Augene: Difference between revisions
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'''Augene''' is a [[regular temperament]] of the [[augmented family]], which means that [[128/125]] is [[tempering out|tempered out]] and three [[5/4]]'s make a [[2/1]]. Augene is distinguished from its relative [[august]] by tempering out [[64/63]], which means that tunings in which the fifth is larger than 7\12 (700 cents) are optimal. Therefore the [[optimal ET sequence]] of augene goes 12, 15, 27, … in constrast to august's which goes 9, 12, 21, …. | '''Augene''' is a [[regular temperament]] of the [[augmented family]], which means that [[128/125]] is [[tempering out|tempered out]] and three [[5/4]]'s make a [[2/1]]. Augene is distinguished from its relative [[august]] by tempering out [[64/63]], which means that tunings in which the fifth is larger than 7\12 (700 cents) are optimal. Therefore the [[optimal ET sequence]] of augene goes 12, 15, 27, … in constrast to august's which goes 9, 12, 21, …. | ||
It is also the unique [[7-limit]] [[regular temperament]] that tempers out the [[essential tempering commas]] of the 5 ([[128/125]])- and 7-limit ([[64/63]], [[126/125]]). | It is also the unique [[7-limit]] [[regular temperament]] that tempers out the [[essential tempering commas]] of the [[5-odd-limit|5-]] ([[128/125]])- and [[7-odd-limit]] ([[64/63]], [[126/125]]). | ||
The first few augene [[mos scale]]s are [[3L 3s]], [[3L 6s]], [[3L 9s]], [[12L 3s]], … and the first edos that reasonably support augene are [[12edo]], [[15edo]], and especially [[27edo]]. | The first few augene [[mos scale]]s are [[3L 3s]], [[3L 6s]], [[3L 9s]], [[12L 3s]], … and the first edos that reasonably support augene are [[12edo]], [[15edo]], and especially [[27edo]]. | ||
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{| class="wikitable center-1 right-2 right-4 right-6" | {| class="wikitable center-1 right-2 right-4 right-6" | ||
|- | |- | ||
! rowspan="2" | | ! rowspan="2" | # | ||
! colspan="2" | Period 0 | ! colspan="2" | Period 0 | ||
! colspan="2" | Period 1 | ! colspan="2" | Period 1 | ||
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|- | |- | ||
! Cents* | ! Cents* | ||
! Approx. | ! Approx. ratios | ||
! Cents* | ! Cents* | ||
! Approx. | ! Approx. ratios | ||
! Cents* | ! Cents* | ||
! Approx. | ! Approx. ratios | ||
|- | |- | ||
| 0 | | 0 | ||
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| 27/22 | | 27/22 | ||
|} | |} | ||
<nowiki />* In 11-odd-limit minimax tuning | <nowiki/>* In 11-odd-limit minimax tuning, octave reduced | ||
== Tuning spectrum == | == Tuning spectrum == | ||
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{| class="wikitable center-all left-4" | {| class="wikitable center-all left-4" | ||
|- | |- | ||
! Edo<br | ! Edo<br>generator | ||
! [[Eigenmonzo|Eigenmonzo<br | ! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]* | ||
! | ! Generator (¢) | ||
! Comments | ! Comments | ||
|- | |- | ||
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| | | | ||
|} | |} | ||
<nowiki />* Besides the octave | <nowiki/>* Besides the octave | ||
== Music == | == Music == | ||