1171edo: Difference between revisions
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rank-2 temperaments |
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{{Harmonics in equal|1171}} | {{Harmonics in equal|1171}} | ||
[[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | [[Category:Equal divisions of the octave|####]] | ||
== Regular temperament properties == | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
!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]] | |||
|}<!-- 4-digit number --> | |||
Revision as of 21:34, 27 September 2023
| ← 1170edo | 1171edo | 1172edo → |
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.
Subsets and supersets
1171edo is the 193rd prime edo.
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) | |
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 |