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 | ||
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.
Though described by Carlos as containing "144 [= 12<sup>2</sup>] distinct pitches to the octave", the twelve scales include 78 notes per octave.
Technically there should then be duplicates and thus 57 pitches . For example, a perfect fifth above G (D) is the major tone above C.