41edt: Difference between revisions
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'''[[Edt|Division of the third harmonic]] into 41 equal parts''' (41edt) is related to [[26edo|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 [[9-odd-limit|10-integer-limit]], with discrepancy for the 11th harmonic. | '''[[Edt|Division of the third harmonic]] into 41 equal parts''' (41edt) is related to [[26edo|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 [[9-odd-limit|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 [[181edo|181]], [[207edo|207]], [[388edo|388]], 569, and 595 EDOs. | 41edt is related to the regular temperament which tempers out 823543/820125 and 2199023255552/2197176384375 in the 7-limit, which is supported by [[181edo|181]], [[207edo|207]], [[388edo|388]], [[569edo|569]], and [[595edo|595]] EDOs. | ||
=Related regular temperaments= | =Related regular temperaments= | ||
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Mapping: [<1 0 7|, <0 41 -121|] | Mapping: [<1 0 7|, <0 41 -121|] | ||
EDOs: 181, 207, 388, 569, 595, 957, 1345 | EDOs: {{EDOs|181, 207, 388, 569, 595, 957, 1345}} | ||
Badness: 17.5651 | Badness: 17.5651 | ||
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Mapping: [<1 0 7 3|, <0 41 -121 -5|] | Mapping: [<1 0 7 3|, <0 41 -121 -5|] | ||
EDOs: 181, 207, 388, 569, 595 | EDOs: {{EDOs|181, 207, 388, 569, 595}} | ||
Badness: 0.6461 | Badness: 0.6461 | ||
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Mapping: [<1 0 7 3 4|, <0 41 -121 -5 -14|] | Mapping: [<1 0 7 3 4|, <0 41 -121 -5 -14|] | ||
EDOs: 181, 207, 388, 569, 595 | EDOs: {{EDOs|181, 207, 388, 569, 595}} | ||
Badness: 0.1362 | Badness: 0.1362 | ||
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Mapping: [<1 0 7 3 4 2|, <0 41 -121 -5 -14 44|] | Mapping: [<1 0 7 3 4 2|, <0 41 -121 -5 -14 44|] | ||
EDOs: 181, 207, 388, 569, 595 | EDOs: {{EDOs|181, 207, 388, 569, 595}} | ||
Badness: 0.0707 | Badness: 0.0707 | ||
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Mapping: [<1 0 7 3 4 2 2|, <0 41 -121 -5 -14 44 54|] | Mapping: [<1 0 7 3 4 2 2|, <0 41 -121 -5 -14 44 54|] | ||
EDOs: 181, 207, 388, 569, 595 | EDOs: {{EDOs|181, 207, 388, 569, 595}} | ||
Badness: 0.0411 | Badness: 0.0411 | ||
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Mapping: [<2 0 -1|, <0 41 73|] | Mapping: [<2 0 -1|, <0 41 73|] | ||
EDOs: 26, 388, 414, 802, 1190, 1578, 1966, 2354 | EDOs: {{EDOs|26, 388, 414, 802, 1190, 1578, 1966, 2354}} | ||
Badness: 3.9285 | Badness: 3.9285 | ||
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Mapping: [<2 0 -1 6|, <0 41 73 -5|] | Mapping: [<2 0 -1 6|, <0 41 73 -5|] | ||
EDOs: 26, 362, 388, 414, 802 | EDOs: {{EDOs|26, 362, 388, 414, 802}} | ||
Badness: 0.4543 | Badness: 0.4543 | ||
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Mapping: [<2 0 -1 6 8|, <0 41 73 -5 -14|] | Mapping: [<2 0 -1 6 8|, <0 41 73 -5 -14|] | ||
EDOs: 26, 362, 388, 414, 802 | EDOs: {{EDOs|26, 362, 388, 414, 802}} | ||
Badness: 0.1020 | Badness: 0.1020 | ||
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Mapping: [<2 0 -1 6 8 4|, <0 41 73 -5 -14 44|] | Mapping: [<2 0 -1 6 8 4|, <0 41 73 -5 -14 44|] | ||
EDOs: 26, 362, 388, 414, 802 | EDOs: {{EDOs|26, 362, 388, 414, 802}} | ||
Badness: 0.0595 | Badness: 0.0595 | ||
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Mapping: [<2 0 -1 6 8 4 4|, <0 41 73 -5 -14 44 54|] | Mapping: [<2 0 -1 6 8 4 4|, <0 41 73 -5 -14 44 54|] | ||
EDOs: 26, 362, 388, 414, 802 | EDOs: {{EDOs|26, 362, 388, 414, 802}} | ||
Badness: 0.0326 | Badness: 0.0326 | ||