189edo: Difference between revisions
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m Infobox ET added |
Adopt template: EDO intro; +prime error table; +subsets and supersets; -redundant categories |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro}} | |||
[[ | The equal temperament [[tempering out|tempers out]] 15625/15552 (kleisma) and 9007199254740992/8578797170610375 in the 5-limit; [[4000/3969]], [[6144/6125]], and 537824/531441 in the 7-limit, supporting the [[hemikleismic]] temperament. Using the [[patent val]], it tempers out [[896/891]], 1331/1323, 1375/1372, and 16896/16807 in the 11-limit; [[169/168]], [[352/351]], [[364/363]], and [[1001/1000]] in the 13-limit. | ||
=== Odd harmonics === | |||
{{Harmonics in equal|189}} | |||
=== Subsets and supersets === | |||
Since 189 factors into {{factorization|189}}, 189edo contains {{EDOs| 3, 7, 9, 21, 27, and 63 }} as its subsets. | |||
Revision as of 15:38, 22 April 2024
| ← 188edo | 189edo | 190edo → |
The equal temperament tempers out 15625/15552 (kleisma) and 9007199254740992/8578797170610375 in the 5-limit; 4000/3969, 6144/6125, and 537824/531441 in the 7-limit, supporting the hemikleismic temperament. Using the patent val, it tempers out 896/891, 1331/1323, 1375/1372, and 16896/16807 in the 11-limit; 169/168, 352/351, 364/363, and 1001/1000 in the 13-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.81 | +0.99 | +2.60 | -0.74 | +1.06 | -2.43 | -2.55 | +2.98 | +0.90 | -0.94 | +0.30 |
| Relative (%) | +44.2 | +15.6 | +41.0 | -11.6 | +16.7 | -38.3 | -40.2 | +47.0 | +14.2 | -14.8 | +4.7 | |
| Steps (reduced) |
300 (111) |
439 (61) |
531 (153) |
599 (32) |
654 (87) |
699 (132) |
738 (171) |
773 (17) |
803 (47) |
830 (74) |
855 (99) | |
Subsets and supersets
Since 189 factors into 33 × 7, 189edo contains 3, 7, 9, 21, 27, and 63 as its subsets.