1012edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|1012}} | {{EDO intro|1012}} | ||
== Theory == | |||
1012edo is a strong 13-limit system, distinctly [[consistent]] through the 15-odd-limit. It is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak edo]], though not zeta integral nor zeta gap. A basis for the 13-limit commas is [[2401/2400]], [[4096/4095]], [[6656/6655]], [[9801/9800]] and {{monzo| 2 6 -1 2 0 4 }}. | 1012edo is a strong 13-limit system, distinctly [[consistent]] through the 15-odd-limit. It is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak edo]], though not zeta integral nor zeta gap. A basis for the 13-limit commas is [[2401/2400]], [[4096/4095]], [[6656/6655]], [[9801/9800]] and {{monzo| 2 6 -1 2 0 4 }}. | ||
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=== Trivia === | === Trivia === | ||
In addition to containing 22edo and 23edo, it contains a [[22L 1s]] scale produced by generator of 45\1012 associated with [[33/32]], and is associated with the 45 & 1012 temperament, making it [[concoctic]]. A comma basis for the 13-limit is 2401/2400, 6656/6655, 123201/123200, {{monzo| 18 15 -12 -1 0 -3 }}. | In addition to containing 22edo and 23edo, it contains a [[22L 1s]] scale produced by generator of 45\1012 associated with [[33/32]], and is associated with the 45 & 1012 temperament, making it [[concoctic]]. A comma basis for the 13-limit is 2401/2400, 6656/6655, 123201/123200, {{monzo| 18 15 -12 -1 0 -3 }}. | ||
== Regular temperament properties == | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
! Periods<br>per 8ve | |||
! Generator<br>(Reduced) | |||
! Cents<br>(Reduced) | |||
! Associated<br>Ratio | |||
! Temperaments | |||
|- | |||
| 1 | |||
| 361\1012 | |||
| 428.066 | |||
| 2800/2187 | |||
| [[Osiris]] | |||
|- | |||
| 2 | |||
| 491\1012 | |||
| 498.023 | |||
| 7/5 | |||
| [[Quarvish]] | |||
|- | |||
| 44 | |||
| 420\1012<br>(6\1012) | |||
| 498.023<br>(7.115) | |||
| 4/3<br>(18375/18304) | |||
| [[Ruthenium]] | |||
|} | |||