2554edo: Difference between revisions
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{{Infobox ET|Consistency=41|Distinct consistency=41}} | |||
{{ED intro}} | |||
2554edo is a remarkable very high limit equal temperament. It is [[consistent]] through the [[41-odd-limit]] distinctly, [[tempering out]] [[3025/3024]], 4675/4674, 6325/6324, 7106/7105, 7216/7215, 7905/7904, 12155/12152, 13300/13299, 13950/13949, 14652/14651, 56265/56252, and 92701/92690. It provides the [[optimal patent val]] for the rank-4 temperament tempering out 3025/3024, the lehmerisma, and [[thor]], the rank-3 temperament also tempering out [[4375/4374]]. It is [[Enfactoring|enfactored]] in the 7-limit, with the same mapping as [[1277edo]]. | |||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|2554|columns=13}} | {{Harmonics in equal|2554|columns=13}} | ||
[[ | === Subsets and supersets === | ||
Since 2554 factors into {{factorization|2554}}, 2554edo contains [[2edo]] and 1277edo as subsets. | |||
[[Category:Lehmerismic]] | [[Category:Lehmerismic]] | ||
[[Category:Thor]] | [[Category:Thor]] | ||
Latest revision as of 22:41, 20 February 2025
| ← 2553edo | 2554edo | 2555edo → |
2554 equal divisions of the octave (abbreviated 2554edo or 2554ed2), also called 2554-tone equal temperament (2554tet) or 2554 equal temperament (2554et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2554 equal parts of about 0.47 ¢ each. Each step represents a frequency ratio of 21/2554, or the 2554th root of 2.
2554edo is a remarkable very high limit equal temperament. It is consistent through the 41-odd-limit distinctly, tempering out 3025/3024, 4675/4674, 6325/6324, 7106/7105, 7216/7215, 7905/7904, 12155/12152, 13300/13299, 13950/13949, 14652/14651, 56265/56252, and 92701/92690. It provides the optimal patent val for the rank-4 temperament tempering out 3025/3024, the lehmerisma, and thor, the rank-3 temperament also tempering out 4375/4374. It is enfactored in the 7-limit, with the same mapping as 1277edo.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.003 | -0.096 | +0.007 | -0.182 | +0.036 | -0.179 | -0.097 | -0.083 | -0.133 | -0.008 | +0.026 | -0.088 |
| Relative (%) | +0.0 | +0.6 | -20.4 | +1.6 | -38.8 | +7.7 | -38.0 | -20.7 | -17.7 | -28.3 | -1.7 | +5.6 | -18.8 | |
| Steps (reduced) |
2554 (0) |
4048 (1494) |
5930 (822) |
7170 (2062) |
8835 (1173) |
9451 (1789) |
10439 (223) |
10849 (633) |
11553 (1337) |
12407 (2191) |
12653 (2437) |
13305 (535) |
13683 (913) | |
Subsets and supersets
Since 2554 factors into 2 × 1277, 2554edo contains 2edo and 1277edo as subsets.