1ed21/20
(Redirected from 21/20 equal-step tuning)
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| ← 0ed21/20 | 1ed21/20 | 2ed21/20 → |
(convergent)
(convergent)
1 equal division of 21/20 (1ed21/20), also known as ambitonal sequence of 21/20 (AS21/20) or 21/20 equal-step tuning, is the equal multiplication of the 21/20 septimal chromatic semitone of 84.467 cents. As such, every interval is a subset of 7-limit just inotation.
It is equal to approximately 14.2067 EDO, and as a result of tethering between compressed 14 and heavily stretched 15 it is quite xenharmonic in its sound. Nonetheless, it is quite a useful scale because it is related to nautilus, sextilififths and floral temperaments.
Harmonics
1ed21/20 offers a good approximation of the no-3s 11-limit, and of the no-3s, no-13s, no-59s 73-limit. It could be used as a dual-fifth tuning.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -17.5 | +40.8 | +1.1 | +9.9 | -12.4 | +36.2 | -5.9 | -29.5 | -22.4 | -1.3 | -32.3 |
| Relative (%) | -20.7 | +48.3 | +1.3 | +11.7 | -14.7 | +42.9 | -6.9 | -34.9 | -26.5 | -1.6 | -38.3 | |
| Step | 14 | 23 | 33 | 40 | 49 | 53 | 58 | 60 | 64 | 69 | 70 | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.8 | -9.6 | -7.5 | +7.4 | -31.7 | +36.1 | -21.6 | -15.1 | -31.1 | +5.3 | +37.5 |
| Relative (%) | -0.9 | -11.3 | -8.9 | +8.8 | -37.5 | +42.7 | -25.6 | -17.9 | -36.8 | +6.3 | +44.4 | |
| Step | 74 | 76 | 77 | 79 | 81 | 84 | 84 | 86 | 87 | 88 | 90 | |