4501edo: Difference between revisions
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Expansion |
41- and 43-limit notability |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|4501}} | {{EDO intro|4501}} | ||
4501edo is a very strong high-limit system, distinctly [[consistent]] through the 39-odd-limit, and has the lowest 31- and 37-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] of any equal temperament until [[16808edo|16808]]. The 4501m val likewise performs well in the 41- and 43-limit, with the lowest relative error of any equal temperament until [[7361edo|7361]]. | |||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|4501}} | {{Harmonics in equal|4501|columns=15}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
4501edo has subset edos [[7edo|7]] and [[643edo|643]]. | 4501edo has subset edos [[7edo|7]] and [[643edo|643]]. | ||
Revision as of 12:11, 20 February 2023
| ← 4500edo | 4501edo | 4502edo → |
4501edo is a very strong high-limit system, distinctly consistent through the 39-odd-limit, and has the lowest 31- and 37-limit relative error of any equal temperament until 16808. The 4501m val likewise performs well in the 41- and 43-limit, with the lowest relative error of any equal temperament until 7361.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.022 | +0.000 | +0.025 | +0.026 | +0.086 | +0.088 | +0.021 | +0.119 | +0.061 | +0.043 | +0.067 | -0.091 | +0.102 | -0.055 |
| Relative (%) | +0.0 | +8.4 | +0.2 | +9.5 | +9.8 | +32.1 | +33.0 | +7.8 | +44.8 | +22.8 | +16.2 | +25.0 | -34.2 | +38.2 | -20.4 | |
| Steps (reduced) |
4501 (0) |
7134 (2633) |
10451 (1449) |
12636 (3634) |
15571 (2068) |
16656 (3153) |
18398 (394) |
19120 (1116) |
20361 (2357) |
21866 (3862) |
22299 (4295) |
23448 (943) |
24114 (1609) |
24424 (1919) |
25001 (2496) | |