1911edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|1911}} | {{EDO intro|1911}} | ||
== Theory == | |||
1911edo is consistent in the 11-limit and tempers out the [[aluminium comma]] in the 5-limit. It provides the [[optimal patent val]] for the [[protactinium]] temperament in the 17-limit. However as may stem from consistency only in the 11-limit, the 13th harmonic has a large relative error. As such, 1911edo is best considered as a 2.3.5.7.11.17.19 subgroup tuning. | 1911edo is consistent in the 11-limit and tempers out the [[aluminium comma]] in the 5-limit. It provides the [[optimal patent val]] for the [[protactinium]] temperament in the 17-limit. However as may stem from consistency only in the 11-limit, the 13th harmonic has a large relative error. As such, 1911edo is best considered as a 2.3.5.7.11.17.19 subgroup tuning. | ||
=== Odd harmonics === | === Odd harmonics === | ||
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=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
!Periods | !Periods<br>per 8ve | ||
per 8ve | !Generator<br>(Reduced) | ||
!Generator | !Cents<br>(Reduced) | ||
(Reduced) | !Associated<br>Ratio | ||
!Cents | |||
(Reduced) | |||
!Associated | |||
Ratio | |||
!Temperaments | !Temperaments | ||
|- | |- | ||
|13 | |13 | ||
|793\1911 | |793\1911<br>(58\1911) | ||
(58\1911) | |497.959<br>(36.421) | ||
|497.959 | |4/3<br>(?) | ||
(36.421) | |||
|4/3 | |||
(?) | |||
|[[Aluminium]] | |[[Aluminium]] | ||
|- | |- | ||
|91 | |91 | ||
|793\1911 | |793\1911<br>(16\1911) | ||
(16\1911) | |497.959<br>(10.047) | ||
|497.959 | |4/3<br>(176/175) | ||
(10.047) | |||
|4/3 | |||
(176/175) | |||
|[[Protactinium]] | |[[Protactinium]] | ||
|} | |} |