27/22: Difference between revisions

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**Imported revision 513546368 - Original comment: **
 
mention its closeness to 13\44
 
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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 = rastmic neutral third, Alpharabian tendoneutral third
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-10 21:42:54 UTC</tt>.<br>
| Color name = 1u3, lu 3rd
: The original revision id was <tt>513546368</tt>.<br>
| Sound = jid_27_22_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>
'''27/22''', conventionally called the '''rastmic neutral third''', is [[243/242]] (7.1{{cent}}) sharp of [[11/9]], and together with 11/9 makes [[3/2]], so that we obtain the two neutral triads, 1-11/9-3/2 and 1-27/22-3/2, with intervals of 11/9 and 27/22. It is the interval between [[10/9]] and [[15/11]], and 11/9 and [[3/2]] and their inversions. As this is the larger of two [[11-limit]] neutral thirds obtained by modifying Pythagorean intervals by [[33/32]], it is dubbed the '''Alpharabian tendoneutral third''' in [[Alpharabian tuning]]. It is extremely close to [[44edo]]'s 13\44 neutral third, however the first multiple of 44edo to map it consistently is [[176edo]].
<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">**27/22**
== Approximation ==
|-1 3 0 0 -1&gt;
{{Interval edo approximation|27/22}}
354.5471 cents
== See also ==
[[media type="file" key="jid_27_22_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_27_22_pluck_adu_dr220.mp3|sound sample]]
* [[24edo]]
</pre></div>
* [[44/27]] – its [[octave complement]]
<h4>Original HTML content:</h4>
* [[11/9]] – its [[fifth complement]]
<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;27_22&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;27/22&lt;/strong&gt;&lt;br /&gt;
* [[Gallery of just intervals]]
|-1 3 0 0 -1&amp;gt;&lt;br /&gt;
* [[Iceface Tuning]]
354.5471 cents&lt;br /&gt;
 
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[[Category:Third]]
[[Category:Neutral third]]
[[Category:Rastmic]]
[[Category:Alpharabian]]

Latest revision as of 16:45, 11 March 2026

Interval information
Ratio 27/22
Factorization 2-1 × 33 × 11-1
Monzo [-1 3 0 0 -1⟩
Size in cents 354.5471¢
Names rastmic neutral third,
Alpharabian tendoneutral third
Color name 1u3, lu 3rd
FJS name [math]\displaystyle{ \text{M3}_{11} }[/math]
Special properties reduced
Tenney norm (log2 nd) 9.21432
Weil norm (log2 max(n, d)) 9.50978
Wilson norm (sopfr(nd)) 22

[sound info]
Open this interval in xen-calc

27/22, conventionally called the rastmic neutral third, is 243/242 (7.1 ¢) sharp of 11/9, and together with 11/9 makes 3/2, so that we obtain the two neutral triads, 1-11/9-3/2 and 1-27/22-3/2, with intervals of 11/9 and 27/22. It is the interval between 10/9 and 15/11, and 11/9 and 3/2 and their inversions. As this is the larger of two 11-limit neutral thirds obtained by modifying Pythagorean intervals by 33/32, it is dubbed the Alpharabian tendoneutral third in Alpharabian tuning. It is extremely close to 44edo's 13\44 neutral third, however the first multiple of 44edo to map it consistently is 176edo.

Approximation

Edo approximations for 27/22 (354.55 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
7 2\7 342.86 -11.69 -6.82
10 3\10 360.00 +5.45 +4.54
17 5\17 352.94 -1.61 -2.28
20 6\20 360.00 +5.45 +9.09
24 7\24 350.00 -4.55 -9.09
27 8\27 355.56 +1.01 +2.27
34 10\34 352.94 -1.61 -4.55
37 11\37 356.76 +2.21 +6.81
44 13\44 354.55 -0.00 -0.01
51 15\51 352.94 -1.61 -6.83
54 16\54 355.56 +1.01 +4.54
61 18\61 354.10 -0.45 -2.28
64 19\64 356.25 +1.70 +9.08
68 20\68 352.94 -1.61 -9.10
71 21\71 354.93 +0.38 +2.26
78 23\78 353.85 -0.70 -4.56

See also

Retrieved from "https://en.xen.wiki/index.php?title=27/22&oldid=225580"