Harmonic scale
The harmonic scale is a "super-just" musical scale allowing extended just intonation, beyond 5-limit to the 19th harmonic (Audio file "19th harmonic on C.mid" not found), 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 | Audio file "Unison on C.mid" not found | 0 |
| C♯ | C17♯ | D♭ | Audio file "Minor diatonic semitone on C.mid" not found | 104.96 |
| D | D | D♮ | Audio file "Major tone on C.mid" not found | 203.91 |
| E♭ | E19♭ | E♭ | Audio file "19th harmonic on C.mid" not found | 297.51 |
| E♮ | E♮ | E↓ | Audio file "Just major third on C.mid" not found | 386.31 |
| F | F7+ | FFile:Half down arrow.png | Audio file "Twenty-first harmonic on C.mid" not found | 470.78 |
| F♯ | F↑ | FFile:Sims flagged arrow down.svg♯ | Audio file "Eleventh harmonic on C.mid" not found | 551.32 |
| G | G | G | Audio file "Just perfect fifth on C.mid" not found | 701.96 |
| A♭ | A13♭ | AFile:Half up arrow.png♭ | Audio file "Tridecimal neutral sixth on C.mid" not found | 840.53 |
| A♮ | A♮+ | A♮ | Audio file "Pythagorean major sixth on C.mid" not found | 905.87 |
| B♭ | B7♭ | BFile:Half down arrow.png♭ | Audio file "Harmonic seventh on C.mid" not found | 968.83 |
| B♮ | B♮ | B♮↓ | Audio file "Just major seventh on C.mid" not found | 1088.27 |
| C' | C' | C' | Audio file "Perfect octave on C.mid" not found | 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. Audio file "Harmonic Scale diatonic on C.mid" not found
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]
Number of notes
[edit | edit source]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.
References
[edit | edit source]- ^ a b Milano, Dominic (November 1986). "A Many-Colored Jungle of Exotic Tunings", Keyboard.
- ^ Benson, Dave (2007). Music: A Mathematical Offering, p. 212. Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value)..
- ^ Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
- ^ Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
External links
[edit | edit source]- "Wendy Carlos Harmonic scale", Microtonal-Synthesis.com.
