135/128: Difference between revisions

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{{Infobox Interval

~~| Ratio = 135/128~~

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

~~| Monzo = -7 3 1~~

~~| Cents = 92.17872~~

| Name = ~~pelogic comma~~, ~~ ~~ major limma, ~~ ~~ major chroma

| Color name = Ly1, layo unison, Layobi comma

~~| FJS name = A15~~

| Sound = jid_135_128_pluck_adu_dr220.mp3

| Comma = yes

}}

The [[5-limit]] interval '''135/128''', about 92.2 [[cent]]s in size, is called the '''~~pelogic comma~~''', '''major limma''' or '''major chroma'''. It is a [[syntonic comma]] away from the ~~pythagorean major~~ semitone [[2187/2048]], and so is tuned justly in 1/7 comma meantone. Flattening by another syntonic comma reaches the even simpler [[25/24]].

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]].

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

== 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.

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.

== 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

~~[[Category:5-limit]]~~

~~[[Category:Medium commas]]~~

[[Category:Semitone]]

[[Category:Chroma]]

[[Category:~~Octave-reduced harmonics]]~~

[[Category:Mavila]]

~~[[Category:Pelogic~~]]

[[Category:Meantone]]

[[Category:Commas named after musical traditions]]

~~{{todo|expand}}~~

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Ratio = 135/128
+| Name = ptolemaic chromatic semitone, major limma, major chroma, mavila comma
-| Monzo = -7 3 1
-| Cents = 92.17872
-| Name = pelogic comma, <br> major limma, <br> major chroma
 | Color name = Ly1, layo unison,<br>Layobi comma
-| FJS name = A1<sup>5</sup>
 | Sound = jid_135_128_pluck_adu_dr220.mp3
+| Comma = yes
 }}
-The [[5-limit]] interval '''135/128''', about 92.2 [[cent]]s in size, is called the '''pelogic comma''', '''major limma''' or '''major chroma'''. It is a [[syntonic comma]] away from the pythagorean major semitone [[2187/2048]], and so is tuned justly in 1/7 comma meantone. Flattening by another syntonic comma reaches the even simpler [[25/24]].
+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]].
-As a [[comma]] it represents the difference between three [[4/3|perfect fourths]] and a [[5/4|just major third]] (plus an [[octave]]).
+== 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.
+/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.
 == 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
-[[Category:5-limit]]
-[[Category:Medium commas]]
 [[Category:Semitone]]
 [[Category:Chroma]]
-[[Category:Octave-reduced harmonics]]
+[[Category:Mavila]]
-[[Category:Pelogic]]
 [[Category:Meantone]]
+[[Category:Commas named after musical traditions]]
-{{todo|expand}}