Everything about Interval Cycle totally explained
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 (for example 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 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.
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.
Further Information
Get more info on 'Interval Cycle'.
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