46edo: Difference between revisions

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46et tempers out 507/500, 91/90, 686/675, 2048/2025, 121/120, 245/243, 126/125, 169/168, 176/175, 896/891, 196/195, 1029/1024, 5120/5103, 385/384, and 441/440 among other intervals, with various consequences. [[Rank_two_temperaments|Rank two temperaments]] it supports include sensi, valentine, shrutar, rodan, leapday and unidec. The [[11-limit|11-limit]] [[Target_tunings|minimax]] tuning for [[Starling_family|valentine temperament]], (11/7)^(1/10), is only 0.01 cents flat of 3/46 octaves. In the opinion of some, 46et is the first equal division to deal adequately with the [[13-limit|13-limit]], though others award that distinction to [[41edo|41edo]]. In fact, while 41 is a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta integral edo]] but not a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta gap edo]], 46 is zeta gap but not zeta integral.

The fifth of 46 equal is 2.39 cents sharp, which some people (eg, Margo Schulter) prefer, sometimes strongly, over both the [https://en.xen.wiki/w/3/2 just fifth] and fifths of temperaments with flat fifths, such as meantone. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad.

The fifth of 46 equal is 2.39 cents sharp, which some people (eg, [https://en.xen.wiki/w/Margo_Schulter Margo Schulter]) prefer, sometimes strongly, over both the [https://en.xen.wiki/w/3/2 just fifth] and fifths of temperaments with flat fifths, such as meantone. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad.

46edo can be treated as two [[23edo|23edo]]'s separated by an interval of 26.087 cents.

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 et tempers out 507/500, 91/90, 686/675, 2048/2025, 121/120, 245/243, 126/125, 169/168, 176/175, 896/891, 196/195, 1029/1024, 5120/5103, 385/384, and 441/440 among other intervals, with various consequences. [[Rank_two_temperaments|Rank two temperaments]] it supports include sensi, valentine, shrutar, rodan, leapday and unidec. The [[11-limit|11-limit]] [[Target_tunings|minimax]] tuning for [[Starling_family|valentine temperament]], (11/7)^(1/10), is only 0.01 cents flat of 3/46 octaves. In the opinion of some, 46et is the first equal division to deal adequately with the [[13-limit|13-limit]], though others award that distinction to [[41edo|41edo]]. In fact, while 41 is a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta integral edo]] but not a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta gap edo]], 46 is zeta gap but not zeta integral.
-The fifth of 46 equal is 2.39 cents sharp, which some people (eg, Margo Schulter) prefer, sometimes strongly, over both the [https://en.xen.wiki/w/3/2 just fifth] and fifths of temperaments with flat fifths, such as meantone. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad.
+The fifth of 46 equal is 2.39 cents sharp, which some people (eg, [https://en.xen.wiki/w/Margo_Schulter Margo Schulter]) prefer, sometimes strongly, over both the [https://en.xen.wiki/w/3/2 just fifth] and fifths of temperaments with flat fifths, such as meantone. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad.
 edo can be treated as two [[23edo|23edo]]'s separated by an interval of 26.087 cents.