114edo: Difference between revisions
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'''114edo''' is the [[Equal_division_of_the_octave|equal division of the octave]] into 114 parts, each of 10.52632 [[cent|cent]]s. In the [[5-limit|5-limit]] it [[tempering_out|tempers out]] 2048/2025, in the [[7-limit|7-limit]] 245/243, in the [[11-limit|11-limit]] 121/120, 176/175 | '''114edo''' is the [[Equal_division_of_the_octave|equal division of the octave]] into 114 parts, each of 10.52632 [[cent|cent]]s. In the [[5-limit|5-limit]] it [[tempering_out|tempers out]] 2048/2025, in the [[7-limit|7-limit]] 245/243, in the [[11-limit|11-limit]] 121/120, 176/175 and [[Quartisma|117440512/117406179]], in the [[13-limit|13-limit]] 196/195 and 325/324, in the [[17-limit|17-limit]] 136/135 and 154/153, in the [[19-limit|19-limit]] 286/285 and 343/342. These commas make for 114edo being an excellent tuning for [[Diaschismic_family|shrutar temperament]]; it is in fact the [[Optimal_patent_val|optimal patent val]] for [[Shrutar|shrutar]] in the 11- 13- 17- and 19-limit, as well as the rank three bisector temperament. | ||
===Period of 19-limit Shrutar=== | ===Period of 19-limit Shrutar=== | ||
Revision as of 20:28, 13 September 2020
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.
Period of 19-limit Shrutar
| Degree | Cents |
|---|---|
| 2 | 21.05263 |
| 3 | 31.57895 |
| 5 | 52.63158 |
| 7 | 73.68421 |
| 8 | 84.21053 |
| 10 | 105.26316 |
| 12 | 126.31579 |
| 13 | 136.842105 |
| 15 | 157.89474 |
| 17 | 178.94737 |
| 18 | 189.47369 |
| 20 | 210.52632 |
| 22 | 231.57895 |
| 23 | 242.10526 |
| 25 | 263.157895 |
| 27 | 284.21053 |
| 29 | 305.26316 |
| 30 | 315.78947 |
| 32 | 336.842105 |
| 34 | 357.89474 |
| 35 | 368.42105 |
| 37 | 389.47368 |
| 39 | 410.52632 |
| 40 | 421.05263 |
| 42 | 442.10526 |
| 44 | 463.157895 |
| 45 | 473.68421 |
| 47 | 494.73684 |
| 49 | 515.78947 |
| 50 | 526.31579 |
| 52 | 547.36842 |
| 54 | 568.42105 |
| 55 | 578.94737 |