2016edo: Difference between revisions

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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
|}

Revision as of 09:39, 10 March 2022

← 2015edo 2016edo 2017edo →
Prime factorization 25 × 32 × 7
Step size 0.595238 ¢ 
Fifth 1179\2016 (701.786 ¢) (→ 131\224)
Semitones (A1:m2) 189:153 (112.5 ¢ : 91.07 ¢)
Consistency limit 5
Distinct consistency limit 5

2016 equal division divides the octave into steps of 595 millicents, or 25/42 cent each.

Theory

Script error: No such module "primes_in_edo". 2016 is a significantly composite number, with its divisors being 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.