Delta scale



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. 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♯, ) to approximate the interval $3:2/5:4$, 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{align}

\frac{50\log_2{\left(\frac32\right)} + 28\log_2{\left(\frac54\right)} + 23\log_2{\left(\frac65\right)}}{50^2+28^2+23^2} = 0.011\,621\,2701 \\ 0.011\,621\,2701 \times 1200 = 13.945\,524\,1627 \end{align}$$



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:
 * 1:1
 * 25:21
 * 9:7
 * 75:49
 * 5:3
 * 9:5
 * 15:7
 * 7:3
 * 25:9
 * 3:1