306edo: Difference between revisions
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The ''306 equal division'' divides the octave into 306 equal parts of 3. | 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 31/53 and before 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]]. | ||
Revision as of 00:06, 30 November 2018
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 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 31/53 and before 389/665 in the sequence of continued fraction approximations to to log2(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as 612edo.