Materials and Techniques of Post-Tonal Music by Stefan Kostka Matthew Santa

Author:Stefan Kostka,Matthew Santa
Language: eng
Format: epub, pdf
ISBN: 9781351859219
Publisher: Taylor & Francis Ltd

SUBSETS

Sometimes pitch-class sets that do not belong to the same set class may be related to each other by sharing common subsets, just as C7 and Cadd6 are closely related because they have the C major triad in common. For example, the pitch-class sets below all have forms of the set class [026] as a subset:

[E, F♯, A, B♭], set class [0146], includes subset [E, F♯, B♭], a form of set class [026]

[D, E♭, G, A], set class [0157], includes [E♭, G, A], another form of [026]

[D♭, D, E♭, F, A], set class [01248], includes [D♭, E♭, A], another form of [026]

These are the pitch-class sets labeled chords 5, 6, and 8 in Example 9-3 (p. 173), and their [026] subsets make them not only related to each other but also to the chords labeled 1 and 2 in that example, both of which are forms of [026] as well. Chord 1 is a literal subset of chord 8 because it shares not just the same intervals but literally the same pitch classes: D♭, E♭, and A. The other subset relationships above are all nonliteral subsets, because those forms of [026] are all related by transposition or inversion, but do not literally share the same three pitch classes.

A special kind of subset is the scalar subset, which is a subset that is derived from a particular scale type, usually diatonic (as in the white keys of the piano), octatonic, or whole tone. For example, even if a passage is not based on a single whole-tone scale, it would be of interest to discover that most or all of its sets are whole-tone subsets. In Example 9-19a, the violin states a figure that, while not octatonic, is constructed from octatonic subsets. The piano a few measures later answers with some octatonic subsets of its own with another non-octatonic figure (Example 9-19b).

EXAMPLE 9-19 Zwilich: Sonata in Three Movements (1974), III

Reprinted by permission of Carl Fischer, LLC.

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