76edo: Difference between revisions

Line 1:

The ''76 equal division'' 5-limit patent val is [[contorted|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|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.

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.

Revision as of 00:00, 17 July 2018 view source Wikispaces>FREEZE No edit summary ← Older edit		Revision as of 23:09, 20 September 2018 view source Keenan Pepper (talk \| contribs) autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops 968 edits m link patent val Tag: Visual edit: Switched Newer edit →
Line 1:		Line 1:
	The ''76 equal division'' 5-limit patent val is [[contorted\|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\|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.

	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.		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.