258008edo: Difference between revisions
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Tristanbay (talk | contribs) Giving most edo pages over 100000 the mathematical interest note |
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{{Mathematical interest}} | |||
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It is notable as a high-limit tuning system and is especially strong in the 13-limit, although it's also somewhat impractical given the vast density of notes. It is the first [[Trivial temperament|non-trivial]] EDO to be consistent in the 36-[[Odd prime sum limit|odd-prime-sum-limit]]. | It is notable as a high-limit tuning system and is especially strong in the 13-limit, although it's also somewhat impractical given the vast density of notes. It is the first [[Trivial temperament|non-trivial]] EDO to be consistent in the 36-[[Odd prime sum limit|odd-prime-sum-limit]]. | ||
Latest revision as of 17:47, 8 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. |
| ← 258007edo | 258008edo | 258009edo → |
258008 equal divisions of the octave (abbreviated 258008edo or 258008ed2), also called 258008-tone equal temperament (258008tet) or 258008 equal temperament (258008et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 258008 equal parts of about 0.00465 ¢ each. Each step represents a frequency ratio of 21/258008, or the 258008th root of 2.
It is notable as a high-limit tuning system and is especially strong in the 13-limit, although it's also somewhat impractical given the vast density of notes. It is the first non-trivial EDO to be consistent in the 36-odd-prime-sum-limit.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00000 | -0.00002 | -0.00011 | -0.00013 | -0.00015 | -0.00024 | -0.00052 | -0.00131 | -0.00081 | +0.00018 | -0.00131 | +0.00166 |
| Relative (%) | +0.0 | -0.5 | -2.4 | -2.9 | -3.3 | -5.1 | -11.3 | -28.2 | -17.3 | +3.9 | -28.2 | +35.6 | |
| Steps (reduced) |
258008 (0) |
408933 (150925) |
599076 (83060) |
724320 (208304) |
892561 (118537) |
954743 (180719) |
1054598 (22566) |
1095999 (63967) |
1167115 (135083) |
1253398 (221366) |
1278222 (246190) |
1344081 (54041) | |