Delta scale

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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 About this soundPlay . 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, About this soundPlay ) to approximate the interval ​3:25:4, which equals 6:5 (E, 315.64 cents, About this soundPlay ). Thus the step is approximately 13.946 cents and there are 86.049 per octave.

(About this soundPlay )

The Bohlen–Pierce delta scale is based on the tritave and the 7:5:3 "wide" triad (About this soundPlay ) and the 9:7:5 "narrow" triad (About this soundPlay ) (rather than the conventional 4:5:6 triad). Notes include:[2]

1:1 About this soundPlay 
25:21 About this soundPlay 
9:7 About this soundPlay 
75:49 About this soundPlay 
5:3 About this soundPlay 
9:5 About this soundPlay 
15:7 About this soundPlay 
7:3 About this soundPlay 
25:9 About this soundPlay 
3:1 About this soundPlay 
interval name size
just ratio just
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[edit]

Further reading[edit]


  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.