2684edo: Difference between revisions

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== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{{comma basis begin}}
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" | Tuning Error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3.5.7
| 2.3.5.7
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| 0.0150
| 0.0150
| 3.36
| 3.36
|}
{{comma basis end}}
* 2684et holds a record for the lowest relative error in the 13-limit, past [[2190edo|2190]] and is only bettered by [[5585edo|5585]], which is more than twice its size. In terms of absolute error, it is narrowly beaten by [[3395edo|3395]].
* 2684et holds a record for the lowest relative error in the 13-limit, past [[2190edo|2190]] and is only bettered by [[5585edo|5585]], which is more than twice its size. In terms of absolute error, it is narrowly beaten by [[3395edo|3395]].
* 2684et is also notable in the 11-limit, where it has the lowest absolute error, past [[1848edo|1848]] and before 3395.  
* 2684et is also notable in the 11-limit, where it has the lowest absolute error, past [[1848edo|1848]] and before 3395.  
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Note: 5-limit temperaments supported by [[1342edo]] are not included.
Note: 5-limit temperaments supported by [[1342edo]] are not included.


{| class="wikitable center-all left-5"
{{rank-2 begin}}
|+Table of rank-2 temperaments by generator
|-
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
|-
| 1
| 1
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|-
|-
| 44
| 44
| 1114\2684<br>(16\2684)
| 1114\2684<br />(16\2684)
| 498.063<br>(7.154)
| 498.063<br />(7.154)
| 4/3<br>(18375/18304)
| 4/3<br />(18375/18304)
| [[Ruthenium]]
| [[Ruthenium]]
|-
|-
| 61
| 61
| 557\2684<br>(29\2684)
| 557\2684<br />(29\2684)
| 249.031<br>(12.965)
| 249.031<br />(12.965)
| 11907/6875<br>(?)
| 11907/6875<br />(?)
| [[Promethium]]
| [[Promethium]]
|}
{{rank-2 end}}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
{{orf}}