The Harmonic Scale is a "super-Just" musical scale allowing extended just intonation, beyond 5-limit to the 19th harmonic ( Play ), and free 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.
For example, if the harmonic scale is tuned to a fundamental of C then harmonics 16-32 are as follows:
It was invented by Wendy Carlos and used on three pieces on her album Beauty in the Beast (1986); Just Imaginings, That's Just It, and Yusae-Aisae. Versions of the scale have also been used by Ezra Sims and Frans Richter Herf.
Number of notes
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.
- 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, JSTOR 3680228
- Carlos, Wendy (1987), "Tuning: At the Crossroads", Computer Music Journal, 11 (1): 29–43, JSTOR 3680176
- "Wendy Carlos Harmonic scale", Microtonal-Synthesis.com.