73709edo: Difference between revisions
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{{EDO intro|73709}} While it is distinctly [[consistent]] through the 11-odd-limit, its notability stems from the fact that it is a very strong 5-limit division, with lower 5-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any smaller edo. However, [[78005edo]], only slightly larger, beats it. It tempers out {{monzo| 21 290 -207 }} and {{monzo| -573 237 85 }} (quark) in the 5-limit. | {{EDO intro|73709}} While it is distinctly [[consistent]] through the 11-odd-limit, its notability stems from the fact that it is a very strong 5-limit division, with lower 5-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any smaller edo. However, [[78005edo]], only slightly larger, beats it. It tempers out {{monzo| 21 290 -207 }} and {{monzo| -573 237 85 }} (quark) in the 5-limit. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|73709}} | {{Harmonics in equal|73709}} | ||
Revision as of 04:05, 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. |
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Template:EDO intro While it is distinctly consistent through the 11-odd-limit, its notability stems from the fact that it is a very strong 5-limit division, with lower 5-limit relative error than any smaller edo. However, 78005edo, only slightly larger, beats it. It tempers out [21 290 -207⟩ and [-573 237 85⟩ (quark) in the 5-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00000 | -0.00002 | +0.00003 | -0.00527 | -0.00399 | +0.00470 | +0.00328 | -0.00796 | -0.00372 | +0.00128 | +0.00235 |
| Relative (%) | +0.0 | -0.1 | +0.2 | -32.4 | -24.5 | +28.9 | +20.1 | -48.9 | -22.8 | +7.9 | +14.4 | |
| Steps (reduced) |
73709 (0) |
116826 (43117) |
171147 (23729) |
206927 (59509) |
254991 (33864) |
272756 (51629) |
301283 (6447) |
313110 (18274) |
333427 (38591) |
358077 (63241) |
365169 (70333) | |