Harmonic Scale

From Wikipedia, the free encyclopedia
Jump to: navigation, search
Harmonic series on C, partials 1-5 numbered About this sound Play .
Harmonic series on G, partials 1-5 numbered About this sound Play .

The Harmonic Scale is a "Super-Just" musical scale allowing extended just intonation, beyond 5-limit to the 19th harmonic (About this sound Play ), and free modulation through the use of synthesizers. It includes 144 (=12×12) notes per octave and two circles of fifths.[a] Transpositions and tuning tables are controlled by 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 C is also the 16th and 32nd harmonics, C is the 17th (About this sound Play ), D the 18th (About this sound Play ), E the 19th (About this sound Play ), E the 20th (About this sound Play ), F the 21st (a natural seventh above G, but not a great interval above C) (About this sound Play ), F the 22nd (About this sound Play ), G the 24th (About this sound Play ), A the 26th (About this sound Play ), A the 27th (a just fifth above D) (About this sound Play ), B the 28th (About this sound Play ), B the 30th (About this sound Play ), and some harmonics are not included.[1] About this sound Play diatonic scale 

Harmonic Scale chromatic on C.
Harmonics: 16, 17, 18, 19, 20, 21, 22, 24, 26, 27, 28, 30, 32[2] About this sound Play chromatic scale 

It was invented by Wendy Carlos and used on Just Imaginings, That's Just It, and Yusae-Aisae from her album Beauty in the Beast (1986).


  1. ^ Technically there should then be duplicates and thus 57 pitches. For example, a perfect fifth above G is the major tone above C.


  1. ^ a b Milano, Dominic (November 1986). "A Many-Colored Jungle of Exotic Tunings", Keyboard.
  2. ^ Benson, Dave (2007). Music: A Mathematical Offering, p.212. ISBN 9780521853873.

External links[edit]