Harmonic series on G, partials 1-5 numbered
Play ( · help ) info
Harmonic Scale is a "super-Just" musical scale allowing extended just intonation, beyond 5- limit to the 19th harmonic ( ), and free Play ( · help ) info modulation through the use of synthesizers. Transpositions and tuning tables are controlled by the left hand on the appropriate note on a one-octave keyboard. [1 ]
For example, if the harmonic scale is tuned to a
fundamental of C then harmonics 16-32 are as follows:
Some harmonics are not included:
23, 25, 29, & 31. The 21st is a natural seventh above G, but not a great interval above C and the 27th is a just fifth above D. [1 ] Play diatonic scale ( · help ) info
It was invented by
Wendy Carlos and used on three pieces on her album (1986); Beauty in the Beast Just Imaginings, That's Just It, and Yusae-Aisae. Versions of the scale have also been used by Ezra Sims and Frans Richter Herf. [3 ]
Number of notes [ edit ]
Though described by Carlos as containing, "
144 [=12 2] distinct pitches to the octave," the twelve scales include [4 ] 78 (= 12(12+1)⁄ 2) notes per octave.
Technically there should then be duplicates and thus 57 (=78-21) pitches (21=
6(6+1)⁄ 2). For example, a perfect fifth above G (D) is the major tone above C.
References [ edit ]
^ a b Milano, Dominic (November 1986). "A Many-Colored Jungle of Exotic Tunings", Keyboard.
^ Benson, Dave (2007). Music: A Mathematical Offering, p.212. ISBN 9780521853873.
^ Sims, Ezra (1987), "Observations on Microtonality Issue: Letters", Computer Music Journal 11 (4): 8–9
^ Carlos, Wendy (1987), "Tuning: At the Crossroads", Computer Music Journal 11 (1): 29–43
External links [ edit ]