181edo and stretched hemififths: Difference between revisions
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| Line 34: | Line 34: | ||
|181 | |181 | ||
|1200.000 | |1200.000 | ||
|2/1 | |'''2/1''' | ||
|} | |} | ||
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!Cents | !Cents | ||
!Approximated Ratios | !Approximated Ratios | ||
(octave-reduced) | |||
|- | |- | ||
|31 | |31 | ||
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|183 | |183 | ||
|1213.260 | |1213.260 | ||
|'''2/1''' | |||
|- | |||
|214 | |||
|1418.785 | |||
|9/8, 8/7 | |||
|- | |||
|236 | |||
|1564.641 | |||
|'''16/13''' | |||
|- | |||
|267 | |||
|1770.166 | |||
|18/13 | |||
|- | |||
|290 | |||
|1922.652 | |||
|3/2 | |||
|- | |||
|321 | |||
|2128.177 | |||
|12/7 | |||
|- | |||
|343 | |||
|2274.033 | |||
|13/7 | |||
|- | |||
|366 | |||
|2426.519 | |||
|2/1 | |2/1 | ||
|} | |} | ||
Revision as of 14:03, 10 March 2023
Normal Hemififths
181edo supports normal Hemififths (MOS 3L 4s) with the mode 31 22 31 22 31 22 22
| #\181 | Cents | Approximated Ratios |
|---|---|---|
| 31 | 205.525 | 9/8 |
| 53 | 351.381 | 11/9 |
| 84 | 556.906 | 11/8 |
| 106 | 702.762 | 3/2 |
| 137 | 908.287 | 22/13 |
| 159 | 1054.144 | 11/6 |
| 181 | 1200.000 | 2/1 |
Stretched Hemififths
This mode can be improved in 181edo by stretching some "s" of the mode with 1 step of 181edo: 31 22 31 23 31 22 23
With this stretched mode, more JI ratios are approximated
| #\181 | Cents | Approximated Ratios
(octave-reduced) |
|---|---|---|
| 31 | 205.525 | 9/8 |
| 53 | 351.381 | 11/9 |
| 84 | 556.906 | 11/8 |
| 107 | 709.392 | 3/2 |
| 138 | 914.917 | 22/13 |
| 160 | 1060.773 | 24/13 |
| 183 | 1213.260 | 2/1 |
| 214 | 1418.785 | 9/8, 8/7 |
| 236 | 1564.641 | 16/13 |
| 267 | 1770.166 | 18/13 |
| 290 | 1922.652 | 3/2 |
| 321 | 2128.177 | 12/7 |
| 343 | 2274.033 | 13/7 |
| 366 | 2426.519 | 2/1 |