on the neck.
t~
..
B string: G (second finger)
So which method is better to find notes
..t..,
G string: Eb, E (second, third finger)
finger)
With these moves, every possible note of that formula in that key, in that zone, has been identified; there are no others. Enjoy the completeness of that. Such a sensation of thoroughness is not typically associated with guitar practicing, given the instrument's melodic and harmonic potential.
eej
To build both skills initially, practice each method separately. Then trv to unify them.
-+ -t --J
"I.•
When are we gonna start making music? Now.
..fa
a
• ••
..t 50
FAQ Part 4
FAQPtlrt4
51
... .• .. a
AN IMPROVISER'S OS FAQ, PART 5 Let
this
Get a metronome. Something with a click that's not too loud or sonically ir ritating or you and your friends, family and neighbors will quickly be driven insane, or more msane.
under my
Don't bother. In this mapping-out process of the formula it's not to run the sequence of available notes up and down to mechanize it and ),1"""1" it to a pattern.
-~
.-~
.-;~ I
..-;.:e
How will I remember it, otherwise? You won't. In fact, that's an important goal: to not remember a single formula's location anywhere on the neck. Instead, every time that access to a formula is needed, it is searched for by note name or function as if for the first time, of how manv times it has been searched for before. for anyone formula makes the search for any other
that much easier. What makes access to 2048 formulas possible is that it isn't
necessary to have memorized their locations, or even to have practiced them
specifically. Instead, one continues the practice of searching for them, in all
keys, all over the neck, increasing one/s skill in finding all formulas in
the process.
. . .;;.l~
.._I...,
patterni::e everytfling.
A of locational awareness is inevitably gained with this exercise. But to take maximum advantage of the concept, it's important that the orientation of the is on searching rather than on If old habits persistently turn formulas into
identify each note name or function, out loud or silently, before it is played. Change keys, formu las and zones often. Don't get too comfortable. Familiarity breeds composition not part of the exercise, for now.
The practice of searching improves the skill of finding. The practice of pattern playing improves the skill of playing patterns.
What else? ueSKHlD
52
fAQ Part 5
cassette recorders, the kind with forward OAT recorders or anything else with are not recommended for this The desktops cost around $30 and last
I assume
tell me
SOOIl
?
Yes. Choose a moderate tempo on the metronome and tum on the cassette recorder. Now, using only the notes of the aforementioned randomly chosen formula Ib235b7 in Eb (Eb, E, G, Bb, Db), in the aforementioned randomly cho sen 4-fret zone (frets 7,8,9 and 10), start improvising melodically.
_'~
What do you mean? ..-~~
-!~ Take a solo. Choose a
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.~)
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I tend to
It's hard to overstate how important these two items are for this kind of practicing .
•
~.
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and . the notes available within those four . on the guitar. slowly enough to not make mistakes, in this case mean ing playing notes other than those in the formula or notes outside the zone. Don't just throw the hand down anywhere by habit; instead, think of the actual notes and functions being played. Remember, it's an exercise of control. Every note matters .
Within the given limitations, try to make as much music as you can .
.. -'::t'»)
.-:eJ How do I know what notes to
... --=1"
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haven't memorized
as II
out the right notes while playing, in tion or both. That's the concept: the search is happening in the moment, with all of one's musical powers brought into play to make the search sound as good as it possibly can within the limitations of formula and zone.
All right; Ifinished my solo. Roll back the tape and listen to it.
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-
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IF-~.
••
fAQPart5
53
4
I
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I don't know. If one can determine why something sounds bad, steps can be taken to make it
sound better. That's the essence of self-teaching, of self-improvement, and it's what makes the tape recorder valuable. Without it, we only have the of what was played, without the measure of objectivity that listening to the tape allows.
5-,"" ... -I-l" .-~
A limitation can't sound bad;
what we do within it can.
The limitation is an opportunity to build improvisational muscle. As noted previously, what makes music sound good isn't which notes and intervals are used, or how many, but how they are used. Miles Davis, among others, proved that one note can sound as good as ten. Accordingly, what is on the tape could sound as musical and good as anything that's ever been played before, by anyone. If it doesn't, there are reasons why. Specifically, what are they? aspect of what has been played can be analyzed and worked on. Generally speaking, what are the elements of good music? To some degree it's a subjec tive question, but whatever musical answers there are can be plugged into this exercise and developed by the practicer. The following are some basic areas of concern, areas that sometimes make the difference between good and bad sounding music. All of them can be worked on within the context of the 4-fret exercise. Time: is the metronome being listened to, or is it just droning inconsequen tially in the background? Check to see if things are lining up with the click in the intended way. Note choice: are they right or wrong? In this exercise, anything out of the formula or zone is considered wrong. Also, even a right note can sometimes be played at the wrong time. Melody: given the limitations of formula and zone, do the melodic lines make sense? Are they purposeful, or random-sounding? Practice achieving effects.
.. .
.. --1't
~~ I
Articulation: are the notes 54
FAQ Part 5
played clearly enough? Too
What is
Groove: aside from the time and how it's lining up with the click, is there a rhythmic happening? Does it make you want to dance, or die? Soul: difficult to quantify, but with few exceptions, if a musician forgets to be involved spiritually and emotionally with the music, the result will be less than great. Add yourself to the music. Math is beautiful and useful, but doesn't often sound good by itself.
"l~
·r~ '~
.l=m Formulas are math: what we do with them is music. .l~
.1:m How do proceed with all this? are any number of things to consider while practicing, including all of .:m There the concerns listed above, plus others of varying importance. While playing, I
.f~ .~~
.-.~
.-~
.~:e
most people can be conscious of only one or two things at a time, so the prac ticer must choose which elements to concentrate on in a given moment. After listening to the first pass on the tape, choose some element of it that is particularly unsatisfying and focus on it in subsequent passes, until an im provement in that element is noticeable in playback. Then shift focus to a dif ferent element. Each pass could last from 30 seconds to some minutes: what ever feels right.
.-:e
...
.-. •• .--.,J-..•
.-;.
.-l-.
.-t.
