1147edo
| ← 1146edo | 1147edo | 1148edo → |
1147 equal divisions of the octave (abbreviated 1147edo or 1147ed2), also called 1147-tone equal temperament (1147tet) or 1147 equal temperament (1147et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1147 equal parts of about 1.05 ¢ each. Each step represents a frequency ratio of 21/1147, or the 1147th root of 2.
1147edo can be defined as the unique ET in the 2.3.7 subgroup that tempers out the Don Page commas among the intervals 9/8, 8/7, and 7/6, and therefore contains 28ed4/3 and 32ed9/7 within it. This edo notably also tempers out the quartisma (117440512/117406179), by virtue of 28ed4/3 mapping 7/6 to a number of steps divisible by 5 (that is, 15). Therefore, the representation of 33/32, as one fifth of 7/6, is accurate and the edo overall excels in the 2.3.7.11 subgroup, with an additional very good prime 43.
In regular temperament terms, in addition to the quartisma, 1147edo also tempers out the elysia (117649/117612), and the Alpharabian schisma ([18 -31 0 0 9⟩), which sets 44/27 equal to 4\9edt (alternatively, it is the difference between the gothic comma and nine rastmas), in the 2.3.7.11 subgroup.
Odd harmonics
One should note that its prime 11 is inherited from 37edo, which is a strong convergent.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | +0.0502 | -0.2631 | -0.0378 | +0.0334 | -0.4230 | -0.3347 | -0.3901 | +0.4964 | -0.1090 | -0.4846 | -0.2542 | -0.1173 | +0.0778 | -0.1187 |
| Relative (%) | +0.0 | +4.8 | -25.2 | -3.6 | +3.2 | -40.4 | -32.0 | -37.3 | +47.4 | -10.4 | -46.3 | -24.3 | -11.2 | +7.4 | -11.3 | |
| Steps (reduced) |
1147 (0) |
1818 (671) |
2663 (369) |
3220 (926) |
3968 (527) |
4244 (803) |
4688 (100) |
4872 (284) |
5189 (601) |
5572 (984) |
5682 (1094) |
5975 (240) |
6145 (410) |
6224 (489) |
6371 (636) | |
Subsets and supersets
Since 1147 factors into 31 × 37, 1147edo has subset edos 31 and 37.
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