1171edo
| ← 1170edo | 1171edo | 1172edo → |
1171 equal divisions of the octave (abbreviated 1171edo or 1171ed2), also called 1171-tone equal temperament (1171tet) or 1171 equal temperament (1171et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1171 equal parts of about 1.02 ¢ each. Each step represents a frequency ratio of 21/1171, or the 1171st root of 2.
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 distinctly 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 | +1 | +2 | -41 | +1 | -21 | -42 | -32 | -9 | +30 | -36 | |
| 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. 2342edo which doubles it, corrects its harmonic 7 to a near-just quality.
Regular temperament properties
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | 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 |
* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct