3395edo: Difference between revisions
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{{EDO intro|3395}} | |||
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}. | 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}. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|3395|columns=11}} | |||
=== Miscellany === | |||
3395 = 5 × 7 × 97, with subset edos 5, 7, 35, 97, 485, and 679. | 3395 = 5 × 7 × 97, with subset edos 5, 7, 35, 97, 485, and 679. | ||
[[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | [[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | ||
[[Category:Jacobin]] | [[Category:Jacobin]] | ||
[[Category:Zeta]] | [[Category:Zeta]] | ||