190537edo: Difference between revisions
Tristanbay (talk | contribs) Giving most edo pages over 100000 the mathematical interest note |
m →Supersets: Fixed links to go to user page |
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=== Supersets === | === Supersets === | ||
* [[571611edo]] (3×) | * [[User:Aura/571611edo|571611edo]] (3×) | ||
* [[762148edo]] (4×) | * [[User:Aura/762148edo|762148edo]] (4×) | ||
* [[1714833edo]] (9×) | * [[User:Aura/1714833edo|1714833edo]] (9×) | ||
* [[1905370edo]] (10×) | * [[User:Aura/1905370edo|1905370edo]] (10×) | ||
* [[2667518edo]] (14×) | * [[User:Aura/2667518edo|2667518edo]] (14×) | ||
* [[4191814edo]] (22×) | * [[User:Aura/4191814edo|4191814edo]] (22×) | ||
[[Category:3-limit record edos|######]] <!-- 6-digit number --> | [[Category:3-limit record edos|######]] <!-- 6-digit number --> | ||
Revision as of 03:53, 28 September 2025
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This page presents a topic of primarily mathematical interest.
While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown. |
| ← 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×)