29edt: Difference between revisions
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'''29EDT''' is the [[Edt|equal division of the third harmonic]] into 29 parts of 65.5847 [[cent|cents]] each, corresponding to 18.2970 [[edo]]. It is related to the temperament | '''29EDT''' is the [[Edt|equal division of the third harmonic]] into 29 parts of 65.5847 [[cent|cents]] each, corresponding to 18.2970 [[edo]]. It is related to the regular temperament supported by [[183edo]], [[311edo]], and [[494edo]]. | ||
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| | | | | 64/51 | ||
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| | 23 | | | 23 | ||
| | 1508.4471 | | | 1508.4471 | ||
| | | | | 153/64 | ||
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| | [[3/2|just perfect fifth]] plus an octave | | | [[3/2|just perfect fifth]] plus an octave | ||
|} | |} | ||
==Related regular temperament== | |||
===5-limit 183&311=== | |||
Comma: |145 -49 -29> | |||
POTE generator: 65.585 | |||
Map: [<1 0 5|, <0 29 -49|] | |||
EDOs: 183, 311, 494, 677, 860, 1171, 1665, 1848, 2159, 2836, 3019, 4007 | |||
Badness: 0.1949 | |||
===7-limit 183&311=== | |||
Commas: 703125/702464, 26843545600/26795786661 | |||
POTE generator: ~8505/8192 = 65.588 | |||
Map: [<1 0 5 8|, <0 29 -49 -95|] | |||
EDOs: 128, 183, 311, 494, 677, 805, 1116, 1299 | |||
Badness: 0.1348 | |||
===11-limit 183&311=== | |||
Commas: 3025/3024, 131072/130977, 703125/702464 | |||
POTE generator: ~5103/4840 = 65.588 | |||
Map: [<1 0 5 8 1|, <0 29 -49 -95 45|] | |||
EDOs: 128, 183, 311, 494, 677, 805, 1299 | |||
===13-limit 183&311=== | |||
Commas: 2080/2079, 3025/3024, 4096/4095, 31250/31213 | |||
POTE generator: ~1404/1331 = 65.588 | |||
Map: [<1 0 5 8 1 -1|, <0 29 -49 -95 45 86|] | |||
EDOs: 128, 183, 311, 494, 677, 805, 1299 | |||
===17-limit 183&311=== | |||
Commas: 1156/1155, 1275/1274, 2080/2079, 2431/2430, 4096/4095 | |||
POTE generator: ~1404/1331 = 65.588 | |||
Map: [<1 0 5 8 1 -1 6|, <0 29 -49 -95 45 86 -35|] | |||
EDOs: 128, 183, 311, 494, 677, 805 | |||
[[Category:Edt]] | [[Category:Edt]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
Revision as of 11:56, 29 January 2019
29EDT is the equal division of the third harmonic into 29 parts of 65.5847 cents each, corresponding to 18.2970 edo. It is related to the regular temperament supported by 183edo, 311edo, and 494edo.
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 65.5847 | 27/26 | |
| 2 | 131.1693 | ||
| 3 | 196.7540 | 28/25 | |
| 4 | 262.3386 | ||
| 5 | 327.9233 | ||
| 6 | 393.5079 | 64/51 | |
| 7 | 459.0926 | ||
| 8 | 524.6772 | 65/48 | |
| 9 | 590.2619 | 45/32 | |
| 10 | 655.8466 | ||
| 11 | 721.4312 | ||
| 12 | 787.0159 | 63/40, 52/33 | |
| 13 | 852.6005 | 18/11 | |
| 14 | 918.1852 | ||
| 15 | 983.7698 | ||
| 16 | 1049.3545 | 11/6 | |
| 17 | 1114.9391 | 99/52, 40/21 | |
| 18 | 1180.5238 | ||
| 19 | 1246.1084 | ||
| 20 | 1311.6931 | 32/15 | |
| 21 | 1377.2778 | 144/65 | |
| 22 | 1442.8624 | ||
| 23 | 1508.4471 | 153/64 | |
| 24 | 1574.0317 | ||
| 25 | 1639.6164 | ||
| 26 | 1705.2010 | 75/28 | |
| 27 | 1770.7857 | ||
| 28 | 1836.3703 | 26/9 | |
| 29 | 1901.9550 | exact 3/1 | just perfect fifth plus an octave |
Related regular temperament
5-limit 183&311
Comma: |145 -49 -29>
POTE generator: 65.585
Map: [<1 0 5|, <0 29 -49|]
EDOs: 183, 311, 494, 677, 860, 1171, 1665, 1848, 2159, 2836, 3019, 4007
Badness: 0.1949
7-limit 183&311
Commas: 703125/702464, 26843545600/26795786661
POTE generator: ~8505/8192 = 65.588
Map: [<1 0 5 8|, <0 29 -49 -95|]
EDOs: 128, 183, 311, 494, 677, 805, 1116, 1299
Badness: 0.1348
11-limit 183&311
Commas: 3025/3024, 131072/130977, 703125/702464
POTE generator: ~5103/4840 = 65.588
Map: [<1 0 5 8 1|, <0 29 -49 -95 45|]
EDOs: 128, 183, 311, 494, 677, 805, 1299
13-limit 183&311
Commas: 2080/2079, 3025/3024, 4096/4095, 31250/31213
POTE generator: ~1404/1331 = 65.588
Map: [<1 0 5 8 1 -1|, <0 29 -49 -95 45 86|]
EDOs: 128, 183, 311, 494, 677, 805, 1299
17-limit 183&311
Commas: 1156/1155, 1275/1274, 2080/2079, 2431/2430, 4096/4095
POTE generator: ~1404/1331 = 65.588
Map: [<1 0 5 8 1 -1 6|, <0 29 -49 -95 45 86 -35|]
EDOs: 128, 183, 311, 494, 677, 805