135/128: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox Interval
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| Name = ptolemaic chromatic semitone, major limma, major chroma, mavila comma
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-22 16:17:34 UTC</tt>.<br>
| Color name = Ly1, layo unison,<br>Layobi comma
: The original revision id was <tt>238246265</tt>.<br>
| Sound = jid_135_128_pluck_adu_dr220.mp3
: The revision comment was: <tt></tt><br>
| Comma = yes
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
}}
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The interval with the [[frequency ratio]] **135/128** ([[monzo]]: |-7 3 1&gt;), 92.179 [[cent]]s in size, is called //[[pelogic comma]]//.


----
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]].
see also [[comma]]</pre></div>
 
<h4>Original HTML content:</h4>
== Temperaments ==
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;135_128&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The interval with the &lt;a class="wiki_link" href="/frequency%20ratio"&gt;frequency ratio&lt;/a&gt; &lt;strong&gt;135/128&lt;/strong&gt; (&lt;a class="wiki_link" href="/monzo"&gt;monzo&lt;/a&gt;: |-7 3 1&amp;gt;), 92.179 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s in size, is called &lt;em&gt;&lt;a class="wiki_link" href="/pelogic%20comma"&gt;pelogic comma&lt;/a&gt;&lt;/em&gt;.&lt;br /&gt;
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.
&lt;br /&gt;
 
&lt;hr /&gt;
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 &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
 
== 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:Semitone]]
[[Category:Chroma]]
[[Category:Mavila]]
[[Category:Meantone]]
[[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

Retrieved from "https://en.xen.wiki/index.php?title=135/128&oldid=174333"