Download Dmitri Tymoczko on Scales

Dmitri Tymoczko on Scales
In A Geometry of Music (Oxford, 2011) Dmitri Tymoczko provides an analysis of scales
used in Western music, including jazz, together with a historical perspective and a theory
on the key techniques used in composing with scales.
Scales
Chapter 4, Scales, provides a definition plus a language for discussing scales. Tymoczko
suggest a series of criteria for a successful scale: it is maximally saturated with consonant
intervals (such as the perfect fifth, major third, and minor third) while also dividing the
octave nearly evenly and containing a reasonably small number of notes.
From these criteria he derives the scales commonly used in Western music
Scale
No of
Intervals
Saturated with
notes
Comparable OCA scale (page
49 of course folder)
Pentatonic
5
2-2-3-2-3
Perfect fifths
Pentatonic
Whole tone
6
2-2-2-2-2-2
Major thirds,
Whole tone
but no perfect
fifths
Hexatonic
6
1-3-1-3-1-3
Major thirds
Diatonic
7
2-2-1-2-2-
Perfect fifths
2-1
Melodic minor,
7
ascending
Harmonic minor
2-1-2-2-2-
Thirds
2-1
7
2-1-2-2-1-
this.
Thirds
3-1
Harmonic major
7
2-2-1-2-1-
8
2-1-2-1-21-2-1
Nine-note scale 1 on G
includes this.
Thirds
3-1
Octatonic
Both nine-note scales include
Nine-note scale 2 on D
includes this.
Minor thirds
Middle Eastern eight-note
Using Tymoczko’s criteria on the scales in the OCA course folder (excluding the
chromatic scale).
Scale
No of
Intervals
Perfect fifths
Major thirds
Minor thirds
6
2-2-2-2-2-2
0
6
0
6
2-2-2-2-2-2
0
6
0
7
1-3-1-2-1-3-1
4
4
7
7
2-1-3-1-1-3-1
4
4
7
8
2-1-2-1-2-1-2-1
4
4
8
8
1-2-1-2-1-2-1-2
4
4
8
9
2-1-2-2-1-1-1-1-
7
6
7
6
7
6
notes
Whole-tone
1
Whole-tone
2
East
European
major
East
European
minor
Middle
Eastern eight
note 1
Middle
Eastern eight
note 2
Nine-note 1
1
Nine-note 2
9
1-1-1-2-1-1-2-21
Scalar techniques
Chapter 9 outlines three scalar techniques that Tymoczko believes underlie many
twentieth century composers use of scales.
1. Chord-first
In this method, the compositional structure comes from the chord progressions, with
different scales being assigned to each chord. An example of this is given from Scriabin’s
prelude, Op. 48 No.2. Other examples are given from

Grieg’s Drommesyn, Op. 62 No.5

Debussy’s Fetes

Michael Nyman’s The Mood That Passes Through You
2. Scale-first
In this method, the music progresses through a series of closely related scales, the
modulations being managed through voice-leading from one scale to the next. An
example is given from Ravel’s Ondine. Other examples are given from

Debussy’s Des Pas Sur la Neige

Janacek’s On An Overgrown Path

Shostakovich’s F♯ Minor Prelude and Fugue

Reich’s New York Counterpoint
3. Subset technique
This technique juxtaposes scales sharing a common set of notes. For example, in
Debussy’s Collines d’Anacapri, has a pentatonic theme B-F♯-C♯-E-G♯-B in three distinct
scalar contexts: B diatonic, E diatonic, E acoustic. The music has five fixed scale degrees
(B C♯ E F♯ G♯) and two mobile degrees (D/D♯ and A/A♯). Other examples are given from

Grieg’s Klokkeklang, Op. 54 No. 6

Stravinsky’s Histoire du Soldat

Reich’s City Life.