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Created page with "'''4ED5/4''' is the equal division of the just major third into four parts of 96.5784 cents each, corresponding to 12.4252 edo. It i..." |
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'''4ED5/4''' is the [[Equal-step tuning|equal division]] of the [[5/4|just major third]] into four parts of 96.5784 [[cent|cents]] each, corresponding to 12. | '''4ED5/4''' is the [[Equal-step tuning|equal division]] of the [[5/4|just major third]] into four parts of 96.5784 [[cent|cents]] each, corresponding to 12.4251 [[edo]]. It is related to the temperament which tempers out 48828125/48771072 and 67108864/66976875 in the 7-limit, which is supported by [[87edo]], [[323edo]], [[410edo]], and [[733edo]] among others. | ||
==Intervals== | ==Intervals== | ||
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| | (5/4)<font style="vertical-align:super;font-size:0.8em;">13</font> = 1220703125/67108864 | | | (5/4)<font style="vertical-align:super;font-size:0.8em;">13</font> = 1220703125/67108864 | ||
|} | |} | ||
==Related regular temperament== | |||
===7-limit 87&323=== | |||
Commas: 48828125/48771072, 67108864/66976875 | |||
POTE generator: ~200/189 = 96.591 | |||
Map: [<1 4 2 -5|, <0 -30 4 97|] | |||
EDOs: 87, 323, 410, 733 | |||
Badness: 0.1793 | |||
===11-limit 87&323=== | |||
Commas: 5632/5625, 14641/14580, 131072/130977 | |||
POTE generator: ~200/189 = 96.587 | |||
Map: [<1 4 2 -5 7|, <0 -30 4 97 -44|] | |||
EDOs: 87, 323, 410, 733e | |||
Badness: 0.1001 | |||
===13-limit 87&323=== | |||
Commas: 676/675, 1001/1000, 4096/4095, 14641/14580 | |||
POTE generator: ~143/135 = 96.586 | |||
Map: [<1 4 2 -5 7 7|, <0 -30 4 97 -44 -41|] | |||
EDOs: 87, 323, 410, 733e | |||
Badness: 0.0462 | |||
[[Category:Major third]] | [[Category:Major third]] | ||
[[Category:Equal-step tuning]] | [[Category:Equal-step tuning]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
Revision as of 07:53, 26 January 2019
4ED5/4 is the equal division of the just major third into four parts of 96.5784 cents each, corresponding to 12.4251 edo. It is related to the temperament which tempers out 48828125/48771072 and 67108864/66976875 in the 7-limit, which is supported by 87edo, 323edo, 410edo, and 733edo among others.
Intervals
| degree | cents value | ratio |
|---|---|---|
| 0 | 0.0000 | 1/1 |
| 1 | 96.5784 | (5/4)1/4 |
| 2 | 193.1569 | (5/4)1/2 |
| 3 | 289.7353 | (5/4)3/4 |
| 4 | 386.3137 | 5/4 |
| 5 | 482.8921 | (5/4)5/4 |
| 6 | 579.4706 | (5/4)3/2 |
| 7 | 676.0490 | (5/4)7/4 |
| 8 | 772.6274 | (5/4)2 = 25/16 |
| 9 | 869.2059 | (5/4)9/4 |
| 10 | 965.7843 | (5/4)5/2 |
| 11 | 1062.3627 | (5/4)11/4 |
| 12 | 1158.9411 | (5/4)3 = 125/64 |
| 13 | 1255.5196 | (5/4)13/4 |
| 14 | 1352.0980 | (5/4)7/2 |
| 15 | 1448.6764 | (5/4)15/4 |
| 16 | 1545.2549 | (5/4)4 = 625/256 |
| 17 | 1641.8333 | (5/4)17/4 |
| 18 | 1738.4117 | (5/4)9/2 |
| 19 | 1834.9901 | (5/4)19/4 |
| 20 | 1931.5686 | (5/4)5 = 3125/1024 |
| 21 | 2028.1470 | (5/4)21/4 |
| 22 | 2124.7254 | (5/4)11/2 |
| 23 | 2221.3039 | (5/4)23/4 |
| 24 | 2317.8823 | (5/4)6 = 15625/4096 |
| 25 | 2414.4607 | (5/4)25/4 |
| 26 | 2511.0391 | (5/4)13/2 |
| 27 | 2607.6176 | (5/4)27/4 |
| 28 | 2704.1960 | (5/4)7 = 78125/16384 |
| 29 | 2800.7744 | (5/4)29/4 |
| 30 | 2897.3529 | (5/4)15/2 |
| 31 | 2993.9313 | (5/4)31/4 |
| 32 | 3090.5097 | (5/4)8 = 390625/65536 |
| 33 | 3187.0881 | (5/4)33/4 |
| 34 | 3283.6666 | (5/4)17/2 |
| 35 | 3380.2450 | (5/4)35/4 |
| 36 | 3476.8234 | (5/4)9 = 1953125/262144 |
| 37 | 3573.4019 | (5/4)37/4 |
| 38 | 3669.9803 | (5/4)19/2 |
| 39 | 3766.5587 | (5/4)39/4 |
| 40 | 3863.1371 | (5/4)10 = 9765625/1048576 |
| 41 | 3959.7156 | (5/4)41/4 |
| 42 | 4056.2940 | (5/4)21/2 |
| 43 | 4152.8724 | (5/4)43/4 |
| 44 | 4249.4509 | (5/4)11 = 48828125/4194304 |
| 45 | 4346.0293 | (5/4)45/4 |
| 46 | 4442.6077 | (5/4)23/2 |
| 47 | 4539.1861 | (5/4)47/4 |
| 48 | 4635.7646 | (5/4)12 = 244140625/16777216 |
| 49 | 4732.3430 | (5/4)49/4 |
| 50 | 4828.9214 | (5/4)25/2 |
| 51 | 4925.4999 | (5/4)51/4 |
| 52 | 5022.0783 | (5/4)13 = 1220703125/67108864 |
Related regular temperament
7-limit 87&323
Commas: 48828125/48771072, 67108864/66976875
POTE generator: ~200/189 = 96.591
Map: [<1 4 2 -5|, <0 -30 4 97|]
EDOs: 87, 323, 410, 733
Badness: 0.1793
11-limit 87&323
Commas: 5632/5625, 14641/14580, 131072/130977
POTE generator: ~200/189 = 96.587
Map: [<1 4 2 -5 7|, <0 -30 4 97 -44|]
EDOs: 87, 323, 410, 733e
Badness: 0.1001
13-limit 87&323
Commas: 676/675, 1001/1000, 4096/4095, 14641/14580
POTE generator: ~143/135 = 96.586
Map: [<1 4 2 -5 7 7|, <0 -30 4 97 -44 -41|]
EDOs: 87, 323, 410, 733e
Badness: 0.0462