102557edo: Difference between revisions
Jump to navigation
Jump to search
Tristanbay (talk | contribs) fixed link to match new title capitalization style Tags: Mobile edit Mobile web edit |
m changed EDO intro to ED intro |
||
| (One intermediate revision by one other user not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
102557edo is notable for being a good high-limit system, and specializes in the [[17-limit]] with a lower [[TE simple badness|relative error]] than any smaller equal temperaments. It is [[consistent]] to the [[39-odd-limit]] and is the first [[trivial temperament|non-trivial]] edo to be consistent in the 32-[[odd prime sum limit|odd-prime-sum-limit]]. | |||
{{Harmonics in equal|columns= | === Prime harmonics === | ||
{{Harmonics in equal|102557|columns=15}} | |||
Latest revision as of 06:49, 20 February 2025
| ← 102556edo | 102557edo | 102558edo → |
102557 equal divisions of the octave (abbreviated 102557edo or 102557ed2), also called 102557-tone equal temperament (102557tet) or 102557 equal temperament (102557et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 102557 equal parts of about 0.0117 ¢ each. Each step represents a frequency ratio of 21/102557, or the 102557th root of 2.
102557edo is notable for being a good high-limit system, and specializes in the 17-limit with a lower relative error than any smaller equal temperaments. It is consistent to the 39-odd-limit and is the first non-trivial edo to be consistent in the 32-odd-prime-sum-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00000 | +0.00001 | +0.00024 | +0.00118 | +0.00084 | +0.00004 | +0.00086 | +0.00349 | +0.00066 | +0.00050 | +0.00572 | +0.00107 | -0.00539 | -0.00508 | +0.00036 |
| Relative (%) | +0.0 | +0.1 | +2.0 | +10.1 | +7.1 | +0.4 | +7.3 | +29.8 | +5.6 | +4.3 | +48.9 | +9.1 | -46.1 | -43.4 | +3.1 | |
| Steps (reduced) |
102557 (0) |
162549 (59992) |
238130 (33016) |
287914 (82800) |
354789 (47118) |
379506 (71835) |
419198 (8970) |
435655 (25427) |
463923 (53695) |
498220 (87992) |
508088 (97860) |
534266 (21481) |
549454 (36669) |
556501 (43716) |
569662 (56877) | |