3395edo: Difference between revisions

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The '''3395''' ~~division~~ divides the octave into 3395 equal steps of 0.35346 ~~cents~~ each. It is an extremely strong 17- and 19-limit system, and a [[~~The_Riemann_Zeta_Function_and_Tuning~~#Zeta EDO lists|zeta peak, integral and gap edo]]. It has a lower 17-limit [[~~Tenney-Euclidean_temperament_measures#~~TE ~~simple badness|~~relative error]] than any edo until [[7033edo|7033]], and a lower 19-limit relative error than any edo until [[8269edo|8269]]. A basis for the 17-limit commas is {6656/6655, 12376/12375, 28561/28560, 31213/31212, 37180/37179, 937125/937024}, and for the 19-limit, {6656/6655, 12376/12375, 12636/12635, 13377/13376, 14365/14364, 23409/23408, 28561/28560}.

The '''3395 equal divisions of the octave''' divides the [[octave]] into 3395 [[equal]] steps of 0.35346 [[cent]]s each.

3395edo is an extremely strong 17- and 19-limit system, and a [[The Riemann Zeta function and tuning #Zeta EDO lists|zeta peak, integral and gap edo]]. It has a lower 17-limit [[TE relative error]] than any edo until [[7033edo|7033]], and a lower 19-limit relative error than any edo until [[8269edo|8269]]. Besides, it provides the [[optimal patent val]] for the 13-limit rank-5 temperament tempering out [[6656/6655]], the jacobin comma. A basis for the 17-limit commas is {6656/6655, 12376/12375, 28561/28560, 31213/31212, 37180/37179, 937125/937024}, and for the 19-limit, {6656/6655, 12376/12375, 12636/12635, 13377/13376, 14365/14364, 23409/23408, 28561/28560}.

[[Category:Equal divisions of the octave]]

[[Category:Jacobin]]

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-The '''3395''' division divides the octave into 3395 equal steps of 0.35346 cents each. It is an extremely strong 17- and 19-limit system, and a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta peak, integral and gap edo]]. It has a lower 17-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than any edo until [[7033edo|7033]], and a lower 19-limit relative error than any edo until [[8269edo|8269]]. A basis for the 17-limit commas is {6656/6655, 12376/12375, 28561/28560, 31213/31212, 37180/37179, 937125/937024}, and for the 19-limit, {6656/6655, 12376/12375, 12636/12635, 13377/13376, 14365/14364, 23409/23408, 28561/28560}.
+The '''3395 equal divisions of the octave''' divides the [[octave]] into 3395 [[equal]] steps of 0.35346 [[cent]]s each.
+edo is an extremely strong 17- and 19-limit system, and a [[The Riemann Zeta function and tuning #Zeta EDO lists|zeta peak, integral and gap edo]]. It has a lower 17-limit [[TE relative error]] than any edo until [[7033edo|7033]], and a lower 19-limit relative error than any edo until [[8269edo|8269]]. Besides, it provides the [[optimal patent val]] for the 13-limit rank-5 temperament tempering out [[6656/6655]], the jacobin comma. A basis for the 17-limit commas is {6656/6655, 12376/12375, 28561/28560, 31213/31212, 37180/37179, 937125/937024}, and for the 19-limit, {6656/6655, 12376/12375, 12636/12635, 13377/13376, 14365/14364, 23409/23408, 28561/28560}.
+[[Category:Equal divisions of the octave]]
+[[Category:Jacobin]]