Escapade comma: Difference between revisions

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**Imported revision 248591417 - Original comment: **
 
Jerdle (talk | contribs)
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Fixed typo. ssp^94 would be very different.
 
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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 = 4294967296/4271484375
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-08-26 03:58:05 UTC</tt>.<br>
| Monzo = 32 -7 -9
: The original revision id was <tt>248591417</tt>.<br>
| Name = escapade comma
: The revision comment was: <tt></tt><br>
| Color name = ssg<sup>9</sup>4, sasa-tritrigu 4th
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| Comma = yes
<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 **escapade comma** |32 -7 -9&gt; has a size of 9.492 [[cent]]s. It is the difference between nine just major thirds and seven just fourths, that is, (4/3)^7/(5/4)^9.  
The '''escapade comma''' ({{monzo|legend=1| 32 -7 -9 }}) is a [[small comma|small]] [[5-limit]] [[comma]] with a size of 9.492 [[cent]]s. It is the difference between nine [[5/4|just major thirds]] and seven [[4/3|just perfect fourths]], that is, (4/3)<sup>7</sup>/(5/4)<sup>9</sup>. This can also be written as (5/3)/(16/15)<sup>8</sup>, that is, the difference between a stack of eight [[16/15|classic diatonic semitones]] and a [[5/3|classic major sixth]]. In terms of commas, it is equal to two [[128/125|lesser dieses]] minus three [[81/80|syntonic commas]] and one [[15625/15552|kleisma]], that is, (128/125)<sup>2</sup>/((15625/15552)(81/80)<sup>3</sup>).


The [[escapade family]] tempers out this [[comma]].</pre></div>
== Temperaments ==
<h4>Original HTML content:</h4>
Temperaments in the [[escapade family]] tempers out this comma.  
<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;escapade comma&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;strong&gt;escapade comma&lt;/strong&gt; |32 -7 -9&amp;gt; has a size of 9.492 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s. It is the difference between nine just major thirds and seven just fourths, that is, (4/3)^7/(5/4)^9. &lt;br /&gt;
 
&lt;br /&gt;
== Etymology ==
The &lt;a class="wiki_link" href="/escapade%20family"&gt;escapade family&lt;/a&gt; tempers out this &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
The escapade comma seems to have been named by [[Paul Erlich]] in 2002, referring to the fact that this comma "escaped" a 5-limit comma search by [[Carl Lumma]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5080.html#5113 Yahoo! Tuning Group | ''Ultimate 5-limit comma list'']</ref>.  
 
== Notes ==
 
[[Category:Escapade]]
[[Category:Commas named following events]]

Latest revision as of 09:30, 13 March 2025

Interval information
Ratio 4294967296/4271484375
Factorization 232 × 3-7 × 5-9
Monzo [32 -7 -9⟩
Size in cents 9.491569¢
Name escapade comma
Color name ssg94, sasa-tritrigu 4th
FJS name [math]\displaystyle{ \text{6d4}_{5,5,5,5,5,5,5,5,5} }[/math]
Special properties reduced,
reduced subharmonic
Tenney height (log2 nd) 63.9921
Weil height (log2 max(n, d)) 64
Wilson height (sopfr(nd)) 130
Comma size small
Open this interval in xen-calc

The escapade comma (monzo: [32 -7 -9⟩) is a small 5-limit comma with a size of 9.492 cents. It is the difference between nine just major thirds and seven just perfect fourths, that is, (4/3)7/(5/4)9. This can also be written as (5/3)/(16/15)8, that is, the difference between a stack of eight classic diatonic semitones and a classic major sixth. In terms of commas, it is equal to two lesser dieses minus three syntonic commas and one kleisma, that is, (128/125)2/((15625/15552)(81/80)3).

Temperaments

Temperaments in the escapade family tempers out this comma.

Etymology

The escapade comma seems to have been named by Paul Erlich in 2002, referring to the fact that this comma "escaped" a 5-limit comma search by Carl Lumma[1].

Notes

  1. ↑ Yahoo! Tuning Group | Ultimate 5-limit comma list
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