8745edo: Difference between revisions
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Created page with "{{Infobox ET}} {{EDO intro|8745}} This dual-fifths system is the largest number EDO which tempers out Mercator's comma. === Prime harmonics === {{Harmonics in equal|8745}}" |
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{{ | {{ED intro}} This dual-fifths system is the largest number EDO which tempers out [[Mercator's comma]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|8745}} | {{Harmonics in equal|8745}} | ||
Latest revision as of 18:26, 19 February 2025
| ← 8744edo | 8745edo | 8746edo → |
8745 equal divisions of the octave (abbreviated 8745edo or 8745ed2), also called 8745-tone equal temperament (8745tet) or 8745 equal temperament (8745et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 8745 equal parts of about 0.137 ¢ each. Each step represents a frequency ratio of 21/8745, or the 8745th root of 2. This dual-fifths system is the largest number EDO which tempers out Mercator's comma.
Prime harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.0682 | -0.0358 | -0.0437 | +0.0008 | +0.0371 | -0.0474 | +0.0332 | +0.0189 | -0.0173 | +0.0253 | +0.0618 |
| Relative (%) | -49.7 | -26.1 | -31.9 | +0.6 | +27.0 | -34.5 | +24.2 | +13.7 | -12.6 | +18.4 | +45.1 | |
| Steps (reduced) |
13860 (5115) |
20305 (2815) |
24550 (7060) |
27721 (1486) |
30253 (4018) |
32360 (6125) |
34166 (7931) |
35745 (765) |
37148 (2168) |
38411 (3431) |
39559 (4579) | |