76edo: Difference between revisions

Line 3:

== 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 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.

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.

=== Odd harmonics ===

This tuning's 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.~~

== Intervals ==

@@ Line 3: / Line 3: @@
 == 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 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.
+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.
+=== Odd harmonics ===
 {{Harmonics in equal|76}}
-This tuning's 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.
 == Intervals ==
 {{Interval table}}