190537edo: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
No edit summary |
||
| Line 1: | Line 1: | ||
{{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]], before [[10590737edo|10590737]] | 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]], before [[10590737edo|10590737]]. | ||
== Theory == | == 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. | 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. | ||
{{Harmonics in equal|190537}} | {{Harmonics in equal|190537}} | ||
[[Category:Equal divisions of the octave|#####]] <!-- 6-digit number --> | [[Category:Equal divisions of the octave|#####]] <!-- 6-digit number --> | ||
Revision as of 12:34, 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, before 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) | |