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{{Infobox ET}} | |||
'''149edo''' is the [[equal division of the octave]] into 149 equal parts of 8.054 [[cent]]s each. | '''149edo''' is the [[equal division of the octave]] into 149 equal parts of 8.054 [[cent]]s each. | ||
Revision as of 19:08, 4 October 2022
| ← 148edo | 149edo | 150edo → |
149edo is the equal division of the octave into 149 equal parts of 8.054 cents each.
Theory
149edo is the smallest division which is uniquely consistent through the 17-odd-limit. It provides the optimal patent val for 7-, 11-, 13-, and 17-limit heinz temperament and the rank-3 temperament ominous in the 13- and 17-limits. It has a general flat tendency, with the fifth 1.28 cents flat, but the major third is a quarter of a cent sharp. In the 5-limit it tempers out the sensipent comma, 78732/78125; in the 7-limit, 1029/1024, 3136/3125 and 19683/19600; in the 11-limit 385/384 and 441/440; in the 13-limit 351/350 and 676/675; in the 17-limit 273/272 and 561/560; in the 19-limit 286/285 and 343/342.
149edo is the 35th prime EDO.
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 | [-236 149⟩ | [⟨149 236]] | +0.405 | 0.405 | 5.03 |
| 2.3.5 | 78732/78125, [-34 20 1⟩ | [⟨149 236 346]] | +0.232 | 0.411 | 5.11 |
| 2.3.5.7 | 1029/1024, 3136/3125, 19683/19600 | [⟨149 236 346 418]] | +0.386 | 0.445 | 5.53 |
| 2.3.5.7.11 | 385/384, 441/440, 3136/3125, 19683/19600 | [⟨149 236 346 418 515]] | +0.521 | 0.481 | 5.97 |
| 2.3.5.7.11.13 | 351/350, 385/384, 441/440, 676/675, 847/845 | [⟨149 236 346 418 515 551]] | +0.567 | 0.451 | 5.60 |
| 2.3.5.7.11.13.17 | 273/272, 351/350, 385/384, 441/440, 676/675, 847/845 | [⟨149 236 346 418 515 551 609]] | +0.495 | 0.453 | 5.62 |
Rank-2 temperaments
| Periods per octave |
Generator (reduced) |
Cents (reduced) |
Associated ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 3\149 | 24.16 | 686/675 | Sengagen |
| 1 | 16\149 | 128.86 | 14/13 | Tertiathirds |
| 1 | 18\149 | 144.97 | 49/45 | Swetneus |
| 1 | 24\149 | 193.29 | 28/25 | Luna / hemithirds |
| 1 | 29\149 | 233.56 | 8/7 | Slendric |
| 1 | 47\149 | 378.52 | 56/45 | Subpental |
| 1 | 55\149 | 442.95 | 162/125 | Sensipent |
| 1 | 57\149 | 459.06 | 125/96 | Majvam |
| 1 | 60\149 | 483.22 | 45/34 | Hemiseven |
| 1 | 61\149 | 491.28 | 3645/2744 | Fifthplus |
| 1 | 68\149 | 547.65 | 11/8 | Heinz |