3395edo: Difference between revisions
Update the prime error table and sectioning |
m now there's rank 2 temperaments |
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{{EDO intro|3395}} | {{EDO intro|3395}} | ||
== Theory == | |||
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}. | ||
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{{Harmonics in equal|3395|columns=11}} | {{Harmonics in equal|3395|columns=11}} | ||
=== | === Divisors === | ||
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. | ||
== Regular temperament properties == | |||
3395edo 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]]. | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
! Periods<br>per 8ve | |||
! Generator<br>(Reduced) | |||
! Cents<br>(Reduced) | |||
! Associated<br>Ratio | |||
! Temperament | |||
|- | |||
| 1 | |||
| 2319\3395 | |||
| 819.676 | |||
| 55115776/34328125 | |||
| [[Gene's jacobin]] | |||
|} | |||
[[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]] | ||