114edo: Difference between revisions
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| Line 144: | Line 144: | ||
| |578.94737 | | |578.94737 | ||
| -3.40557¢ | | -3.40557¢ | ||
|} | |} | ||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
[[Category:Shrutar]] | [[Category:Shrutar]] | ||
Revision as of 21:17, 30 May 2023
| ← 113edo | 114edo | 115edo → |
114edo is the equal division of the octave into 114 parts, each of 10.52632 cents. In the 5-limit it tempers out 2048/2025, in the 7-limit 245/243, in the 11-limit 121/120, 176/175 and 117440512/117406179, in the 13-limit 196/195 and 325/324, in the 17-limit 136/135 and 154/153, in the 19-limit 286/285 and 343/342. These commas make for 114edo being an excellent tuning for shrutar temperament; it is in fact the optimal patent val for shrutar in the 11- 13- 17- and 19-limit, as well as the rank three bisector temperament.
Prime harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.31 | +3.16 | -0.40 | -3.91 | -3.95 | +1.58 | -4.06 | +0.31 | -2.78 | +2.90 | +3.30 |
| Relative (%) | +31.4 | +30.0 | -3.8 | -37.1 | -37.5 | +15.0 | -38.6 | +2.9 | -26.4 | +27.6 | +31.4 | |
| Steps (reduced) |
181 (67) |
265 (37) |
320 (92) |
361 (19) |
394 (52) |
422 (80) |
445 (103) |
466 (10) |
484 (28) |
501 (45) |
516 (60) | |
Period of 19-limit Shrutar
| Degree | Cents | Difference from 68edo |
|---|---|---|
| 2 | 21.05263 | 3.40557¢ |
| 3 | 31.57895 | -3.71517¢ |
| 5 | 52.63158 | -0.3096¢ |
| 7 | 73.68421 | 3.096¢ |
| 8 | 84.21053 | -4.02477¢ |
| 10 | 105.26316 | -0.619195¢ |
| 12 | 126.31579 | 2.78638¢ |
| 13 | 136.842105 | -4.334365¢ |
| 15 | 157.89474 | -0.9288¢ |
| 17 | 178.94737 | 2.47678¢ |
| 18 | 189.47369 | -4.644¢ |
| 20 | 210.52632 | -1.23839¢ |
| 22 | 231.57895 | 2.16718¢ |
| 23 | 242.10526 | -4.953560372 |
| 25 | 263.157895 | -1.548¢ |
| 27 | 284.21053 | 1.857585¢ |
| 29 | 305.26316 | 5.26316¢ |
| 30 | 315.78947 | -1.857585¢ |
| 32 | 336.842105 | 1.548¢ |
| 34 | 357.89474 | 4.95356¢ |
| 35 | 368.42105 | -2.16718¢ |
| 37 | 389.47368 | 1.23839¢ |
| 39 | 410.52632 | 4.64396¢ |
| 40 | 421.05263 | -2.47678¢ |
| 42 | 442.10526 | 0.92879¢ |
| 44 | 463.157895 | 4.334365¢ |
| 45 | 473.68421 | -2.78638¢ |
| 47 | 494.73684 | 0.619195¢ |
| 49 | 515.78947 | 4.02477¢ |
| 50 | 526.31579 | -3.095975¢ |
| 52 | 547.36842 | 0.3096¢ |
| 54 | 568.42105 | 3.71517¢ |
| 55 | 578.94737 | -3.40557¢ |