Interval cycle

From Academic Kids

In music, interval cycles, "unfold a single recurrent interval in a series that closes with a return to the initial pitch class", and are notated by George Perle using the letter "C", for cycle, with an interval class integer to distinguish the interval. Thus the diminished seventh chord would be C3 and the augmented triad would be C4. A superscript may be added to distinguish between transpositions, using 0-11 to indicate the lowest pitch class in the cycle. "These interval cycles play a fundamental role in the harmonic organization of post-diatonic music and can easily be identified by naming the cycle." (Perle, 1990)

Missing image
Interval_cycles_C1-C4_and_C6.PNG
Interval cycles C1–C4 and C6

Interval cycles are symmetrical and thus non-diatonic. However, a seven pitch segment of C5 will produce the diatonic major scale. (Perle, 1990) This is known also known as a generated collection.

Missing image
7-note_segment_of_C5.png
7 note segment of C5

A minimum of three pitches are needed to represent a interval cycle. (Perle, 1990)

Cyclic tonal progressions in the works of Romantic composers such as Gustav Mahler and Richard Wagner form a link with the cyclic pitch successions in the atonal music of Modernists such as Bela Bartok, Alexander Scriabin, Edgard Varese, and the second Vienna school (Arnold Schoenberg, Alban Berg, and Anton Webern). At the same time, these progressions signal the end of tonality. (Perle, 1990)

Interval cycles are also important in jazz, such as in Coltrane changes.

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