140edo: Difference between revisions

Regular temperament properties: 17- to 23-limit notability
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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
| 2.3.5
| 15625/15552, {{monzo| 35 -25 2 }}
| 15625/15552, {{monzo| 35 -25 2 }}
| {{mapping| 140 222 325 }}
| {{mapping| 140 222 325 }}
| -0.104
| &minus;0.104
| 0.346
| 0.346
| 4.03
| 4.03
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| 2401/2400, 5120/5103, 15625/15552
| 2401/2400, 5120/5103, 15625/15552
| {{mapping| 140 222 325 393 }}
| {{mapping| 140 222 325 393 }}
| -0.055
| &minus;0.055
| 0.311
| 0.311
| 3.63
| 3.63
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| 0.396
| 0.396
| 4.62
| 4.62
|}
{{comma basis end}}
* 140et has lower absolute errors than any previous equal temperaments in the 17-, 19-, and 23-limit, and perhaps beyond. In the 17-limit it is the first to beat [[121edo|121]] and is superseded by [[171edo|171]]. In the 19- and 23-limit it is the first to beat [[130edo|130]] and is superseded by [[152edo|152fg]].  
* 140et has lower absolute errors than any previous equal temperaments in the 17-, 19-, and 23-limit, and perhaps beyond. In the 17-limit it is the first to beat [[121edo|121]] and is superseded by [[171edo|171]]. In the 19- and 23-limit it is the first to beat [[130edo|130]] and is superseded by [[152edo|152fg]].  


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| 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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|-
|-
| 2
| 2
| 41\140<br>(29\140)
| 41\140<br />(29\140)
| 351.43<br>(248.57)
| 351.43<br />(248.57)
| 49/40<br>(15/13)
| 49/40<br />(15/13)
| [[Semihemi]]
| [[Semihemi]]
|-
|-
| 4
| 4
| 37\140<br>(2\140)
| 37\140<br />(2\140)
| 317.14<br>(17.14)
| 317.14<br />(17.14)
| 6/5<br>(126/125)
| 6/5<br />(126/125)
| [[Quadritikleismic]]
| [[Quadritikleismic]]
|-
|-
| 4
| 4
| 58\140<br>(12\140)
| 58\140<br />(12\140)
| 497.14<br>(102.86)
| 497.14<br />(102.86)
| 4/3<br>(35/33)
| 4/3<br />(35/33)
| [[Undim]]
| [[Undim]]
|-
|-
| 5
| 5
| 43\140<br>(13\140)
| 43\140<br />(13\140)
| 368.57<br>(111.43)
| 368.57<br />(111.43)
| 1024/891<br>(16/15)
| 1024/891<br />(16/15)
| [[Quintosec]]
| [[Quintosec]]
|-
|-
| 10
| 10
| 29\140<br>(1\140)
| 29\140<br />(1\140)
| 248.57<br>(8.57)
| 248.57<br />(8.57)
| 15/13<br>(176/175)
| 15/13<br />(176/175)
| [[Decoid]]
| [[Decoid]]
|-
|-
| 20
| 20
| 54\140<br>(2\140)
| 54\140<br />(2\140)
| 497.14<br>(17.14)
| 497.14<br />(17.14)
| 4/3<br>(126/125)
| 4/3<br />(126/125)
| [[Degrees]]
| [[Degrees]]
|-
|-
| 28
| 28
| 54\140<br>(2\140)
| 54\140<br />(2\140)
| 497.14<br>(17.14)
| 497.14<br />(17.14)
| 4/3<br>(126/125)
| 4/3<br />(126/125)
| [[Oquatonic]]
| [[Oquatonic]]
|}
{{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}}


[[Category:Countercata]]
[[Category:Countercata]]