Interval cycle

In music, an interval cycle is a collection of pitch classes created from a sequence of the same interval class. In other words, a collection of pitches 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". See: .

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.".

Here are interval cycles C1, C2, C3, C4 and C6:

Interval cycles assume the use of equal temperament and may not work in other systems such as just intonation. For example, if the C4 interval cycle used justly-tuned major thirds it would fall flat of an octave return by an interval known as the diesis. Put another way, a major third above G♯ is B♯, which is only enharmonically the same as C in systems such as equal temperament, in which the diesis has been tempered out.

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