358edo: Difference between revisions
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Created page with "{{Infobox ET}} {{EDO intro|358}} == Theory == 358et is consistent to the 7-odd-limit and the harmonic 3 is about halfway its steps. It is suitable for use with the 2...." |
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== Theory == | == Theory == | ||
358et is consistent to the [[7-odd-limit]] and the [[harmonic]] 3 is about halfway its steps. It is suitable for use with the 2.9.5.7.11.17.23.29.37.41 [[subgroup]]. Using the patent val, it tempers out 283115520/282475249, 26873856/26796875, 48828125/48771072, [[2100875/2097152]] and 200120949/200000000 in the 7-limit; 20155392/20131375, 234375/234256, 29296875/29218112, 46656/46585, 1953125/1951488, 226492416/226474325, [[540/539]], 107495424/107421875, 5788125/5767168, 5767168/5764801, 1375/1372, [[3025/3024]], 766656/765625, 4108797/4096000 and 644204/643125 in the 11-limit. It | 358et is consistent to the [[7-odd-limit]] and the [[harmonic]] 3 is about halfway its steps. It is suitable for use with the 2.9.5.7.11.17.23.29.37.41 [[subgroup]]. Using the patent val, it tempers out 283115520/282475249, 26873856/26796875, 48828125/48771072, [[2100875/2097152]] and 200120949/200000000 in the 7-limit; 20155392/20131375, 234375/234256, 29296875/29218112, 46656/46585, 1953125/1951488, 226492416/226474325, [[540/539]], 107495424/107421875, 5788125/5767168, 5767168/5764801, 1375/1372, [[3025/3024]], 766656/765625, 4108797/4096000 and 644204/643125 in the 11-limit. It [[support]]s [[hypnos]] and [[lee]]. | ||
=== Odd harmonics === | === Odd harmonics === | ||
Revision as of 12:36, 30 December 2023
| ← 357edo | 358edo | 359edo → |
Theory
358et is consistent to the 7-odd-limit and the harmonic 3 is about halfway its steps. It is suitable for use with the 2.9.5.7.11.17.23.29.37.41 subgroup. Using the patent val, it tempers out 283115520/282475249, 26873856/26796875, 48828125/48771072, 2100875/2097152 and 200120949/200000000 in the 7-limit; 20155392/20131375, 234375/234256, 29296875/29218112, 46656/46585, 1953125/1951488, 226492416/226474325, 540/539, 107495424/107421875, 5788125/5767168, 5767168/5764801, 1375/1372, 3025/3024, 766656/765625, 4108797/4096000 and 644204/643125 in the 11-limit. It supports hypnos and lee.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.40 | -0.84 | -0.11 | +0.56 | -1.60 | +0.81 | +1.12 | -1.04 | +0.81 | -1.51 | -1.46 |
| Relative (%) | -41.7 | -25.0 | -3.3 | +16.7 | -47.7 | +24.3 | +33.3 | -31.2 | +24.2 | -45.0 | -43.5 | |
| Steps (reduced) |
567 (209) |
831 (115) |
1005 (289) |
1135 (61) |
1238 (164) |
1325 (251) |
1399 (325) |
1463 (31) |
1521 (89) |
1572 (140) |
1619 (187) | |
Subset and supersets
358 factors into 2 × 179, with 2edo and 179edo as its subset edos. 716edo, which doubles it, gives a good correction to the harmonic 3.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.9 | [1135 -358⟩ | [⟨358 1135]] | -0.0882 | 0.0882 | 2.63 |
| 2.9.5 | [3 -9 11⟩, [-98 17 19⟩ | [⟨358 1135 831]] | +0.0616 | 0.2238 | 6.68 |
| 2.9.5.7 | 390625/388962, 4802000/4782969, 2100875/2097152 | [⟨358 1135 831 1005]] | +0.0561 | 0.1941 | 5.79 |