46edo: Difference between revisions
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== Theory == | == Theory == | ||
{| | {{Odd harmonics in edo|edo=46}} | ||
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 temperament]]s it supports include [[sensi]], [[valentine]], [[shrutar]], [[rodan]], [[leapday]] and [[unidec]]. The [[11-limit]] [[minimax tuning]] for valentine temperament, (11/7)<sup>1/10</sup>, 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]], though others award that distinction to [[41-EDO]]. 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. | 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 temperament]]s it supports include [[sensi]], [[valentine]], [[shrutar]], [[rodan]], [[leapday]] and [[unidec]]. The [[11-limit]] [[minimax tuning]] for valentine temperament, (11/7)<sup>1/10</sup>, 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]], though others award that distinction to [[41-EDO]]. 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. | ||