12/11: 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 neutral second, Alpharabian tendoneutral second
: This revision was by author [[User:Sarzadoce|Sarzadoce]] and made on <tt>2011-08-09 00:51:45 UTC</tt>.<br>
| Color name = 1u2, lu 2nd
: The original revision id was <tt>244975507</tt>.<br>
| Sound = jid_12_11_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>
{{Wikipedia|Neutral second}}
<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 (lesser) neutral second is a strangely exotic interval found between the 11th and 12th partials of the harmonic series. In Just Intonation it is represented by the ratio 12/11, and is about 150.64 [[cent|cents]] large. One step of [[8edo|8-edo]] is an excellent approximation of the just neutral second.</pre></div>
'''12/11''', the '''undecimal neutral second''' or '''(lesser) neutral second''', is an interval found between the 11th and 12th partials of the [[harmonic series]]. In [[just intonation]] it is represented by the [[superparticular]] ratio 12/11, and is about 150.6 [[cent]]s large. One step of [[8edo]] is an excellent approximation of the just neutral second, and eight of them exceed the octave by the comma [[Undecimal_octatonic_comma|(12/11)<sup>8</sup>/2 = {{Monzo|15 8 0 0 -8}}]]. It follows that EDOs which are multiples of 8, such as [[16edo]] and [[24edo]], will also represent this interval well. In [[Alpharabian tuning]] it is known as the '''Alpharabian tendoneutral second'''.
<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;12_11&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The (lesser) neutral second is a strangely exotic interval found between the 11th and 12th partials of the harmonic series. In Just Intonation it is represented by the ratio 12/11, and is about 150.64 &lt;a class="wiki_link" href="/cent"&gt;cents&lt;/a&gt; large. One step of &lt;a class="wiki_link" href="/8edo"&gt;8-edo&lt;/a&gt; is an excellent approximation of the just neutral second.&lt;/body&gt;&lt;/html&gt;</pre></div>
12/11 differs from the larger undecimal neutral second [[11/10]] (~165 cents) by [[121/120]] (~14.4 cents). Temperaments which conflate the two (thus tempering out 121/120) include [[15edo]], [[22edo]], [[31edo]], [[orwell]], [[porcupine]], [[mohajira]], [[valentine]], etc.
 
Many Western listeners might describe 12/11 as sounding "exotic".
 
== See also ==
* [[11/6]] – its [[octave complement]]
* [[11/8]] – its [[fifth complement]]
* [[11/9]] – its [[fourth complement]]
* [[Iceface Tuning]]
* [[Gallery of just intervals]]
* [[List of superparticular intervals]]
 
[[Category:Second]]
[[Category:Neutral second]]
[[Category:Over-11 intervals]]

Latest revision as of 23:53, 16 August 2025

Interval information
Ratio 12/11
Factorization 22 × 3 × 11-1
Monzo [2 1 0 0 -1⟩
Size in cents 150.6371¢
Names undecimal neutral second,
Alpharabian tendoneutral second
Color name 1u2, lu 2nd
FJS name [math]\displaystyle{ \text{M2}_{11} }[/math]
Special properties superparticular,
reduced
Tenney height (log2 nd) 7.04439
Weil height (log2 max(n, d)) 7.16993
Wilson height (sopfr(nd)) 18

[sound info]
Open this interval in xen-calc
English Wikipedia has an article on:

12/11, the undecimal neutral second or (lesser) neutral second, is an interval found between the 11th and 12th partials of the harmonic series. In just intonation it is represented by the superparticular ratio 12/11, and is about 150.6 cents large. One step of 8edo is an excellent approximation of the just neutral second, and eight of them exceed the octave by the comma (12/11)8/2 = [15 8 0 0 -8⟩. It follows that EDOs which are multiples of 8, such as 16edo and 24edo, will also represent this interval well. In Alpharabian tuning it is known as the Alpharabian tendoneutral second.

12/11 differs from the larger undecimal neutral second 11/10 (~165 cents) by 121/120 (~14.4 cents). Temperaments which conflate the two (thus tempering out 121/120) include 15edo, 22edo, 31edo, orwell, porcupine, mohajira, valentine, etc.

Many Western listeners might describe 12/11 as sounding "exotic".

See also

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