182edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|182}} | {{EDO intro|182}} | ||
== Theory == | == Theory == | ||
182edo is | 182edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings suitable for the 11-limit: {{val| 182 288 423 511 630 }} ([[patent val]]), {{val| 182 289 423 511 630 }} (182b), and {{val| 182 288 422 511 629 }} (182ce). It does have a potential as a 2.9.15.7.17.19 [[subgroup]] temperament. | ||
Using the patent val, it tempers out the mynic comma, 10077696/9765625 and {{monzo| -27 20 -2 }} in the 5-limit; [[126/125]], [[1728/1715]], and {{monzo| -28 18 1 -1 }} in the 7-limit; 2187/2156, 2835/2816, [[5632/5625]], and 14700/14641 in the 11-limit; [[364/363]], [[676/675]], [[1287/1280]], and 1701/1690 in the 13-limit. Using the 182f val, [[144/143]], [[847/845]], [[1001/1000]], and [[1716/1715]] are tempered out in the 13-limit. | |||
Using the 182ce val, it tempers out the kleisma, [[15625/15552]] and the [[python comma]], 43046721/41943040 in the 5-limit; [[2430/2401]], 33075/32768, and 78125/76832 in the 7-limit; [[243/242]], [[385/384]], 2420/2401, and [[6250/6237]] in the 11-limit; [[351/350]], [[1188/1183]], 1287/1280, [[1575/1573]], and 1625/1617 in the 13-limit. | |||
Using the | |||
Using the 182b val, it tempers out the [[ | Using the 182b val, it tempers out the diaschisma, [[2048/2025]] and {{monzo| -4 -37 27 }}; in the 5-limit; [[245/243]], [[6144/6125]], and 9882516/9765625 in the 7-limit; [[3025/3024]], 3773/3750, and [[4000/3993]] in the 11-limit. Using the 182bf val, [[196/195]], [[325/324]], 364/363, and 1001/1000 are tempered out in the 13-limit. The 182bef val supports the [[shrutar]] temperament in the 19-limit and [[petrtri]] in the 2.11/5.13/5 subgroup. | ||
=== Odd harmonics === | |||
{{Harmonics in equal|182}} | |||
Revision as of 09:09, 25 April 2024
| ← 181edo | 182edo | 183edo → |
Theory
182edo is inconsistent to the 5-odd-limit and higher limits, with three mappings suitable for the 11-limit: ⟨182 288 423 511 630] (patent val), ⟨182 289 423 511 630] (182b), and ⟨182 288 422 511 629] (182ce). It does have a potential as a 2.9.15.7.17.19 subgroup temperament.
Using the patent val, it tempers out the mynic comma, 10077696/9765625 and [-27 20 -2⟩ in the 5-limit; 126/125, 1728/1715, and [-28 18 1 -1⟩ in the 7-limit; 2187/2156, 2835/2816, 5632/5625, and 14700/14641 in the 11-limit; 364/363, 676/675, 1287/1280, and 1701/1690 in the 13-limit. Using the 182f val, 144/143, 847/845, 1001/1000, and 1716/1715 are tempered out in the 13-limit.
Using the 182ce val, it tempers out the kleisma, 15625/15552 and the python comma, 43046721/41943040 in the 5-limit; 2430/2401, 33075/32768, and 78125/76832 in the 7-limit; 243/242, 385/384, 2420/2401, and 6250/6237 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1575/1573, and 1625/1617 in the 13-limit.
Using the 182b val, it tempers out the diaschisma, 2048/2025 and [-4 -37 27⟩; in the 5-limit; 245/243, 6144/6125, and 9882516/9765625 in the 7-limit; 3025/3024, 3773/3750, and 4000/3993 in the 11-limit. Using the 182bf val, 196/195, 325/324, 364/363, and 1001/1000 are tempered out in the 13-limit. The 182bef val supports the shrutar temperament in the 19-limit and petrtri in the 2.11/5.13/5 subgroup.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -3.05 | +2.70 | +0.40 | +0.49 | +2.53 | -3.17 | -0.36 | +0.54 | -0.81 | -2.65 | -1.90 |
| Relative (%) | -46.3 | +40.9 | +6.1 | +7.4 | +38.3 | -48.0 | -5.4 | +8.2 | -12.3 | -40.2 | -28.8 | |
| Steps (reduced) |
288 (106) |
423 (59) |
511 (147) |
577 (31) |
630 (84) |
673 (127) |
711 (165) |
744 (16) |
773 (45) |
799 (71) |
823 (95) | |