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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:spt3125|spt3125]] and made on <tt>2014-06-07 16:01:40 UTC</tt>.<br>
| | | Color name = 1u2, lu 2nd |
| : The original revision id was <tt>513195536</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>
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| <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">**12/11**
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| |2 1 0 0 -1> | |
| 150.63706 cents
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| [[media type="file" key="jid_12_11_pluck_adu_dr220.mp3" width="240" height="20"]] [[file:xenharmonic/jid_12_11_pluck_adu_dr220.mp3|sound sample]]
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| 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 [[superparticular]] ratio 12/11, and is about 150.6 [[cent|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.
| | '''12/11''', conventionally the '''(lesser) undecimal 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. |
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| 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]] and [[valentine]].</pre></div>
| | In [[Alpharabian tuning]] it is known as the '''Alpharabian tendoneutral second''', which contrasts [[88/81]], the other undecimal neutral 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"><html><head><title>12_11</title></head><body><strong>12/11</strong><br />
| | The name ''lesser undecimal neutral second'' is said as opposed to [[11/10]], the larger undecimal neutral second or undecimal submajor second (~165 cents), from which it differs by [[121/120]] (~14.4 cents). [[Regular temperament|Temperaments]] which conflate the two (thus [[tempering out]] 121/120) include [[orwell]], [[porcupine]], [[mohajira]], [[valentine]], and their [[support]]ing [[edo]]s: [[15edo]], [[22edo]], [[31edo]], etc. |
| |2 1 0 0 -1&gt;<br />
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| 150.63706 cents<br />
| | Many Western listeners might describe 12/11 as sounding "exotic". |
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| <br />
| | == Approximation == |
| 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 <a class="wiki_link" href="/superparticular">superparticular</a> ratio 12/11, and is about 150.6 <a class="wiki_link" href="/cent">cents</a> large. One step of <a class="wiki_link" href="/8edo">8edo</a> 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&gt;. It follows that EDOs which are multiples of 8, such as <a class="wiki_link" href="/16edo">16edo</a> and <a class="wiki_link" href="/24edo">24edo</a>, will also represent this interval well.<br />
| | 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. |
| <br />
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| 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 <a class="wiki_link" href="/15edo">15edo</a>, <a class="wiki_link" href="/22edo">22edo</a>, <a class="wiki_link" href="/31edo">31edo</a>, <a class="wiki_link" href="/orwell">orwell</a>, <a class="wiki_link" href="/porcupine">porcupine</a>, <a class="wiki_link" href="/mohajira">mohajira</a> and <a class="wiki_link" href="/valentine">valentine</a>.</body></html></pre></div> | | {{Interval edo approximation|12/11}} |
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| | == 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]] |
12/11, conventionally the (lesser) undecimal 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.
In Alpharabian tuning it is known as the Alpharabian tendoneutral second, which contrasts 88/81, the other undecimal neutral second.
The name lesser undecimal neutral second is said as opposed to 11/10, the larger undecimal neutral second or undecimal submajor second (~165 cents), from which it differs by 121/120 (~14.4 cents). Temperaments which conflate the two (thus tempering out 121/120) include orwell, porcupine, mohajira, valentine, and their supporting edos: 15edo, 22edo, 31edo, etc.
Many Western listeners might describe 12/11 as sounding "exotic".
Approximation
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.
Edo approximations for 12/11 (150.64 ¢)
≤ 80edo, relative error ≤ 10%
| Edo |
Step size |
Cents (¢) |
Absolute error (¢) |
Relative error (%)
|
| 8 |
1\8 |
150.00 |
-0.64 |
-0.42
|
| 16 |
2\16 |
150.00 |
-0.64 |
-0.85
|
| 24 |
3\24 |
150.00 |
-0.64 |
-1.27
|
| 32 |
4\32 |
150.00 |
-0.64 |
-1.70
|
| 40 |
5\40 |
150.00 |
-0.64 |
-2.12
|
| 48 |
6\48 |
150.00 |
-0.64 |
-2.55
|
| 55 |
7\55 |
152.73 |
+2.09 |
+9.58
|
| 56 |
7\56 |
150.00 |
-0.64 |
-2.97
|
| 63 |
8\63 |
152.38 |
+1.74 |
+9.16
|
| 64 |
8\64 |
150.00 |
-0.64 |
-3.40
|
| 71 |
9\71 |
152.11 |
+1.48 |
+8.73
|
| 72 |
9\72 |
150.00 |
-0.64 |
-3.82
|
| 79 |
10\79 |
151.90 |
+1.26 |
+8.31
|
| 80 |
10\80 |
150.00 |
-0.64 |
-4.25
|
See also
