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.

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

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

See also

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References

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  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.

Further reading

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