Marvel temperaments: Difference between revisions
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This page discusses | This page discusses miscellaneous rank-2 temperaments tempering out {{monzo|-5 2 2 -1}} = [[225/224]], the marvel comma or septimal kleisma. | ||
Temperaments considered in families and clans are: | |||
* [[Dicot family #Sharp|sharp]] ({25/24, 28/27}, dicot family) | |||
* [[Pelogic family #Pelogic|pelogic]] ({21/20, 135/128}, pelogic family) | |||
* [[Augmented family #August|august]] ({36/35, 128/125}, augmented family) | |||
* [[Diaschismic family #Pajara|pajara]] ({50/49, 64/63}, diaschismic family / jubilismic clan / archytas clan) | |||
* [[Meantone family #Septimal meantone|meantone]] ({81/80, 126/125}, meantone family) | |||
* [[Magic family|magic]] ({225/224, 245/243}, magic family) | |||
* [[Gamelismic clan #Miracle|miracle]] ({225/224, 1029/1024}, gamelismic clan) | |||
* [[Semicomma family #Orwell|orwell]] ({225/224, 1728/1715}, semicomma family) | |||
* [[Schismatic family #Garibaldi|garibaldi]] ({225/224, 3125/3087}, schismatic family) | |||
* [[Kleismic family #Catakleismic|catakleismic]] ({225/224, 4375/4374}, kleismic family) | |||
* [[Cloudy clan #Decic|decic]] ({225/224, 16807/16384}, cloudy clan) | |||
* [[Escapade family #Escapade|escapade]] ({225/224, 65625/65536}, escapade family) | |||
* [[Pythagorean family #Compton|compton]] ({225/224, 250047/250000}, pythagorean family) | |||
* [[Qintosec family|qintosec]] ({225/224, 2560000/2470629}, qintosec family) | |||
Considered below are negri, wizard, tritonic, septimin, slender, triton, merman, marvo, marvolo, amavil, enneaportent, submajor, and alphorn. | |||
Since (5/4)<sup>2</sup> = 225/224 × 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess a version of the augmented triad where each third approximates either 5/4 or 9/7. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds. | Since (5/4)<sup>2</sup> = 225/224 × 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess a version of the augmented triad where each third approximates either 5/4 or 9/7. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds. | ||