135/128: Difference between revisions

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~~'''135/128'''~~

{{Infobox Interval

|~~-7 3 1>~~

| Name = ptolemaic chromatic semitone, major limma, major chroma, mavila comma

| Color name = Ly1, layo unison,<br>Layobi comma

| Sound = jid_135_128_pluck_adu_dr220.mp3

| Comma = yes

}}

92.~~1787 cents~~

The [[5-limit]] interval '''135/128''', about 92.2 [[cent]]s in size, is called the '''ptolemaic chromatic semitone''', the '''major limma''' or the '''major chroma'''. It is a [[syntonic comma]] away from the Pythagorean chromatic semitone [[2187/2048]], and so is tuned justly in [[1/7-comma meantone]]. Flattening by another syntonic comma reaches the even simpler [[25/24]]. In regular 5-limit diatonic systems, it is the chromatic semitone that compliments [[16/15]], as the two semitones add up to [[9/8]].

[[~~File:jid_135_128_pluck_adu_dr220~~.~~mp3~~]] [[~~:File:jid_135_128_pluck_adu_dr220~~.~~mp3|sound sample~~]]

== Temperaments ==

If 135/128 is treated as a comma to be [[tempering out|tempered out]], it may be called the '''mavila comma'''. It represents the difference between three [[4/3|perfect fourth]]s and a [[5/4|just major third]] (plus an [[octave]]). Tempering it out results in the [[mavila]] temperament.

~~The 5-limit interval~~ 135/128~~, about 92.2~~ [[~~cent|cent~~]]s in ~~size, is called the ''[[pelogic_comma~~|~~pelogic comma]]'', ''[[major_limma~~|~~major limma]]'' or ''~~[[~~major_chroma|major chroma~~]]''.

135/128 is very close to one step of [[13edo]], in fact being a {{w|Continued fraction|semiconvergent}}. [[Aluminium]] temperament realizes this through a regular temperament lens.

~~As a~~ [[~~Comma|~~comma]] ~~it represents~~ the difference between ~~three~~ [[4/~~3|perfect fourths~~]] ~~and a~~ [[~~5/4|~~just ~~major third~~]] ~~(plus an~~ [[~~Octave|octave~~]]).

== See also ==

* [[256/135]] – its [[octave complement]]

* [[Aluminium comma]] - the difference between a stack of 13 instances of this interval and [[2/1]]

* [[Gallery of just intervals]]

* [[Medium comma]]

* [[:File:Ji-135-128-csound-foscil-220hz.mp3]] – another sound example

~~See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]~~ [[Category:~~comma~~]]

[[Category:Semitone]]

[[Category:~~comma_name~~]]

[[Category:Chroma]]

[[Category:~~interval~~]]

[[Category:Mavila]]

[[Category:~~pelogic~~]]

[[Category:Meantone]]

[[Category:~~ratio~~]]

[[Category:Commas named after musical traditions]]

@@ Line 1: / Line 1: @@
-'''135/128'''
+{{Infobox Interval
-|-7 3 1&gt;
+| Name = ptolemaic chromatic semitone, major limma, major chroma, mavila comma
+| Color name = Ly1, layo unison,<br>Layobi comma
+| Sound = jid_135_128_pluck_adu_dr220.mp3
+| Comma = yes
+}}
-.1787 cents
+The [[5-limit]] interval '''135/128''', about 92.2 [[cent]]s in size, is called the '''ptolemaic chromatic semitone''', the '''major limma''' or the '''major chroma'''. It is a [[syntonic comma]] away from the Pythagorean chromatic semitone [[2187/2048]], and so is tuned justly in [[1/7-comma meantone]]. Flattening by another syntonic comma reaches the even simpler [[25/24]].  In regular 5-limit diatonic systems, it is the chromatic semitone that compliments [[16/15]], as the two semitones add up to [[9/8]].
-[[File:jid_135_128_pluck_adu_dr220.mp3]] [[:File:jid_135_128_pluck_adu_dr220.mp3|sound sample]]
+== Temperaments ==
+If 135/128 is treated as a comma to be [[tempering out|tempered out]], it may be called the '''mavila comma'''. It represents the difference between three [[4/3|perfect fourth]]s and a [[5/4|just major third]] (plus an [[octave]]). Tempering it out results in the [[mavila]] temperament.
-The 5-limit interval 135/128, about 92.2 [[cent|cent]]s in size, is called the ''[[pelogic_comma|pelogic comma]]'', ''[[major_limma|major limma]]'' or ''[[major_chroma|major chroma]]''.
+/128 is very close to one step of [[13edo]], in fact being a {{w|Continued fraction|semiconvergent}}. [[Aluminium]] temperament realizes this through a regular temperament lens.
-As a [[Comma|comma]] it represents the difference between three [[4/3|perfect fourths]] and a [[5/4|just major third]] (plus an [[Octave|octave]]).
+== See also ==
+* [[256/135]] – its [[octave complement]]
+* [[Aluminium comma]] - the difference between a stack of 13 instances of this interval and [[2/1]]
+* [[Gallery of just intervals]]
+* [[Medium comma]]
+* [[:File:Ji-135-128-csound-foscil-220hz.mp3]] – another sound example
-See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]      [[Category:comma]]
+[[Category:Semitone]]
-[[Category:comma_name]]
+[[Category:Chroma]]
-[[Category:interval]]
+[[Category:Mavila]]
-[[Category:pelogic]]
+[[Category:Meantone]]
-[[Category:ratio]]
+[[Category:Commas named after musical traditions]]