Magic family: Difference between revisions
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[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[5-odd-limit]]: ~5/4 = {{monzo| 0 1/5 0 }} | * [[5-odd-limit]]: ~5/4 = {{monzo| 0 1/5 0 }} | ||
: [[eigenmonzo basis| | : [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3 | ||
[[Tuning ranges]]: | [[Tuning ranges]]: | ||
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225/224 is the [[marvel family|marvel]] comma. Because the augmented triad is the simplest triad in magic temperaments, it is especially significant in magic temperament. 245/243, the [[sensamagic family|sensamagic]] comma, leads to another essentially tempered 9-odd-limit triad with two thirds approximating 9/7 and the other 6/5. It also divides the approximate 3/2 into two steps of 7/6 and one of 10/9. | 225/224 is the [[marvel family|marvel]] comma. Because the augmented triad is the simplest triad in magic temperaments, it is especially significant in magic temperament. 245/243, the [[sensamagic family|sensamagic]] comma, leads to another essentially tempered 9-odd-limit triad with two thirds approximating 9/7 and the other 6/5. It also divides the approximate 3/2 into two steps of 7/6 and one of 10/9. | ||
By adding [[100/99]] to the list of commas, magic can be extended to an 11-limit version | By adding [[100/99]] to the list of commas, magic can be extended to an 11-limit version. For this, [[104edo]] provides an excellent tuning, as it does also for the rank-3 temperaments tempering out 100/99 with 225/224, 245/243 or 875/864. Septimage (see below) is also an excellent 11-limit magic tuning. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* 7- and [[9-odd-limit]]: ~5/4 = {{monzo| 0 1/5 0 0 }} | * 7- and [[9-odd-limit]]: ~5/4 = {{monzo| 0 1/5 0 0 }} | ||
: [[eigenmonzo basis| | : [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3 | ||
[[Tuning ranges]]: | [[Tuning ranges]]: | ||
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Minimax tuning: | Minimax tuning: | ||
* 11-odd-limit: ~5/4 = {{monzo| 1/3 1/9 0 0 -1/18 }} | * 11-odd-limit: ~5/4 = {{monzo| 1/3 1/9 0 0 -1/18 }} | ||
: | : unchanged-interval (eigenmonzo) basis: 2.11/9 | ||
Tuning ranges: | Tuning ranges: | ||
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== Trismegistus == | == Trismegistus == | ||
{{See also| No-threes subgroup temperaments #Mabilic }} | {{See also| No-threes subgroup temperaments #Mabilic }}{{Main|Mabilic and trismegistus}} | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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Badness (Smith): 0.033081 | Badness (Smith): 0.033081 | ||
=== 2.3.5.7.11.13.19 subgroup === | |||
Subgroup: 2.3.5.7.11.13.19 | |||
Comma list: 105/104, 144/143, 441/440, 210/209, 625/616 | |||
Sval mapping: {{mapping| 1 10 4 0 13 11 2| 0 -15 -3 5 -17 -13 4}} | |||
Optimal tunings: | |||
* CWE: ~2 = 1200.000, ~22/15 = 673.363 | |||
{{Optimal ET sequence|legend=0| 16, 25e, 41, 98c }} | |||
== Quadrimage == | == Quadrimage == | ||
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[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Pages with mostly numerical content]] | |||
[[Category:Magic family| ]] <!-- main article --> | [[Category:Magic family| ]] <!-- main article --> | ||
[[Category:Magic| ]] <!-- key article --> | [[Category:Magic| ]] <!-- key article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
[[Category:Listen]] | [[Category:Listen]] | ||