190537edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
The '''190537edo''' divides the octave into 190537 equal parts of 0.0063 cents each. It is the denominator of the next convergent for log<sub>2</sub>3 past [[111202edo|111202]], | The '''190537edo''' divides the octave into 190537 equal parts of 0.0063 cents each. It is the denominator of the next convergent for log<sub>2</sub>3 past [[111202edo|111202]], with another such convergent not occurring until [[10590737edo|10590737]]. | ||
== Theory == | == Theory == | ||
Revision as of 13:27, 22 December 2022
| ← 190536edo | 190537edo | 190538edo → |
(convergent)
The 190537edo divides the octave into 190537 equal parts of 0.0063 cents each. It is the denominator of the next convergent for log23 past 111202, with another such convergent not occurring until 10590737.
Theory
190537edo has a consistency limit of 11, which is rather impressive for a convergent. However, it's strongest in the 2.3.7.17.23 subgroup. Notably, it's the first EDO with a 3-2 telicity k-strength greater that 1 since 665edo and it even surpasses 665edo in telicity k-strength.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00000 | +0.00000 | -0.00134 | +0.00010 | +0.00175 | +0.00200 | +0.00058 | -0.00230 | +0.00048 | -0.00079 | +0.00187 |
| Relative (%) | +0.0 | +0.0 | -21.3 | +1.5 | +27.8 | +31.7 | +9.3 | -36.5 | +7.6 | -12.5 | +29.8 | |
| Steps (reduced) |
190537 (0) |
301994 (111457) |
442413 (61339) |
534905 (153831) |
659150 (87539) |
705071 (133460) |
778813 (16665) |
809387 (47239) |
861906 (99758) |
925625 (163477) |
943958 (181810) | |