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]] | ||
|} | |} | ||
Revision as of 11:14, 29 September 2023
| ← 1170edo | 1171edo | 1172edo → |
Theory
1171edo is a very strong 5-limit division, being the first one past 612 with a lower 5-limit relative error. It has a 5-limit comma basis consisting of the monzisma, [54 -37 2⟩ and whoosh, [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
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.009 | +0.023 | -0.423 | +0.006 | -0.220 | -0.429 | -0.331 | -0.093 | +0.312 | -0.373 |
| Relative (%) | +0.0 | +0.9 | +2.2 | -41.3 | +0.6 | -21.5 | -41.9 | -32.3 | -9.1 | +30.4 | -36.4 | |
| Steps (reduced) |
1171 (0) |
1856 (685) |
2719 (377) |
3287 (945) |
4051 (538) |
4333 (820) |
4786 (102) |
4974 (290) |
5297 (613) |
5689 (1005) |
5801 (1117) | |
Subsets and supersets
1171edo is the 193rd prime edo.
Regular temperament properties
Rank-2 temperaments
| Periods per 8ve |
Generator (Reduced) |
Cents (Reduced) |
Associated Ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 129\1171 | 132.195 | [-38 5 13⟩ | Astro |
| 1 | 243\1171 | 249.018 | [-26 18 -1⟩ | Monzismic |
| 1 | 315\1171 | 322.801 | [-6 23 -13⟩ | Senior |
| 1 | 335\1171 | 343.296 | 8000/6561 | Raider |
| 1 | 547\1171 | 560.547 | 864/625 | Whoosh |