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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 = just minor third, classic(al) minor third, ptolemaic minor third |
| : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-07 11:54:39 UTC</tt>.<br>
| | | Color name = g3, gu 3rd |
| : The original revision id was <tt>513182808</tt>.<br>
| | | Sound = jid_6_5_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|Minor third}} |
| <h4>Original Wikitext content:</h4>
| | In [[5-limit]] [[just intonation]], '''6/5''' is the '''just minor third''', '''classic(al) minor third''', or '''ptolemaic minor third'''<ref>For reference, see [[5-limit]]. </ref>, measuring about 315.6[[cent|¢]]. It is sharp of the [[Pythagorean]] minor third of [[32/27]] (about 294.1¢) as well as the 300¢ minor third of [[4edo]], [[12edo]] and all other 4n-[[EDO|edos]]. It arises in the [[harmonic series]] between the 5th and 6th harmonics and appears in the [[5-limit]] otonal triad of 4:5:6. A 5-limit minor triad in just intonation can be written 10:12:15, with 6/5 falling between 10 and 12, [[5/4]] falling between 12 and 15, and [[3/2]] falling between 10 and 15. |
| <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">**6/5**
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| |1 1 -1>
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| 315.64129 cents
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| [[media type="file" key="jid_6_5_pluck_adu_dr220.mp3"]] | |
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| In [[5-limit]] [[Just Intonation]], **6/5** is the classic minor third, measuring about 315.6[[Cent|¢]]. It is sharp of the [[Pythagorean]] minor third of [[32_27|32/27]] (about 294.1¢) as well as the 300¢ minor third of [[4edo]], [[12edo]] and all other 4n-[[edo]]s. It arises in the [[OverToneSeries|harmonic series]] between the 5th and 6th overtones and appears in the [[5-limit]] otonal triad of 4:5:6. A 5-limit minor triad in just intonation can be written 10:12:15, with 6/5 falling between 10 and 12, [[5_4|5/4]] falling between 12 and 15, and [[3_2|3/2]] falling between 10 and 15. | | In higher-limit JI, 6/5 is only one of many minor thirds. A popular one in the [[7-limit]] is [[7/6]] (about 266.9¢), the septimal subminor third, which is [[36/35]] (about 48.8¢) flat of 6/5. Another in the [[13-limit]] is [[13/11]] (about 289.2¢), which is [[66/65]] (about 26.4¢) flat of 6/5. Both of these are more complex intervals than 6/5 and have their own character to them. |
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| In higher-limit JI, 6/5 is only one of many minor thirds. A popular one in the [[7-limit]] is [[7_6|7/6]] (about 266.9¢), the septimal subminor third, which is [[36_35|36/35]] (about 48.8¢) flat of 6/5. Another in the [[13-limit]] is [[13_11|13/11]] (about 289.2¢), which is [[66_65|66/65]] (about 26.4¢) flat of 6/5. Both of these are more complex intervals than 6/5 and have their own character to them.
