38edo: Difference between revisions
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m improved linking, added 3 digits to cent size in the intro to be consistent with the interval table, a better solution would be to reduce all of these phone numbers. |
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'''38edo''' divides the octave into 38 equal parts of 31. | '''38edo''' divides the octave into 38 equal parts of 31.578947 [[cent]]s. Since 38 = 2*19, it can be thought of as two parallel [[19edo]]s. It [[tempers out]] the same [[5-limit]] commas as 19edo, namely [[81/80]], [[3125/3072]] and [[15625/15552]]. In the [[7-limit]], we can add [[50/49]], and tempering out 81/80 and 50/49 gives [[injera]] temperament, for which 38 is the [[optimal patent val]]. In the [[11-limit]], we can add 121/120 and 176/175. | ||
== Intervals == | == Intervals == | ||
Revision as of 10:34, 6 December 2020
38edo divides the octave into 38 equal parts of 31.578947 cents. Since 38 = 2*19, it can be thought of as two parallel 19edos. It tempers out the same 5-limit commas as 19edo, namely 81/80, 3125/3072 and 15625/15552. In the 7-limit, we can add 50/49, and tempering out 81/80 and 50/49 gives injera temperament, for which 38 is the optimal patent val. In the 11-limit, we can add 121/120 and 176/175.
Intervals
| Step | Cents |
|---|---|
| 0 | 0.0000 |
| 1 | 31.5789 |
| 2 | 63.1579 |
| 3 | 94.7368 |
| 4 | 126.3157 |
| 5 | 157.8947 |
| 6 | 189.4737 |
| 7 | 221.0526 |
| 8 | 252.6316 |
| 9 | 284.2105 |
| 10 | 315.7895 |
| 11 | 347.3684 |
| 12 | 378.9474 |
| 13 | 410.5263 |
| 14 | 442.1053 |
| 15 | 473.6843 |
| 16 | 505.2632 |
| 17 | 536.8421 |
| 18 | 568.4211 |
| 19 | 600.0000 |
| 20 | 631.5789 |
| 21 | 663.1579 |
| 22 | 694.7368 |
| 23 | 726.3157 |
| 24 | 757.8947 |
| 25 | 789.4737 |
| 26 | 821.0526 |
| 27 | 852.6316 |
| 28 | 884.2105 |
| 29 | 915.7895 |
| 30 | 947.3684 |
| 31 | 978.9474 |
| 32 | 1010.5263 |
| 33 | 1042.1053 |
| 34 | 1073.6843 |
| 35 | 1105.2632 |
| 36 | 1136.8421 |
| 37 | 1168.4211 |
| 38 | 1200.0000 |