182edo: Difference between revisions
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{{Infobox ET}} | |||
{{ED intro}} | |||
[[ | 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 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}} | |||
=== Octave stretch === | |||
182edo’s approximations of 3/1, 5/1, 7/1 and 13/1 are all improved by the [[Gallery of arithmetic pitch sequences#APS of tinas|Argentina scale]] (APS47tina), a [[Octave stretch|stretched-octave]] version of 182edo. The trade-off is a slightly worse 2/1 and 11/1. | |||
There are also several nearby [[Zeta peak index]] (ZPI) tunings which can be used for this same purpose: 1199zpi, 1200zpi, 1201zpi, 1202zpi, 1203zpi, 1204zpi and 1205zpi. | |||
The details of each of those ZPI tunings are visible in [[User:Contribution]]’s gallery of [[User:Contribution/Gallery of Zeta Peak Indexes (1 - 10 000)|Zeta Peak Indexes (1 - 10 000)]]. Warning: due to its length, that page may slow down your device while it is open. The effect will go away after you close the page. | |||
=== Subsets and supersets === | |||
Since 182 factors into {{factorization|182}}, 182edo has subset edos {{EDOs| 2, 7, 13, 14, 26, and 91 }}. | |||
Latest revision as of 16:38, 20 February 2025
| ← 181edo | 182edo | 183edo → |
182 equal divisions of the octave (abbreviated 182edo or 182ed2), also called 182-tone equal temperament (182tet) or 182 equal temperament (182et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 182 equal parts of about 6.59 ¢ each. Each step represents a frequency ratio of 21/182, or the 182nd root of 2.
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) | |
Octave stretch
182edo’s approximations of 3/1, 5/1, 7/1 and 13/1 are all improved by the Argentina scale (APS47tina), a stretched-octave version of 182edo. The trade-off is a slightly worse 2/1 and 11/1.
There are also several nearby Zeta peak index (ZPI) tunings which can be used for this same purpose: 1199zpi, 1200zpi, 1201zpi, 1202zpi, 1203zpi, 1204zpi and 1205zpi.
The details of each of those ZPI tunings are visible in User:Contribution’s gallery of Zeta Peak Indexes (1 - 10 000). Warning: due to its length, that page may slow down your device while it is open. The effect will go away after you close the page.
Subsets and supersets
Since 182 factors into 2 × 7 × 13, 182edo has subset edos 2, 7, 13, 14, 26, and 91.