User:Francium/7247edo
| ← 7246edo | 7247edo | 7248edo → |
7247 equal divisions of the octave (abbreviated 7247edo or 7247ed2), also called 7247-tone equal temperament (7247tet) or 7247 equal temperament (7247et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 7247 equal parts of about 0.166 ¢ each. Each step represents a frequency ratio of 21/7247, or the 7247th root of 2.
Theory
7247edo is consistent to the 7-limit, due to its harmonic 11 being halfway between its steps. It is strong in the 2.3.5.7.13.17.31 subgroup, tempering out 5832/5831, 10881/10880, 903168/903125, 17577/17576, 5688387/5687500 and 24810913575/24806539264. It supports eternal revolutionary in the 2.5.11.13 subgroup.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | -0.0370 | -0.0021 | +0.0164 | +0.0826 | -0.0143 | +0.0260 | +0.0446 | -0.0420 | +0.0351 | -0.0100 |
| Relative (%) | +0.0 | -22.3 | -1.3 | +9.9 | +49.9 | -8.7 | +15.7 | +26.9 | -25.3 | +21.2 | -6.1 | |
| Steps (reduced) |
7247 (0) |
11486 (4239) |
16827 (2333) |
20345 (5851) |
25071 (3330) |
26817 (5076) |
29622 (634) |
30785 (1797) |
32782 (3794) |
35206 (6218) |
35903 (6915) | |
Subsets and supersets
7247edo is the 927th prime edo. 21741edo, which triples it, gives a good correction to its harmonic 11.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-11486 7247⟩ | [⟨7247 11486]] | 0.0117 | 0.0117 | 7.07 |
| 2.3.5 | [-69 45 -1⟩, [170 133 -164⟩ | [⟨7247 11486 16827]] | 0.0081 | 0.0108 | 6.52 |
| 2.3.5.7 | 184528125/184473632, [44 6 -17 -5⟩, [-20 41 -23 3⟩ | [⟨7247 11486 16827 20345]] | 0.0046 | 0.0111 | 6.70 |