--t·
-1-
.1. .-~
.--«'
So, two identification of a specific weakness and then a focus on that weakness while improvising. These methods of attack take place within the context of a controlled tonality (formula) and in a specific 4-fret zone. One initial goal might be to play the right notes, in time, soulfully. Accom
plishing that should sound acceptable, at least. Once that basic goal is attained
whether in minutes, hours, days or weeks - other issues can be explored .
Is this uvvusetl to sound like
1
Phrasing: unless otherwise specified by the practicer, the form - which can have a big impact on phrasing, or how the melody is being organized - is unde fined. Try using 4 or 8-bar forms to improvise in to begin with, if it sounds like the lines are rambling or disorganized.
Rhythmic content: without it, things can get dull. Use it to activate the melodies.
Sound: is the instrument's sound pleasing on tape? If not, even great playing .-:~ can sound bad.
.~
Maybe it sounds bad because of the limitation.
the desired effect? Decide, then try to accomplish it.
J .......
·r..-r
It can sound like anything. The chosen rhythmic feel and sound of the impro visation will determine whether it swings, whether it's syncopated, whether it's sustained. The stylistic element, whether it's jazz, reggae, rock, blues, another idiom, or no idiom - is applied by the practicer after the formula, key and zone are chosen.
FAQ Part 5
55
What do YOll mean, "no idiom"? Formulas have no inherent idiomatic content of their own, so improvising with them is an opportunity to create beyond idiomatic boundaries. If the impro viser can conceive of melody, harmony and rhythm without stylistic reference, then the stage is set for a more personalized kind of music to emerge that may not be so easilv defined.
/ see...so in addition to being a study of tonality, this is a method of practicing all the llIusical skills that might make somebody a better improviser, and mal/be e(1en a llIore individualized one?
r couldn't have said it better myself.
.'.: ..,..' .' . 6
AN IMPROVISER'S OS FAQ, PART 6 I'm bored with the exercise. Make it more musicaL Within its defined limits the 4-fret exercise provides significant creative opportunity. Exploit it. Change the speed of the metronome, the sound, the time signature, the feel, the intent. All articulations - including bending notes - are acceptable, as long they resolve into notes of the chosen formula.
a a a
As with all things having to do with practicing it's essential to make it fun, which is a creative exercise in itself. Without fun, any kind of practicing is an endeavor without much appeal. One idea is to play along harmonically with the recorded melodic improvisation - but first, some routines:
._l.:e
.-~) .-~)
._l:el • -I~'
-l--)
-1~1
_i-:S
I
-i-' -i-"
I
·i"1l) • t-:tl l
·t-:il .-. .-. ••
.- __ 1-" ..--_..•.•.. . .• -_
After playing melodically with the formula in one key, continue the exercise with the same formula in twelve without changing the zone. Keep one finger to each fret. After that, continue the exercise with the same formula in one key, but play it in all 4-fret zones, up and down the neck. Then do the same in all keys. After that, continue the exercise with the same formula, but leave the zone - open up the whole neck, move through some different keys, still searching for each note and concentrating on name and function. If it's tempting to stick to familiar areas, force the hand into unfamiliar territory, playing fewer notes if necessary to avoid making mistakes. It will be easier to find the formula everywhere on the neck after first explor
ing the zones - not from memorizing locations, but because the search for those notes and intervals will become more familiar and the basic skill of searching will be improved. Make it musicaL Record it. Listen to it. Fix it. Try it again.
I get stuck
I
out the next l10te to play.
However long it takes to figure it out - ten seconds or thirty, a minute, five minutes - just make sure to come back in musically, in time, with a right note. H doesn't matter how long the rests are. That "figuring it out" period is very, very good practicing. That's the process. One practices searching, becoming increasingly able to find things more quickly and musically. It can be difficult, especially in the beginning. Don't be afraid of that; embrace
it. That will make it easier, sooner.
-
56
l-AQ Parf 5
-
<---it
FAQ Part 6
57
..'., I.r
Initially the concentration required may be exhausting. If very many wrong notes start cropping up, layoff immediately or the point of the exercise will be lost. Do it for as long as it can be done with controt even if that's just five min utes with five notes, and build it up from there in subsequent practice sessions.
should J start with? It doesn't really matter. It might be practical to start with the common triads
Ib35, Ib3b5, 13b6 and some common seventh chords, say 1357, Ib357, Ib35b7, Ib3b5b7, 135b7, Ib3b56, 13b67, 13b5b7. But what's most important is to pick something anything and start looking for it as musically as you can within the defined limitations.
11lention these triads and seventh chords; I thought we were talking
and playing melodically - I'm confused.
YOli
Those are three-note and four-note formulas that are common enough to have names: major, minor, diminished and augmented triads, and major seven, minor-major seven, minor seven, minor seven flat-five, dominant seven, dimin ished seven, major seven sharp-five and dominant seven flat-five chords. Most formulas don't have names; sequences like Ib24, 16b7, Ib22b3, 14b55 can best be described just by their functions, as formulas. But whether common or uncommon, named or unnamed, all formulas invite exactly the same melodic and harmonic treatment. Even though those named formulas are often thought of as chords, at the mo ment we're accessing them as melody, one note at a time.
Like an arpeggio? Yes, but as with the words "scale" and "chord", the word "arpeggio" is so loaded with pattern references that it's of minimal relevance to this exercise. Whatever can be achieved within the concepts of scak chord and arpeggio can be covered by formula as melody or harmony, but to a greater improvisational degree. After playing melodically with the formula, practice playing those same avail able notes harmonically: two or more notes at a time. Use the same methods of access - note name and function - but play the notes simultaneously.
1.'1
.'.'r,
a'r
Which ones? Any that are within the zone. A formula's notes are all equal, all available . Experiment with the different possible harmonic combinations, from two to six strings. Unlike chord forms, which are accessed by shape, formula voic ings are created spontaneously, without shape or pattern reference, by locating available notes of the formula via note name or function and playing them simultaneously. Practice this harmonic playing just as the melodic playing was practiced, with
aj the recorder and metronome, working on chosen areas of focus, keeping it as
a, a, a,
.,., . ,
,,., .,
tI1 tI1 I::' tI1-:::'
tI,-Si tIT-~
musical as possible. Don't get attached to any particular key, location or for mula - keep it moving. Again; the goal is not to memorize, but to explore. This is where melody and harmony meet: it's the same concept of improvi sation coming from the same tonal source, the difference being the melodic and harmonic effects of playing one note at a time or multiple notes at a time. Depending on how it's applied by the improviser, this unification of "scale" playing and "chord" playing can have significant creative implications . After experimenting with harmonic improvisation, try recording a melodic improvisation, and then playa simple harmonic groove from the same formula against it as you listen back to it.
