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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 = septimal whole tone, supermajor second, septimal major second, septimal supermajor second |
| : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2014-06-14 05:39:04 UTC</tt>.<br>
| | | Color name = r2, ru 2nd |
| : The original revision id was <tt>513928358</tt>.<br>
| | | Sound = jid_8_7_pluck_adu_dr220.mp3 |
| : The revision comment was: <tt>corrected cent value</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|Septimal whole tone}} |
| <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">**8/7**
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| |3 0 0 -1> | |
| 231,17409 cents
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| [[media type="file" key="jid_8_7_pluck_adu_dr220.mp3" width="240" height="20"]] [[file:xenharmonic/jid_8_7_pluck_adu_dr220.mp3|sound sample]]
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| In [[Just Intonation]], 8/7 is the "septimal supermajor second" of approximately 231.2¢. Although it falls between the familiar major second and minor third of [[12edo]], it generally sounds more like a wide second than a narrow third. It can be found between the 7th and 8th overtones in the harmonic series and is thus a [[superparticular]] ratio. In [[7-limit]] JI and higher, it is treated as a consonance, particularly in the context of a chord such as 4:5:6:7:8, where it appears between the harmonic seventh ([[7_4|7/4]]) and octave. It differs from the Pythagorean major third of [[9_8|9/8]] by [[64_63|64/63]], a microtone of about 27.3¢. | | In [[just intonation]], 8/7 is the '''septimal major second''', or '''septimal supermajor second''', of approximately 231.2{{cent}}. Although it falls between the familiar major second and minor third of [[12edo]], most people think of it more like a wide second than a narrow third. It can be found between the 7th and 8th [[harmonic]]s and is thus a [[superparticular]] ratio. In [[7-limit]] JI and higher, it is treated as a consonance, particularly in the context of a chord such as 4:5:6:7:8, where it appears between the harmonic seventh ([[7/4]]) and octave. It differs from the Pythagorean major second of [[9/8]] by [[64/63]], a microtone of about 27.3{{cent}}. It is close in size to 5edo's 240{{c}} step. |
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| See the Wikipedia article for [[http://en.wikipedia.org/wiki/Septimal_whole_tone|Septimal whole tone]].
| | A stack of three supermajor seconds is close to a perfect fifth ([[3/2]]). The difference is [[1029/1024]] (about 8.4{{c}}), which is tempered out in [[slendric]] systems like [[31edo]]. |
| See also: [[Gallery of Just Intervals]]</pre></div>
| | == Approximation == |
| <h4>Original HTML content:</h4>
| | {{Interval edo approximation|8/7}} |
| <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>8_7</title></head><body><strong>8/7</strong><br />
| | == See also == |
| |3 0 0 -1&gt;<br />
| | * [[7/4]] – its [[octave complement]] |
| 231,17409 cents<br />
| | * [[21/16]] – its [[fifth complement]] |
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| | * [[7/6]] – its [[fourth complement]] |
| <br />
| | * [[Gallery of just intervals]] |
| In <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 8/7 is the &quot;septimal supermajor second&quot; of approximately 231.2¢. Although it falls between the familiar major second and minor third of <a class="wiki_link" href="/12edo">12edo</a>, it generally sounds more like a wide second than a narrow third. It can be found between the 7th and 8th overtones in the harmonic series and is thus a <a class="wiki_link" href="/superparticular">superparticular</a> ratio. In <a class="wiki_link" href="/7-limit">7-limit</a> JI and higher, it is treated as a consonance, particularly in the context of a chord such as 4:5:6:7:8, where it appears between the harmonic seventh (<a class="wiki_link" href="/7_4">7/4</a>) and octave. It differs from the Pythagorean major third of <a class="wiki_link" href="/9_8">9/8</a> by <a class="wiki_link" href="/64_63">64/63</a>, a microtone of about 27.3¢.<br />
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| <br />
| | [[Category:Second]] |
| See the Wikipedia article for <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_whole_tone" rel="nofollow">Septimal whole tone</a>.<br />
| | [[Category:Supermajor second]] |
| See also: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div>
| | [[Category:Over-7 intervals]] |
In just intonation, 8/7 is the septimal major second, or septimal supermajor second, of approximately 231.2 ¢. Although it falls between the familiar major second and minor third of 12edo, most people think of it more like a wide second than a narrow third. It can be found between the 7th and 8th harmonics and is thus a superparticular ratio. In 7-limit JI and higher, it is treated as a consonance, particularly in the context of a chord such as 4:5:6:7:8, where it appears between the harmonic seventh (7/4) and octave. It differs from the Pythagorean major second of 9/8 by 64/63, a microtone of about 27.3 ¢. It is close in size to 5edo's 240 ¢ step.
A stack of three supermajor seconds is close to a perfect fifth (3/2). The difference is 1029/1024 (about 8.4 ¢), which is tempered out in slendric systems like 31edo.
Approximation
Edo approximations for 8/7 (231.17 ¢)
≤ 80edo, relative error ≤ 10%
| Edo |
Step size |
Cents (¢) |
Absolute error (¢) |
Relative error (%)
|
| 5 |
1\5 |
240.00 |
+8.83 |
+3.68
|
| 10 |
2\10 |
240.00 |
+8.83 |
+7.35
|
| 16 |
3\16 |
225.00 |
-6.17 |
-8.23
|
| 21 |
4\21 |
228.57 |
-2.60 |
-4.55
|
| 26 |
5\26 |
230.77 |
-0.40 |
-0.88
|
| 31 |
6\31 |
232.26 |
+1.08 |
+2.80
|
| 36 |
7\36 |
233.33 |
+2.16 |
+6.48
|
| 42 |
8\42 |
228.57 |
-2.60 |
-9.11
|
| 47 |
9\47 |
229.79 |
-1.39 |
-5.43
|
| 52 |
10\52 |
230.77 |
-0.40 |
-1.75
|
| 57 |
11\57 |
231.58 |
+0.40 |
+1.92
|
| 62 |
12\62 |
232.26 |
+1.08 |
+5.60
|
| 67 |
13\67 |
232.84 |
+1.66 |
+9.28
|
| 68 |
13\68 |
229.41 |
-1.76 |
-9.99
|
| 73 |
14\73 |
230.14 |
-1.04 |
-6.31
|
| 78 |
15\78 |
230.77 |
-0.40 |
-2.63
|
See also
