Английская Википедия:Delta scale

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Файл:Just diatonic semitone on C.png

Minor second Шаблон:Audio

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 Шаблон:Audio. 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, AШаблон:MusicШаблон:Music, Шаблон:Audio) to approximate the interval Шаблон:Frac, which equals 6:5 (EШаблон:Music, 315.64 cents, Шаблон:Audio). Thus the step is approximately 13.946 cents, and there are 86.049 steps per octave.

<math>\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}</math>

(Шаблон:Audio)

The Bohlen–Pierce delta scale is based on the tritave and the 7:5:3 "wide" triad (Шаблон:Audio) and the 9:7:5 "narrow" triad (Шаблон:Audio) (rather than the conventional 4:5:6 triad). Notes include:

1:1 Шаблон:Audio

25:21 Шаблон:Audio

9:7 Шаблон:Audio

75:49 Шаблон:Audio

5:3 Шаблон:Audio

9:5 Шаблон:Audio

15:7 Шаблон:Audio

7:3 Шаблон:Audio

25:9 Шаблон:Audio

3:1 Шаблон:Audio

interval name	size (steps)	size (cents)	just ratio	just (cents)	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

See also

• Alpha scale
• Beta scale
• Gamma scale

Further reading

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

Шаблон:Music-theory-stub