Why don't 1 just make a
track first and then play along with it?
That's a different exercise, one that's more for the ear than for the head. For
now, the goal is to be able to access any tonality without relying on a backing
track. The head decides what the available notes will be, then the ear organizes
those available notes as music.
Also, accompanying one's own improvisation can illuminate which areas to
tIT--= focus on as a practicer. tlI--= .,-~
.,-:-=
.,-' -=
&.--'::11
&--~
&. _(:::e
What's the point ofall this, again? So far it's a melodic and harmonic study of all the tonalities that exist in the chromatic scale. At the same time it's an improvisational exercise that can be used to isolate and develop assorted playing skills, with maximized applica tion to actual performance.
&---r &--_,-::e Is that all? No.
~-!~
58
FAQ Part 6
5-11
.-1~
fAQ Pari 6
59
·r·
-i·'
1
AN IMPROVISER'S OS FAQ, PART 7 All ri'lht: what else can be done
Formulas contain modes and potential harmonies. Modes are derived by defining each function of a given formula in turn as 1/1", and then calculating the interval relationships of the formula's other functions to each new root. For example, random formula 1b56b7 has four potential roots / modes. To calculate them, first translate the formula into a key: 1b56b7 in C C,Gb,A,Bb mode #2 contains the same notes and order, but begins with Gb: Gb,A,Bb,C mode #3 begins with A: A,Bb,C,Gb mode #4: Bb,C,Gb,A Now, analyze each mode in the key of its new root to derive the formulas: mode #1 mode #2 mode #3 mode #4
(C,Gb,A,Bb) in C:= 1b56b7
(Gb,A,Bb,C) in Gb := Ib33b5
(A,Bb,C,Gb) in A Ib2b36
(Bb,C,Gb,A) in Bb := 12b67
What is the value affiguring alit the modes?
Primarily as a means to generate new formulas from an existing one. The relationship between a formula and its modes is mathematically specific but musically vague. Every formula (other than the formula 1/1") has modes, and every formula (other than the formula "lb22b334b55b66b77") is a mode of some other formula. Unless the musician dictates otherwise, where a mode comes from is less significant than the independent tonal personality it has as a unique formula. Another way to generate new formulas from an existing one - in a way that has significant creative implications for the improviser - is by defining its subsets.
"Subsets"?
Yes
formulas that are contained within other, larger formulas.
All formulas (except the formula "1") contain subsets, and all formulas (except the formula "lb22b334b55b66b77") are subsets of larger formulas, and ulti mately of the chromatic scale.
60
FAQ Pari 7
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·1-l1' ·1=f1'i ·1-11"
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Formula 135b7 contains the following 28 subsets, derived by defining each function of the formula in turn as "1 ", then calculating the interval relation ships of the other functions to each new root.
I thought that's llOI!) the modes were determined and subsets?
what's the d~fference between modes
Modes always have the same number of functions as the formula from which
they're derived, and exist in only one combination from each degree. Subsets
are always smaller than the original formula and have multiple combinations
from each degree,
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...
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.~ .~
For example, in the key of C (mode is 135b7 / C,E,G,Ub):
subsets from function 1:
1 (C)
13 (C,E)
15 (C,G)
1b7 (C,Bb)
135 (C,E,G)
13b7 (C,E,Bb)
15b7 (C,G,Bb)
.11'
• .11'
subsets from function 3 (mode is Ib3b5b6/ E,G,Bb,C):
.:e
--(-~
.-"fI'
.--1Ift
1 ,
1b3 (E,G)
Ib5 (E,Bb)
1b6 (E,C)
1b3b5 (E,G,Bb)
1b3b6 (E,G,C)
Ib5b6 (E,Bb,C)
.L-e
.>-e subsets from function 5 (mode is Ib346 / G,Bb,C,E):
.---e 1 (G)
(G,Bb)
• t. 14Ib3(G,C)
•••
.!.
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16 (G,E)
Ib34 (G,Bb,C)
1b36 (G,Bb,E)
146 (G,C,E)
.~.
.~
•••
FAQ Pari 7
61
subsets from function b7 (mode is 12b56 I Bb,C,E,G): 1 (Bb)
12 (Bb,C)
1b5 (Bb,E)
16 (Bb,G)
12b5 (Bb,C,E)
126 (Bb,C,G)
1b56 (Bb,E,G)
The potential harmonies of a formula are defined by its subsets. Some of these harmonies will have names, as in the example above: major triad (135) from 1 and diminished triad (lb3b5) from 3. Many are unnamed. But all are available when played two or more notes at a time as harmonic voicings of the formula.
1 thought hannonu was built in thirds? Tertial harmony but in a formula all harmonic combinations are valid, regardless of interval.
I notice in some of the examples above - 135 from 1 and 146 from 5, for example - the notes end up being the same. Why are they considered A formula's root has a critical role in the way the formula is organized by the musician and subsequently perceived by the ear. Playing 135 in C creates a dif ferent effect than playing 146 in G, even though the pitches are the same. When the center (root) of the formula changes, the interval relationships of the other functions to that root change and the nature of the music changes perceptibly - sometimes slightly, sometimes significantly. The subsets of a formula are like the facets of a diamond; as each small angle contributes to the unique character of the stone, so each subset illuminates a different facet of the formula's tonality. A subset is always "of" the formula that contains it, so it is always in tonal agreement with that formula. But the subset is made up of a selective group of that formula's functions and high lights them exclusively. That can create some interesting effects, melodically and harmonically.
How can I use that? Consider the familiar 7-note tonality of Dorian: 12b3456b7 The 441 subset formulas it contains are calculated in order, as follows.
