12edo: Difference between revisions
No exaggerated language bs. |
→Regular temperament properties: no more relative error note beyond its monotonicity capability. Reduce duplication. - rank-3 stuff |
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* 12et | * 12et is monotonic to the [[11-odd-limit]]. It is the first equal temperament to achieve this. | ||
* 12et has a lower relative error than any previous equal temperaments in the [[3-limit|3-]], [[5-limit|5-]], [[7-limit|7-]], and [[11-limit]]. The next equal temperaments doing better in those subgroups are [[41edo|41]], [[19edo|19]], 19, [[22edo|22]], respectively. | |||
* 12et is even more prominent in the 2.3.5.7.17.19 subgroup, and the next equal temperament that does this better is [[72edo|72]]. | * 12et is even more prominent in the 2.3.5.7.17.19 subgroup, and the next equal temperament that does this better is [[72edo|72]]. | ||
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* [[List of 12et rank two temperaments by complexity]] | * [[List of 12et rank two temperaments by complexity]] | ||
* [[List of edo-distinct 12f rank two temperaments]] | * [[List of edo-distinct 12f rank two temperaments]] | ||
{| class="wikitable center-1 center-2" | {| class="wikitable center-1 center-2" | ||
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<nowiki>*</nowiki> [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | <nowiki>*</nowiki> [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | ||
Rank-2 temperaments to which 12et can be [[ | Rank-2 temperaments to which 12et can be [[detempering|detempered]] include [[compton]] (12 & 72), [[schismic]] (12 & 53), and [[diaschismic]] (46 & 58). See [[Schismic–commatic equivalence continuum]] for a more comprehensive list. | ||
== Octave stretch or compression == | == Octave stretch or compression == | ||