The harmonic scale is a "super-just" musical scale allowing extended just intonation, beyond 5- limit to the 19th harmonic ( ), 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 | 0 | |
C♯ | C
![]() |
D♭ | 104.96 | |
D | D | D♮ | 203.91 | |
E♭ | E
![]() |
E♭ | 297.51 | |
E♮ | E♮ | E↓ | 386.31 | |
F | F
![]() |
F
![]() |
470.78 | |
F♯ | F↑ | F
![]() |
551.32 | |
G | G | G | 701.96 | |
A♭ | A
![]() |
A
![]() |
840.53 | |
A♮ | A♮+ | A♮ | 905.87 | |
B♭ | B
![]() |
B
![]() |
968.83 | |
B♮ | B♮ | B♮↓ | 1088.27 | |
C' | C' | C' | 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.
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]
Though described by Carlos as containing " 144 [= 122] distinct pitches to the octave", [4] the twelve scales include 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.
The harmonic scale is a "super-just" musical scale allowing extended just intonation, beyond 5- limit to the 19th harmonic ( ), 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 | 0 | |
C♯ | C
![]() |
D♭ | 104.96 | |
D | D | D♮ | 203.91 | |
E♭ | E
![]() |
E♭ | 297.51 | |
E♮ | E♮ | E↓ | 386.31 | |
F | F
![]() |
F
![]() |
470.78 | |
F♯ | F↑ | F
![]() |
551.32 | |
G | G | G | 701.96 | |
A♭ | A
![]() |
A
![]() |
840.53 | |
A♮ | A♮+ | A♮ | 905.87 | |
B♭ | B
![]() |
B
![]() |
968.83 | |
B♮ | B♮ | B♮↓ | 1088.27 | |
C' | C' | C' | 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.
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]
Though described by Carlos as containing " 144 [= 122] distinct pitches to the octave", [4] the twelve scales include 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.