152edo: Difference between revisions
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The '''152 equal divisions of the octave''' ('''152edo''') or '''152(-tone) equal temperament''' ('''152tet''', '''152et''') when viewed from a [[regular temperament]] perspective, is the tuning system derived by dividing the [[octave]] into 152 [[equal]]ly sized parts of 7. | The '''152 equal divisions of the octave''' ('''152edo''') or '''152(-tone) equal temperament''' ('''152tet''', '''152et''') when viewed from a [[regular temperament]] perspective, is the tuning system derived by dividing the [[octave]] into 152 [[equal]]ly sized parts of about 7.89 [[cent]]s each. | ||
== Theory == | == Theory == | ||
Revision as of 19:36, 16 September 2021
| ← 151edo | 152edo | 153edo → |
The 152 equal divisions of the octave (152edo) or 152(-tone) equal temperament (152tet, 152et) when viewed from a regular temperament perspective, is the tuning system derived by dividing the octave into 152 equally sized parts of about 7.89 cents each.
Theory
152et is a strong 11-limit system, with the 3, 5, 7, and 11 slightly sharp. It tempers out 1600000/1594323, the amity comma, in the 5-limit; 4375/4374, 5120/5103, 6144/6125 and 16875/16807 in the 7-limit; 540/539, 1375/1372, 4000/3993, 5632/5625 and 9801/9800 in the 11-limit.
It has two reasonable mappings for 13, with the 152f val scoring much better. The patent val tempers out 169/168, 325/324, 351/350, 364/363, 1001/1000, and 4096/4095. The 152f val tempers out 352/351, 625/624, 640/637, 729/728, 847/845, 1575/1573, 1716/1715 and 2080/2079.
It provides the optimal patent val for the 11-limit grendel and kwai linear temperaments, the 13-limit rank two temperament octopus, the 11-limit planar temperament laka, and the rank five temperament tempering out 169/168.
Paul Erlich has suggested that 152edo could be considered a sort of universal tuning.
152 = 8 × 19, with divisors 2, 4, 8, 19, 38, 76.
Prime harmonics
Script error: No such module "primes_in_edo".
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 octave |
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 |
| 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 |