45/44: 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 = undecimal 1/5-tone, cake comma

~~: This revision was by author [[User:xenjacob~~|~~xenjacob]] and made on <tt>2014~~-~~04-23 18:05:58 UTC</tt>.<br>~~

| Color name = 1uy1, luyo 1sn,<br>Luyo comma

~~: The original revision id was <tt>504157944</tt>.<br>~~

| Sound = Ji-45-44-csound-foscil-220hz.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">~~45/44, ~38.906 cents, the undecimal 1/~~5th~~ tone, is the interval between [[~~11_9|~~11/9]] and [[~~5_4|~~5/4]], ~~and also~~ between [[~~11_10|~~11/10]] and [[~~9_8|~~9/8]]. It is ~~tempered out by the patent vals for~~ [[~~12edo|12~~]], [[~~19edo|19~~]], and [[~~26edo|26~~]] ~~equal~~.~~</pre></div>~~

'''45/44''', ~38.906 cents, the '''undecimal 1/5-tone''', is the interval between [[11/9]] and [[5/4]], between [[11/10]] and [[9/8]], and between [[22/15]] and [[3/2]].

~~<h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>45_44</title></head><body>45/44, ~~~38~~.~~906 cents~~, the ~~undecimal 1/5th tone~~, is the ~~interval between <~~a ~~class=~~"~~wiki_link" href="/11_9">~~11/9~~</a> and <a class="wiki_link" href="/5_4">~~5/4~~</a>~~, ~~and also between <a class="wiki_link" href="~~/~~11_10">11/10</a> and <a class="wiki_link" href="/9_8">9/8</a>~~. It is ~~tempered out~~ by the patent ~~vals~~ for ~~<a class="wiki_link" href="/~~12edo~~">~~12~~</a>~~, ~~<a class="wiki_link" href="/~~19edo~~">~~19~~</a>~~, and ~~<a class~~=~~"wiki_link" href~~="/~~26edo">26<~~/~~a> equal~~.~~<~~/~~body><~~/~~html><~~/~~pre><~~/~~div>~~

== Approximation ==

45/44 is extremely close to a single step of [[31edo]], and is represented consistently there as well. When one uses 45/44 as an interval in its own right, it has properties akin to a sort of [[chroma]], and it differs from [[8192/8019]], the Alpharabian inframinor second, by the [[schisma]].

== Temperaments ==

[[File:Oceania's cake.jpg|thumb|Ocean's cake]]

45/44 is also known as the '''cake comma''', from when [[Ocean Stegosaurus Tardigrade]] was baking a cake and misread flour and sugar measurements on his scale, leading to the inclusion of 11/9 times the amount suggested in his recipe. To compensate, he writes "I increased all the other ingredients by a neutral third, except the eggs, which I increased by a major third because I couldn't be bothered to measure out eight ninths of an egg." We see here the equating of 11/9 with 5/4, leading to the [[tempering out]] of 45/44. The cake turned out fine but slightly burnt on the top.

This temperament is the [[Catalog of rank-4 temperaments #Cake (45/44)|cake temperament]], [[support]]ed by the [[patent val]]s for [[12edo|12-]], [[19edo|19-]], and [[26edo|26-tone equal temperament]].

== Notation ==

=== Sagittal notation ===

In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal | (!( }} and is called the '''11/5 small diesis''', or '''11/5S''' for short, because the simplest interval it notates is 11/5 (equiv. 11/10), as for example in C–D{{nbhsp}}{{sagittal | (!( }}. The upward version is called '''5/11S''' or '''11/5S up''' and is represented by {{sagittal| (|( }}.

== See also ==

* [[88/45]] – its [[octave complement]]

* [[22/15]] – its [[fifth complement]]

* [[Gallery of just intervals]]

* [[List of superparticular intervals]]

* [[Medium comma]]

[[Category:Cake]]

[[Category:Commas named following events]]

@@ Line 1: / Line 1: @@
-<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 = undecimal 1/5-tone, cake comma
-: This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2014-04-23 18:05:58 UTC</tt>.<br>
+| Color name = 1uy1, luyo 1sn,<br>Luyo comma
-: The original revision id was <tt>504157944</tt>.<br>
+| Sound = Ji-45-44-csound-foscil-220hz.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">45/44, ~38.906 cents, the undecimal 1/5th tone, is the interval between [[11_9|11/9]] and [[5_4|5/4]], and also between [[11_10|11/10]] and [[9_8|9/8]]. It is tempered out by the patent vals for [[12edo|12]], [[19edo|19]], and [[26edo|26]] equal.</pre></div>
+'''45/44''', ~38.906 cents, the '''undecimal 1/5-tone''', is the interval between [[11/9]] and [[5/4]], between [[11/10]] and [[9/8]], and between [[22/15]] and [[3/2]].
-<h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;45_44&lt;/title&gt;&lt;/head&gt;&lt;body&gt;45/44, ~38.906 cents, the undecimal 1/5th tone, is the interval between &lt;a class="wiki_link" href="/11_9"&gt;11/9&lt;/a&gt; and &lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt;, and also between &lt;a class="wiki_link" href="/11_10"&gt;11/10&lt;/a&gt; and &lt;a class="wiki_link" href="/9_8"&gt;9/8&lt;/a&gt;. It is tempered out by the patent vals for &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, and &lt;a class="wiki_link" href="/26edo"&gt;26&lt;/a&gt; equal.&lt;/body&gt;&lt;/html&gt;</pre></div>
+== Approximation ==
+/44 is extremely close to a single step of [[31edo]], and is represented consistently there as well. When one uses 45/44 as an interval in its own right, it has properties akin to a sort of [[chroma]], and it differs from [[8192/8019]], the Alpharabian inframinor second, by the [[schisma]].
+== Temperaments ==
+[[File:Oceania's cake.jpg|thumb|Ocean's cake]]
+/44 is also known as the '''cake comma''', from when [[Ocean Stegosaurus Tardigrade]] was baking a cake and misread flour and sugar measurements on his scale, leading to the inclusion of 11/9 times the amount suggested in his recipe. To compensate, he writes "I increased all the other ingredients by a neutral third, except the eggs, which I increased by a major third because I couldn't be bothered to measure out eight ninths of an egg." We see here the equating of 11/9 with 5/4, leading to the [[tempering out]] of 45/44. The cake turned out fine but slightly burnt on the top.
+This temperament is the [[Catalog of rank-4 temperaments #Cake (45/44)|cake temperament]], [[support]]ed by the [[patent val]]s for [[12edo|12-]], [[19edo|19-]], and [[26edo|26-tone equal temperament]].
+== Notation ==
+=== Sagittal notation ===
+In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal | (!( }} and is called the '''11/5 small diesis''', or '''11/5S''' for short, because the simplest interval it notates is 11/5 (equiv. 11/10), as for example in C–D{{nbhsp}}{{sagittal | (!( }}. The upward version is called '''5/11S''' or '''11/5S up''' and is represented by {{sagittal| (|( }}.
+== See also ==
+* [[88/45]] – its [[octave complement]]
+* [[22/15]] – its [[fifth complement]]
+* [[Gallery of just intervals]]
+* [[List of superparticular intervals]]
+* [[Medium comma]]
+[[Category:Cake]]
+[[Category:Commas named following events]]