62
FAQ Part 7
at"
·1~
Subsets from 1 (mode is 12b3456b7) :
·1~
.....
•
~
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_ff"
-i~
-r'"
_1=1'1
-r'"
-r'"
-i""
-i~
One-note: 1
Two-note: 12,lb3,14,15,16,lb7
Three-note: 12b3,124,125,126,12b7,lb34,lb35,lb36,1 b3b7,145,146,14b7,
156,15b7,16b7
Four-note : 12b34,12b35,12b36,12b3b7,1245,1246,124b7,1256,125b7,
126b7,1b345,1b346,l b34b7,lb356,lb35b7,1 b36b7,1456,145b7,146b7,
156b7
Five_note:12b345,12b346,12b34b7,12b356,12b35b7,12b36b7,12456,
1245b7,1246b7,1256b7,lb3456,1b345b7,lb346b7,lb356b7,1456b7
Six-note: 12b3456,12b345b7,12b346b7,12b356b7,12456b7,lb3456b7
Subsets from 2 (mode is Ib2b345b6b7) :
One-note:1
Two-note: Ib2,1b3,14,15,1b6,lb7
-r~ Three-note: Ib2b3,1b24,lb25,1b2b6,l b2b7,1b34,1b35,Ib3b6,1b3b7,145,
-r~ 14b6,14b7,15b6,15b7,lb6b7
-~ .~
Four-note: Ib2b34,1b2b35,1b2b3b6,lb2b3b7/lb245,1b24b6,lb24b7,
1b25b6,lb25b7, Ib2b6b7,l b345,lb34b6,1b34b7,lb35b6,Ib35b7,1b3b6b7,
145b6,145b7,14b6b7,15b6b7
.:e Five-note: Ib2b345,l b2b34b6,Ib2b34b7,Ib2b35b6,l b2b35b7,
.~ .~
Ib2b3b6b7,lb245b6,lb245b7,lb24b6b7,lb25b6b7,lb345b6,lb345b7,
1b34b6b7, Ib35b6b7,145b6b7
.-:e
...-.
.... -
.".
.:e
Six-note:1b2b345b6,lb2b345b7,lb2b34b6b7,lb2b35b6b7,lb245b6b7,
1b345b6b7
.. -= Subsets from b3 (mode is 123b5567) :
One-note: 1
Two-note:12,13,lb5,15,l6,17
Three-note:123,12b5,125,126,127,13b5,135,136,137,lb55,lb56,lb57,
156,157,167
•..-. -.
....
•
Four-note: 123b5,1235,1236,1237,I2b55,12b56,12b57,1256,1257,
1267,13b55,13b56,13b57,1356,l357,1367,lb556,1b557, 1b567,1567
.~
FAQ Part 7
63
~ Five-note: 123b55,123b56,123b57, 12356,12357, 12367,
12b556,12b557,12b567,12567,13b556,13b557,13b567,
Ib5567
13b5567 Subsets from 4 (mode is 123456b7) :
One-note: 1
Two-note:12,13,14,15,16,lb7
Three-note: 123,124,125,126,12b7, 134, 135,136,13b7, 145,
146,14b7,156,15b7,16b7
Four-note: 1234,1235,1236,123b7,1245,1246,124b7, 1256,
125b7,126b7,1345,1346,134b7,1356,135b7,136b7,1456,
12456,1245b7,1246b7,1256b7,13456,1345b7,1346b7, 1356b7,1456b7 Six-note: 123456, 12345b7,12346b7,12356b7,12456b7, 13456b7 Subsets from 5 (mode is 12b345b6b7) : One-note: 1
ii; ti,
Two-note:1 b2,l b3,14,lb5,i b6, 1b7 Three-note:lb2b3,lb24,lb2b5,lb2b6,lb2b7,lb34,lb3b5,lb3b6, 1b3b7,14b5,14b6,14b7,lb5b6,lb5b7,lb6b7
.~.""?r Ii.- . 4i.
~l~ Five-note: Ib2b34b5,lb2b34b6,lb2b34b7,lb2b3b5b6,lb2b3b5b7,
e
Ib2b3b6b7,l b24b5b6, 1b24b5b7,lb24b6b7,lb2b5b6b7,lb34b5b6, Ib34b5b7,lb34b6b7,lb3b5b6b7,14b5b6b7
t5i~
:t~
·1~ ·i~ ·f~ ·1~
Subsets from b7 (mode is 1234567): One-note: 1 Two-note: 12,13,14,15,16,17 Three-note: 123,124,125,126,127,134,135,136,137,145,146, 147,156,157,167
·r~
·f~ ·t~
Four-note: 1234)235,1236)237,1245,1246,1247,1256, 1257,1267,1345,134611347,1356,1357,1367,1456,1457, 1467,1567
-t·:e
.~)
.I~
.t~)
Four-note: 12b34,12b35,12b3b6, 12b3b7,1245, 124b6,124b7,125b6, 125b7,12b6b7,lb345,1 b34b6,lb34b7, 1b35b6, 1b35b7, 1b3b6b7, 145b6,145b7,14b6b7,15b6b7 Five-note: 12b345, 12b34b6, 12b34b7,12b35b6, 12b35b7112b3b6b7, 1245b6,1245b7,124b6b7,125b6b7,lb345b6, Ib345b7, 1b34b6b7, 1b35b6b7, 145b6b7 Six-note: 12b345b6,12b345b7,12b34b6b7,12b35b6b7,
1245b6b7,lb345b6b7
Subsets from 6 One-note: 1
is 1b2b34b5b6b7) :
Six-note: 1b2b34b5b6, 1b2b34b5b7,1 b2b34b6b7,l b2b3b5b6b7, 1b24b5b6b7,lb34b5b6b7
Five-note:12345,12346, 12347, 12356,12357,12367, 12456,12457,12467,12567,13456,13457,13467,
•...J·f~ .. .t..
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)-.
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What do [ do with all these?
