188edo: Difference between revisions
+prime error table; +subsets and supersets; -redundant categories |
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{{EDO intro|188}} | {{EDO intro|188}} | ||
188edo is closely related to [[94edo]], but the [[patent val]]s differ on the mapping for [[5/1|5]]. The equal temperament [[tempering out|tempers out]] 129140163/128000000 ([[graviton]]) and 268435456/263671875 ([[mabila comma]]) in the 5-limit; [[2401/2400]], [[19683/19600]], and 110592/109375 in the 7-limit. | 188edo is closely related to [[94edo]], but the [[patent val]]s differ on the mapping for [[5/1|5]]. The equal temperament [[tempering out|tempers out]] 129140163/128000000 ([[graviton]]) and 268435456/263671875 ([[mabila comma]]) in the 5-limit; [[2401/2400]], [[19683/19600]], and 110592/109375 in the 7-limit. It [[support]]s [[harry]] and [[newt]], and provides the [[optimal patent val]] for [[tuskaloosa]], the 77 & 111 temperament. | ||
Using the [[patent val]], it tempers out [[176/175]], 1331/1323, 3773/3750, and 16896/16807 in the 11-limit; [[351/350]], [[352/351]], [[676/675]], [[1573/1568]], and 16848/16807 in the 13-limit. | Using the [[patent val]], it tempers out [[176/175]], 1331/1323, 3773/3750, and 16896/16807 in the 11-limit; [[351/350]], [[352/351]], [[676/675]], [[1573/1568]], and 16848/16807 in the 13-limit; supporting 13-limit tuskaloosa. Using the alternative 188e val, [[243/242]], [[441/440]], [[540/539]], [[8019/8000]], and [[9801/9800]] in the 11-limit; 351/350, [[1716/1715]], and [[2080/2079]] in the 13-limit; supporting 13-limit harry. | ||
188cef val is a tuning for the [[hemigari]] temperament in the 11- and 13-limit. | The 188cef val is a tuning for the [[hemigari]] temperament in the 11- and 13-limit. | ||
=== Odd harmonics === | === Odd harmonics === | ||
Revision as of 16:03, 22 April 2024
| ← 187edo | 188edo | 189edo → |
188edo is closely related to 94edo, but the patent vals differ on the mapping for 5. The equal temperament tempers out 129140163/128000000 (graviton) and 268435456/263671875 (mabila comma) in the 5-limit; 2401/2400, 19683/19600, and 110592/109375 in the 7-limit. It supports harry and newt, and provides the optimal patent val for tuskaloosa, the 77 & 111 temperament.
Using the patent val, it tempers out 176/175, 1331/1323, 3773/3750, and 16896/16807 in the 11-limit; 351/350, 352/351, 676/675, 1573/1568, and 16848/16807 in the 13-limit; supporting 13-limit tuskaloosa. Using the alternative 188e val, 243/242, 441/440, 540/539, 8019/8000, and 9801/9800 in the 11-limit; 351/350, 1716/1715, and 2080/2079 in the 13-limit; supporting 13-limit harry.
The 188cef val is a tuning for the hemigari temperament in the 11- and 13-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.17 | +3.05 | +1.39 | +0.35 | -2.38 | +2.03 | -3.16 | -2.83 | +2.49 | +1.56 | -2.74 |
| Relative (%) | +2.7 | +47.8 | +21.7 | +5.4 | -37.3 | +31.7 | -49.5 | -44.3 | +39.0 | +24.4 | -43.0 | |
| Steps (reduced) |
298 (110) |
437 (61) |
528 (152) |
596 (32) |
650 (86) |
696 (132) |
734 (170) |
768 (16) |
799 (47) |
826 (74) |
850 (98) | |
Subsets and supersets
Since 188 factors into 22 × 47, 188edo contains subset edos 2, 4, 47, and 94.