1171edo: Difference between revisions
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== Theory == | == Theory == | ||
1171edo is a very strong 5-limit division, being the first one past [[612edo|612]] with a lower 5-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]. It has a 5-limit [[comma basis]] consisting of the [[monzisma]], {{monzo| 54 -37 2 }} and whoosh, {{monzo| 37 25 -33 }}. While not a strong higher-limit system, it is uniquely consistent through the [[27-odd-limit]], and is very strong on the 2.3.5.11 subgroup. | 1171edo is a very strong 5-limit division, being the first one past [[612edo|612]] with a lower 5-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]. It has a 5-limit [[comma basis]] consisting of the [[monzisma]], {{monzo| 54 -37 2 }} and whoosh, {{monzo| 37 25 -33 }}. While not a strong higher-limit system, it is uniquely consistent through the [[27-odd-limit]], and is very strong on the 2.3.5.11 subgroup. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|1171}} | {{Harmonics in equal|1171}} | ||
[[ | === Subsets and supersets === | ||
1171edo is the 193rd [[prime edo]]. | |||
== Regular temperament properties == | == Regular temperament properties == | ||
| Line 16: | Line 14: | ||
=== 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 | ! Temperaments | ||
(Reduced) | |||
!Associated | |||
Ratio | |||
!Temperaments | |||
|- | |- | ||
|1 | | 1 | ||
|129\1171 | | 129\1171 | ||
|132.195 | | 132.195 | ||
|{{Monzo|-38 5 13}} | | {{Monzo| -38 5 13 }} | ||
|[[Astro]] | | [[Astro]] | ||
|- | |- | ||
|1 | |1 | ||
|243\1171 | | 243\1171 | ||
|249.018 | | 249.018 | ||
|{{Monzo|-26 18 -1}} | | {{Monzo| -26 18 -1 }} | ||
|[[Monzismic]] | | [[Monzismic]] | ||
|- | |- | ||
|1 | |1 | ||
|315\1171 | | 315\1171 | ||
|322.801 | | 322.801 | ||
|{{Monzo|-6 23 -13}} | | {{Monzo| -6 23 -13 }} | ||
|[[Senior]] | | [[Senior]] | ||
|- | |- | ||
|1 | | 1 | ||
|335\1171 | | 335\1171 | ||
|343.296 | | 343.296 | ||
|8000/6561 | | 8000/6561 | ||
|[[Raider]] | | [[Raider]] | ||
|- | |- | ||
|1 | | 1 | ||
|547\1171 | | 547\1171 | ||
|560.547 | | 560.547 | ||
|864/625 | | 864/625 | ||
|[[Whoosh]] | | [[Whoosh]] | ||
|} | |} | ||