The δ (delta) scale is a non-octave repeating

musical scale In music theory, a scale is any set of musical notes ordered by fundamental frequency or pitch. A scale ordered by increasing pitch is an ascending scale, and a scale ordered by decreasing pitch is a descending scale. Often, especially in the ...

. It may be regarded as the

beta scale The β (beta) scale is a non-octave-repeating musical scale invented by Wendy Carlos and first used on her album ''Beauty in the Beast'' (1986). It is derived from approximating just intervals using multiples of a single interval without, as is ...

's reciprocal, since it is "as far 'down' the ( 0 3 6 9) circle from α as β is 'up'".Taruskin, Richard (1996). ''Stravinsky and the Russian Traditions: A Biography of the Works through Mavra'', p. 1394. . As such it would split the

minor second A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically. It is defined as the interval between two adjacent no ...

(presumably 16:15) into eight equal parts of approximately 14 cents each . This would total approximately 85.7 steps per octave. The

scale step In Schenkerian theory, a scale-step (german: Stufe) is a triad (based on one of the diatonic scale degrees) that is perceived as an organizing force for a passage of music (in accordance with the principle of composing-out). In ''Harmony'', ...

may also precisely be derived from using 50:28 (25:14, 1003.8 cents, A, ) to approximate the interval , which equals 6:5 (E, 315.64 cents, ). Thus the step is approximately 13.946 cents, and there are 86.049 steps per octave. :

\begin
 \frac = 0.011\,621\,2701 \\
 0.011\,621\,2701 \times 1200 = 13.945\,524\,1627
\end

() The Bohlen–Pierce delta scale is based on the tritave and the 7:5:3 "wide" triad () and the 9:7:5 "narrow" triad () (rather than the conventional 4:5:6 triad). Notes include:"What about BP tonality?"
''The Bohlen-Pierce Site''. : 1:1 :25:21 : 9:7 :75:49 : 5:3 : 9:5 : 15:7 : 7:3 : 25:9 : 3:1

See also

References

Further reading