156edo: Difference between revisions
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Linking; style; switch to prime harmonics since the odd harmonics table doesn't add much; -redundant categories |
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{{EDO intro}} | {{EDO intro}} | ||
It supports [[compton]] | It supports [[compton]]. It is the smallest edo to contain both [[12edo]] and [[13edo]] as subsets. | ||
The equal temperament [[tempering out|tempers out]] 531441/524288 ([[Pythagorean comma]]) and 1220703125/1207959552 (ditonmic comma) in the 5-limit, as well as 1224440064/1220703125 ([[parakleisma]]); [[225/224]], [[250047/250000]], and [[589824/588245]] in the 7-limit. Using the patent val, it tempers out [[441/440]], 1375/1372, 4375/4356, and 65536/65219 in the 11-limit; [[351/350]], [[364/363]], [[625/624]], 1625/1617, and 13122/13013 in the 13-limit. Using the 156e val, it tempers out [[385/384]], [[540/539]], 1331/1323, and 78408/78125 in the 11-limit; 351/350, 625/624, [[847/845]], and [[1001/1000]] in the 13-limit. | |||
== | === Prime harmonics === | ||
{{Harmonics in equal|156}} | {{Harmonics in equal|156|intervals=prime}} | ||
{{stub}} | {{stub}} | ||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
Revision as of 09:06, 11 May 2024
| ← 155edo | 156edo | 157edo → |
It supports compton. It is the smallest edo to contain both 12edo and 13edo as subsets.
The equal temperament tempers out 531441/524288 (Pythagorean comma) and 1220703125/1207959552 (ditonmic comma) in the 5-limit, as well as 1224440064/1220703125 (parakleisma); 225/224, 250047/250000, and 589824/588245 in the 7-limit. Using the patent val, it tempers out 441/440, 1375/1372, 4375/4356, and 65536/65219 in the 11-limit; 351/350, 364/363, 625/624, 1625/1617, and 13122/13013 in the 13-limit. Using the 156e val, it tempers out 385/384, 540/539, 1331/1323, and 78408/78125 in the 11-limit; 351/350, 625/624, 847/845, and 1001/1000 in the 13-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -1.96 | -1.70 | +0.40 | +2.53 | -2.07 | +2.74 | +2.49 | +2.49 | +1.19 | +1.12 |
| Relative (%) | +0.0 | -25.4 | -22.1 | +5.3 | +32.9 | -26.9 | +35.6 | +32.3 | +32.4 | +15.5 | +14.5 | |
| Steps (reduced) |
156 (0) |
247 (91) |
362 (50) |
438 (126) |
540 (72) |
577 (109) |
638 (14) |
663 (39) |
706 (82) |
758 (134) |
773 (149) | |
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