2016edo: Difference between revisions
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== Theory == | == Theory == | ||
{{ | {{Harmonics in equal|2016}} | ||
2016 is a significantly composite number, with its divisors being {{EDOs|1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 672, 1008}}. It's abundancy index is 2.25. | 2016 is a significantly composite number, with its divisors being {{EDOs|1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 672, 1008}}. It's abundancy index is 2.25. | ||
Prime harmonics (below 61) with less than 22% error in 2016edo are: 2, 5, 11, 13, 19, 41, 47. With next error being 26% on the 37th harmonic, it is reasonable to make cutoff here. | |||
2016 shares the mapping for 3 with [[224edo]], albeit with a 28 relative cent error. Using the 2016f val gives the same mapping for 13 as [[224edo]], and unleashes the full power of 224edo's 13 limit chords. | 2016 shares the mapping for 3 with [[224edo]], albeit with a 28 relative cent error. Using the 2016f val gives the same mapping for 13 as [[224edo]], and unleashes the full power of 224edo's 13 limit chords. | ||
== Regular temperament properties == | |||
{| class="wikitable center-4 center-5 center-6" | |||
! rowspan="2" |Subgroup | |||
! rowspan="2" |[[Comma list]] | |||
(zeroes skipped for clarity) | |||
! rowspan="2" |[[Mapping]] | |||
! rowspan="2" |Optimal | |||
8ve stretch (¢) | |||
! colspan="2" |Tuning error | |||
|- | |||
![[TE error|Absolute]] (¢) | |||
![[TE simple badness|Relative]] (%) | |||
|- | |||
|2.3.5 | |||
| | |||
| | |||
| | |||
| | |||
| | |||
|- | |||
|2.5.11.13 | |||
|{{monzo|5 -6 9 6}}, {{monzo|-38 12 4 -1}}, {{monzo|0 -22 3 11}} | |||
| | |||
|0.013 | |||
|0.015 | |||
|2.5 | |||
|} | |||