3395edo: Difference between revisions
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It provides the OPV for jacobin |
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The '''3395''' | 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]] | |||
Revision as of 10:46, 6 October 2021
The 3395 equal divisions of the octave divides the octave into 3395 equal steps of 0.35346 cents each.
3395edo is an extremely strong 17- and 19-limit system, and a zeta peak, integral and gap edo. It has a lower 17-limit TE relative error than any edo until 7033, and a lower 19-limit relative error than any edo until 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}.