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 . 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, 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}
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+ |
28log | ||||
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2+23 | ||||
23log | ||||
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2}=0.0116212701\\ 0.0116212701 x 1200=13.9455241627 \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:[2]
25:21
75:49
align=center bgcolor="#ffffb4" | interval name | align=center bgcolor="#ffffb4" | size (steps) | align=center bgcolor="#ffffb4" | size (cents) | align=center bgcolor="#ffffb4" | just ratio | align=center bgcolor="#ffffb4" | just (cents) | align=center bgcolor="#ffffb4" | 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 |