Harmonic Scale

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. It includes 144 notes per octave and two circles of fifths.

For example, if the harmonic scale is tuned to a fundamental of C then C is also the 16th and 32nd harmonics, C♯ is the 17th ( Play ), D the 18th ( Play ), E♭ the 19th ( Play ), E♮ the 20th ( Play ), F the 21st (a natural seventh above G, but not a great interval above C) ( Play ), F♯ the 22nd ( Play ), G the 24th ( Play ), A♭ the 26th ( Play ), A♮ the 27th (a just fifth above D) ( Play ), B♭ the 28th ( Play ), B♮ the 30th ( Play ), and some harmonics are not included.  Play diatonic scale 

Harmonic Scale chromatic on C.  Play chromatic scale 

It was invented by Wendy Carlos and used on her album Beauty in the Beast (1986). Transpositions and tuning tables are controlled by left-hand on the appropriate note on a one-octave keyboard.