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Negri comma: Difference between revisions

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**Imported revision 282668146 - Original comment: **
+ 7-limit factorizations
 
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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>
| Ratio = 16875/16384
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-12-05 21:46:08 UTC</tt>.<br>
| Name = negri comma
: The original revision id was <tt>282668146</tt>.<br>
| Color name = Ly<sup>4</sup>-2, Laquadyo comma
: 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>
'''16875/16384''' is the 51.120 [[cent]] interval called the '''negri comma''' or double augmentation diesis. It is the amount by which four classical major thirds exceed three fourths, that is, ([[5/4]])<sup>4</sup>/([[4/3]])<sup>3</sup>, and is also the amount by which three [[16/15|diatonic semitones (16/15)]] fall short of a classical major third, that is, (5/4)/(16/15)<sup>3</sup>. Another characterization of this comma is the difference between the [[256/243|Pythagorean limma (256/243)]] and a stack of two [[25/24|classical chromas (25/24)]].
<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">16875/16384 is the 51.120 cent interval called the negri [[comma]] or double augmentation diesis. It is the amount by which four major thirds exceed three fourths, that is, (5/4)^4/(4/3)^3, and is also the amount by which three [[16_15|diatonic semitones]] fall short of a major third, that is, (5/4)/(16/15)^3. Tempering it out leads to [[5-limit]] [[Negri|negri temperament]], which is closely associated with [[19edo]].</pre></div>
 
<h4>Original HTML content:</h4>
It factors into simpler commas as ([[81/80]])⋅([[3125/3072]]), the syntonic comma and the magic comma. In the [[7-limit]], it factors into ([[225/224]])⋅([[525/512]]), (225/224)<sup>2</sup>⋅([[49/48]]), or (225/224)<sup>3</sup>⋅([[686/675]]).
<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;negri comma&lt;/title&gt;&lt;/head&gt;&lt;body&gt;16875/16384 is the 51.120 cent interval called the negri &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt; or double augmentation diesis. It is the amount by which four major thirds exceed three fourths, that is, (5/4)^4/(4/3)^3, and is also the amount by which three &lt;a class="wiki_link" href="/16_15"&gt;diatonic semitones&lt;/a&gt; fall short of a major third, that is, (5/4)/(16/15)^3. Tempering it out leads to &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Negri"&gt;negri temperament&lt;/a&gt;, which is closely associated with &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
 
== Temperaments ==
Tempering it out leads to [[5-limit]] [[negri]] temperament, which is closely associated with [[19edo]].  
 
== Etymology ==
The corresponding temperament was discovered first, dubbed ''negri'' by [[Paul Erlich]] in late 2001<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_31054.html#31065 Yahoo! Tuning Group | ''The grooviest linear temperaments for 7-limit music'']</ref> after John Negri's 10-out-of-19 maximally even scale<ref>"The Nineteen-Tone System as Ten Plus Nine". [https://interval.xentonic.org/tables-of-contents.html  ''Interval, Journal of Music Research and Development''], pp. 11–13 of Volume 5, Number 3 (Winter 1986–1987). John Negri. </ref>. The comma was at one point dubbed ''negrisma'' by [[Gene Ward Smith]] in late 2002, though it was ''negri comma'' that stuck<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5025.html Yahoo! Tuning Group | ''5-limit comma names'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5080.html#5113 Yahoo! Tuning Group | ''Ultimate 5-limit comma list'']</ref>.
 
== See also ==
* [[Medium comma]]
 
== Notes ==
 
[[Category:Negri]]
[[Category:Commas named after composers]]
[[Category:Commas named after music theorists]]
Retrieved from "https://en.xen.wiki/w/Negri_comma"