4L 3s: Difference between revisions
→Tuning ranges: being careful about saying that a certain set of JI interpretations "is" a certain temperament (given that many different abstract temperaments use the same name) |
Updated for consistency with 5L 3s |
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| Line 57: | Line 57: | ||
| 1 | | 1 | ||
| L | | L | ||
| perfect | | perfect mosthird | ||
| 1L + 1s | | 1L + 1s | ||
| -1 | | -1 | ||
| O | | O | ||
| perfect | | perfect mossixth | ||
| 3L + 2s | | 3L + 2s | ||
|- | |- | ||
| Line 158: | Line 158: | ||
Parasoft smitonic EDOs include [[18edo]], [[25edo]], and [[43edo]]. | Parasoft smitonic EDOs include [[18edo]], [[25edo]], and [[43edo]]. | ||
* 18edo can be used to make large and small steps more distinct (the step ratio is 3/2, thus 18edo smitonic is distorted [[19edo]] diatonic), or for its nearly pure 9/8. It also makes rising fifths (733.3c, a perfect | * 18edo can be used to make large and small steps more distinct (the step ratio is 3/2, thus 18edo smitonic is distorted [[19edo]] diatonic), or for its nearly pure 9/8. It also makes rising fifths (733.3c, a perfect mossixth) and falling fifths (666.7c, a major mosfifth) almost equally off from a just fifth. 18edo is also more suited for conventionally jazz styles due to its 6-fold symmetry. | ||
* [[25edo]] can be used to make the augmented mosthird a good [[5/4]] (384¢). | * [[25edo]] can be used to make the augmented mosthird a good [[5/4]] (384¢). | ||
| Line 217: | Line 217: | ||
| -7 | | -7 | ||
|- | |- | ||
| dim. | | dim. mos2nd | ||
| 1\18, 66.7 | | 1\18, 66.7 | ||
| 2\25, 96.0 | | 2\25, 96.0 | ||
| Line 249: | Line 249: | ||
| -10 | | -10 | ||
|-bgcolor="#eaeaff" | |-bgcolor="#eaeaff" | ||
| dim. | | dim. mos3rd | ||
| 4\18, 266.7 | | 4\18, 266.7 | ||
| 6\25, 288.0 | | 6\25, 288.0 | ||
| Line 281: | Line 281: | ||
| -13 | | -13 | ||
|- | |- | ||
| dim. | | dim. mos4th | ||
| 6\18, 400.0 | | 6\18, 400.0 | ||
| 9\25, 432.0 | | 9\25, 432.0 | ||
| Line 313: | Line 313: | ||
| -9 | | -9 | ||
|-bgcolor="#eaeaff" | |-bgcolor="#eaeaff" | ||
| dim. | | dim. mos5th | ||
| 9\18, 600.0 | | 9\18, 600.0 | ||
| 13\25, 624.0 | | 13\25, 624.0 | ||
| Line 345: | Line 345: | ||
| -12 | | -12 | ||
|- | |- | ||
| doubly dim. | | doubly dim. mos6th | ||
| 11\18, 733.3 | | 11\18, 733.3 | ||
| 16\25, 768.0 | | 16\25, 768.0 | ||
| Line 353: | Line 353: | ||
| +13 | | +13 | ||
|- | |- | ||
| dim. | | dim. mos6th | ||
| 12\18, 800.0 | | 12\18, 800.0 | ||
| 17\25, 816.0 | | 17\25, 816.0 | ||
| Line 377: | Line 377: | ||
| -8 | | -8 | ||
|-bgcolor="#eaeaff" | |-bgcolor="#eaeaff" | ||
| dim. | | dim. mos7th | ||
| 14\18, 933.3 | | 14\18, 933.3 | ||
| 20\25, 960.0 | | 20\25, 960.0 | ||
| Line 409: | Line 409: | ||
| -11 | | -11 | ||
|- | |- | ||
| dim. | | dim. mosoctave | ||
| 17\18, 1133.3 | | 17\18, 1133.3 | ||
| 24\25, 1152.0 | | 24\25, 1152.0 | ||
| Line 509: | Line 509: | ||
| -5 | | -5 | ||
|- | |- | ||
| dim. | | dim. mos6th | ||
| 19\29, 786.2 | | 19\29, 786.2 | ||
| O@ | | O@ | ||
| Line 649: | Line 649: | ||
| -5 | | -5 | ||
|- | |- | ||
| dim. | | dim. mos6th | ||
| 7\11, 763.6 | | 7\11, 763.6 | ||
| 9\15, 720.0 | | 9\15, 720.0 | ||
| Line 801: | Line 801: | ||
| -5 | | -5 | ||
|- | |- | ||
| dim. | | dim. mos6th | ||
| 11\19, 694.7 | | 11\19, 694.7 | ||
| 20\34, 705.9 | | 20\34, 705.9 | ||