149edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
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| 0.453 | | 0.453 | ||
| 5.62 | | 5.62 | ||
{{comma basis end}} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
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| 1 | | 1 | ||
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| 11/8 | | 11/8 | ||
| [[Heinz]] | | [[Heinz]] | ||
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{{orf}} | |||
[[Category:Heinz]] | [[Category:Heinz]] | ||
Revision as of 04:25, 16 November 2024
| ← 148edo | 149edo | 150edo → |
Theory
149edo is the smallest division which is uniquely consistent through the 17-odd-limit. 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. 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-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -1.28 | +0.26 | -2.38 | -3.67 | -2.94 | -0.26 | +0.47 | -0.09 | +1.30 | -1.41 |
| Relative (%) | +0.0 | -15.9 | +3.3 | -29.6 | -45.5 | -36.6 | -3.2 | +5.9 | -1.1 | +16.1 | -17.5 | |
| Steps (reduced) |
149 (0) |
236 (87) |
346 (48) |
418 (120) |
515 (68) |
551 (104) |
609 (13) |
633 (37) |
674 (78) |
724 (128) |
738 (142) | |
Subsets and supersets
149edo is the 35th prime edo.
Regular temperament properties
Template:Comma basis begin |- | 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 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin |- | 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 | 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 Template:Rank-2 end Template:Orf