31202edo: Difference between revisions
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mostly copied from 15601edo because it seems notable. idk how to explain why though |
Explain its xenharmonic value (not much but it's something) |
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{{Infobox ET}} | {{Infobox ET}} | ||
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31202edo approximates all harmonics up to the [[23-odd-limit]] with less than 25% [[relative interval error|relative error]]. | |||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
31202edo doubles [[15601edo]], from which the approximations of the 3rd, 19th, and 23rd harmonics are derived. | 31202edo doubles [[15601edo]], from which the approximations of the 3rd, 19th, and 23rd harmonics are derived. | ||
Latest revision as of 14:39, 31 July 2025
| ← 31201edo | 31202edo | 31203edo → |
31202 equal divisions of the octave (abbreviated 31202edo or 31202ed2), also called 31202-tone equal temperament (31202tet) or 31202 equal temperament (31202et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 31202 equal parts of about 0.0385 ¢ each. Each step represents a frequency ratio of 21/31202, or the 31202nd root of 2.
31202edo approximates all harmonics up to the 23-odd-limit with less than 25% relative error.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | +0.0000 | +0.0077 | -0.0034 | -0.0071 | -0.0046 | -0.0006 | +0.0064 | -0.0069 | +0.0107 | +0.0064 |
| Relative (%) | +0.0 | +0.0 | +20.0 | -8.8 | -18.5 | -12.0 | -1.6 | +16.6 | -18.0 | +27.7 | +16.7 | |
| Steps (reduced) |
31202 (0) |
49454 (18252) |
72449 (10045) |
87595 (25191) |
107941 (14335) |
115461 (21855) |
127537 (2729) |
132544 (7736) |
141144 (16336) |
151579 (26771) |
154581 (29773) | |
Subsets and supersets
31202edo doubles 15601edo, from which the approximations of the 3rd, 19th, and 23rd harmonics are derived.