342edo: Difference between revisions
→Regular temperament properties: +13-limit branches |
+rank-2 temperaments |
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* 342et is lower in relative error than any previous ETs in the 11-limit. Not until 612 do we find a better ET in terms of absolute error, and not until 1848 do we find one in terms of relative error. | * 342et is lower in relative error than any previous ETs in the 11-limit. Not until 612 do we find a better ET in terms of absolute error, and not until 1848 do we find one in terms of relative error. | ||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+Table of rank-2 temperaments by generator | |||
! Periods<br>per octave | |||
! Generator<br>(reduced) | |||
! Cents<br>(reduced) | |||
! Associated<br>ratio | |||
! Temperaments | |||
|- | |||
| 1 | |||
| 11\342 | |||
| 38.60 | |||
| 45/44 | |||
| [[Hemitert]] | |||
|- | |||
| 2 | |||
| 50\342 | |||
| 175.44 | |||
| 448/405 | |||
| [[Bisesqui]] | |||
|- | |||
| 2 | |||
| 124\342<br>(47\342) | |||
| 435.09<br>(164.91) | |||
| 9/7<br>(11/10) | |||
| [[Semisupermajor]] | |||
|- | |||
| 2 | |||
| 142\342<br>(29\342) | |||
| 498.25<br>(101.75) | |||
| 4/3<br>(35/33) | |||
| [[Bipont]] | |||
|- | |||
| 3 | |||
| 71\342<br>(43\342) | |||
| 249.12<br>(150.88) | |||
| 15/13<br>(12/11) | |||
| [[Hemiterm]] | |||
|- | |||
| 6 | |||
| 142\342<br>(28\342) | |||
| 498.25<br>(98.25) | |||
| 4/3<br>(200/189) | |||
| [[Semiterm]] | |||
|- | |||
| 9 | |||
| 63\342<br>(13\342) | |||
| 221.05<br>(45.61) | |||
| 25/22<br>(77/75) | |||
| [[Quadraennealimmal]] | |||
|- | |||
| 18 | |||
| 71\342<br>(5\342) | |||
| 249.12<br>(17.54) | |||
| 15/13<br>(99/98) | |||
| [[Hemiennealimmal]] | |||
|- | |||
| 38 | |||
| 142\342<br>(2\342) | |||
| 498.25<br>(7.02) | |||
| 4/3<br>(225/224) | |||
| [[Hemienneadecal]] | |||
|} | |||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||