76edo: Difference between revisions

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== Theory ==

76edo's [[patent val]] is [[contorted]] in the 5-limit, reflecting the fact that 76 = 4 × 19. In the 7-limit it [[tempering out|tempers out]] [[2401/2400]] in addition to [[81/80]], and so [[support]]s the [[squares]] temperament. In the 11-limit, it tempers out [[245/242]] and [[385/384]], and supports [[pombe]], the {{nowrap|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 [[hornbostel]] temperament's [[POTE]] fifth, whereas its sharp fifth, 45\76, makes for an excellent [[superpyth]] fifth. Hence you can do hornbostel/mavila, squares/meantone, and superpyth all with the same equal division.

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

Using the 76dgh val, 76edo provides an excellent tuning for [[teff]] temperament, a low-complexity, medium-accuracy, and high-limit (17- or 19-limit) temperament.

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