15900edo: Difference between revisions
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Created page with "{{Infobox ET}} The '''15900 equal divisions of the octave''', or the 15900-tone equal temperament (15900tet), 15900 equal temperament (15900et) when viewed from a regular temp..." |
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== Theory == | == Theory == | ||
15900edo tempers out the [[magnetisma]] in the 2.3.29.43 subgroup. It is consistent in the 23-odd-limit and has 10% or less errors on prime harmonics 3, 7, 11, 13, 19, 29, 41, 47, 53, 59, 71. | |||
=== Divisors === | |||
15900edo has subset EDOs {{EDOs|1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 53, 60, 75, 100, 106, 150, 159, 212, 265, 300, 318, 530, 636, 795, 1060, 1325, 1590, 2650, 3180, 3975, 5300, 7950}}. | |||
A single step of 15900edo is the [[relative cent]] of [[159edo]]. | |||
=== Prime harmonics === | |||
{{Harmonics in equal|15900}} | {{Harmonics in equal|15900}} | ||
[[Category:Equal divisions of the octave|####]] <!-- 5-digit number --> | [[Category:Equal divisions of the octave|#####]] <!-- 5-digit number --> | ||
Latest revision as of 06:10, 9 July 2023
| ← 15899edo | 15900edo | 15901edo → |
The 15900 equal divisions of the octave, or the 15900-tone equal temperament (15900tet), 15900 equal temperament (15900et) when viewed from a regular temperament perspective, divides the octave into 15900 equal parts of about 0.075 cents each.
Theory
15900edo tempers out the magnetisma in the 2.3.29.43 subgroup. It is consistent in the 23-odd-limit and has 10% or less errors on prime harmonics 3, 7, 11, 13, 19, 29, 41, 47, 53, 59, 71.
Divisors
15900edo has subset EDOs 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 53, 60, 75, 100, 106, 150, 159, 212, 265, 300, 318, 530, 636, 795, 1060, 1325, 1590, 2650, 3180, 3975, 5300, 7950.
A single step of 15900edo is the relative cent of 159edo.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | +0.0073 | +0.0259 | +0.0043 | +0.0028 | +0.0006 | +0.0257 | -0.0036 | +0.0275 | +0.0077 | +0.0210 |
| Relative (%) | +0.0 | +9.6 | +34.3 | +5.7 | +3.7 | +0.8 | +34.1 | -4.7 | +36.5 | +10.2 | +27.9 | |
| Steps (reduced) |
15900 (0) |
25201 (9301) |
36919 (5119) |
44637 (12837) |
55005 (7305) |
58837 (11137) |
64991 (1391) |
67542 (3942) |
71925 (8325) |
77242 (13642) |
78772 (15172) | |