62edo: Difference between revisions
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'''62edo''' divides the octave into 62 equal parts of 19.35484 cents each. | '''62edo''' divides the octave into 62 equal parts of 19.35484 cents each. | ||
62 = 2 × 31 and the [[patent val]] is a contorted [[31edo]] through the 11-limit; in the 13-limit it tempers out [[169/168]], [[1188/1183]], [[847/845]] and [[676/675]]. It provides the [[optimal patent val]] for [[31 comma temperaments #Gallium|gallium]], [[Starling temperaments #Valentine|semivalentine]] and [[Meantone_family#Hemimeantone|hemimeantone]] temperaments. | 62 = 2 × 31 and the [[patent val]] is a contorted (or [[enfactored]]) [[31edo]] through the 11-limit; in the 13-limit it tempers out [[169/168]], [[1188/1183]], [[847/845]] and [[676/675]]. It provides the [[optimal patent val]] for [[31 comma temperaments #Gallium|gallium]], [[Starling temperaments #Valentine|semivalentine]] and [[Meantone_family#Hemimeantone|hemimeantone]] temperaments. | ||
Using the 35\62 generator, which leads to the {{val| 62 97 143 173 }} val, 62edo is also an excellent tuning for septimal mavila temperament; alternatively {{val| 62 97 143 172 }} supports hornbostel. | Using the 35\62 generator, which leads to the {{val| 62 97 143 173 }} val, 62edo is also an excellent tuning for septimal mavila temperament; alternatively {{val| 62 97 143 172 }} supports hornbostel. | ||
Revision as of 19:38, 29 September 2021
62edo divides the octave into 62 equal parts of 19.35484 cents each.
62 = 2 × 31 and the patent val is a contorted (or enfactored) 31edo through the 11-limit; in the 13-limit it tempers out 169/168, 1188/1183, 847/845 and 676/675. It provides the optimal patent val for gallium, semivalentine and hemimeantone temperaments.
Using the 35\62 generator, which leads to the ⟨62 97 143 173] val, 62edo is also an excellent tuning for septimal mavila temperament; alternatively ⟨62 97 143 172] supports hornbostel.
Intervals
| ARMODUE NOMENCLATURE 8;3 RELATION |
|---|
|
| # | Cents | Armodue notation | Approximate intervals |
|---|---|---|---|
| 0 | 0.000 | 1 | |
| 1 | 19.355 | 1Ɨ | 90/89 |
| 2 | 38.710 | 1‡ (9#) | 45/44 |
| 3 | 58.065 | 2b | 30/29 |
| 4 | 77.419 | 1◊2 | 23/22 |
| 5 | 96.774 | 1# | 37/35, 18/17, 19/18 |
| 6 | 116.129 | 2v | 31/29, 15/14, 16/15 |
| 7 | 135.484 | 2⌐ | 27/25, 13/12, 14/13 |
| 8 | 154.839 | 2 | 12/11 |
| 9 | 174.194 | 2Ɨ | 11/10 |
| 10 | 193.548 | 2‡ | 19/17, 9/8, 10/9 |
| 11 | 212.903 | 3b | 17/15, 9/8 |
| 12 | 232.258 | 2◊3 | 8/7 |
| 13 | 251.613 | 2# | 15/13 |
| 14 | 270.968 | 3v | 7/6 |
| 15 | 290.323 | 3⌐ | |
| 16 | 309.677 | 3 | 6/5 |
| 17 | 329.032 | 3Ɨ | |
| 18 | 348.387 | 3‡ | 11/9 |
| 19 | 367.742 | 4b | · |
| 20 | 387.097 | 3◊4 | 5/4 |
| 21 | 406.452 | 3# | |
| 22 | 425.806 | 4v (5b) | |
| 23 | 445.161 | 4⌐ | |
| 24 | 464.516 | 4 | |
| 25 | 483.871 | 4Ɨ (5v) | |
| 26 | 503.226 | 5⌐ (4‡) | 4/3 |
| 27 | 522.581 | 5 | · |
| 28 | 541.935 | 5Ɨ | |
| 29 | 561.290 | 5‡ (4#) | |
| 30 | 580.645 | 6b | 7/5 |
| 31 | 600.000 | 5◊6 | |
| 32 | 619.355 | 5# | 10/7 |
| 33 | 638.710 | 6v | |
| 34 | 658.065 | 6⌐ | |
| 35 | 677.419 | 6 | · |
| 36 | 696.774 | 6Ɨ | 3/2 |
| 37 | 716.129 | 6‡ | |
| 38 | 735.484 | 7b | |
| 39 | 754.839 | 6◊7 | |
| 40 | 774.194 | 6# | |
| 41 | 793.548 | 7v | |
| 42 | 812.903 | 7⌐ | 8/5 |
| 43 | 832.258 | 7 | · |
| 44 | 851.613 | 7Ɨ | 18/11 |
| 45 | 870.968 | 7‡ | |
| 46 | 890.323 | 8b | 5/3 |
| 47 | 909.677 | 7◊8 | |
| 48 | 929.032 | 7# | 12/7 |
| 49 | 948.387 | 8v | 26/15 |
| 50 | 967.742 | 8⌐ | 7/4 |
| 51 | 987.097 | 8 | 16/9 |
| 52 | 1006.452 | 8Ɨ | |
| 53 | 1025.806 | 8‡ | |
| 54 | 1045.161 | 9b | |
| 55 | 1064.516 | 8◊9 | |
| 56 | 1083.871 | 8# | |
| 57 | 1103.226 | 9v (1b) | |
| 58 | 1122.581 | 9⌐ | |
| 59 | 1141.936 | 9 | |
| 60 | 1161.290 | 9Ɨ (1v) | |
| 61 | 1180.645 | 1⌐ (9‡) | |
| 62 | 1200.000 | 1 |