343edo: Difference between revisions

BudjarnLambeth (talk | contribs)
Theory: add line about optimal ET sequences
BudjarnLambeth (talk | contribs)
m Move my addition to reg temp section
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343edo is only [[consistent]] to the [[3-odd-limit]] since its errors of [[harmonic]]s [[3/1|3]] and [[5/1|5]] are quite large. To start with, consider the 2.9.15.7 [[subgroup]], where it [[tempering out|tempers out]] 5250987/5242880. In the 2.5.7 subgroup it tempers out 2100875/2097152 and in the 2.3.7 subgroup it tempers out 118098/117649.  
343edo is only [[consistent]] to the [[3-odd-limit]] since its errors of [[harmonic]]s [[3/1|3]] and [[5/1|5]] are quite large. To start with, consider the 2.9.15.7 [[subgroup]], where it [[tempering out|tempers out]] 5250987/5242880. In the 2.5.7 subgroup it tempers out 2100875/2097152 and in the 2.3.7 subgroup it tempers out 118098/117649.  


For the full 7-limit, the 343c [[val]] tempers out [[4375/4374]] and [[5120/5103]], [[support]]ing [[amity]]. The 343cdd val tempers out [[16875/16807]] and 65536/64827. The [[patent val]] tempers out [[10976/10935]] and 390625/387072.
For the full 7-limit, the 343c [[val]] tempers out [[4375/4374]] and [[5120/5103]], [[support]]ing [[amity]]. The 343cdd val tempers out [[16875/16807]] and 65536/64827. The [[patent val]] tempers out [[10976/10935]] and 390625/387072.
 
343edo is on the [[optimal ET sequence]] of [[gammy]] temperament (10\343 generator, 2/1 period), [[protolangwidge]] temperament (200\343 g, 2/1 p) and [[anthoine]] temperament (110\343 g, 2/1 p).


=== Odd harmonics ===
=== Odd harmonics ===
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== Regular temperament properties ==
== Regular temperament properties ==
343edo is on the [[optimal ET sequence]] of [[gammy]] temperament (10\343 generator, 2/1 period), [[protolangwidge]] temperament (200\343 g, 2/1 p) and [[anthoine]] temperament (110\343 g, 2/1 p).
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
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