190537edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ED intro}} 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]]. | |||
190537edo has a [[consistency]] limit of 11, which is rather impressive for a convergent. However, it is strongest in the 2.3.7.17.23 subgroup. Notably, it is the first member of the log<sub>2</sub>3 convergent series with a 3-2 [[Telicity #k-Strong Telicity|telicity ''k''-strength]] greater than 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]]. | |||
== Theory == | == Theory == | ||
=== Prime harmonics === | |||
{{Harmonics in equal|190537|columns=12}} | |||
=== Supersets === | |||
* [[571611edo]] (3×) | |||
* [[762148edo]] (4×) | |||
* [[1714833edo]] (9×) | |||
* [[1905370edo]] (10×) | |||
* [[2667518edo]] (14×) | |||
* [[4191814edo]] (22×) | |||
[[Category: | [[Category:3-limit record edos|######]] <!-- 6-digit number --> | ||
Latest revision as of 14:01, 31 July 2025
| ← 190536edo | 190537edo | 190538edo → |
(convergent)
190537 equal divisions of the octave (abbreviated 190537edo or 190537ed2), also called 190537-tone equal temperament (190537tet) or 190537 equal temperament (190537et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 190537 equal parts of about 0.0063 ¢ each. Each step represents a frequency ratio of 21/190537, or the 190537th root of 2. It is the denominator of the next convergent for log23 past 111202, with another such convergent not occurring until 10590737.
190537edo has a consistency limit of 11, which is rather impressive for a convergent. However, it is strongest in the 2.3.7.17.23 subgroup. Notably, it is the first member of the log23 convergent series with a 3-2 telicity k-strength greater than 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.
Theory
Prime harmonics
| 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) | |
Supersets
- 571611edo (3×)
- 762148edo (4×)
- 1714833edo (9×)
- 1905370edo (10×)
- 2667518edo (14×)
- 4191814edo (22×)