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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'". 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, 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.

${\displaystyle {\begin{aligned}{\frac {50\log _{2}{\left({\frac {3}{2}}\right)}+28\log _{2}{\left({\frac {5}{4}}\right)}+23\log _{2}{\left({\frac {6}{5}}\right)}}{50^{2}+28^{2}+23^{2}}}=0.011\,621\,2701\\0.011\,621\,2701\times 1200=13.945\,524\,1627\end{aligned}}}$

(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:

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

See also

• Alpha scale
• Beta scale
• Gamma scale

References

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

• Bohlen, Heinz: "13 Tonstufen in der Duodezime", Acustica, vol. 39 no. 2, S. Hirzel Verlag, Stuttgart, 1978, pp. 76–86. (in German)

v t e Microtonal music
Composers	Richard Barrett Béla Bartók Easley Blackwood Jr. Heinz Bohlen Julián Carrillo Franklin Cox Mildred Couper John Eaton Brian Ferneyhough Michael Finnissy Bjørn Fongaard Alois Hába Christiaan Huygens Charles Ives Ben Johnston György Ligeti Stu Mackenzie Claus-Steffen Mahnkopf Joel Mandelbaum Joe Maneri Roger Redgate John Schneider Sevish Ezra Sims Nicola Vicentino Claude Vivier Elaine Walker Ivan Wyschnegradsky La Monte Young
Inventors	Glenn Branca Wendy Carlos Ivor Darreg Adriaan Fokker Lou Harrison Yuri Landman Harry Partch Tui St. George Tucker Nicola Vicentino
Tunings and scales	Non-octave- repeating scales Alpha scale Beta scale Gamma scale Delta scale Lambda scale (Bohlen–Pierce scale) Equal temperament 15 17 19 22 23 24 31 34 41 53 58 72 96 Just intonation Harry Partch's 43-tone scale Double diatonic
Concepts and techniques	Limit Otonality and Utonality Semitone Sonido 13 Xenharmonicity Tonality diamond
Groups and publications	Boston Microtonal Society Genesis of a Music Huygens-Fokker Foundation
Compositions	Beauty in the Beast quarter tone pieces just pieces Mother Sonata for Microtonal Piano Suite for Microtonal Piano Twelve Microtonal Etudes for Electronic Music Media Flying Microtonal Banana K.G. L.W.
Other topics	Enharmonic keyboard Generalized keyboard Modernism (music)

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