Starling temperaments: Difference between revisions
Cmloegcmluin (talk | contribs) adding parenthetical "(unchanged intervals)" to eigenmonzo lists |
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* [[Schismatic family #Grackle|grackle]] ({126/125, 32805/32768}, schismatic family) | * [[Schismatic family #Grackle|grackle]] ({126/125, 32805/32768}, schismatic family) | ||
* [[Würschmidt family #Worschmidt|worschmidt]] ({126/125, 33075/32768}, würschmidt family) | * [[Würschmidt family #Worschmidt|worschmidt]] ({126/125, 33075/32768}, würschmidt family) | ||
* [[Vishnuzmic family #Vishnean|vishnean]] ({126/125, 540225/524288}, vishnuzmic family) | |||
Since (6/5)<sup>3</sup> = 126/125 × 12/7, these temperaments tend to have a relatively small complexity for 6/5. They also possess the [[starling tetrad]], the 6/5-6/5-6/5-7/6 versions of the diminished seventh chord. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before [[12edo|12EDO]] established itself as the standard tuning, it is arguably more authentic to tune it as three stacked minor thirds and an augmented second, which is what it is in meantone, than as the modern version of four stacked very flat minor thirds. | Since (6/5)<sup>3</sup> = 126/125 × 12/7, these temperaments tend to have a relatively small complexity for 6/5. They also possess the [[starling tetrad]], the 6/5-6/5-6/5-7/6 versions of the diminished seventh chord. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before [[12edo|12EDO]] established itself as the standard tuning, it is arguably more authentic to tune it as three stacked minor thirds and an augmented second, which is what it is in meantone, than as the modern version of four stacked very flat minor thirds. | ||
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Badness: 0.016687 | Badness: 0.016687 | ||
=== Dwynwen === | ==== Dwynwen ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.023461 | Badness: 0.023461 | ||
=== Lupercalia === | ==== Lupercalia ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.021328 | Badness: 0.021328 | ||
=== Valentino === | ==== Valentino ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.020665 | Badness: 0.020665 | ||
=== Semivalentine === | ==== Semivalentine ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||