Each one expresses a unique tonal component of the original formula. Together they represent 441 different ways to imply Dorian, melodically and harmoni cally. None of them include all the notes of Dorian and they don't have to - they are fragments of that sound, in complete tonal agreement with it and use ful as potential substitutes for it. For example: Chord
minor seven choice: 12b3456b7 subset choice from Dorian: 1b35b7 from 2
-j-"
64
[J1Q Pari 7
.1~
FAQ Pari
65
Playing this subset melodically or harmonically over the chord change inciden tally highlights the 1,2,4,6 of Dorian in that key. Since it happens to be a subset with a common name, minor seven, it's easy to remember that this specific Dorian color is created by playing II minor seven over a I minor seven chord; i.e., Ib35b7 in C# over B-7, lb35b7 in Eb over Db-7, etc. Using subsets is an excellent way to get a variety of tonal colors from a single formula or scale.
How do I remember the subsets that don'l haDe common names? In fact, how do I remember all these hundreds of subsets and formulas, period? It's not necessary to remember them, just to explore them. In the course of that exploration, favored sounds will be discovered and memorized either by name or number. A stable of current formulas will develop that will gradually expand and transform as new sounds replace old ones. It's an ongoing process that reflects the transience and evolution of improvisation itself. It may be easier to remember a formula by name than by number.
Many nameless formulas can be referenced by other, named formulas: 157 can be called major seven no 3, for example. Ib34b5b7 can be minor seven flat five with 4. Ib23b6b7, augmented seven with b2. Searching initially for the previously mentioned common triads and seventh chords will give the practicer a good foundation to refer to in the process of relating unfamiliar formulas to familiar ones, making them easier to access.
What about a bigger formula, like the lO-note lb2b34b55b66b77...what do I call that? At some point, it becomes easier to think of a formula as a subtraction from the chromatic scale rather than as an addition to common 7 or 8-note formulas. For example, the lO-note formula above could be called chromatic no 2/ no 3. To access it, play chromatically but avoid functions 2 and 3; i.e., in the key of Eb, all notes are available except for F and G.
Cmon; isn't that going to sound just like a chromatic scale? Not exactly. It may take time for the ear to discern the difference, but it's tan gible. If an art is to be judged by the range of its subtleties, then music, with but its twelve notes, must reign as queen.
•• _::wn
-1=-' -i~
-1:
Huh? Conversely, an 8-note formula like 1b2b33b55b6b7 can be thought of as Altered w / 5; i.e., Ab Altered plus the note Eb.
:l:
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.~ ~ .~
.=p>
•
-.:f')
So, there are a number of ways for the improviser to describe urmamed formu las that can facilitate access on the instrument. The chosen name can also have an effect on the resulting sound of the improvisation. For example, accessing Ib22b34b55b66b7 as chromatic no 3/ no 7 will sound different than playing it as Phrygian w / II major triad, because of how the musician will tend to orga nize these notes with these descriptions in mind.
OK; makes sense.
Good; let's move on.
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.
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·t
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;-:
66
FAQ Part 7
I
FAQ Pari 7
67
AN IMPROVISER'S OS FAQ, PART 8 In addition to containing subsets that highlight each tonal facet of a formula, all formulas (except the 12-note chromatic formula) are themselves subsets of other Consider the aforementioned formula with its 28 subsets. To discover other, larger formulas of which it is a part, first analyze it as it moves by step through the chromatic scale, highlighting specific functions as it goes: from 1: 135b7
from b2: b24b67
from 2: 2b561
from b3: b35b7b2
from 3: 3b672
from 4: 461b3
from b5: b5b7b23
from 5: 5724
from b6: b61 b3b5
from 6: 6b235
from b7: b724b6
from 7: 7b3b56
Now organize these functions as formulas, in order and starting with 1. The results will imply some larger, common formulas: from 1: 135b7 (+ the functions 246) Mixolydian
from b2: 1b24b67 (+ 35) Double harmonic major
(+ 357)
from 2: 12b56 Symmetrical diminished
from b3: 1b2b35b7 (+ 3b56) Lydian #5
from 3: 123b67 (+ b56) from 4: 1b346 (+ 257) = Melodic minor from b5: 1b23b5b7 (+ b3b6) = Altered (+ 36) Ionian
from 5: 12457 from b6: 1b3b5b6 (+ b23b7) Altered
from 6: 1b2356 4b7) ~ Mixolydian b2
from b7: 124b6b7 (+ b35) = Aeolian from 7: Ib3b567 (+ 24b6) Diminished This means that the formula 135b7 can be played melodically and harmonically as a subset in the following situations, among hundreds of others: from 1 of a dom 7 chord from bII of maj 7 b2 b6 chord from 11 of a maj 7 #11 chord
68
FAQParf 8
.•.
~.-~'
-~) ,-~
.\., .,.,
..
~
from bIII of a dam 7 #9 13 chord from III of maj 7 #5 chord from IV of min/maj 7 chord from b V of dam 7 #9 13 chord from V of maj 7 sus 4 chord from bVI of dom 7 b9 b13 chord from VI of dom 7 #9 13 chord from b VII of min 7 b6 chord from VII of dim 7 chord
e-, 1';
How would I know those chords go with these "implied formulas"?
Ih_~i
That's chord scale theory, which this book doesn't specifically address. But it's available knowledge that can be had from most good books on the subject of jazz improvisation, from Mick Goodrick's to Jamey Aebersold's. Most of it is common sense, once one understands how seventh chords are made.
.,-~)
.,-~'
..,;;1)
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To make the connections between formulas and which chord scales they might fit into requires knowing those chord scales as formulas - i.e., that the Lydian scale is 123b5567, the Altered scale is 1b2b33b5b6b7, etc. - so the functions can be matched up easily.
How am I going to know those particular formulas? Learn them. Memorize the formulas for the most common scales: the major and minor modes, the diminished scales, the blues scales, triads, seventh chords and anything else that seems useful. Get them down, cold. Once those functions are memorized they can be more easily accessed as formulas rather than scale patterns.
I'm getting lost here - what's tile point of all these different kinds
again?
So far, formulas have been used in the following ways:
17
1. As a tonal center: each of the 2048 formulas contained within the chromatic scale is a unique tonal entity to be explored melodically and harmonically. Makes possible a systematic study of tonality on the instrument, which the 4 fret exercise further defines as a means to develop improvisational skills.
