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. Music is an Art form in which the medium is Sound organized in Time. In Music, a pitch class is a set of all pitches that are a whole number of Octaves apart e In Music theory, the term interval describes the relationship between the pitches of two Notes Intervals may be described as vertical 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". In Music theory, the term interval describes the relationship between the pitches of two Notes Intervals may be described as vertical In Music, a pitch class is a set of all pitches that are a whole number of Octaves apart e

Interval cycles are notated by George Perle using the letter "C" (for cycle), with an interval class integer to distinguish the interval. George Perle (born May 6, 1915 in Bayonne New Jersey) is a Composer and music theorist. In Musical set theory, an interval class (usual abbreviation ic) is the shortest distance in Pitch class space between two unordered Pitch classes Thus the diminished seventh chord would be C3 and the augmented triad would be C4. In Music theory, a diminished seventh ( is an interval encompassing nine Semitones or a particular chord containing this interval In music an augmented triad ( is a triad consisting of two Major thirds Harmonic considerations Whereas a Major triad, such as C-E-G A superscript may be added to distinguish between transpositions, using 0–11 to indicate the lowest pitch class in the cycle. In Music transposition refers to the process of moving a collection of notes ( pitches) up or down in pitch by a constant interval. "These interval cycles play a fundamental role in the harmonic organization of post-diatonic music and can easily be identified by naming the cycle. In Acoustics and Telecommunication, the harmonic of a Wave is a component Frequency of the signal that is an Integer Atonality in its broadest sense describes Music that lacks a tonal center, or key. " (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. Equal temperament is a Musical temperament, or a system of tuning in which every pair of adjacent notes has an identical Frequency ratio. In music just intonation is any Musical tuning in which the frequencies of Notes are related by Ratios of Whole numbers Any interval 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. A major third ( is one of two commonly occurring Musical intervals that span three Diatonic scale degrees the other being the Minor third. A diesis is a comma type of Musical interval, usually meaning the difference between three justly tuned major thirds (tuned in the Frequency 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. Symmetry generally conveys two primary meanings The first is an imprecise sense of harmonious or aesthetically-pleasing proportionality and balance such that it reflects beauty or However, a seven-pitch segment of C5 will produce the diatonic major scale (Perle, 1990):

This is known also known as a generated collection. In Music theory, a diatonic scale (from the Greek διατονικος, meaning " through tones" also known as the heptatonia prima and In Diatonic set theory a generated collection is a collection or scale formed by repeatedly adding a constant interval in Integer notation 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). A chord progression (also chord sequence and harmonic progression or sequence) is a series of chords played in order Béla Viktor János Bartók (March 25 1881&ndashSeptember 26 1945 was a Hungarian Composer and Pianist, considered to be one of the greatest Alexander Nikolayevich Scriabin (Алекса́ндр Никола́евич Скря́бин Aleksandr Nikolaevič Skrjabin; sometimes transliterated as Skriabin WikipediaWikiProject Composers#Lead section --> Edgard Victor Achille Charles Varèse, whose name was also spelled Edgar Varèse The Second Viennese School is the term generally used in English -speaking countries to denote the group of Composers that comprised Arnold Schoenberg Arnold Schoenberg ( pronounced ˈʃøːnbɛrk (13 September 1874 &ndash 13 July 1951 was an Austrian and later American Composer, associated with Alban Maria Johannes Berg (February 9 1885 &ndash December 24 1935 was an Austrian Composer. WikipediaWikiProject Composers#Lead section --> Anton Webern (December 3 1883 &ndash September 15 1945 was an Austrian Composer At the same time, these progressions signal the end of tonality. Tonality is a system of Music in which specific hierarchical pitch relationships are based on a key "center" or tonic. (Perle, 1990)

Interval cycles are also important in jazz, such as in Coltrane changes. Jazz is an American Musical art form which originated in the beginning of the 20th century in African American communities in the Southern United States In Jazz harmony, the Coltrane changes ( Coltrane Matrix or cycle) are a harmonic progression variation using substitute chords over common jazz chord progressions

External links

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

References

• Perle, George (1990). George Perle (born May 6, 1915 in Bayonne New Jersey) is a Composer and music theorist. The Listening Composer, p. 21. California: University of California Press. ISBN 0-520-06991-9.

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