The γ (gamma) scale is a non-octave repeating

musical scale In music theory, a scale is any set of musical notes ordered by fundamental frequency or pitch. A scale ordered by increasing pitch is an ascending scale, and a scale ordered by decreasing pitch is a descending scale. Often, especially in the ...

invented by

Wendy Carlos Wendy Carlos (born Walter Carlos, November 14, 1939) is an American musician and composer best known for her electronic music and film scores. Born and raised in Rhode Island, Carlos studied physics and music at Brown University before moving ...

while preparing ''

Beauty in the Beast ''Beauty in the Beast'' is a studio album from the American keyboardist and composer Wendy Carlos, released in 1986, on Audion Records, her first for a label other than Columbia Records since 1968. The album uses alternate musical tunings and s ...

'' (1986) though it does not appear on the album. It is derived from approximating

just interval In music, just intonation or pure intonation is the tuning of musical intervals as whole number ratios (such as 3:2 or 4:3) of frequencies. An interval tuned in this way is said to be pure, and is called a just interval. Just intervals (and c ...

s using multiples of a single interval without, as is standard in

equal temperament An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, wh ...

s, requiring an

octave In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...

(2:1). It may be approximated by splitting the

perfect fifth In music theory, a perfect fifth is the Interval (music), musical interval corresponding to a pair of pitch (music), pitches with a frequency ratio of 3:2, or very nearly so. In classical music from Western culture, a fifth is the interval fro ...

(3:2) into 20 equal parts (3:2≈35.1 cents), by splitting the

neutral third A neutral third is a musical interval wider than a minor third but narrower than a major third , named by Jan Pieter Land in 1880. Land makes reference to the neutral third attributed to Zalzal (8th c.), described by Al-Farabi (10th c.) as c ...

into two equal parts, or ten equal parts of approximately 35.1 cents each () for 34.188 steps per octave.Carlos, Wendy (1989–96)
"Three Asymmetric Divisions of the Octave"
''WendyCarlos.com''. The

scale step In Schenkerian theory, a scale-step (german: Stufe) is a triad (based on one of the diatonic scale degrees) that is perceived as an organizing force for a passage of music (in accordance with the principle of composing-out). In ''Harmony'', ...

may also precisely be derived from using 20:11 (B, 1035 cents, ) to approximate the interval , which equals 6:5 (E, 315.64 cents, ). Thus the step is approximately 35.099 cents and there are 34.1895 per octave.Benson, Dave (2006). ''Music: A Mathematical Offering'', p.232-233. . "Carlos has 34.188 γ-scale degrees to the octave, corresponding to a scale degree of 35.1 cents."

\frac=0.0292487852

and

0.0292487852\times1200=35.0985422804

() "It produces nearly perfect triads."Milano, Dominic (November 1986)
"A Many-Colored Jungle of Exotic Tunings"
''Keyboard''. "A 'third flavor', sort of intermediate to 'alpha' and 'beta', although a melodic

diatonic scale In music theory, a diatonic scale is any heptatonic scale that includes five whole steps (whole tones) and two half steps (semitones) in each octave, in which the two half steps are separated from each other by either two or three whole steps, ...

is easily available."

References

Equal temperaments Non–octave-repeating scales Wendy Carlos {{music-theory-stub

See also

References