46edo: Difference between revisions

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== Theory ==

In the opinion of some, 46edo is the first equal division to deal adequately with the [[13-limit]], though others award that distinction to [[41edo]]. In fact, while 41 is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak and 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 peak or zeta integral. (Their sum, [[87edo]], does better than both in the 13-limit at the expense of a high note count.) Like 41, 46 is distinctly [[consistent]] in the [[9-odd-limit]], and it is consistent to the [[13-odd-limit]] or the no-15 no-19 [[23-odd-limit]]. 46edo's fifth is slightly sharp of just, which some people (e.g. [[Margo Schulter]]) prefer, sometimes strongly, over both the [[3/2|just fifth]] and fifths of temperaments with flat fifths, such as meantone. Many say that sharp fifths give a characteristic bright sound to 5-limit triads, and consider the sound of meantone triads to be more mellow in comparison.

In the opinion of some{{Who}}, 46edo is the first equal division to deal adequately with the [[13-limit]], though others award that distinction to [[41edo]]. In fact, while 41 is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak and 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 peak or zeta integral. (Their sum, [[87edo]], does better than both in the 13-limit at the expense of a high note count.) Like 41, 46 is distinctly [[consistent]] in the [[9-odd-limit]], and it is consistent to the [[13-odd-limit]] or the no-15 no-19 [[23-odd-limit]]. 46edo's fifth is slightly sharp of just, which some people (e.g. [[Margo Schulter]]) prefer, sometimes strongly, over both the [[3/2|just fifth]] and fifths of temperaments with flat fifths, such as meantone. Many say that sharp fifths give a characteristic bright sound to 5-limit triads, and consider the sound of meantone triads to be more mellow in comparison.

[[Rank-2 temperament]]s it [[support]]s include [[sensi]], [[valentine]], [[shrutar]], [[rodan]], [[leapday]] and [[unidec]]. The [[11-odd-limit]] [[minimax tuning]] for valentine, (11/7)<sup>1/10</sup>, is only 0.01 cents flat of 3\46 octaves.

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 == Theory ==
-In the opinion of some, 46edo is the first equal division to deal adequately with the [[13-limit]], though others award that distinction to [[41edo]]. In fact, while 41 is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak and 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 peak or zeta integral. (Their sum, [[87edo]], does better than both in the 13-limit at the expense of a high note count.) Like 41, 46 is distinctly [[consistent]] in the [[9-odd-limit]], and it is consistent to the [[13-odd-limit]] or the no-15 no-19 [[23-odd-limit]]. 46edo's fifth is slightly sharp of just, which some people (e.g. [[Margo Schulter]]) prefer, sometimes strongly, over both the [[3/2|just fifth]] and fifths of temperaments with flat fifths, such as meantone. Many say that sharp fifths give a characteristic bright sound to 5-limit triads, and consider the sound of meantone triads to be more mellow in comparison.
+In the opinion of some{{Who}}, 46edo is the first equal division to deal adequately with the [[13-limit]], though others award that distinction to [[41edo]]. In fact, while 41 is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak and 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 peak or zeta integral. (Their sum, [[87edo]], does better than both in the 13-limit at the expense of a high note count.) Like 41, 46 is distinctly [[consistent]] in the [[9-odd-limit]], and it is consistent to the [[13-odd-limit]] or the no-15 no-19 [[23-odd-limit]]. 46edo's fifth is slightly sharp of just, which some people (e.g. [[Margo Schulter]]) prefer, sometimes strongly, over both the [[3/2|just fifth]] and fifths of temperaments with flat fifths, such as meantone. Many say that sharp fifths give a characteristic bright sound to 5-limit triads, and consider the sound of meantone triads to be more mellow in comparison.
 [[Rank-2 temperament]]s it [[support]]s include [[sensi]], [[valentine]], [[shrutar]], [[rodan]], [[leapday]] and [[unidec]]. The [[11-odd-limit]] [[minimax tuning]] for valentine, (11/7)<sup>1/10</sup>, is only 0.01 cents flat of 3\46 octaves.