Description
This collection would be great for anyone who is trying to learn the music theory, and it's important for any musician.
This book is licensed under a Creative Commons by-nc-sa 3.0 (http://creativecommons.org/licenses/by-nc-sa/ 3.0/) license. This book was accessible as of December 29, 2012, and it was downloaded then by Andy Schmitz (http://lardbucket.org) in an effort to preserve the availability of this book.
Study Set Content:
Each whole tone scale replicates itself when re-ordered in a revolving manner.
Pitch-classes remain identical, the “spacing” remains identical, although
enharmonic spellings are freely used.
Figure 3.26
Revolving Whole Tone Scales
Audio 17
Whole Tone Scale Rotations
Because of these properties there are only two whole tone scales aurally. All other
versions are re-orderings of either
WT I
or
WT II
, but will assume individual
identities according to their use is specific contexts.
Octatonic Scale
Another commonly used symmetrical scale is called the
Octatonic
Scale
26
.Theoretically, any scale with eight constituent members is an octatonic
scale. The versions described here are those most commonly used. In Jazz pedagogy,
these versions are called “diminished scales” or “symmetrical diminished scales”
because of the structures formed by alternate scale degrees. The two related forms
of the Octatonic Scale divide the octave into eight portions consisting of either
alternating half steps and whole steps, or alternating whole and half steps.
26. An eight-tone scale. The most
common form is the
symmetrical division of the
octave into eight portions of
either alternating half steps
and whole steps, or alternating
whole steps and half steps
Chapter 3 The Foundations Scale-Steps and Scales
3.5 Other Commonly Used Scales
115
Figure 3.27
Octatonic I (Oct I) and Octatonic II (Oct II)
Audio 18
Octatonic Scales
Oct I
and
Oct II
have only three forms each.
Figure 3.28 "Octatonic Rotations"
shows
Oct I
with additional re-orderings on successively higher scale degrees. Observe
that, after the original form and two additional transpositions have been listed, the
fourth ordering is equivalent to the first, the fifth is equivalent to the second, and
so forth. The same holds true for
Oct II
.
Figure 3.28
Octatonic Rotations
“Augmented” Scale
Another commonly used hexatonic scale pattern is sometimes called the
“Augmented” scale
27
.This hexachord, along with the Whole Tone, Octatonic, and
Chromatic scales are labeled “Modes of Limited Transposition” in 20th-century
composer Olivier Messiaen’s
Techniques de mon langage musical
. This label refers to
the chords built upon alternate scale degrees. This is also a symmetrical construct,
evenly dividing the octave by the pattern, “half step and a step and a half.” It’s
related counterpart divides the octave by the reverse pattern, “step and a half and
halfstep.”
27. A hexatonic scale that
symmetrically divides the
octave by alternating half step
and step-and-a-half, or the
reverse.
Chapter 3 The Foundations Scale-Steps and Scales
3.5 Other Commonly Used Scales
116
Figure 3.29
“Augmented” Scale
Audio 19
The “Augmented” Scale
“Nearly” Whole Tone and Lydian-Mixolydian
Two other scales having great currency in 20th Century music are identical in pitch
content and identical in their potential origin, but vastly different in context and
usage.
Figure 3.30 "“Nearly” Whole Tone and Lydian-Mixolydian"
compares the
Whole Tone scale to the
“Nearly” Whole Tone
28
Hexachord and the
Lydian-
Dominant
29
scale.Lydian-Dominant is only one label for this scale and is used here
as a convenience only. Other names are Lydian-Dominant (common to Jazz
pedagogy) or (the proper name) the Overtone Scale. These additional names will
not acquire meaning until the student has acquired additional information. Observe
that, despite differing orderings, the pitch-class content is identical for the
“Nearly” Whole Tone and Lydian-Dominant scales.
Figure 3.30
“Nearly” Whole Tone and Lydian-Mixolydian
Audio 20
“Nearly” Whole Tone and Lydian-Mixolydian
The Nearly Whole Tone hexachord is just that: all whole steps except for an initial
half step. The Lydian-Mixolydian scale is so-named because the first tetrachord
28. A six-tone scale that is an
altered whole tone scale. One
pitch is altered to create a
single half step in the
collection. In this chapter it
has been listed half step first.
In other sources, there are
other orderings.
29. A heptatonic scale wherein the
first tetrachord resembles
Lydian mode (raised 4) and the
second tetrachord resembles
Mixolydian mode (lowered 7).
Chapter 3 The Foundations Scale-Steps and Scales
3.5 Other Commonly Used Scales
117
resembles the first tetrachord of the Lydian mode, and the second tetrachord
resembles the second tetrachord of the Mixolydian mode.
Both scales have their potential postulated origin in the naturally occurring
acoustical phenomenon called the Overtone (or Harmonic) Series, discussed in
.The Nearly Whole Tone hexachord is the source set that forms
the basis of Russian composer Alexander Scriabin’s
Mystic Chord
, an important
component of his personalized compositional syntax.
These are but a few of the many scales that have been recognized and used in
contemporaneous theory and composition. While the primary focus of the student
should be upon Major and Minor scales at this juncture, at least a passing
familiarity with other scalar constructs is desirable.
One cannot begin to understand and perform early music without an understanding
of modes. Much music since 1900 has been composed using modes or, at least,
modal “flavors.” One cannot improvise credibly in the Jazz style without
understanding and employing modes.
These same remarks may be made concerning the other scales discussed. One
cannot begin to understand and perform modern music without an understanding
of these various scale patterns. In time, with the proper investment of effort, these
scales (and others) will open new worlds in a deepening musical experience.
K E Y T A K E A W A Y S
The student should understand:
• The Pentatonic Scale.
• Whole Tone Scales, Octatonic Scales, Augmented Scales.
• “Nearly” Whole Tone and Lydian-Mixolydian.
Chapter 3 The Foundations Scale-Steps and Scales
3.5 Other Commonly Used Scales
118
E X E R C I S E S
1. In your
Scale Thesaurus
:
a. Construct Pentatonic on C.
b. Using this as a model, construct the same on F, G, Eb, A, and
B.
2. In your
Scale Thesaurus
:
a. Construct WT I and WT II from F.
b. Oct I and Oct II from G.
c. Augmented I and II from Eb.
Chapter 3 The Foundations Scale-Steps and Scales
3.5 Other Commonly Used Scales
119
3.6 Summary
This chapter provides an overview and discussion of the scalar resources used by
composers. The student should focus upon Major and Minor scales at this point.
Modes and other scales will become valuable assets in time. There are numerous
additional scale patterns that are recognized in various pedagogical practices. The
examples given here are those that are the most common.
In the next chapters, Major and Minor scales will become affiliated with specific
tonal “regions” or keys. They will also be added to our arsenal of useful tools.
Chapter 3 The Foundations Scale-Steps and Scales
120
