2016edo: Difference between revisions
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'''2016 equal division''' divides the octave into steps of 595 millicents, or 25/42 cent each. | '''2016 equal division''' divides the octave into steps of 595 millicents, or 25/42 cent each. | ||
== Theory == | == Theory == | ||
{{Primes in edo|2016|columns=18}} | {{Primes in edo|2016|columns=18}} | ||
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 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]] | |||
! rowspan="2" |[[Mapping]] | |||
! rowspan="2" |Optimal | |||
8ve stretch (¢) | |||
! colspan="2" |Tuning error | |||
|- | |||
![[TE error|Absolute]] (¢) | |||
![[TE simple badness|Relative]] (%) | |||
|- | |||
|2.3 | |||
|{{monzo| -355 224 }} | |||
|[{{val| 2016 3195}}] | |||
| +1.99 | |||
|1.99 | |||
|11.43 | |||
|- | |||
|2.3.5 | |||
|81/80, {{monzo| -41 1 17 }} | |||
|[{{val| 69 109 160 }}] | |||
| +1.86 | |||
|1.64 | |||
|9.40 | |||
|- | |||
|2.3.5.7 | |||
|81/80, 126/125, 4117715/3981312 | |||
|[{{val| 69 109 160 193 }}] (69d) | |||
| +2.49 | |||
|1.79 | |||
|10.28 | |||
|- | |||
|2.3.5.7 | |||
|81/80, 3125/3087, 6144/6125 | |||
|[{{val| 69 109 160 194 }}] (69) | |||
| +0.94 | |||
|2.13 | |||
|12.23 | |||
|} | |||