2016edo: Difference between revisions
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-rank-2 temps (until they're named; otherwise there would be infinitely many); misc cleanup |
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| Step size = 0.59524¢ | | Step size = 0.59524¢ | ||
| Fifth = 1179\2016 (701.79¢) (→[[224edo|131\224]]) | | Fifth = 1179\2016 (701.79¢) (→[[224edo|131\224]]) | ||
|Semitones=342:153}} | | Semitones = 342:153}} | ||
The '''2016 equal divisions of the octave''' ('''2016edo'''), or the '''2016-tone equal temperament''' ('''2016tet'''), '''2016 equal temperament''' ('''2016et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 2016 [[equal]] parts of about 595 milli[[cent]]s each. | The '''2016 equal divisions of the octave''' ('''2016edo'''), or the '''2016-tone equal temperament''' ('''2016tet'''), '''2016 equal temperament''' ('''2016et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 2016 [[equal]] parts of about 595 milli[[cent]]s each. | ||
== Theory == | == Theory == | ||
{{Harmonics in equal|2016}} | {{Harmonics in equal|2016}} | ||
| Line 26: | Line 27: | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
! rowspan="2" |Subgroup | ! rowspan="2" | '[[Subgroup]] | ||
! rowspan="2" |[[Comma list]] | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | Optimal<br>8ve stretch (¢) | ||
! rowspan="2" |Optimal | ! colspan="2" | Tuning error | ||
8ve stretch (¢) | |||
! colspan="2" |Tuning error | |||
|- | |- | ||
![[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
![[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
|{{Monzo|-83 | | {{Monzo| -83 26 18 }}, {{Monzo| 30 47 -45 }} | ||
|[{{Val|2016 3195 4681}}] | | [{{Val| 2016 3195 4681 }}] | ||
|0.036 | | 0.036 | ||
|0.050 | | 0.050 | ||
|8.4 | | 8.4 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|250047/250000, {{monzo|7 | | 250047/250000, {{monzo| 7 18 -2 -11 }}, {{monzo| 43 -1 -13 -4 }} | ||
|[{{Val|2016 3195 4681 5660}}] | | [{{Val| 2016 3195 4681 5660 }}] | ||
|0.007 | | 0.007 | ||
|0.066 | | 0.066 | ||
|11.1 | | 11.1 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|5250987/5242880, 40353607/40310784, {{monzo|14 | | 5250987/5242880, 40353607/40310784, {{monzo| 14 11 -22 7 }} | ||
|[{{Val|2016 3195 4681 5659}}] (2016d) | | [{{Val| 2016 3195 4681 5659 }}] (2016d) | ||
|0.060 | | 0.060 | ||
|0.060 | | 0.060 | ||
|10.1 | | 10.1 | ||
|- | |- | ||
| | | 2.5.11.13 | ||
| | | {{monzo| 5 -6 9 6 }}, {{monzo| -38 12 4 -1 }}, {{monzo| 0 -22 3 11 }} | ||
| | | [{{Val| 2016 4681 6974 7460 }}] | ||
| | | 0.013 | ||
| 0.015 | |||
| 2.5 | |||
|- | |- | ||
| | | 2.5.11.13.19.41.47 | ||
| | | 7943/7942, 322465/322373, 415292/415207, 511225/511024, <br>5078491/5078125, 22151168/22150865 | ||
| | | {{Val| 2016 4681 6974 7460 8564 10801 11198 }} | ||
| | | 0.002 | ||
| 0.019 | |||
| 3.2 | |||
|} | |} | ||