4007edo
| ← 4006edo | 4007edo | 4008edo → |
4007 equal divisions of the octave (abbreviated 4007edo or 4007ed2), also called 4007-tone equal temperament (4007tet) or 4007 equal temperament (4007et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 4007 equal parts of about 0.299 ¢ each. Each step represents a frequency ratio of 21/4007, or the 4007th root of 2.
Theory
4007edo is consistent to the 15-odd-limit, tempering out 10648/10647, 1990656/1990625, 1146880/1146717, 105644/105625 and 140625/140608 in the 13-limit. It is strong in the 2.3.5.7.11.23.29 subgroup, tempering out 30625/30624, 150920/150903, 151263/151250, 53361/53360, 25921/25920 and 1507328/1507275. Using the 11-limit, it tempers out 1771561/1771470. Using the 2.3.5.7.11.13.41 subgroup, it tempers out 6930/6929.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.017 | +0.010 | -0.021 | +0.017 | +0.101 | -0.139 | -0.133 | +0.026 | +0.021 | -0.139 |
| Relative (%) | +0.0 | +5.5 | +3.4 | -7.1 | +5.8 | +33.8 | -46.4 | -44.6 | +8.7 | +7.0 | -46.5 | |
| Steps (reduced) |
4007 (0) |
6351 (2344) |
9304 (1290) |
11249 (3235) |
13862 (1841) |
14828 (2807) |
16378 (350) |
17021 (993) |
18126 (2098) |
19466 (3438) |
19851 (3823) | |
Subsets and supersets
4007edo is the 553rd prime edo.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [6351 -4007⟩ | [⟨4007 6351]] | −0.0052 | 0.0052 | 1.74 |
| 2.3.5 | [-36 -52 51⟩, [145 -49 -29⟩ | [⟨4007 6351 9304]] | −0.0049 | 0.0043 | 1.44 |
| 2.3.5.7 | 78125000/78121827, [-1 -18 -3 13⟩, [-48 0 11 8⟩ | [⟨4007 6351 9304 11249]] | −0.0018 | 0.0066 | 2.20 |
| 2.3.5.7.11 | 151263/151250, 21437500/21434787, 184549376/184528125, 246071287/246037500 | [⟨4007 6351 9304 11249 13862]] | −0.0024 | 0.0060 | 2.00 |
| 2.3.5.7.11.13 | 10648/10647, 1990656/1990625, 1146880/1146717, 105644/105625, 140625/140608 | [⟨4007 6351 9304 11249 13862 14828]] | −0.0066 | 0.0108 | 3.61 |