56edf: Difference between revisions
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m Fix broken table (it was broken cause they said rowspan but wanted colspan, causing the glitchy look). Also add subheading for the table, and todo:complete table because it’s barebones as-is. |
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'''56EDF''' is the [[EDF|equal division of the just perfect fifth]] into 56 parts of 12.5349 [[cent|cents]] each, corresponding to 95.7326 [[edo]]. It is related to the regular temperament which tempers out 2401/2400 and |91 -80 13 2> in the 7-limit, which is supported by [[383edo|383]], [[670edo|670]], [[1053edo|1053]], 1436, and 1723 EDOs. | '''56EDF''' is the [[EDF|equal division of the just perfect fifth]] into 56 parts of 12.5349 [[cent|cents]] each, corresponding to 95.7326 [[edo]]. It is related to the regular temperament which tempers out 2401/2400 and |91 -80 13 2> in the 7-limit, which is supported by [[383edo|383]], [[670edo|670]], [[1053edo|1053]], 1436, and 1723 EDOs. | ||
== Intervals== | |||
{| class="wikitable" | {| class="wikitable" | ||
! | ! colspan="2" |56ed3/2 | ||
|- | |- | ||
|1 | |1 | ||
| Line 344: | Line 342: | ||
|1403.91 | |1403.91 | ||
|} | |} | ||
{{todo|inline=1|complete table|text=Add a third column that comments on the intervals, either what [[JI]] they approximate, what they are named, or how they can be used musically.}} | |||
==Related regular temperaments== | ==Related regular temperaments== | ||
Revision as of 03:43, 18 December 2024
| ← 55edf | 56edf | 57edf → |
56EDF is the equal division of the just perfect fifth into 56 parts of 12.5349 cents each, corresponding to 95.7326 edo. It is related to the regular temperament which tempers out 2401/2400 and |91 -80 13 2> in the 7-limit, which is supported by 383, 670, 1053, 1436, and 1723 EDOs.
Intervals
| 56ed3/2 | |
|---|---|
| 1 | 12.5349 |
| 2 | 25.0698 |
| 3 | 37.6047 |
| 4 | 50.1396 |
| 5 | 62.67455 |
| 6 | 75.2095 |
| 7 | 87.7444 |
| 8 | 100.2793 |
| 9 | 112.8142 |
| 10 | 125.3491 |
| 11 | 137.884 |
| 12 | 150.4189 |
| 13 | 162.9538 |
| 14 | 175.48875 |
| 15 | 188.2366 |
| 16 | 200.5586 |
| 17 | 213.0935 |
| 18 | 225.6284 |
| 19 | 238.1633 |
| 20 | 250.6982 |
| 21 | 263.2331 |
| 22 | 275.768 |
| 23 | 288.30295 |
| 24 | 300.8379 |
| 25 | 313.3728 |
| 26 | 325.9077 |
| 27 | 338.4426 |
| 28 | 350.9775 |
| 29 | 363.5214 |
| 30 | 376.0473 |
| 31 | 388.5822 |
| 32 | 401.1171 |
| 33 | 413.65205 |
| 34 | 426.187 |
| 35 | 438.7219 |
| 36 | 451.2568 |
| 37 | 463.7917 |
| 38 | 476.3266 |
| 39 | 488.8615 |
| 40 | 501.3964 |
| 41 | 513.9313 |
| 42 | 526.46625 |
| 43 | 539.0012 |
| 44 | 551.536 |
| 45 | 564.071 |
| 46 | 576.6059 |
| 47 | 589.1408 |
| 48 | 601.6757 |
| 49 | 614.2106 |
| 50 | 626.7455 |
| 51 | 639.28045 |
| 52 | 651.8154 |
| 53 | 664.3503 |
| 54 | 676.8852 |
| 55 | 689.4201 |
| 56 | 701.955 |
| 57 | 714.4899 |
| 58 | 727.0248 |
| 59 | 739.5597 |
| 60 | 752.0946 |
| 61 | 764.62955 |
| 62 | 777.1645 |
| 63 | 789.6994 |
| 64 | 802.2343 |
| 65 | 814.7692 |
| 66 | 827.3041 |
| 67 | 839.839 |
| 68 | 852.3739 |
| 69 | 864.9088 |
| 70 | 877.44375 |
| 71 | 889.9787 |
| 72 | 902.5136 |
| 73 | 915.0485 |
| 74 | 927.5834 |
| 75 | 940.1183 |
| 76 | 952.6532 |
| 77 | 965.1881 |
| 78 | 977.723 |
| 79 | 990.25795 |
| 80 | 1002.7929 |
| 81 | 1015.3278 |
| 82 | 1027.8627 |
| 83 | 1040.3976 |
| 84 | 1052.9325 |
| 85 | 1065.4674 |
| 86 | 1078.0023 |
| 87 | 1090.5372 |
| 88 | 1103.0721 |
| 89 | 1115.6071 |
| 90 | 1128.142 |
| 91 | 1140.6769 |
| 92 | 1153.2118 |
| 93 | 1165.7467 |
| 94 | 1178.2816 |
| 95 | 1190.8165 |
| 96 | 1203.3514 |
| 97 | 1215.8863 |
| 98 | 1228.42125 |
| 99 | 1240.9561 |
| 100 | 1253.4911 |
| 101 | 1266.026 |
| 102 | 1278.5609 |
| 103 | 1291.0958 |
| 104 | 1303.6307 |
| 105 | 1316.1656 |
| 106 | 1328.7005 |
| 107 | 1341.23545 |
| 108 | 1353.7704 |
| 109 | 1366.3053 |
| 110 | 1378.8418 |
| 111 | 1391.3751 |
| 112 | 1403.91 |
|
Todo: complete table
Add a third column that comments on the intervals, either what JI they approximate, what they are named, or how they can be used musically. |
Related regular temperaments
7-limit 383&670
Commas: 2401/2400, |91 -80 13 2>
POTE generator: ~|-33 32 -4 -3> = 12.5357
Mapping: [<1 1 -1 1|, <0 56 318 173|]
EDOs: 383, 670, 1053, 1436, 1723
11-limit 383&670
Commas: 2401/2400, [[1]], [[2]]
POTE generator: ~13504609503/13421772800 = 12.5359
Mapping: [<1 1 -1 1 3|, <[56 318 173|0 56 318 173] 44|]