Mabila family: Difference between revisions

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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]]. This gives 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.

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" 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

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: [[error map]]: {{val| -0.646 +0.173 +1.240 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~375/256 = 670.2921{{c}}

: error map: {{val| -0.~~646~~ +0.~~173~~ +1.~~240~~ }}

: error map: {{val| 0.000 +0.966 +2.810 }}

[[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 ==

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| ~~34d~~ & 43 }} temperament.

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

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Semabila tempers out [[49/48]] and may be described as the {{nowrap| 25 ~~& 34~~ }} temperament.

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.

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== References ==

[[Category:Mabila family| ]]

[[Category:Temperament families]]

[[Category:~~Mabila family| ]] <!~~-~~- main article -->~~

[[Category:Catalogs of rank-2 temperaments]]

~~[[Category:Rank~~ 2]]

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 {{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]]. This gives 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.
+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" 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
@@ Line 16: / Line 20: @@
 : [[error map]]: {{val| -0.646 +0.173 +1.240 }}
 * [[CWE]]: ~2 = 1200.0000{{c}}, ~375/256 = 670.2921{{c}}
-: error map: {{val| -0.646 +0.173 +1.240 }}
+: error map: {{val| 0.000 +0.966 +2.810 }}
 {{Optimal ET sequence|legend=1| 9, 25, 34, 77, 111, 145, 256c }}
 [[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 ==
-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| 34d & 43 }} temperament.
+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
@@ Line 104: / Line 113: @@
 {{See also| No-threes subgroup temperaments #Mabilic }}
-Semabila tempers out [[49/48]] and may be described as the {{nowrap| 25 & 34 }} temperament.
+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.
@@ Line 582: / Line 591: @@
 == References ==
+[[Category:Mabila family| ]] <!-- main article -->
 [[Category:Temperament families]]
-[[Category:Mabila family| ]] <!-- main article -->
+[[Category:Catalogs of rank-2 temperaments]]
-[[Category:Rank 2]]