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]]

Latest revision as of 07:26, 3 January 2025

Interval information
Ratio 135/128
Factorization 2-7 × 33 × 5
Monzo [-7 3 1⟩
Size in cents 92.17872¢
Names ptolemaic chromatic semitone,
major limma,
major chroma,
mavila comma
Color name Ly1, layo unison,
Layobi comma
FJS name [math]\displaystyle{ \text{A1}^{5} }[/math]
Special properties reduced,
reduced harmonic
Tenney height (log2 nd) 14.0768
Weil height (log2 max(n, d)) 14.1536
Wilson height (sopfr(nd)) 28
Comma size medium
S-expression S3 / S4

[sound info]
Open this interval in xen-calc

The 5-limit interval 135/128, about 92.2 cents 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.

Temperaments

If 135/128 is treated as a comma to be tempered out, it may be called the mavila comma. It represents the difference between three perfect fourths and a 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 semiconvergent. Aluminium temperament realizes this through a regular temperament lens.

See also

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