41edt: Difference between revisions
→Related regular temperaments: adding badness Tags: Mobile edit Mobile web edit |
Cmloegcmluin (talk | contribs) map → mapping |
||
| Line 10: | Line 10: | ||
POTE generator: ~|140 -59 -20> = 46.3927 | POTE generator: ~|140 -59 -20> = 46.3927 | ||
Mapping: [<1 0 7|, <0 41 -121|] | |||
EDOs: 181, 207, 388, 569, 595, 957, 1345 | EDOs: 181, 207, 388, 569, 595, 957, 1345 | ||
| Line 21: | Line 21: | ||
POTE generator: ~131072/127575 = 46.3932 | POTE generator: ~131072/127575 = 46.3932 | ||
Mapping: [<1 0 7 3|, <0 41 -121 -5|] | |||
EDOs: 181, 207, 388, 569, 595 | EDOs: 181, 207, 388, 569, 595 | ||
| Line 32: | Line 32: | ||
POTE generator: ~352/343 = 46.3934 | POTE generator: ~352/343 = 46.3934 | ||
Mapping: [<1 0 7 3 4|, <0 41 -121 -5 -14|] | |||
EDOs: 181, 207, 388, 569, 595 | EDOs: 181, 207, 388, 569, 595 | ||
| Line 43: | Line 43: | ||
POTE generator: ~352/343 = 46.3921 | POTE generator: ~352/343 = 46.3921 | ||
Mapping: [<1 0 7 3 4 2|, <0 41 -121 -5 -14 44|] | |||
EDOs: 181, 207, 388, 569, 595 | EDOs: 181, 207, 388, 569, 595 | ||
| Line 54: | Line 54: | ||
POTE generator: ~187/182 = 46.3918 | POTE generator: ~187/182 = 46.3918 | ||
Mapping: [<1 0 7 3 4 2 2|, <0 41 -121 -5 -14 44 54|] | |||
EDOs: 181, 207, 388, 569, 595 | EDOs: 181, 207, 388, 569, 595 | ||
| Line 66: | Line 66: | ||
POTE generator: ~|-16 57 -32> = 46.3883 | POTE generator: ~|-16 57 -32> = 46.3883 | ||
Mapping: [<2 0 -1|, <0 41 73|] | |||
EDOs: 26, 388, 414, 802, 1190, 1578, 1966, 2354 | EDOs: 26, 388, 414, 802, 1190, 1578, 1966, 2354 | ||
| Line 77: | Line 77: | ||
POTE generator: ~17294403/16777216 = 46.3835 | POTE generator: ~17294403/16777216 = 46.3835 | ||
Mapping: [<2 0 -1 6|, <0 41 73 -5|] | |||
EDOs: 26, 362, 388, 414, 802 | EDOs: 26, 362, 388, 414, 802 | ||
| Line 88: | Line 88: | ||
POTE generator: ~352/343 = 46.3827 | POTE generator: ~352/343 = 46.3827 | ||
Mapping: [<2 0 -1 6 8|, <0 41 73 -5 -14|] | |||
EDOs: 26, 362, 388, 414, 802 | EDOs: 26, 362, 388, 414, 802 | ||
| Line 99: | Line 99: | ||
POTE generator: ~352/343 = 46.3825 | POTE generator: ~352/343 = 46.3825 | ||
Mapping: [<2 0 -1 6 8 4|, <0 41 73 -5 -14 44|] | |||
EDOs: 26, 362, 388, 414, 802 | EDOs: 26, 362, 388, 414, 802 | ||
| Line 110: | Line 110: | ||
POTE generator: ~187/182 = 46.3824 | POTE generator: ~187/182 = 46.3824 | ||
Mapping: [<2 0 -1 6 8 4 4|, <0 41 73 -5 -14 44 54|] | |||
EDOs: 26, 362, 388, 414, 802 | EDOs: 26, 362, 388, 414, 802 | ||
Revision as of 19:50, 5 November 2021
Division of the third harmonic into 41 equal parts (41edt) is related to 26 edo, but with the 3/1 rather than the 2/1 being just. The octave is about 6.1178 cents stretched and the step size is about 46.3891 cents. Unlike 26edo, it is only consistent up to the 10-integer-limit, with discrepancy for the 11th harmonic.
41edt is related to the regular temperament which tempers out 823543/820125 and 2199023255552/2197176384375 in the 7-limit, which is supported by 181, 207, 388, 569, and 595 EDOs.
Related regular temperaments
181&207 temperament
5-limit
Comma: |287 -121 -41>
POTE generator: ~|140 -59 -20> = 46.3927
Mapping: [<1 0 7|, <0 41 -121|]
EDOs: 181, 207, 388, 569, 595, 957, 1345
Badness: 17.5651
7-limit
Commas: 823543/820125, 2199023255552/2197176384375
POTE generator: ~131072/127575 = 46.3932
Mapping: [<1 0 7 3|, <0 41 -121 -5|]
EDOs: 181, 207, 388, 569, 595
Badness: 0.6461
11-limit
Commas: 42592/42525, 43923/43904, 184877/184320
POTE generator: ~352/343 = 46.3934
Mapping: [<1 0 7 3 4|, <0 41 -121 -5 -14|]
EDOs: 181, 207, 388, 569, 595
Badness: 0.1362
13-limit
Commas: 847/845, 4096/4095, 4459/4455, 17303/17280
POTE generator: ~352/343 = 46.3921
Mapping: [<1 0 7 3 4 2|, <0 41 -121 -5 -14 44|]
EDOs: 181, 207, 388, 569, 595
Badness: 0.0707
17-limit
Commas: 833/832, 847/845, 1089/1088, 2058/2057, 2431/2430
POTE generator: ~187/182 = 46.3918
Mapping: [<1 0 7 3 4 2 2|, <0 41 -121 -5 -14 44 54|]
EDOs: 181, 207, 388, 569, 595
Badness: 0.0411
26&388 temperament
5-limit
Comma: |-41 146 -82>
POTE generator: ~|-16 57 -32> = 46.3883
Mapping: [<2 0 -1|, <0 41 73|]
EDOs: 26, 388, 414, 802, 1190, 1578, 1966, 2354
Badness: 3.9285
7-limit
Commas: 4375/4374, |-62 -1 2 21>
POTE generator: ~17294403/16777216 = 46.3835
Mapping: [<2 0 -1 6|, <0 41 73 -5|]
EDOs: 26, 362, 388, 414, 802
Badness: 0.4543
11-limit
Commas: 3025/3024, 4375/4374, 5931980229/5905580032
POTE generator: ~352/343 = 46.3827
Mapping: [<2 0 -1 6 8|, <0 41 73 -5 -14|]
EDOs: 26, 362, 388, 414, 802
Badness: 0.1020
13-limit
Commas: 2200/2197, 3025/3024, 4375/4374, 50421/50336
POTE generator: ~352/343 = 46.3825
Mapping: [<2 0 -1 6 8 4|, <0 41 73 -5 -14 44|]
EDOs: 26, 362, 388, 414, 802
Badness: 0.0595
17-limit
Commas: 833/832, 1089/1088, 1225/1224, 1701/1700, 2200/2197
POTE generator: ~187/182 = 46.3824
Mapping: [<2 0 -1 6 8 4 4|, <0 41 73 -5 -14 44 54|]
EDOs: 26, 362, 388, 414, 802
Badness: 0.0326