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In music
Music

Music is an art form whose media is sound organized in time. Common elements of music are pitch , rhythm , dynamics , and the sonic qualities of timbre and texture ....
, an interval cycle is the collection of pitch
Pitch class

In music, a pitch class is a set of all Pitch that are a whole number of octaves apart, e.g. the pitch class C consists of the Cs in all octaves....
es created by starting with a certain note and going up by a certain interval
Interval (music)

In music theory, the term interval describes the relationship between the pitch of two notes.Intervals may be described as:*vertical if the two notes sound simultaneously...
 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
Interval (music)

In music theory, the term interval describes the relationship between the pitch of two notes.Intervals may be described as:*vertical if the two notes sound simultaneously...
 in a series that closes with a return to the initial pitch class
Pitch class

In music, a pitch class is a set of all Pitch that are a whole number of octaves apart, e.g. the pitch class C consists of the Cs in all octaves....
".

Interval cycles are notated by George Perle
George Perle

George Perle was a composer and music theory. He was born in Bayonne, New Jersey. A student of Ernst Krenek, Perle composed with a technique of his own devising called "twelve-tone tonality," which is different from, but related to, twelve-tone technique ....
 using the letter "C" (for cycle), with an interval class
Interval class

In musical set theory, an interval class is the shortest distance in pitch class space between two unordered pitch classes. For example, the interval class between pitch classes 4 and 9 is 5 because 9 − 4 = 5 is less than 4 − 9 = −5 = 7 ....
 integer to distinguish the interval.






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In music
Music

Music is an art form whose media is sound organized in time. Common elements of music are pitch , rhythm , dynamics , and the sonic qualities of timbre and texture ....
, an interval cycle is the collection of pitch
Pitch class

In music, a pitch class is a set of all Pitch that are a whole number of octaves apart, e.g. the pitch class C consists of the Cs in all octaves....
es created by starting with a certain note and going up by a certain interval
Interval (music)

In music theory, the term interval describes the relationship between the pitch of two notes.Intervals may be described as:*vertical if the two notes sound simultaneously...
 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
Interval (music)

In music theory, the term interval describes the relationship between the pitch of two notes.Intervals may be described as:*vertical if the two notes sound simultaneously...
 in a series that closes with a return to the initial pitch class
Pitch class

In music, a pitch class is a set of all Pitch that are a whole number of octaves apart, e.g. the pitch class C consists of the Cs in all octaves....
".

Interval cycles are notated by George Perle
George Perle

George Perle was a composer and music theory. He was born in Bayonne, New Jersey. A student of Ernst Krenek, Perle composed with a technique of his own devising called "twelve-tone tonality," which is different from, but related to, twelve-tone technique ....
 using the letter "C" (for cycle), with an interval class
Interval class

In musical set theory, an interval class is the shortest distance in pitch class space between two unordered pitch classes. For example, the interval class between pitch classes 4 and 9 is 5 because 9 − 4 = 5 is less than 4 − 9 = −5 = 7 ....
 integer to distinguish the interval. Thus the diminished seventh chord
Diminished seventh chord

A diminished seventh chord is a four note chord comprising a diminished chord plus the interval of a diminished seventh above the root . Thus it is , or enharmonically , of any major scale; for example, C diminished-seventh would be , or enharmonically ....
 would be C3 and the augmented triad
Augmented triad

In music, an augmented triad is a triad consisting of two major thirds....
 would be C4. A superscript may be added to distinguish between transpositions
Transposition (music)

In music transposition refers to the process of moving a collection of notes up or down in pitch by a constant interval . For example, one might transpose an entire piece of music into another Key ....
, using 0–11 to indicate the lowest pitch class in the cycle. "These interval cycles play a fundamental role in the harmonic
Harmonic

In acoustics and telecommunication, a harmonic of a wave is a component frequency of the Signalling that is an integer multiple of the fundamental frequency....
 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 C1 C4 and C6
Interval cycles assume the use of equal temperament
Equal temperament

Equal temperament is a musical temperament, or a system of Musical tuning in which every pair of adjacent notes has an identical frequency ratios....
 and may not work in other systems such as just intonation
Just intonation

