76edo: Difference between revisions

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The ''76 equal division'' 5-limit [[patent val]] is [[contorted]] in the 5-limit, reflecting the fact that 76 = 4 * 19. In the 7-limit it tempers out 2401/2400 as well as 81/80, and so ~~supports~~ [[Meantone_family#Squares|squares temperament]]. In the 11-limit, it tempers out 245/242 and 385/384, and supports the 24&26 temperament. In the 13-limit, it tempers out 105/104, 144/143, 351/350 and 364/363. While the 44\76 = 11\19 fifth is already flat, the 43\76 fifth, even flatter, is an almost perfect approximation to the [[Pelogic_family|hornbostel temperament]] POTE fifth, whereas its sharp fifth, 45\76, makes for an excellent [[Archytas_clan#Superpyth|superpyth]] fifth. Hence you can do hornbostel/mavila, squares/meantone, and superpyth all with the same equal division.

The ''76 equal division'' 5-limit [[patent val]] is [[contorted]] in the 5-limit, reflecting the fact that 76 = 4 * 19. In the 7-limit it tempers out 2401/2400 as well as 81/80, and so [[support]]s [[Meantone_family#Squares|squares temperament]]. In the 11-limit, it tempers out 245/242 and 385/384, and supports the 24&26 temperament. In the 13-limit, it tempers out 105/104, 144/143, 351/350 and 364/363. While the 44\76 = 11\19 fifth is already flat, the 43\76 fifth, even flatter, is an almost perfect approximation to the [[Pelogic_family|hornbostel temperament]] POTE fifth, whereas its sharp fifth, 45\76, makes for an excellent [[Archytas_clan#Superpyth|superpyth]] fifth. Hence you can do hornbostel/mavila, squares/meantone, and superpyth all with the same equal division.

Using non-patent vals, 76edo provides an excellent tuning for [[Teff|teff]] temperament, a low complexity, medium accuracy, and high limit (17 or 19) temperament.

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-The ''76 equal division'' 5-limit [[patent val]] is [[contorted]] in the 5-limit, reflecting the fact that 76 = 4 * 19. In the 7-limit it tempers out 2401/2400 as well as 81/80, and so supports [[Meantone_family#Squares|squares temperament]]. In the 11-limit, it tempers out 245/242 and 385/384, and supports the 24&amp;26 temperament. In the 13-limit, it tempers out 105/104, 144/143, 351/350 and 364/363. While the 44\76 = 11\19 fifth is already flat, the 43\76 fifth, even flatter, is an almost perfect approximation to the [[Pelogic_family|hornbostel temperament]] POTE fifth, whereas its sharp fifth, 45\76, makes for an excellent [[Archytas_clan#Superpyth|superpyth]] fifth. Hence you can do hornbostel/mavila, squares/meantone, and superpyth all with the same equal division.
+The ''76 equal division'' 5-limit [[patent val]] is [[contorted]] in the 5-limit, reflecting the fact that 76 = 4 * 19. In the 7-limit it tempers out 2401/2400 as well as 81/80, and so [[support]]s [[Meantone_family#Squares|squares temperament]]. In the 11-limit, it tempers out 245/242 and 385/384, and supports the 24&amp;26 temperament. In the 13-limit, it tempers out 105/104, 144/143, 351/350 and 364/363. While the 44\76 = 11\19 fifth is already flat, the 43\76 fifth, even flatter, is an almost perfect approximation to the [[Pelogic_family|hornbostel temperament]] POTE fifth, whereas its sharp fifth, 45\76, makes for an excellent [[Archytas_clan#Superpyth|superpyth]] fifth. Hence you can do hornbostel/mavila, squares/meantone, and superpyth all with the same equal division.
 Using non-patent vals, 76edo provides an excellent tuning for [[Teff|teff]] temperament, a low complexity, medium accuracy, and high limit (17 or 19) temperament.
 {{harmonics in equal|76}}