289/288: Difference between revisions
m →Semitonic: having two different sets of generators one of which used by the mapping seems unnecessarily confusing (and using reduced generators usually makes the numbers in the mapping simpler which is useful musically) |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = semitonisma | | Name = semitonisma, septendecimal semitones comma, septendecimal 6-cent comma | ||
| Color name = 17oo2, soso 2nd,<br>Soso comma | | Color name = 17oo2, soso 2nd,<br>Soso comma | ||
| Comma = yes | | Comma = yes | ||
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== Temperaments == | == Temperaments == | ||
Tempering out this comma results in the rank- | Tempering out this comma in the full 17-limit results in the rank-6 '''semitonismic temperament''', or in the 2.3.17 subgroup, the rank-2 '''semitonic temperament'''. In either case the [[octave]] is split into two equal parts, each representing 17/12~24/17, and thus so is the whole tone, each representing 17/16~18/17. Odd edos cannot temper it out. | ||
=== Semitonic === | === Semitonic === | ||
[[ | See [[No-fives subgroup temperaments #Semitonic]]. | ||
=== Semitonismic === | === Semitonismic === | ||
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[[Optimal tuning]] ([[CTE]]): ~17/12 = 1\2, ~3/2 = 702.3472, 5/4, 7/4, 11/8, 13/8 | [[Optimal tuning]] ([[CTE]]): ~17/12 = 1\2, ~3/2 = 702.3472, 5/4, 7/4, 11/8, 13/8 | ||
{{Optimal ET sequence|legend=1| 34d, 38df, 46, 58, 72, 130, 140, 190g, 212g, 270g, 342fg, 402defgg, 460gg, 532dfggg, 672defggg }} | {{Optimal ET sequence|legend=1| 34d, 38df, 46, 58, 72, 130, 140, 190g, 212g, 270g, 342fg, 402defgg, 460gg, 532dfggg, 672defggg }}* | ||
<nowiki>*</nowiki> [[optimal patent val]]: [[280edo|280]] | |||
== Etymology == | == Etymology == | ||
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[[Category:Semitonismic]] | [[Category:Semitonismic]] | ||
[[Category:Commas named for the intervals they stack]] | |||