190537edo: Difference between revisions
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{{Infobox ET}} | {{novelty}}{{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]], with another such convergent not occurring until [[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]], with another such convergent not occurring until [[10590737edo|10590737]]. | ||
Revision as of 04:02, 9 July 2023
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This page presents a novelty topic.
It may contain ideas which are less likely to find practical applications in music, or numbers or structures that are arbitrary or exceedingly small, large, or complex. Novelty topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks. |
| ← 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) | |