Mabila family: Difference between revisions
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{{Technical data page}} | {{Technical data page}} | ||
The '''mabila family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[mabila comma]] ({{monzo|legend=1| 28 -3 -10 }}, [[ratio]]: 268435456/263671875) in the [[5-limit]] | The '''mabila family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[mabila comma]] ({{monzo|legend=1| 28 -3 -10 }}, [[ratio]]: 268435456/263671875) in the [[5-limit]]. | ||
== Mabila == | == Mabila == | ||
: ''"Mabila" redirects here. For the temperaments that used to go by this name, see [[Semabila]] and [[Mabilic]].'' | |||
Mabila has a temperament structure superficially similar to [[mavila]], with extremely sharp fourths/flat fifths, three of which make a major third. However, unlike mavila, 10 of these bad fifths reach a more in tune one, which is useful for creating resolutions when using a large enough gamut, such as the [[9L 7s]] [[mos]] which has 3 good major and minor chords. | |||
Mabila is part of the [[diaschismic–gothmic equivalence continuum]] with {{nowrap| ''n'' {{=}} 5 }}. | |||
[[Subgroup]]: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
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: [[error map]]: {{val| -0.646 +0.173 +1.240 }} | : [[error map]]: {{val| -0.646 +0.173 +1.240 }} | ||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~375/256 = 670.2921{{c}} | * [[CWE]]: ~2 = 1200.0000{{c}}, ~375/256 = 670.2921{{c}} | ||
: error map: {{val| | : error map: {{val| 0.000 +0.966 +2.810 }} | ||
{{Optimal ET sequence|legend=1| 9, 25, 34, 77, 111, 145, 256c }} | {{Optimal ET sequence|legend=1| 9, 25, 34, 77, 111, 145, 256c }} | ||
[[Badness]] (Sintel): 5.45 | [[Badness]] (Sintel): 5.45 | ||
=== Overview to extensions === | |||
The second comma in the comma list defines which 7-limit family member we are looking at. Amavil (9 & 43) adds [[225/224]], semabila (9 & 25) adds [[49/48]], tuscaloosa (77 & 111) adds [[19683/19600]], muscogee (43 & 77) adds [[126/125]]. These all use the same generators as mabila. | |||
Cohemimabila (25 & 43) tempers out [[3136/3125]], splitting the subfifth in two. Hemimabila (9 & 68) tempers out [[6144/6125]], splitting the subtwelfth in two. Trimabila (9 & 111) tempers out [[1728/1715]], with a 1/3-octave period. | |||
== Amavil == | == Amavil == | ||
Named by [[Petr Pařízek]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>, amavil tempers out [[225/224]] and may be described as the {{nowrap| | Named by [[Petr Pařízek]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>, amavil tempers out [[225/224]] and may be described as the {{nowrap| 9 & 43 }} temperament. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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{{See also| No-threes subgroup temperaments #Mabilic }} | {{See also| No-threes subgroup temperaments #Mabilic }} | ||
Semabila | Semabila tempers out [[49/48]] and may be described as the {{nowrap| 9 & 25 }} temperament. | ||
This temperament used to known as ''septimal mabila''. Semabila, by [[Lériendil]] in 2024, was so named because it was a semaphore temperament. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Tuskaloosa == | == Tuskaloosa == | ||
Named by [[Xenllium]] in 2022, tuskaloosa tempers out [[19683/19600]] and may be described as the {{nowrap| 34d & 77 }} temperament. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Muscogee == | == Muscogee == | ||
Named by [[Xenllium]] in 2022, muscogee tempers out [[126/125]] and may be described as the {{nowrap| 43 & 77 }} temperament. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Cohemimabila == | == Cohemimabila == | ||
Named by [[Xenllium]] in 2022, cohemimabila tempers out [[3136/3125]] as well as [[65536/64827]] and may be described as the {{nowrap| 43 & 68 }} temperament. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Trimabila == | == Trimabila == | ||
Named by [[Xenllium]] in 2022, trimabila tempers out [[1728/1715]] and may be described as the {{nowrap| 9 & 111 }} temperament. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== References == | == References == | ||
[[Category:Mabila family| ]] <!-- main article --> | |||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category: | [[Category:Catalogs of rank-2 temperaments]] | ||