The Harmonic scale is a "super-just" musical scale allowing extended just intonation, beyond 5-limit to the 19th harmonic (
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.
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, Franz Richter Herf and Gosheven.
Number of notes
Technically there should then be duplicates and thus 57 (= 78 − 21) pitches (21 = 6(6+1)/). 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.