1012edo: Difference between revisions
rank 2 temperaments |
m Better not to advertise the 2.3.7.11.101 subgroup property |
||
| Line 3: | Line 3: | ||
== Theory == | == 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 }}. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|1012}} | {{Harmonics in equal|1012}} | ||
=== | === Subsets and supersets === | ||
1012 has subset edos {{EDOs| 2, 4, 11, 22, 23, 44, 46, 92, 253, 506 }}. | 1012 has subset edos {{EDOs| 2, 4, 11, 22, 23, 44, 46, 92, 253, 506 }}. | ||
=== 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 }}. | ||
In the 2.3.7.11.101, it tempers out [[7777/7776]] and is a tuning for the [[neutron star]] temperament. | |||
== Regular temperament properties == | == Regular temperament properties == | ||