415edt: Difference between revisions

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'''415edt''' is the [[EDT|equal division of the third harmonic]] into 415 parts of 4.5830 [[cent|cents]] each, corresponding to 261.8358 [[edo]]. It is notable for its impressive [[consistency]] records in very high no-evens [[odd limit#Nonoctave equaves|throdd limit]]s: specifically, it is consistent to the entirety of the no-23s no-47s no-59s add-71 65-throdd limit, and all additional intervals if primes 59, 67, and 73 are added to this are within 60.2% of a step of their [[patent val]] approximation. This makes it a potential candidate for the tritave-based version of [[311edo]], although its performance is not quite as spectacular as that miracle edo.

'''415edt''' is the [[EDT|equal division of the third harmonic]] into 415 parts of 4.5830 [[cent|cents]] each, corresponding to 261.8358 [[edo]]. It is notable for its impressive [[consistency]] records in very high no-evens [[odd limit#Nonoctave equaves|throdd limit]]s: specifically, it is consistent to the entirety of the no-23s no-47s no-59s add-71 add-77 65-throdd limit, and all additional intervals if primes 59, 67, and 73 are added to this are within 60.2% of a step of their [[patent val]] approximation. This makes it a potential candidate for the tritave-based version of [[311edo]], although its performance is not quite as spectacular as that miracle edo.

== Harmonics ==

{{Harmonics in equal|415|3|1|intervals=odd|start=18|columns=22|collapsed=1|title=Approximation of odd harmonics in 415edt (continued)}}

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 {{Infobox ET}}
-'''415edt''' is the [[EDT|equal division of the third harmonic]] into 415 parts of 4.5830 [[cent|cents]] each, corresponding to 261.8358 [[edo]]. It is notable for its impressive [[consistency]] records in very high no-evens [[odd limit#Nonoctave equaves|throdd limit]]s: specifically, it is consistent to the entirety of the no-23s no-47s no-59s add-71 65-throdd limit, and all additional intervals if primes 59, 67, and 73 are added to this are within 60.2% of a step of their [[patent val]] approximation. This makes it a potential candidate for the tritave-based version of [[311edo]], although its performance is not quite as spectacular as that miracle edo.
+'''415edt''' is the [[EDT|equal division of the third harmonic]] into 415 parts of 4.5830 [[cent|cents]] each, corresponding to 261.8358 [[edo]]. It is notable for its impressive [[consistency]] records in very high no-evens [[odd limit#Nonoctave equaves|throdd limit]]s: specifically, it is consistent to the entirety of the no-23s no-47s no-59s add-71 add-77 65-throdd limit, and all additional intervals if primes 59, 67, and 73 are added to this are within 60.2% of a step of their [[patent val]] approximation. This makes it a potential candidate for the tritave-based version of [[311edo]], although its performance is not quite as spectacular as that miracle edo.
 == Harmonics ==
 {{Harmonics in equal|415|3|1|intervals=odd|columns=17}}
 {{Harmonics in equal|415|3|1|intervals=odd|start=18|columns=22|collapsed=1|title=Approximation of odd harmonics in 415edt (continued)}}