58edo: Difference between revisions
m Partially completed a hemipyth column |
m →Regular temperament properties: cleanup |
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| 2.3.5 | | 2.3.5 | ||
| 2048/2025, [[Unicorn comma|1594323/1562500]] | | 2048/2025, [[Unicorn comma|1594323/1562500]] | ||
| | | {{mapping| 58 92 135 }} | ||
| −1.29 | | −1.29 | ||
| 1.22 | | 1.22 | ||
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| 2.3.5.7 | | 2.3.5.7 | ||
| 126/125, 1728/1715, 2048/2025 | | 126/125, 1728/1715, 2048/2025 | ||
| | | {{mapping| 58 92 135 163 }} | ||
| −1.29 | | −1.29 | ||
| 1.05 | | 1.05 | ||
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| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 126/125, 176/175, 243/242, 896/891 | | 126/125, 176/175, 243/242, 896/891 | ||
| | | {{mapping| 58 92 135 163 201 }} | ||
| −1.45 | | −1.45 | ||
| 1.00 | | 1.00 | ||
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| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 126/125, 144/143, 176/175, 196/195, 364/363 | | 126/125, 144/143, 176/175, 196/195, 364/363 | ||
| | | {{mapping| 58 92 135 163 201 215 }} | ||
| −1.56 | | −1.56 | ||
| 0.94 | | 0.94 | ||
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| 2.3.5.7.11.13.17 | | 2.3.5.7.11.13.17 | ||
| 126/125, 136/135, 144/143, 176/175, 196/195, 364/363 | | 126/125, 136/135, 144/143, 176/175, 196/195, 364/363 | ||
| | | {{mapping| 58 92 135 163 201 215 237 }} | ||
| −1.28 | | −1.28 | ||
| 1.10 | | 1.10 | ||
| 5.33 | | 5.33 | ||
|} | |} | ||
* 58et has a lower relative error than any previous equal temperaments in the 13-limit, and the next equal temperament that does better in this subgroup is [[72edo|72]]. | |||
58et has a lower relative error than any previous equal temperaments in the 13-limit, and the next equal temperament that does better in this subgroup is [[72edo|72]]. | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
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|- | |- | ||
! Period<br>per 8ve | ! Period<br>per 8ve | ||
! Generator | ! Generator* | ||
! Cents | ! Cents* | ||
! Associated | ! Associated<br>Ratio* | ||
! Temperament | ! Temperament | ||
|- | |- | ||
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| [[Mystery]] | | [[Mystery]] | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
58et can also be detempered to [[semihemi]] (58 & 140), [[supers]] (58 & 152), [[condor]] (58 & 159), and [[eagle]] (58 & 212). | 58et can also be detempered to [[semihemi]] (58 & 140), [[supers]] (58 & 152), [[condor]] (58 & 159), and [[eagle]] (58 & 212). | ||