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2. As a mode: a given formula can create new formulas of interesting way to generate formulas.
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3. As a container of subsets: a formula consists of smaller formulas that are in tonal agreement with the original, yet have their own distinct identities. A FAQ Part 8
69
good way to get a variety of sounds from a single formula I scale. Also useful over fast-moving changes, when there may not be time to play complete 7 or 8-note formulas. 4. As a subset of other formulas: a formula can be superimposed into other tonalities that share its functions. Uses a single formula - perhaps one the musician is already comfortable searching for and finds multiple tonalities into which it fits. Also can facilitate improvising over difficult chord changes or scales by substituting familiar subsets for unfamiliar formulas.
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Doesn't that contradict the idea offearlessly taking on new formulas? Isn't it a cop-out to use a known formula instead of truinq a new one? It can be, if one never bothers trying the new one. But tonal situations
arise that require improvisers to deal with something in the moment that haven't considered before. Until it can be practiced further, an immediate strat egy is required. Using familiar subsets as substitutions in those cases can be a practical solution.
Formulas present an opportunity to improvise, which puts the musician in a potentially vulnerable position. There is an inherent risk to the art that even a master improviser is subject to. But within that vulnerability, the magic of spontaneous creation - maybe the most powerful, transforming phenomenon in the universe -lives and breathes. To invoke it, the security of composition is relinquished for the creative moment. Playing compositional Dorian in the situation above will create one kind of effect; playing improvisational Phrygian will create another. It's up to the mu sician to try to balance these effects, to focus on one or the other, or to master them both.
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How long does that take?
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As long as it takes to master anything else, or longer. But on the way there lots of great music can be made.
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Good news for musicians and audiences, huh?
Here are a few examples:
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You said it.
135 from 3 for maj 7 #5 (Lydian #5) 135b7 from 2 for maj 7 #11 (Lydian) 12356 from b5 for dom 7 b9,b 13 (Altered) Ib34b5b7 from 3 for dam 7 (Mixolydian)
" 17
Players sometimes regularly substitute one mode for another that they find more difficult, like using III Lydian #5 or bI! Melodic minor instead of the Al tered scale, or the reverse. One drawback in doing that is that the roots of those substitutions will likely be stressed - 3 and b2 of Altered, in this case which may not be desirable. On the other hand, substitutions like these can create some interesting effects. Ultimately, being able to decide what formula to use by choice rather than necessity the player the most creative leeway. Accessing formulas does not require pattern memorization, so the improviser is invited to be equally comfortable with all permutations, regardless of size, key or location.
but what if 1can really burn with Dorian more than with Phrygian? Wouldn't 1 be betteroffplayil1g my Dorian stufffrom bVll the Phrygian chord? Composition is an opportunity to play something that you know sounds good. Improvisation is an opportunity to play something that sounds better than what you know.
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AN IMPROVISER'S OS FAQ, PART 9
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is that it for There is one more way to use formulas offered here: as superimpositions into tonalities that don't contain them as subsets. For example:
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Random formula: 135
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Random chord change: C7 (Mixolydian 123456b7 = C,D,E,F,G,A,Bb) Move 135 through the chromatic scale in it emphasizes: from 1: 135 from b2: b24b6 from 2: 2b56 from b3: b35b7 from 3: 3b67 from 4: 461 from b5: b5b7b2 from 5: 572 from b6: b61b3 from 6: 6b23 from b7: b724 from 7: 7b3b5
key of C to see which functions
(C,E,G)
(Db,F,Ab)
(D,Gb,A)
(Eb,G,Bb)
(E,Ab,B)
(F,A,C)
(Gb,Bb,Db)
(G,B,D)
(Ab,C,Eb)
(A,Db,E)
(Bb,D,F)
(B,Eb,Gb)
Superimposing 135 from 1,4 or b7 of the key will match the functions of Mix olydian. However, to varying degree, the functions do not match from any of the other nine locations. From 2, for example, one note (Gb) is not Mixolydian, from b5, two notes (Gb,Db) are not, from 7, none is. Using 135 from these chromatic degrees of the key creates an "outside" effect, a sound that is outside the specified tonality of Mixolydian. This effect can have significant creative implications.
I don't
aren't these
wrong notes that will sound bad?
note, right or wrong, can sound good or bad, depending on how the musi cian handles it. The following are a few considerations: WHY: superimposing formulas that are not in tonal agreement with the chord or formula I scale they are played over is one way to create tension in music. Whether melodic, harmonic, rhythmic or sonic, the dynamic of tension and its resolution propels a piece of music forward.
72
FIlQ Part 9
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WHEN: some musical situations lend themselves to playing outside the
tonality more than others. Trust the ear more than the head to determine if this
is an appropriate effect and how much to use it.
WHERE: one way to place tension is to consider the basic sequence of Tonic I Dominant I Tonic I Dominant. The Tonic begins at rest, but needs tension to stay alive. The Dominant pro
vides the tension, then wants to resolve it, perpetuating the cycle.
If that cycle is used as a template within a phrase of
time, it might look like this over C7, with C Mixolydian in the Tonic role and B maj. triad (random from the example above) in the Dominant role: I C Mixolydian I C Mixolydian C Mixolydian C Mixolydian C Mixolydian
I I I I B trio I I II C Mixolydian I I I I B trL I I I I or I I I I I I B trL I I C Mixolydian I I I I I I B trL I I or I B trL I I C Mixolydian I B trio I I or I I B trL I C Mixolydian I I B trL I or I I I I C Mixolydian I I I I C Mixolydian I I I I B trio I I I I
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or any other phrase structure in similar order. The words Tonic and Dominant are not used here in the strict sense, but as euphemisms for resolution and tension.
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The least obtrusive place to superimpose an outside formula is where tension already exists; ie, in place of the Dominant function above.
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of the Tonic - at the top of a phrase, for example - can maximize the outside effect.
WHAT: there are any number of ways to select which outside formula to use to create tension. Here are a few:
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1.
The tonic formula in use, but in a different key
2.
