For other uses, see Harmonic scale (disambiguation).
Harmonic series on C, partials 1–5 numbered Playⓘ.Harmonic series on G, partials 1–5 numbered Playⓘ.
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.[1]
For example, if the harmonic scale is tuned to a fundamental of C, then harmonics 16–32 are as follows:
Notation
Harmonics[2]
Cents
C
C
C
16ⓘ
0
C♯
C♯
D♭
17ⓘ
104.96
D
D
D♮
18ⓘ
203.91
E♭
E♭
E♭
19ⓘ
297.51
E♮
E♮
E↓
20ⓘ
386.31
F
F+
F
21ⓘ
470.78
F♯
F↑
F♯
22ⓘ
551.32
G
G
G
24ⓘ
701.96
A♭
A♭
A♭
26ⓘ
840.53
A♮
A♮+
A♮
27ⓘ
905.87
B♭
B♭
B♭
28ⓘ
968.83
B♮
B♮
B♮↓
30ⓘ
1088.27
C'
C'
C'
32ⓘ
1200
Some harmonics are not included:[1] 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. Play diatonic scaleⓘ
Harmonic-scales chromatic on C and G. Play chromatic scale on Cⓘ
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.[3]
^ abMilano, 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, doi:10.2307/3680228, JSTOR 3680228
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Global Information
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♯
♭
♭