306edo: Difference between revisions
Tristanbay (talk | contribs) Added mention of 306edo's association with Valotti temperament Tags: Mobile edit Mobile web edit |
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306edo provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[patent val]] [[tempering out|tempers out]] 78732/78125 ([[sensipent comma]]), whereas the alternative 306c val tempers out 32805/32768 ([[schisma]]). 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]]. | 306edo provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[patent val]] [[tempering out|tempers out]] 78732/78125 ([[sensipent comma]]), whereas the alternative 306c val tempers out 32805/32768 ([[schisma]]). 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]]. | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 306 factors into {{factorization|306}}, 306edo has subset edos {{EDOs| 2, 3, 6, 9, 17, 18, 34, 51, 102, and 153 }}. | Since 306 factors into {{factorization|306}}, 306edo has subset edos {{EDOs| 2, 3, 6, 9, 17, 18, 34, 51, 102, and 153 }}. | ||
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Latest revision as of 12:47, 12 July 2025
| ← 305edo | 306edo | 307edo → |
(convergent)
306 equal divisions of the octave (abbreviated 306edo or 306ed2), also called 306-tone equal temperament (306tet) or 306 equal temperament (306et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 306 equal parts of about 3.92 ¢ each. Each step represents a frequency ratio of 21/306, or the 306th root of 2.
306edo provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the patent val tempers out 78732/78125 (sensipent comma), whereas the alternative 306c val tempers out 32805/32768 (schisma). 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.
306edo provides an excellent approximation of Valotti temperament due to its representation of the Pythagorean comma as 6 steps.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.006 | +1.922 | -0.198 | +1.623 | -1.312 | +0.927 | +0.526 | -0.823 | +1.795 | +0.062 |
| Relative (%) | +0.0 | +0.1 | +49.0 | -5.1 | +41.4 | -33.5 | +23.6 | +13.4 | -21.0 | +45.8 | +1.6 | |
| Steps (reduced) |
306 (0) |
485 (179) |
711 (99) |
859 (247) |
1059 (141) |
1132 (214) |
1251 (27) |
1300 (76) |
1384 (160) |
1487 (263) |
1516 (292) | |
Subsets and supersets
Since 306 factors into 2 × 32 × 17, 306edo has subset edos 2, 3, 6, 9, 17, 18, 34, 51, 102, and 153.