144/125: Difference between revisions

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**Imported revision 513417364 - Original comment: **
 
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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 = classic(al) diminished third, triptolemaic diminished third
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-09 22:27:32 UTC</tt>.<br>
| Color name = g<sup>3</sup>3, trigu 3rd
: The original revision id was <tt>513417364</tt>.<br>
| Sound = jid_144_125_pluck_adu_dr220.mp3
: The revision comment was: <tt></tt><br>
}}
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">**144/125**
|4 2 -3&gt;
244.9689 cents
[[media type="file" key="jid_144_125_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_144_125_pluck_adu_dr220.mp3|sound sample]]


The classic ([[5-limit]]) diminished third.
'''144/125''', the '''classic diminished third''', about 245 [[cent]]s in size, is a just interval in the [[5-limit]]. It can be obtained by subtracting [[6/5]], the classic minor third, by [[25/24]], the classic chroma. It is also the Pythagorean diminished third (65536/59049) flattened by three [[81/80|syntonic commas]], which lends itself to the term ''triptolemaic''.
</pre></div>
 
<h4>Original HTML content:</h4>
== Approximation ==
<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;144_125&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;144/125&lt;/strong&gt;&lt;br /&gt;
This interval is especially close to the 10th step of [[49edo]].  
|4 2 -3&amp;gt;&lt;br /&gt;
 
244.9689 cents&lt;br /&gt;
== Temperaments ==
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In any [[kleismic]] system, it is tuned to an exact semifourth, tempered together with [[125/108]]. The [[university]] temperament treats it as a [[comma]].
&lt;br /&gt;
 
The classic (&lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt;) diminished third.&lt;/body&gt;&lt;/html&gt;</pre></div>
== See also ==
* [[125/72]] – its [[octave complement]]
* [[125/96]] – its [[fifth complement]]
* [[Gallery of just intervals]]
 
[[Category:Third]]
[[Category:Diminished third]]
[[Category:Interseptimal intervals]]
[[Category:Semifourth]]
[[Category:University]]

Latest revision as of 10:24, 1 January 2025

Interval information
Ratio 144/125
Factorization 24 × 32 × 5-3
Monzo [4 2 -3
Size in cents 244.9689¢
Names classic(al) diminished third,
triptolemaic diminished third
Color name g33, trigu 3rd
FJS name [math]\displaystyle{ \text{d3}_{5,5,5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 14.1357
Weil norm (log2 max(n, d)) 14.3399
Wilson norm (sopfr(nd)) 29

[sound info]
Open this interval in xen-calc

144/125, the classic diminished third, about 245 cents in size, is a just interval in the 5-limit. It can be obtained by subtracting 6/5, the classic minor third, by 25/24, the classic chroma. It is also the Pythagorean diminished third (65536/59049) flattened by three syntonic commas, which lends itself to the term triptolemaic.

Approximation

This interval is especially close to the 10th step of 49edo.

Temperaments

In any kleismic system, it is tuned to an exact semifourth, tempered together with 125/108. The university temperament treats it as a comma.

See also