5941edo: Difference between revisions
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Rework to get rid of the overlong table |
m changed EDO intro to ED intro |
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{{Infobox ET}} | {{Infobox ET}} | ||
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As the [[zeta|zeta valley]] edo after [[79edo]], it approximates [[prime harmonic]]s with very high errors. In particular, the 7th, 9th, 11th and 23rd harmonics are off by nearly half a step. In light of this, 5941edo can be seen as excelling in the 2.9<sup>2</sup>.7<sup>2</sup>.11<sup>2</sup>.23<sup>2</sup> subgroup. Otherwise, it is strong in the 2.45.35.49.19.(31.51) subgroup. | As the [[zeta|zeta valley]] edo after [[79edo]], it approximates [[prime harmonic]]s with very high errors. In particular, the 7th, 9th, 11th and 23rd harmonics are off by nearly half a step. In light of this, 5941edo can be seen as excelling in the 2.9<sup>2</sup>.7<sup>2</sup>.11<sup>2</sup>.23<sup>2</sup> subgroup. Otherwise, it is strong in the 2.45.35.49.19.(31.51) subgroup. | ||
Latest revision as of 06:59, 20 February 2025
| ← 5940edo | 5941edo | 5942edo → |
5941 equal divisions of the octave (abbreviated 5941edo or 5941ed2), also called 5941-tone equal temperament (5941tet) or 5941 equal temperament (5941et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 5941 equal parts of about 0.202 ¢ each. Each step represents a frequency ratio of 21/5941, or the 5941st root of 2.
As the zeta valley edo after 79edo, it approximates prime harmonics with very high errors. In particular, the 7th, 9th, 11th and 23rd harmonics are off by nearly half a step. In light of this, 5941edo can be seen as excelling in the 2.92.72.112.232 subgroup. Otherwise, it is strong in the 2.45.35.49.19.(31.51) subgroup.
Rather fittingly, it has a consistency limit of 3.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | 25 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.0530 | +0.0859 | -0.1001 | +0.0961 | -0.0976 | -0.0631 | +0.0329 | +0.0774 | +0.0127 | +0.0489 | -0.0973 | -0.0302 |
| Relative (%) | -26.2 | +42.5 | -49.6 | +47.6 | -48.3 | -31.2 | +16.3 | +38.3 | +6.3 | +24.2 | -48.2 | -15.0 | |
| Steps (reduced) |
9416 (3475) |
13795 (1913) |
16678 (4796) |
18833 (1010) |
20552 (2729) |
21984 (4161) |
23211 (5388) |
24284 (520) |
25237 (1473) |
26095 (2331) |
26874 (3110) |
27589 (3825) | |
| Harmonic | 27 | 29 | 31 | 33 | 35 | 37 | 39 | 41 | 43 | 45 | 47 | 49 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0431 | -0.0535 | +0.0242 | +0.0514 | -0.0142 | -0.0732 | +0.0859 | -0.0437 | -0.0887 | -0.0200 | +0.0379 | +0.0018 |
| Relative (%) | +21.3 | -26.5 | +12.0 | +25.5 | -7.0 | -36.2 | +42.5 | -21.6 | -43.9 | -9.9 | +18.8 | +0.9 | |
| Steps (reduced) |
28249 (4485) |
28861 (5097) |
29433 (5669) |
29969 (264) |
30473 (768) |
30949 (1244) |
31401 (1696) |
31829 (2124) |
32237 (2532) |
32627 (2922) |
33000 (3295) |
33357 (3652) | |