201edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|210}} | {{EDO intro|210}} | ||
201edo is only [[consistent]] to the [[5-odd-limit]], and [[harmonic]] [[3/1|3]] is about halfway between its steps. | |||
Using the [[patent val]], it [[tempering out|tempers out]] 393216/390625 ([[würschmidt comma]]) and {{monzo| 25 -26 7 }} in the 5-limit; [[245/243]], [[50421/50000]], and [[2100875/2097152]] in the 7-limit; [[385/384]], [[896/891]], 1331/1323, and 47432/46875 in the 11-limit; [[196/195]], [[325/324]], [[2080/2079]], [[2200/2197]], and 3146/3125 in the 13-limit. | Using the [[patent val]], it [[tempering out|tempers out]] 393216/390625 ([[würschmidt comma]]) and {{monzo| 25 -26 7 }} in the 5-limit; [[245/243]], [[50421/50000]], and [[2100875/2097152]] in the 7-limit; [[385/384]], [[896/891]], 1331/1323, and 47432/46875 in the 11-limit; [[196/195]], [[325/324]], [[2080/2079]], [[2200/2197]], and 3146/3125 in the 13-limit. | ||
Using the 201e val, it tempers out [[441/440]], [[2200/2187]], [[3388/3375]], and [[65536/65219]] in the 11-limit; 196/195, 325/324, [[352/351]], [[1001/1000]], and 106496/105875 in the 13-limit. | |||
Using the 201de val, it tempers out [[4000/3969]], [[10976/10935]], and 4194304/4134375 in the 7-limit; [[540/539]], 896/891, 1375/1372, and 234375/234256 in the 11-limit; 325/324, 352/351, [[364/363]], [[640/637]], and [[4394/4375]] in the 13-limit (supporting the [[pluto]] temperament). | |||
Using the 201b val, it tempers out 1990656/1953125 (valentine comma) and {{monzo| -31 24 -3 }} in the 5-limit; [[126/125]], [[1029/1024]], and {{monzo| -2 19 0 -10 }} in the 7-limit; 540/539, 1944/1925, 2835/2816, and 483153/480200 in the 11-limit; [[1287/1280]], [[1575/1573]], [[1716/1715]], 2200/2197, and 3146/3125 in the 13-limit. | Using the 201b val, it tempers out 1990656/1953125 (valentine comma) and {{monzo| -31 24 -3 }} in the 5-limit; [[126/125]], [[1029/1024]], and {{monzo| -2 19 0 -10 }} in the 7-limit; 540/539, 1944/1925, 2835/2816, and 483153/480200 in the 11-limit; [[1287/1280]], [[1575/1573]], [[1716/1715]], 2200/2197, and 3146/3125 in the 13-limit. | ||
Using the 201bcf val, it tempers out 15625/15552 ([[15625/15552|kleisma]]) and {{monzo| -56 31 3 }} in the 5-limit; 1029/1024, [[250047/250000]], and 273375/268912 in the 7-limit; 385/384, 441/440, [[4000/3993]], and 295245/290521 in the 11-limit; [[351/350]], 975/968, 1287/1280, [[1573/1568]], and 10935/10816 in the 13-limit. | Using the 201bcf val, it tempers out 15625/15552 ([[15625/15552|kleisma]]) and {{monzo| -56 31 3 }} in the 5-limit; 1029/1024, [[250047/250000]], and 273375/268912 in the 7-limit; 385/384, 441/440, [[4000/3993]], and 295245/290521 in the 11-limit; [[351/350]], 975/968, 1287/1280, [[1573/1568]], and 10935/10816 in the 13-limit. | ||
=== Odd harmonics === | === Odd harmonics === | ||
{{Harmonics in equal|201}} | {{Harmonics in equal|201}} | ||
Revision as of 12:05, 15 April 2024
| ← 200edo | 201edo | 202edo → |
201edo is only consistent to the 5-odd-limit, and harmonic 3 is about halfway between its steps.
Using the patent val, it tempers out 393216/390625 (würschmidt comma) and [25 -26 7⟩ in the 5-limit; 245/243, 50421/50000, and 2100875/2097152 in the 7-limit; 385/384, 896/891, 1331/1323, and 47432/46875 in the 11-limit; 196/195, 325/324, 2080/2079, 2200/2197, and 3146/3125 in the 13-limit.
Using the 201e val, it tempers out 441/440, 2200/2187, 3388/3375, and 65536/65219 in the 11-limit; 196/195, 325/324, 352/351, 1001/1000, and 106496/105875 in the 13-limit.
Using the 201de val, it tempers out 4000/3969, 10976/10935, and 4194304/4134375 in the 7-limit; 540/539, 896/891, 1375/1372, and 234375/234256 in the 11-limit; 325/324, 352/351, 364/363, 640/637, and 4394/4375 in the 13-limit (supporting the pluto temperament).
Using the 201b val, it tempers out 1990656/1953125 (valentine comma) and [-31 24 -3⟩ in the 5-limit; 126/125, 1029/1024, and [-2 19 0 -10⟩ in the 7-limit; 540/539, 1944/1925, 2835/2816, and 483153/480200 in the 11-limit; 1287/1280, 1575/1573, 1716/1715, 2200/2197, and 3146/3125 in the 13-limit.
Using the 201bcf val, it tempers out 15625/15552 (kleisma) and [-56 31 3⟩ in the 5-limit; 1029/1024, 250047/250000, and 273375/268912 in the 7-limit; 385/384, 441/440, 4000/3993, and 295245/290521 in the 11-limit; 351/350, 975/968, 1287/1280, 1573/1568, and 10935/10816 in the 13-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.52 | +1.75 | -1.66 | -0.92 | -2.06 | +1.26 | -1.70 | +2.51 | +0.99 | +0.86 | -1.41 |
| Relative (%) | +42.3 | +29.2 | -27.8 | -15.5 | -34.6 | +21.2 | -28.5 | +42.0 | +16.7 | +14.4 | -23.6 | |
| Steps (reduced) |
319 (118) |
467 (65) |
564 (162) |
637 (34) |
695 (92) |
744 (141) |
785 (182) |
822 (18) |
854 (50) |
883 (79) |
909 (105) | |