interval cycle

In music, an interval cycle is the collection of pitches created by starting with a certain note and going up by a certain interval until the original note is reached (e.g. starting from C, going up by 3 semitones repeatedly until eventually C is again reached - the cycle is the collection of all the notes met on the way). In other words, interval cycles "unfold a single recurrent interval in a series that closes with a return to the initial pitch class".

Interval cycles 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).

Here are interval cycles C1, C2, C3, 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. A minimum of three pitches are needed to represent an 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 Béla Bartók, Alexander Scriabin, Edgard Varèse, and the Second Viennese 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.

External links

• The "Giant Steps" Progression and Cycle Diagrams by Dan Adler

References

• Perle, George (1990). The Listening Composer, p. 21. California: University of California Press. ISBN 0-520-06991-9.

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