443edo: Difference between revisions
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Created page with "{{Infobox ET}} {{EDO intro|443}} == Theory == 443et tempers out 67108864/66976875, 6144/6125 and 32805/32768 in the 7-limit; 806736/805255, 35156250/35153041, 759375/7..." |
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== Theory == | == Theory == | ||
443et tempers out 67108864/66976875, [[6144/6125]] and [[32805/32768]] in the 7-limit; 806736/805255, 35156250/35153041, 759375/758912, [[131072/130977]], [[540/539]], 184549376/184528125, [[5632/5625]], [[8019/8000]], 160083/160000, 391314/390625, 202397184/201768035, 3294225/3294172 and 20614528/20588575 in the 11-limit. | 443et tempers out 67108864/66976875, [[6144/6125]] and [[32805/32768]] in the 7-limit; 806736/805255, 35156250/35153041, 759375/758912, [[131072/130977]], [[540/539]], 184549376/184528125, [[5632/5625]], [[8019/8000]], 160083/160000, 391314/390625, 202397184/201768035, 3294225/3294172 and 20614528/20588575 in the 11-limit. | ||
=== | ===Prime harmonics=== | ||
{{Harmonics in equal|443}} | {{Harmonics in equal|443}} | ||
===Subsets and supersets=== | ===Subsets and supersets=== | ||
443edo is the 86th [[prime edo]]. 886edo, which doubles it, gives a good correction until the 11-limit. | 443edo is the 86th [[prime edo]]. 886edo, which doubles it, gives a good correction until the 11-limit. | ||
Revision as of 20:13, 10 May 2023
| ← 442edo | 443edo | 444edo → |
Theory
443et tempers out 67108864/66976875, 6144/6125 and 32805/32768 in the 7-limit; 806736/805255, 35156250/35153041, 759375/758912, 131072/130977, 540/539, 184549376/184528125, 5632/5625, 8019/8000, 160083/160000, 391314/390625, 202397184/201768035, 3294225/3294172 and 20614528/20588575 in the 11-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.37 | +1.05 | +0.93 | +1.28 | -0.80 | +0.69 | +0.46 | +0.17 | -0.23 | +0.79 |
| Relative (%) | +0.0 | -13.8 | +38.6 | +34.2 | +47.2 | -29.5 | +25.4 | +16.8 | +6.2 | -8.6 | +29.1 | |
| Steps (reduced) |
443 (0) |
702 (259) |
1029 (143) |
1244 (358) |
1533 (204) |
1639 (310) |
1811 (39) |
1882 (110) |
2004 (232) |
2152 (380) |
2195 (423) | |
Subsets and supersets
443edo is the 86th prime edo. 886edo, which doubles it, gives a good correction until the 11-limit.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-702 443⟩ | ⟨443 702] | 0.1183 | 0.1183 | 4.37 |
Rank-2 temperaments
| Periods per 8ve |
Generator (reduced) |
Cents (reduced) |
Associated ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 92\443 | 249.21 | 81/70 | Hemischis (7-limit) |