3395edo: Difference between revisions
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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]] | ||
Revision as of 19:15, 28 January 2023
| ← 3394edo | 3395edo | 3396edo → |
Theory
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}.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.018 | +0.019 | +0.011 | +0.081 | +0.003 | +0.022 | +0.101 | -0.174 | +0.055 | -0.175 |
| Relative (%) | +0.0 | +5.2 | +5.4 | +3.0 | +23.0 | +0.7 | +6.4 | +28.6 | -49.3 | +15.5 | -49.6 | |
| Steps (reduced) |
3395 (0) |
5381 (1986) |
7883 (1093) |
9531 (2741) |
11745 (1560) |
12563 (2378) |
13877 (297) |
14422 (842) |
15357 (1777) |
16493 (2913) |
16819 (3239) | |
Divisors
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 7033, and a lower 19-limit relative error than any edo until 8269.
Rank-2 temperaments
| Periods per 8ve |
Generator (Reduced) |
Cents (Reduced) |
Associated Ratio |
Temperament |
|---|---|---|---|---|
| 1 | 2319\3395 | 819.676 | 55115776/34328125 | Gene's jacobin |