Any diminished (12b34b5b667) or symmetrical diminished (lb2b33b556b7) subset in the key of the tonic formula
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3. Any altered (lb2b33b5b6b7) or symmetrical diminished subset in the "V" key of the tonic formula
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Any random formula, in any key
HOW: along with where an outside formula is placed in the phrase, how it connects with the tonic formula can be important. To begin with, the 4-fret exercise, choose two formulas; one as the tonic and another as a superimposed outside (dominant) formula. Using the phrase templates above as a guide, try to connect the two formulas by the smallest
possible interval to create the smoothest transitions between them.
FAQ l'arl9
73
. Think of it as weaving; creating a fabric in which one color flows impercep tibly into another, then back again. Once that effect is achieved, it's easier to create more radical transitions. As is usual with the 4-fret exercise, use the metronome and the tape recorder and play it as music, not as a scale exercise. During playback, playa tonic groove / chord / chords against it to hear the effect of the
If that's true, why bother getting better at playing anything spec{fic; why not just wing it and try to make it sound good?
It sounds like you're saying "anything goes".
If it sounds good, anything does go. That transcends any conversation about music theory, as anyone who has played music understands. At the same time, everything that goes, goes a certain way based on its tonal (and rhythmic and content. It's for the musician to decide whether to rely on the ear to un derstand that content - and to imagine what other content there might be and how it might be used or to get the head involved in the process as well. The musician is responsible for transforming each bit of acquired knowledge, no matter how technical or theoretical, into music that transcends the math. If that obligation isn't fulfilled, what has been acquired can obstruct the music more than enhance it. But if the energy is generated to apply the math as music, inspiring things can happen that may not occur otherwise.
It's
a little m,m'7nhn
all these
One could explore each of the 2048 all included in thing in music, a realization inevitably filled encouragement for all concerned.
how will I get to it all? it's a finite number and to the bottom of every and
By unifying the disparate concepts of scale, chord and arpeggio, formulas make the study of tonality more manageable, and potentially more comprehen sive, by reducing the tonal context, whether melodic or harmonic, to its most basic elements: the functions involved. In doing so, the distinction between math and music is never clearer, since formulas having no compositional patterns or to confuse with improvisation - are completely inert and are organized creatively by the musician.
the terms of
in this tion without externally imposed idiomatic As mentioned ously, that freedom can encourage more personal sensibilities to come forward.
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So you're
this isn't a good way to
or rock?
Working to enhance the control of tonality on the instrument, along with the other areas of focus associated with the 4-fret can only improve one's musicianship. That will have a positive effect on almost any musical endeavor.
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not addressed in this book. That said: the sound, rhythmic feel, articulation and phrasing of any idiom can be used when practicing formulas. The result may well the idiom without quoting it specifically, often creating some interesting
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I could lise a way to break out of some of these ruts ...
Done .
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AN IMPROVISER'S OS FAQ, PART 10
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Wllat abou t composition?
Once a musician breaks from the routine of using standardized shapes and patterns to practice tonal melody and harmony, unfamiliar sounds and combi nations come up that will inspire composition. Working with formulas can be a catalyst in that process. Whether or not one chooses to compositionally develop a newly something as simple as a voicing or a melodic line that occurs during improvisation can be identified, memorized and used again later as a lick I compositional playing.
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this difference, playing formula 1357 over a major seven chord in C-MI Tothehear same key. Then try 12357. Then 12b556. 1b2b66. Notice the effect as you get
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c How do I know whether to develop an idea as between a compositional idea and an
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Beyond the definitions described earlier, the question is a personal one. Here possibilities: does a new idea have the feeling of something profound; is it particularly evocative of some tangible or intangible thing of import, can it stand on its own? If so, it could be a compositional idea. If it sounds more generally suggestive of a feeling, is dependent on context or is reiterative, then it might best be left as improvisation. An improvisational idea enters one's awareness like a passing butterfly. The improviser simply observes and appreciates the transient nature of its brief appearance, while the composer actually captures it to preserve it. Part of be ing an improviser is the faith that another butterfly will come, perhaps one even more beautiful. Part of being a composer is knowing which butterfly won't fade under
What about rhythm?
Beyond being invaluable when making music with the 4-fret exercise, neither rhythm nor sonics have specifically been integrated into the approach de scribed in this book. That shouldn't stop anyone from trying to do so, if care to.
What about playing over changes?
When choosing formulas to improvise with, whether it's over one chord or a hundred, keep the following in mind:
76
FAQ Part 10
The more chord tones one uses in a formula - Le., the root, third, fifth and sev enth of the corresponding chord change - the more explicit that chord sound will be. Using non-chord tones in a formula results in a more colorful sound that is less descriptive of the basic chord. It's for the musician to decide how important it is to define chord sound in a !!iven situation and to choose the formulas
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further away from the chord tones.
When playing over a lot of changes people often play more chord tones, both to make it easier for the ear to follow the chords and to make it sound like they know what they're doing. Needless to say this is not a rule and leaves much room for experimentation.
A few more
to consider:
1. If changes are going by quickly, it can make sense to choose smaller formulas
to use with them, as there may not be time to improvise with larger ones. 2. Though chord-tone formulas from the root of the matching chord can sound bland, those same formulas can sound colorful and strong when superimposed from other scale degrees. Some examples: 1b3b5b7 from the root of a -7b5 chord (defines chord 1b3b5b7 from bVII of a -7b5 chord (creates altered dominant 1b3b5b7 from II of a -7b5 chord (creates locrian natural 2 sound) 1b3b5b7 from bIlL bV, or VI of a -7b5 chord symmetrical diminished 3. The 4-fret exercise is a good way to practice playing changes. First, go through the chords and decide which formulas - tonic formulas, subsets or superimpositions - you will use, considering the points above. Then choose a zone on the guitar, turn on the tape recorder and metronome and improvise over the changes with the chosen formulas strictly within those four frets. As you listen back, play the appropriately to hear what it sounds like. Then move through some other zones. As before, try initially to connect the formulas with the smallest interval pos sible. Don't be afraid of rests but keep the time constant. If it's too difficult to make the changes at first, ignore some of them. Or make each chord last twice, or even four times, as long. Or slow down the metro nome. Isolate the difficult changes and cycle them. As things become easier, gradually return to the original form. What matters most is that music is being
FAQ Part 10
77
made within the defined limitations. Speed can come later.
