190537edo: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
No edit summary |
||
| Line 6: | Line 6: | ||
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 member of the log<sub>2</sub>3 convergent series with a 3-2 [[Telicity #k-Strong Telicity|telicity k-strength]] greater that 1 since [[665edo]] and it even surpasses 665edo in telicity k-strength. However, the downside is that the step size is many times smaller than the JND. The 3-limit comma this EDO tempers out has been named the [[Archangelic comma]]. | 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 member of the log<sub>2</sub>3 convergent series with a 3-2 [[Telicity #k-Strong Telicity|telicity k-strength]] greater that 1 since [[665edo]] and it even surpasses 665edo in telicity k-strength. However, the downside is that the step size is many times smaller than the JND. The 3-limit comma this EDO tempers out has been named the [[Archangelic comma]]. | ||
{{Harmonics in equal|190537}} | {{Harmonics in equal|190537|columns=12}} | ||
[[Category:Equal divisions of the octave|######]] <!-- 6-digit number --> | [[Category:Equal divisions of the octave|######]] <!-- 6-digit number --> | ||
Revision as of 12:03, 23 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 member of the log23 convergent series with a 3-2 telicity k-strength greater that 1 since 665edo and it even surpasses 665edo in telicity k-strength. However, the downside is that the step size is many times smaller than the JND. The 3-limit comma this EDO tempers out has been named the Archangelic comma.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00000 | +0.00000 | -0.00134 | +0.00010 | +0.00175 | +0.00200 | +0.00058 | -0.00230 | +0.00048 | -0.00079 | +0.00187 | +0.00242 |
| Relative (%) | +0.0 | +0.0 | -21.3 | +1.5 | +27.8 | +31.7 | +9.3 | -36.5 | +7.6 | -12.5 | +29.8 | +38.4 | |
| Steps (reduced) |
190537 (0) |
301994 (111457) |
442413 (61339) |
534905 (153831) |
659150 (87539) |
705071 (133460) |
778813 (16665) |
809387 (47239) |
861906 (99758) |
925625 (163477) |
943958 (181810) |
992594 (39909) | |