342edo: Difference between revisions
→Regular temperament properties: +semiseptichrome |
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| Line 31: | Line 23: | ||
| 1.59 | | 1.59 | ||
|- | |- | ||
| 2.3.5.7.11.13 | |||
| 676/675, 1001/1000, 1716/1715, 3025/3024, 19773/19712 | |||
| {{mapping| 342 542 794 960 1183 1265 }} (342f) | |||
| +0.178 | |||
| 0.1618 | |||
| 4.61 | |||
|- | |- style="border-top: double;" | ||
| 2.3.5.7.11.13 | |||
| 625/624, 729/728, 847/845, 1575/1573, 4096/4095 | |||
| {{mapping| 342 542 794 960 1183 1266 }} (342) | |||
| +0.020 | |||
| 0.2061 | |||
| 5.87 | |||
{{comma basis end}} | |||
* 342et is lower in relative error than any previous equal temperaments in the 11-limit, being the first to beat [[270edo|270]]. Not until [[612edo|612]] do we find a better equal temperament in terms of absolute error, and not until [[1848edo|1848]] do we find one in terms of relative error. | * 342et is lower in relative error than any previous equal temperaments in the 11-limit, being the first to beat [[270edo|270]]. Not until [[612edo|612]] do we find a better equal temperament in terms of absolute error, and not until [[1848edo|1848]] do we find one in terms of relative error. | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 75: | Line 61: | ||
|- | |- | ||
| 2 | | 2 | ||
| 124\342<br>(47\342) | | 124\342<br />(47\342) | ||
| 435.09<br>(164.91) | | 435.09<br />(164.91) | ||
| 9/7<br>(11/10) | | 9/7<br />(11/10) | ||
| [[Semisupermajor]] | | [[Semisupermajor]] | ||
|- | |- | ||
| 2 | | 2 | ||
| 142\342<br>(29\342) | | 142\342<br />(29\342) | ||
| 498.25<br>(101.75) | | 498.25<br />(101.75) | ||
| 4/3<br>(35/33) | | 4/3<br />(35/33) | ||
| [[Bipont]] | | [[Bipont]] | ||
|- | |- | ||
| 3 | | 3 | ||
| 71\342<br>(43\342) | | 71\342<br />(43\342) | ||
| 249.12<br>(150.88) | | 249.12<br />(150.88) | ||
| 15/13<br>(12/11) | | 15/13<br />(12/11) | ||
| [[Hemiterm]] | | [[Hemiterm]] | ||
|- | |- | ||
| 6 | | 6 | ||
| 97\342<br>(17\342) | | 97\342<br />(17\342) | ||
| 340.35<br>(59.65) | | 340.35<br />(59.65) | ||
| 162/133<br>(88/85) | | 162/133<br />(88/85) | ||
| [[Semiseptichrome]] | | [[Semiseptichrome]] | ||
|- | |- | ||
| 6 | | 6 | ||
| 142\342<br>(28\342) | | 142\342<br />(28\342) | ||
| 498.25<br>(98.25) | | 498.25<br />(98.25) | ||
| 4/3<br>(18/17) | | 4/3<br />(18/17) | ||
| [[Semiterm]] | | [[Semiterm]] | ||
|- | |- | ||
| 9 | | 9 | ||
| 63\342<br>(13\342) | | 63\342<br />(13\342) | ||
| 221.05<br>(45.61) | | 221.05<br />(45.61) | ||
| 25/22<br>(77/75) | | 25/22<br />(77/75) | ||
| [[Quadraennealimmal]] | | [[Quadraennealimmal]] | ||
|- | |- | ||
| 18 | | 18 | ||
| 71\342<br>(5\342) | | 71\342<br />(5\342) | ||
| 249.12<br>(17.54) | | 249.12<br />(17.54) | ||
| 15/13<br>(99/98) | | 15/13<br />(99/98) | ||
| [[Hemiennealimmal]] | | [[Hemiennealimmal]] | ||
|- | |- | ||
| 38 | | 38 | ||
| 142\342<br>(2\342) | | 142\342<br />(2\342) | ||
| 498.25<br>(7.02) | | 498.25<br />(7.02) | ||
| 4/3<br>(225/224) | | 4/3<br />(225/224) | ||
| [[Hemienneadecal]] | | [[Hemienneadecal]] | ||
{{rank-2 end}} | |||
{{orf}} | |||