SOUND PATTERNS

A Structural Examination of Tonality, Vocabulary, Texture,
Sonorities, and Time Organization in Western Art Music

by PHILLIP MAGNUSON

NON-TRADITIONAL SCALES


AP 2.1 SCALE PATTERNS

For the purposes of this presentation, a SCALE will be defined as a group of five or more pitch classes divided somewhat equally over an octave. This will preclude stepwise groupings such as tetrachords, pentachords, and hexachords. Also omitted are the traditional major and minor scales as well as the traditional modes (dorian, phrygian, lydian, mixolydian, aeolian, and ionian), which can all be found in Chapter 2. Vocabulary of this text.

For organization, tonic will always be G and will always be presented in treble clef. All of the scales can be constructed with the twelve pitch classes of traditional Western music. Solid noteheads represent repeated pitch classes.

Scales found below:

The next three sections are not scales by the definition above, but they do present an important view of symmetrical divisions of the octave.

AP 2.2 DIVISIONS OF 2

A TRITONE divides the octave into two equal parts (A4/d5):

AP 2.3 DIVISIONS OF 3

An AUGMENTED TRIAD divides the octave into three equal parts (M3/d4):

AP 2.4 DIVISIONS OF 4

A FULLY DIMINISHED SEVENTH CHORD divides the octave into four equal parts (m3/A2):

AP 2.5 DIVISIONS OF 5

PENTATONIC scales:

  1. HEMITONIC (with half-steps):

  2. ANHEMITONIC (no half-steps):

AP 2.6 DIVISIONS OF 6

  1. BLUES scales:

  2. WHOLE TONE scale, divides the octave into six equal parts (M2/d3):

  3. HEXATONIC (aka AUGMENTED) scales (symmetric alternations m2 and m3/A2):
  4. PROMETHEUS scale:

AP 2.7 DIVISIONS OF 7

  1. MODAL VARIATIONS:

AP 2.8 DIVISIONS OF 8

  1. BEBOP scales (characterized by chromatic passing tones):

  2. OCTATONIC (aka DIMINISHED) scales (symmetric alternations of m2 and M2):

AP 2.9 DIVISIONS OF 9

Strictly speaking, 9-note scales do not exist. However, it is possible to consider the MELODIC MINOR scale as a 9-pitch collection:

AP 2.10 DIVISIONS OF 10

As with the previous section, 10-note scales do not exist. Yet again, it is possible to project two important concepts to create 10-pitch collections.

  1. The ascending melodic minor scale differs from the major scale by one note, the raised third. If one were to present an ascending major scale followed by a descending natural minor, a 10-pitch collection results:

  2. The black keys on a piano form a pentatonic scale. If the black key pentatonic is paired with any one of the white key pentatonics, a 10-pitch collection results (gray pentatonic?):

AP 2.11 DIVISIONS OF 11

It seems impossible to use the machinations of the previous two sections to create an 11-note scale, but you, the reader, is challenged to use a search engine online and see what results with "11-note scale". You may be surprised. If not, search "9-note scale", "10-note scale", "nonatonic scale", "decaphonic scale", or any grouping you like. The author's favorite is the Klingon nonatonic scale (from fictional Star Trek) which is inexplicably an octatonic scale.

AP 2.12 DIVISIONS OF 12

Since there are only 12 distinct pitch classes in Western music, there is only one 12-pitch collection: the CHROMATIC scale, which divides the octave into twelve equal parts (all half steps):

ADDENDUM

Non-western scales can contain a great variety of pitch classes, and are frequently MICROTONAL (containing intervals that cannot be measured with half-steps or whole-steps). They cannot be written in the limited Western system, but some examples:

LOCATIONPRIMARY TRADITIONPITCH SYSTEM
Indonesia GAMELANPELOG and SLENDRO
IndiaCARNATIC and HINDUSTANIRAGA
ArabianumerousMAQAM

Copyright 2008-2009 by Phillip Magnuson.

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