612edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | |||
! rowspan="2" | [[Comma list]] | |||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal<br />8ve stretch (¢) | |||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
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| 0.0917 | | 0.0917 | ||
| 4.68 | | 4.68 | ||
|} | |||
* 612et has a lower relative error than any previous equal temperaments in the 5-limit. Not until [[1171edo|1171]] do we find a better equal temperament in terms of either absolute error or relative error. | * 612et has a lower relative error than any previous equal temperaments in the 5-limit. Not until [[1171edo|1171]] do we find a better equal temperament in terms of either absolute error or relative error. | ||
* It also has a lower absolute error in the 7- and 11-limit than any previous equal temperaments, and is only bettered by [[935edo|935]] and [[836edo|836]], respectively. | * It also has a lower absolute error in the 7- and 11-limit than any previous equal temperaments, and is only bettered by [[935edo|935]] and [[836edo|836]], respectively. | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {| class="wikitable center-all left-5" | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |||
! Periods<br />per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br />ratio* | |||
! Temperaments | |||
|- | |- | ||
| 1 | | 1 | ||
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| 231/200<br />(99/98) | | 231/200<br />(99/98) | ||
| [[Hemiennealimmal]] (11-limit) | | [[Hemiennealimmal]] (11-limit) | ||
|} | |||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
== Music == | == Music == |