Delta scale

Minor second Play
The delta scale's approximations compared with the just values
Twelve-tone equal temperament vs. just

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.

The scale step may also precisely be derived from using 50:28 (25:14, 1003.8 cents, A7 upside-down, Play) to approximate the interval 3:25:4, 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.

(Play)

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
  1. ^ Taruskin, Richard (1996). Stravinsky and the Russian Traditions: A Biography of the Works through Mavra, p. 1394. ISBN 978-0-520-07099-8.
  2. ^ "What about BP tonality?", The Bohlen-Pierce Site.