140edo: Difference between revisions
→Regular temperament properties: 17- to 23-limit notability |
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 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 | ||
| 0.346 | | 0.346 | ||
| 4.03 | | 4.03 | ||
| Line 35: | Line 27: | ||
| 2401/2400, 5120/5103, 15625/15552 | | 2401/2400, 5120/5103, 15625/15552 | ||
| {{mapping| 140 222 325 393 }} | | {{mapping| 140 222 325 393 }} | ||
| | | −0.055 | ||
| 0.311 | | 0.311 | ||
| 3.63 | | 3.63 | ||
| Line 59: | Line 51: | ||
| 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 In the 17-limit it is the first to beat [[121edo|121]] and is superseded by [[171edo|171]]. In the 19- and 23-limit it is the first to beat [[130edo|130]] and is superseded by [[152edo|152fg]].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 In the 17-limit it is the first to beat [[121edo|121]] and is superseded by [[171edo|171]]. In the 19- and 23-limit it is the first to beat [[130edo|130]] and is superseded by [[152edo|152fg]].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 === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 120: | Line 106: | ||
|- | |- | ||
| 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}} | |||
{{orf}} | |||
[[Category:Countercata]] | [[Category:Countercata]] | ||