In music, just intonation is any musical tuning in which the frequency of notes are related by ratios of whole numbers. Any interval tuned in this way is called a just interval; in other words, the two notes are members of the same harmonic series ....
. For example, if the C4 interval cycle used justly-tuned major third
Major third

A major third is one of two commonly occurring musical intervals that span three diatonic scale degrees, the other being the minor third. It is denoted 'major' because it is the larger of the two: the major third is a leap of four semitones, the minor third three....
s it would fall flat of an octave return by an interval known as the diesis
Diesis

A diesis is a Comma type of musical interval, usually meaning the difference between three just intonation major thirds and an octave , equal to 128:125 or about 41.06 Cent s....
. 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
Generated collection

In diatonic set theory a generated collection is a set or scale formed by repeatedly adding a constant interval in integer notation, the generator, also known as an interval cycle, around the chromatic circle until a complete collection or scale is formed....
. A minimum of three pitches are needed to represent an interval cycle. (Perle, 1990)

Cyclic tonal progressions
Chord progression

A chord progression is series of chord s played in order. Chord progressions are central to most modern music and the principal study of harmony....
 in the works of Romantic composers such as Gustav Mahler
Gustav Mahler

Gustav Mahler was a Bohemian-born Austrian composer and conducting. He was best known during his own lifetime as one of the leading orchestral and operatic conductors of the day....
 and Richard Wagner
Richard Wagner

Wilhelm Richard Wagner was a German composer, Conducting, theatre director and essayist, primarily known for his operas . Unlike most other great opera composers, Wagner wrote both the scenario and libretto for his works....
 form a link with the cyclic pitch successions in the atonal music of Modernists such as Béla Bartók
Béla Bartók

B?la Viktor J?nos Bart?k was a Hungarian people composer and pianist, considered to be one of the greatest composers of the 20th century. Through his collection and analytical study of folk music, he was one of the founders of ethnomusicology....
, Alexander Scriabin
Alexander Scriabin

Alexander Nikolayevich Scriabin was a Russian composer and pianist who initially developed a highly lyrical and idiosyncratic tonal language inspired by the music of Chopin....
, Edgard Varčse
Edgard Varčse

Edgard Victor Achille Charles Var?se, whose name was also spelled Edgar Var?se , was an innovative French-born composer who spent the greater part of his career in the United States....
, and the Second Viennese School
Second Viennese School

The Second Viennese School is the term generally used in English language-speaking countries to denote the group of composers that comprised Arnold Schoenberg and his pupils and close associates in early 20th century Vienna, Austria, where, with breaks, he lived and taught between 1903 and 1925....
 (Arnold Schoenberg
Arnold Schoenberg

Arnold Schoenberg was an Austrian and later American composer, associated with the expressionist movement in German poetry and art, and leader of the Second Viennese School....
, Alban Berg
Alban Berg

Alban Maria Johannes Berg was an Austrian composer. He was a member of the Second Viennese School with Arnold Schoenberg and Anton Webern, and produced compositions that combined Gustav Mahler Romantic music with a personal adaptation of Schoenberg's twelve-tone technique....
, and Anton Webern
Anton Webern

Anton Webern was an Austrian composer and Conducting. He was a member of the Second Viennese School. As a student and significant follower of Arnold Schoenberg, he became one of the best-known proponents of the twelve-tone technique; in addition, his innovations regarding schematic organization of pitch, rhythm and dynamics were formative...
). At the same time, these progressions
Succession

Succession is the act or process of following in order or sequence. .Succession may further refer to, within the context of "order" and "sequence":...
 signal the end of tonality
Tonality

Tonality is a system of music in which specific hierarchy pitch relationships are based on a Key "center" or Tonic . The term tonalit? originated with Alexandre-?tienne Choron and was borrowed by Fran?ois-Joseph F?tis in 1840 ....
. (Perle, 1990)

Interval cycles are also important in jazz
Jazz

Jazz is a primarily American musical art form which originated at the beginning of the 20th century in African American communities in the Southern United States from a confluence of African and European music traditions....
, such as in Coltrane changes
Coltrane changes

In jazz harmony, the Coltrane changes are a chord progression variation using substitute chords over common jazz chord progressions. These substitution patterns were first demonstrated by jazz musician John Coltrane on the album Blue Train_ on the tunes Lazy Bird and Moment's Notice....
.

External links

  • by Dan Adler