684edo: 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]] (%)
|-
|-
| 2.3.5.7.11.13
| 2.3.5.7.11.13
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| 0.0800
| 0.0800
| 4.56
| 4.56
|}
{{comma basis end}}
* 684et is the first equal temperament past [[494edo|494]] with a lower 13-limit absolute error. The next equal temperament that is better tuned is [[764edo|764]].  
* 684et is the first equal temperament past [[494edo|494]] with a lower 13-limit absolute error. The next equal temperament that is better tuned is [[764edo|764]].  


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Note: 11-limit temperaments supported by [[342edo|342et]] are not shown.  
Note: 11-limit temperaments supported by [[342edo|342et]] are not shown.  


{| 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
|-
|-
| 18
| 18
| 271\684<br>(5\684)
| 271\684<br />(5\684)
| 475.44<br>(8.77)
| 475.44<br />(8.77)
| 1053/800<br>(1287/1280)
| 1053/800<br />(1287/1280)
| [[Semihemiennealimmal]]
| [[Semihemiennealimmal]]
|-
|-
| 38
| 38
| 151\684<br>(7\684)
| 151\684<br />(7\684)
| 264.91<br>(12.28)
| 264.91<br />(12.28)
| 500/429<br>(144/143)
| 500/429<br />(144/143)
| [[Semihemienneadecal]]
| [[Semihemienneadecal]]
|}
{{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}}