Harmonic scale

Harmonic scale may refer to:

See also

Harmonic Scale

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:

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.  Play diatonic scale 

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

Though described by Carlos as containing, "144 [=12²] distinct pitches to the octave," 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.