306edo: Difference between revisions

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~~The '''306 equal division''' divides the octave into 306 equal parts of 3.9216 cents each, and thereby~~ provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[Patent_val|patent val]] tempers out 78732/78125, whereas the alternative 306c val tempers out 32805/32768. In the 7-limit the patent val tempers out 6144/6125, whereas 306c tempers out 16875/16807. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo|31\53]] and before [[665edo|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].

It provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[Patent_val|patent val]] tempers out 78732/78125, whereas the alternative 306c val tempers out 32805/32768. In the 7-limit the patent val tempers out 6144/6125, whereas 306c tempers out 16875/16807. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo|31\53]] and before [[665edo|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].

==Harmonics==

[[Category:Equal divisions of the octave|###]]

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 {{Infobox ET}}
-The '''306 equal division''' divides the octave into 306 equal parts of  3.9216 cents each, and thereby provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[Patent_val|patent val]] tempers out 78732/78125, whereas the alternative 306c val tempers out 32805/32768. In the 7-limit the patent val tempers out 6144/6125, whereas 306c tempers out 16875/16807. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo|31\53]] and before [[665edo|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].
+{{EDO intro}}
+It provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[Patent_val|patent val]] tempers out 78732/78125, whereas the alternative 306c val tempers out 32805/32768. In the 7-limit the patent val tempers out 6144/6125, whereas 306c tempers out 16875/16807. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo|31\53]] and before [[665edo|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].
+==Harmonics==
 {{harmonics in equal|306|start=2|prec=3|intervals=prime}}
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->