![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/9/94/Delta_scale_chromatic_circle.png/640px-Delta_scale_chromatic_circle.png&w=640&q=50)
Delta scale
From Wikipedia, the free encyclopedia
The δ (delta) scale is a non-octave repeating musical scale. It may be regarded as the beta scale's reciprocal, since it is "as far 'down' the (0 3 6 9) circle from α as β is 'up'".[1] As such it would split the minor second (presumably 16:15) into eight equal parts of approximately 14 cents each Playⓘ. This would total approximately 85.7 steps per octave.
![](http://upload.wikimedia.org/wikipedia/commons/thumb/c/c0/Just_diatonic_semitone_on_C.png/320px-Just_diatonic_semitone_on_C.png)
The scale step may also precisely be derived from using 50:28 (25:14, 1003.8 cents, A♯, Playⓘ) to approximate the interval 3:2⁄5:4, which equals 6:5 (E♭, 315.64 cents, Playⓘ). Thus the step is approximately 13.946 cents, and there are 86.049 steps per octave.
The Bohlen–Pierce delta scale is based on the tritave and the 7:5:3 "wide" triad (Playⓘ) and the 9:7:5 "narrow" triad (Playⓘ) (rather than the conventional 4:5:6 triad). Notes include:[2]
- 1:1 Playⓘ
- 25:21 Playⓘ
- 9:7 Playⓘ
- 75:49 Playⓘ
- 5:3 Playⓘ
- 9:5 Playⓘ
- 15:7 Playⓘ
- 7:3 Playⓘ
- 25:9 Playⓘ
- 3:1 Playⓘ
interval name | size (steps) |
size (cents) |
just ratio | just (cents) |
error |
minor third | 23 | 321.23 | 6:5 | 315.64 | +5.59 |
major third | 28 | 391.06 | 5:4 | 386.31 | +4.75 |
perfect fifth | 50 | 698.32 | 3:2 | 701.96 | −3.63 |