What about technical exercises? As far as this book is concerned, the practicing of improvisation, especially when working with a metronome, is essentially the best technical exercise there is since it integrates the physical control needed to playa given idea clearly, in time, with the making of music. In this process, technique is a servant and, like a good waiter, brings the food and clears the plates almost invisibly, without drawing attention to itself.
basic suggestions: Choose any formula at random from the list, memorize its functions and plug it into the exercises described previously. One formula per practice session might be enough. Being open minded about which formulas are used will facil itate becoming comfortable with the search for any and all formulas. If something more specific is desirable, choose a formula based on the number or tonal content of its functions - Le., six note formulas with 2 and bS.
Formulas that are similar to common but contain an extra function or two, such as 1234Sb667 (major scale w / b6) or Ib33Sb6 (major triad w / b3,b6) are interesting substitutes for common sounds.
In some music, technique itself is a focus; generally this requires a more compositional kind of playing, since few people, if any, have managed to play improvisationally i.e., without using preconceived ideas or hand moves - at the extreme technical limits of what's possible. As mentioned earlier, that could and probablv will change.
As one encounters formulas that seem particularly useful as unique tonal cen ters, subsets of common larger formulas or superimpositions, they can be put into regular rotation and explored more thoroughly.
Are you saying it's bad to practice scales the traditional way, up and down, in
What about ,1""",1,..",;.. my own exercises?
It depends on the practicer's goal. If the goal is solely to build technique, strict
As musicians, we're all basically trying to figure out what we're going to play up there. This book encourages the use of one's own imagination to address that issue and all its ramifications.
pattern playing can be useful. It's less effective in realizing musical or improvi sational goals unless the exercise is modified to reflect that. An example: the common major scale pattern that begins on the sixth string root with the second finger and goes up and back after an octave or two, with a metronome in sequential order, creates a strictly technical exercise. However, if the pattern is simply used as a template indicating which notes to play and the order and rate of those notes are broken up in an impro visational or compositional way, it can become a musical exercise as well. Don't stop with the pattern; it just dictates what's available. Put those available notes together as music and it'll be more fun and more useful in actual playing situations.
Singing them can be helpful.
The idea that exercises can be created by the practicer to answer any musical question was inspired here by the methods of the great teacher Charles Bana cos. The idea that a personalized approach is necessary to achieve a personal sound was inspired by all great musicians, each of whom managed to tran the voices of their teachers and heroes. The concepts described here give a lot of creative leeway to the practicer while still enabling a thorough look at what's possible. Ultimately, the reader will decide what is useful, what isn't, what can be adapted and what exercises can be designed in order for them to reach new ground. It might unfold something like this:
What about multi-octave scales? Since this book formulas as a series of functions that are the same in all octaves, specific organizations of functions beyond the octave fall under the category of composition and are not a focus here.
What's the best way to use that gigantic list offormulas you provided?
I want my lines to be more rhythmic what makes lines rhythmic? scalewise movement isn't doin£!: it. .. do I need to use more what are intervals? two notes with distance between them where on the guitar could I play some distance? maybe between the second and sixth string
There are any number of ways to creatively approach the material. A few fAQ Pari 10 78
FAQ Part 10
79
I'll choose a formula and a
and limit the playing to those two
bouncing the line back and forth let's see if that works...
~-~
them
To conceive of an exercise is a creative act, accomplished by first defining a desire or problem, then looking inward for a possible solution and fine-tuning it as necessary. In doing so, a personal direction is taken; a step that is always open to anyone, at any level.
How do!
what the exercise should be?
Trial and error. Using the tape see if a given self-generated exercise takes the playing in the desired direction. Jt will soon become clear or not it works, or how it might be modified to work. Some exercises will be discarded immediately, the more promising ones will stay in rotation until eventually become obsolete. A few may prove more indestructable and become long-term practicing commitments, as most of the concepts and exercises in this book have done for about the last ten years.
Do formulas sum up your playing; is everything coming from this study when play?
YOli
As mentioned before, the study of tonality described here is one way for the practicer to confront a huge, essentially mathematical subject without sacrific the musical aesthetic that makes that study worthwhile. In terms of bridg ing theory and music on the instrument, it's an approach with minimal creative ("'1\t"nnrOl""l"'\lCC
But with all of that, there is no kind of practici confused with actual playing, no matter how imaginative the method. This is because the nature of performance is ultimately unpredictable and inhabits a world more of magic than math. As anyone who has played music knows, it's difficult to describe that particular state of being. Sex comes close, and it's all love, of course. Poets describe it. Musicians play about it. And it transcends any preparation we're capable of. At best, the practicing informs the playing without inhibiting the music. That's about all one can hope for. And that's enough.
What's so great about To create, and to perceive
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direct way. The maker and the perceiver are awakened to an immediacy of be
ing and are transformed. In an environment of ritual and complacency, creativ
ity speaks the truth of the moment and suggests that of the infinite.
The results can't always be pleasant. Birth might not be pretty - but it
the creation of all good beautiful. There is
more meaningful, more enlightening, more important than creation and im
provisation, the forging of music in real time, defines the essense of creation in
music. It's the soul, the creative spark, of composition; it's the uniqueness and
relevance of performance.
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In our time, improvisation may offer more unexplored territory to the artist
than composition, possibly because compositional playing is often mistaken
for improvisation, leaving improvisation itself less realized by comparison. Of
course, some have gone far with it. But at a time when composition and com
positional playing have reached heights that can seem unsurpassable, improvi
sation still offers an uncluttered horizon to those who care to reach for it.
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The vulnerability inherent to improvising can be a
it's not embraced more often. Once musicians find things that work, they tend
not to be inclined to them up for the next butterfly that comes along. The
resulting compositional approach comes with some additional guarantees. It
also runs a risk of becoming ritualized and complacent.
The approach described in this book strives to prepare one to be less vulner able as an improviser. Still, improvisation will require some faith on the part of both the artist and the audience. It's a faith that can be significantly rewarded. In this lifetime.
Oh. U/n, huh? What?
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