152edo: Difference between revisions
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== Theory == | == Theory == | ||
152edo is a strong 11-limit system, with the [[3/1|3]], [[5/1|5]], [[7/1|7]], and [[11/1|11]] slightly sharp. It [[tempering out|tempers out]] 1600000/1594323 ([[amity comma]]) and {{monzo| 32 -7 -9 }} ([[escapade comma]]) in the 5-limit; [[4375/4374]], [[5120/5103]], [[6144/6125]] and [[16875/16807]] in the 7-limit; [[540/539]], [[1375/1372]], [[3025/3024]], [[4000/3993]], [[5632/5625]] and [[9801/9800]] in the 11-limit. It provides the [[optimal patent val]] for the 11-limit linear temperaments [[amity]], [[grendel]], and [[kwai]], and the 11-limit planar temperament [[laka]]. | |||
It has two reasonable mappings for 13, with the 152f val scoring much better. The [[ | It has two reasonable mappings for 13, with the 152f val scoring much better. The 152f val tempers out [[352/351]], [[625/624]], [[640/637]], [[729/728]], [[847/845]], [[1188/1183]], [[1575/1573]], [[1716/1715]] and [[2080/2079]], [[support]]ing and giving an excellent tuning for amity, kwai, and laka. The [[patent val]] tempers out [[169/168]], [[325/324]], [[351/350]], [[364/363]], [[1001/1000]], [[1573/1568]], and [[4096/4095]], providing the optimal patent val for the 13-limit rank-5 temperament tempering out 169/168, as well as some further temperaments thereof, such as [[octopus]]. | ||
[[Paul Erlich]] has suggested that 152edo could be considered a sort of [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3038.html#3041 universal tuning]. | [[Paul Erlich]] has suggested that 152edo could be considered a sort of [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3038.html#3041 universal tuning]. | ||
Revision as of 08:41, 14 May 2024
| ← 151edo | 152edo | 153edo → |
Theory
152edo is a strong 11-limit system, with the 3, 5, 7, and 11 slightly sharp. It tempers out 1600000/1594323 (amity comma) and [32 -7 -9⟩ (escapade comma) in the 5-limit; 4375/4374, 5120/5103, 6144/6125 and 16875/16807 in the 7-limit; 540/539, 1375/1372, 3025/3024, 4000/3993, 5632/5625 and 9801/9800 in the 11-limit. It provides the optimal patent val for the 11-limit linear temperaments amity, grendel, and kwai, and the 11-limit planar temperament laka.
It has two reasonable mappings for 13, with the 152f val scoring much better. The 152f val tempers out 352/351, 625/624, 640/637, 729/728, 847/845, 1188/1183, 1575/1573, 1716/1715 and 2080/2079, supporting and giving an excellent tuning for amity, kwai, and laka. The patent val tempers out 169/168, 325/324, 351/350, 364/363, 1001/1000, 1573/1568, and 4096/4095, providing the optimal patent val for the 13-limit rank-5 temperament tempering out 169/168, as well as some further temperaments thereof, such as octopus.
Paul Erlich has suggested that 152edo could be considered a sort of universal tuning.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.68 | +0.53 | +2.23 | +1.31 | -3.69 | -2.32 | +2.49 | +3.30 | -3.26 | -0.30 |
| Relative (%) | +0.0 | +8.6 | +6.7 | +28.2 | +16.6 | -46.7 | -29.4 | +31.5 | +41.9 | -41.3 | -3.8 | |
| Steps (reduced) |
152 (0) |
241 (89) |
353 (49) |
427 (123) |
526 (70) |
562 (106) |
621 (13) |
646 (38) |
688 (80) |
738 (130) |
753 (145) | |
Subsets and supersets
Since 152 factors into 23 × 19, 152edo has subset edos 2, 4, 8, 19, 38, 76.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [241 -152⟩ | [⟨152 241]] | -0.213 | 0.213 | 2.70 |
| 2.3.5 | 1600000/1594323, [32 -7 -9⟩ | [⟨152 241 353]] | -0.218 | 0.174 | 2.21 |
| 2.3.5.7 | 4375/4374, 5120/5103, 16875/16807 | [⟨152 241 353 427]] | -0.362 | 0.291 | 3.69 |
| 2.3.5.7.11 | 540/539, 1375/1372, 4000/3993, 5120/5103 | [⟨152 241 353 427 526]] | -0.365 | 0.260 | 3.30 |
| 2.3.5.7.11.13 | 352/351, 540/539, 625/624, 729/728, 1575/1573 | [⟨152 241 353 427 526 563]] (152f) | -0.494 | 0.373 | 4.73 |
Rank-2 temperaments
| Periods per 8ve |
Generator (reduced) |
Cents (reduced) |
Associated ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 7\152 | 55.26 | 33/32 | Escapade / alphaquarter |
| 1 | 31\152 | 244.74 | 15/13 | Subsemifourth |
| 1 | 39\152 | 307.89 | 3200/2673 | Familia |
| 1 | 43\152 | 339.47 | 243/200 | Amity |
| 1 | 49\152 | 386.84 | 5/4 | Grendel |
| 1 | 63\152 | 497.37 | 4/3 | Kwai |
| 1 | 71\152 | 560.53 | 242/175 | Whoosh / whoops |
| 2 | 7\152 | 55.26 | 33/32 | Biscapade |
| 2 | 9\152 | 71.05 | 25/24 | Vishnu / acyuta (152f) / ananta (152) |
| 2 | 43\152 (33\152) |
339.47 (260.53) |
243/200 (64/55) |
Hemiamity |
| 2 | 55\152 (21\152) |
434.21 (165.79) |
9/7 (11/10) |
Supers |
| 4 | 63\152 (13\152) |
497.37 (102.63) |
4/3 (35/33) |
Undim / unlit |
| 8 | 63\152 (6\152) |
497.37 (47.37) |
4/3 (36/35) |
Twilight |
| 8 | 74\152 (2\152) |
584.21 (15.79) |
7/5 (126/125) |
Octoid (152f) / octopus (152) |
| 19 | 63\152 (1\152) |
497.37 (7.89) |
4/3 (225/224) |
Enneadecal |
| 38 | 63\152 (1\152) |
497.37 (7.89) |
4/3 (225/224) |
Hemienneadecal |