3041edo
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| ← 3040edo | 3041edo | 3042edo → |
3041 equal divisions of the octave (abbreviated 3041edo or 3041ed2), also called 3041-tone equal temperament (3041tet) or 3041 equal temperament (3041et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3041 equal parts of about 0.395 ¢ each. Each step represents a frequency ratio of 21/3041, or the 3041st root of 2.
Theory
3041edo is consistent to the 25-odd-limit, tempering out 4375/4374, 12376/12375, 10241/10240, 13377/13376, 5929/5928, 89376/89375, 5104/5103, 25025/25024 and 10626/10625 in the 29-limit. Using the 2.5.11.29.37 subgroup, it tempers out 9251/9250.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.051 | +0.007 | -0.066 | -0.052 | -0.015 | +0.010 | +0.021 | -0.060 | -0.047 | +0.114 |
| Relative (%) | +0.0 | +12.9 | +1.7 | -16.6 | -13.2 | -3.7 | +2.5 | +5.2 | -15.2 | -12.0 | +28.9 | |
| Steps (reduced) |
3041 (0) |
4820 (1779) |
7061 (979) |
8537 (2455) |
10520 (1397) |
11253 (2130) |
12430 (266) |
12918 (754) |
13756 (1592) |
14773 (2609) |
15066 (2902) | |
Subsets and supersets
3041edo is the 436th prime edo.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [4820 -3041⟩ | [⟨3041 4820]] | −0.0161 | 0.0161 | 4.08 |
| 2.3.5 | [91 -12 -31⟩, [41 -83 39⟩ | [⟨3041 4820 7061]] | −0.0117 | 0.0145 | 3.67 |
| 2.3.5.7 | 4375/4374, [51 -13 -1 -10⟩, [37 -20 -18 13⟩ | [⟨3041 4820 7061 8537]] | −0.0029 | 0.0197 | 4.99 |
| 2.3.5.7.11 | 4375/4374, 151263/151250, 1395654656/1395032625, 13423439799/13421772800 | [⟨3041 4820 7061 8537 10520]] | +0.0007 | 0.0190 | 4.81 |
| 2.3.5.7.11.13 | 4375/4374, 10648/10647, 196625/196608, 105644/105625, 1063348/1063125 | [⟨3041 4820 7061 8537 10520 11253]] | +0.0012 | 0.0174 | 4.41 |
| 2.3.5.7.11.13.17 | 4375/4374, 12376/12375, 131648/131625, 194481/194480, 196625/196608, 4685824/4685625 | [⟨3041 4820 7061 8537 10520 11253 12430]] | +0.0007 | 0.0162 | 4.11 |
| 2.3.5.7.11.13.17.19 | 4375/4374, 12376/12375, 10241/10240, 13377/13376, 5929/5928, 89376/89375, 27456/27455 | [⟨3041 4820 7061 8537 10520 11253 12430 12918]] | +0.0000 | 0.0152 | 3.85 |