User:MisterShafXen/32ed77: Difference between revisions
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Prime factorization
25
Step size
235.004 ¢
Octave
5\32ed77 (1175.02 ¢)
Twelfth
8\32ed77 (1880.04 ¢) (→ 1\4ed77)
Consistency limit
10
Distinct consistency limit
4
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Latest revision as of 14:44, 1 August 2025
| ← 31ed77 | 32ed77 | 33ed77 → |
32 equal divisions of the 77th harmonic (abbreviated 32ed77) is a nonoctave tuning system that divides the interval of 77/1 into 32 equal parts of about 235 ¢ each. Each step represents a frequency ratio of 771/32, or the 32nd root of 77.
Intervals
| Steps | Cents | Approximate ratios | Note names (9\46) |
|---|---|---|---|
| 0 | 0 | 1/1 | C |
| 1 | 235 | 8/7, 23/20 | ^D |
| 2 | 470 | 17/13, 21/16, 25/19 | vF |
| 3 | 705 | 3/2 | G |
| 4 | 940 | 12/7, 19/11 | ^A |
| 5 | 1175 | vC | |
| 6 | 1410 | 9/4 | D |
| 7 | 1645 | 13/5 | … |
| 8 | 1880 | ||
| 9 | 2115 | 17/5, 27/8 | |
| 10 | 2350 | ||
| 11 | 2585 | ||
| 12 | 2820.1 | ||
| 13 | 3055.1 | ||
| 14 | 3290.1 | 20/3 | |
| 15 | 3525.1 | 23/3 | |
| 16 | 3760.1 | ||
| 17 | 3995.1 | 10/1 | |
| 18 | 4230.1 | 23/2 | |
| 19 | 4465.1 | ||
| 20 | 4700.1 | ||
| 21 | 4935.1 | ||
| 22 | 5170.1 | ||
| 23 | 5405.1 | ||
| 24 | 5640.1 | ||
| 25 | 5875.1 | ||
| 26 | 6110.1 | ||
| 27 | 6345.1 | ||
| 28 | 6580.1 | ||
| 29 | 6815.1 | ||
| 30 | 7050.1 | ||
| 31 | 7285.1 | ||
| 32 | 7520.1 |