POLYTONAL AND ATONAL RAMIFICATIONS: NEOCLASSICISM, DISSONANT COUNTERPOINT, GEBRAUCHSMUSIK, QUARTER-TONES, ETHER-MUSIC
POLYTONALITY is just what the term implies--many tonalities --that is, the simultaneous use of different tonalities (page 213). When only two keys are heard, it is frequently called bitonal. Another variant is polymelodic, which implies several melodies woven together either dissonantly or consonantly. The term, polyharmony has been explained (page 199) as the juxtaposition of two or more chords. These may be the combination of dissonant keys or closely related keys. By an analysis of the natural harmonic series (page 104) many polychordal combinations may be explained:
As the study of a polychordal system is new, it is still very much in the experimental stage. Henry Cowell suggests combining three triads fifths apart, as C, G, and F played simultaneously; thirds apart, C, E, and A; then seconds apart, C, D, and B. Using both major and minor chords, this would give a wide variety of polychords without including chromatic steps.
Darius Milhaud, in an article in La Revue Musicale ( Polytonalité et Atonalité, February, 1923) gives a very simple recipe of taking the chord of C major and superposing each of the eleven other major triads. Every chord can be expressed in four different ways:
|major + major||(c e g + d f# a)|
|minor + major||(c e♭ g + d f# a)|
|major + minor||(c e g + d f a)|
|minor + minor||(c e♭ g + d f a)|