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]]. | 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]]. | ||
{{harmonics in equal|306|start=2|intervals=prime}} | {{harmonics in equal|306|start=2|prec=3|intervals=prime}} | ||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
Revision as of 03:20, 3 October 2022
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.
| Harmonic | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.006 | +1.922 | -0.198 | +1.623 | -1.312 | +0.927 | +0.526 | -0.823 | +1.795 | +0.062 | -0.364 |
| Relative (%) | +0.1 | +49.0 | -5.1 | +41.4 | -33.5 | +23.6 | +13.4 | -21.0 | +45.8 | +1.6 | -9.3 | |
| Steps (reduced) |
485 (179) |
711 (99) |
859 (247) |
1059 (141) |
1132 (214) |
1251 (27) |
1300 (76) |
1384 (160) |
1487 (263) |
1516 (292) |
1594 (64) | |