58973edo: Difference between revisions
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{{Infobox ET|Consistency=47|Distinct consistency=47}} | {{Infobox ET|Consistency=47|Distinct consistency=47}} | ||
{{ | {{ED intro}} | ||
58973edo is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak, integral, and gap edo]]. It is distinctly [[consistent]] in the 47-odd-limit, and has lower [[relative error]]s than any smaller equal temperaments in the [[37-limit]] and way beyond. | |||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|58973|prec=5|columns= | {{Harmonics in equal|58973|prec=5|intervals=prime|columns=9}} | ||
{{Harmonics in equal|58973|prec=5|intervals=prime|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 58973edo (continued)}} | |||
Latest revision as of 14:08, 30 July 2025
| ← 58972edo | 58973edo | 58974edo → |
58973 equal divisions of the octave (abbreviated 58973edo or 58973ed2), also called 58973-tone equal temperament (58973tet) or 58973 equal temperament (58973et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 58973 equal parts of about 0.0203 ¢ each. Each step represents a frequency ratio of 21/58973, or the 58973rd root of 2.
58973edo is a zeta peak, integral, and gap edo. It is distinctly consistent in the 47-odd-limit, and has lower relative errors than any smaller equal temperaments in the 37-limit and way beyond.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00000 | +0.00013 | -0.00133 | -0.00289 | -0.00124 | -0.00064 | +0.00110 | -0.00060 | -0.00039 |
| Relative (%) | +0.0 | +0.6 | -6.6 | -14.2 | -6.1 | -3.1 | +5.4 | -2.9 | -1.9 | |
| Steps (reduced) |
58973 (0) |
93470 (34497) |
136931 (18985) |
165558 (47612) |
204013 (27094) |
218226 (41307) |
241050 (5158) |
250513 (14621) |
266768 (30876) | |
| Harmonic | 29 | 31 | 37 | 41 | 43 | 47 | 53 | 59 | 61 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00584 | +0.00368 | -0.00190 | +0.00174 | -0.00227 | +0.00471 | +0.00706 | -0.00221 | -0.00759 |
| Relative (%) | +28.7 | +18.1 | -9.3 | +8.6 | -11.1 | +23.2 | +34.7 | -10.9 | -37.3 | |
| Steps (reduced) |
286490 (50598) |
292164 (56272) |
307217 (12352) |
315951 (21086) |
320003 (25138) |
327571 (32706) |
337793 (42928) |
346917 (52052) |
349753 (54888) | |