Starling temperaments: Difference between revisions
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Temperaments discussed in families and clans are: | Temperaments discussed in families and clans are: | ||
* [[ | * ''[[Pater]]'', {16/15, 126/125} → [[Father family #Pater]] | ||
* [[ | * ''[[Flat]]'', {21/20, 25/24} → [[Dicot family #Flat]] | ||
* [[ | * ''[[Opossum]]'', {28/27, 126/125} → [[Trienstonic clan #Opossum]] | ||
* [[ | * ''[[Diminished]]'', {36/35, 50/49} → [[Dimipent family #Diminished]] / [[Jubilismic clan #Diminished]] | ||
* [[ | * [[Keemun]], {49/48, 126/125} → [[Kleismic family #Keemun]] | ||
* [[ | * ''[[Augene]]'', {64/63, 126/125} → [[Augmented family #Augene]] | ||
* [[Meantone | * [[Meantone]], {81/80, 126/125} → [[Meantone family #Septimal meantone]] | ||
* [[ | * [[Mavila]], {126/125, 135/128} → [[Pelogic family #Mavila]] | ||
* [[ | * [[Sensi]], {126/125, 245/243}, [[Sensipent family #Sensi]] / [[Sensamagic clan #Sensi]] | ||
* [[ | * ''[[Gilead]]'', {126/125, 343/324} → [[Shibboleth family #Gilead]] | ||
* [[ | * ''[[Muggles]]'', {126/125, 525/512} → [[Magic family #Muggles]] | ||
* [[Diaschismic | * ''[[Diaschismic]]'', {126/125, 2048/2025} → [[Diaschismic family #Diaschismic]] | ||
* [[ | * ''[[Wollemia]]'', {126/125, 2240/2187} → [[Tetracot family #Wollemia]] | ||
* [[Unicorn | * ''[[Unicorn]]'', {126/125, 10976/10935} → [[Unicorn family #Unicorn]] | ||
* [[ | * ''[[Coblack]]'', {126/125, 16807/16384} → [[Cloudy clan #Coblack]] | ||
* [[ | * ''[[Grackle]]'', {126/125, 32805/32768} → [[Schismatic family #Grackle]] | ||
* [[ | * ''[[Worschmidt]]'', {126/125, 33075/32768} → [[Würschmidt family #Worschmidt]] | ||
* [[ | * ''[[Passionate]]'', {126/125, 131072/127575} → [[Passion family #Passionate]] | ||
* ''[[Vishnean]]'', ({126/125, 540225/524288} → [[Vishnuzmic family #Vishnean]] | |||
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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Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
[[Comma list]]: {{monzo|11 18 -17}} = 793437161472/762939453125 | [[Comma list]]: {{monzo| 11 18 -17 }} = 793437161472/762939453125 | ||
[[Mapping]]: [{{val| 1 6 7 }}, {{val| 0 -17 -18 }}] | [[Mapping]]: [{{val| 1 6 7 }}, {{val| 0 -17 -18 }}] | ||
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Badness: 0.035582 | Badness: 0.035582 | ||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||