| | == Approximation == |
| | 6/5 is very accurately approximated by [[19edo]] (5\19), and hence the [[enneadecal]] temperament. |
| | {{Interval edo approximation}} |
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| See: [[Gallery of Just Intervals]], [[List of root-3rd-P5 triads in JI]]</pre></div> | | == See also == |
| <h4>Original HTML content:</h4>
| | * [[5/3]] – its [[octave 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"><html><head><title>6_5</title></head><body><strong>6/5</strong><br />
| | * [[5/4]] – its [[fifth complement]] |
| |1 1 -1&gt;<br />
| | * [[10/9]] – its [[fourth complement]] |
| 315.64129 cents<br />
| | * [[Gallery of just intervals]] |
| <!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_6_5_pluck_adu_dr220.mp3?h=20&amp;w=240&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;jid_6_5_pluck_adu_dr220.mp3&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;20&quot; width=&quot;240&quot;/&gt; --><embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="240" height="20" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252Fjid_6_5_pluck_adu_dr220.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=240&height=20"></embed><!-- ws:end:WikiTextMediaRule:0 --><br />
| | * [[List of superparticular intervals]] |
| <br />
| | * [[:File:Ji-6-5-csound-foscil-220hz.mp3]] – another sound example |
| In <a class="wiki_link" href="/5-limit">5-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, <strong>6/5</strong> is the classic minor third, measuring about 315.6<a class="wiki_link" href="/Cent">¢</a>. It is sharp of the <a class="wiki_link" href="/Pythagorean">Pythagorean</a> minor third of <a class="wiki_link" href="/32_27">32/27</a> (about 294.1¢) as well as the 300¢ minor third of <a class="wiki_link" href="/4edo">4edo</a>, <a class="wiki_link" href="/12edo">12edo</a> and all other 4n-<a class="wiki_link" href="/edo">edo</a>s. It arises in the <a class="wiki_link" href="/OverToneSeries">harmonic series</a> between the 5th and 6th overtones and appears in the <a class="wiki_link" href="/5-limit">5-limit</a> otonal triad of 4:5:6. A 5-limit minor triad in just intonation can be written 10:12:15, with 6/5 falling between 10 and 12, <a class="wiki_link" href="/5_4">5/4</a> falling between 12 and 15, and <a class="wiki_link" href="/3_2">3/2</a> falling between 10 and 15.<br />
| | |
| <br />
| | == Notes == |
| In higher-limit JI, 6/5 is only one of many minor thirds. A popular one in the <a class="wiki_link" href="/7-limit">7-limit</a> is <a class="wiki_link" href="/7_6">7/6</a> (about 266.9¢), the septimal subminor third, which is <a class="wiki_link" href="/36_35">36/35</a> (about 48.8¢) flat of 6/5. Another in the <a class="wiki_link" href="/13-limit">13-limit</a> is <a class="wiki_link" href="/13_11">13/11</a> (about 289.2¢), which is <a class="wiki_link" href="/66_65">66/65</a> (about 26.4¢) flat of 6/5. Both of these are more complex intervals than 6/5 and have their own character to them.<br />
| | <references/> |
| <br />
| | |
| See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a>, <a class="wiki_link" href="/List%20of%20root-3rd-P5%20triads%20in%20JI">List of root-3rd-P5 triads in JI</a></body></html></pre></div>
| | [[Category:Third]] |
| | [[Category:Minor third]] |
| | [[Category:Over-5 intervals]] |
In 5-limit just intonation, 6/5 is the just minor third, classic(al) minor third, or ptolemaic minor third[1], measuring about 315.6¢. It is sharp of the Pythagorean minor third of 32/27 (about 294.1¢) as well as the 300¢ minor third of 4edo, 12edo and all other 4n-edos. It arises in the harmonic series between the 5th and 6th harmonics and appears in the 5-limit otonal triad of 4:5:6. A 5-limit minor triad in just intonation can be written 10:12:15, with 6/5 falling between 10 and 12, 5/4 falling between 12 and 15, and 3/2 falling between 10 and 15.
In higher-limit JI, 6/5 is only one of many minor thirds. A popular one in the 7-limit is 7/6 (about 266.9¢), the septimal subminor third, which is 36/35 (about 48.8¢) flat of 6/5. Another in the 13-limit is 13/11 (about 289.2¢), which is 66/65 (about 26.4¢) flat of 6/5. Both of these are more complex intervals than 6/5 and have their own character to them.
Approximation
6/5 is very accurately approximated by 19edo (5\19), and hence the enneadecal temperament.
Edo approximations for 6/5 (315.64 ¢)
≤ 80edo, relative error ≤ 10%
| Edo |
Step size |
Cents (¢) |
Absolute error (¢) |
Relative error (%)
|
| 4 |
1\4 |
300.00 |
-15.64 |
-5.21
|
| 15 |
4\15 |
320.00 |
+4.36 |
+5.45
|
| 19 |
5\19 |
315.79 |
+0.15 |
+0.23
|
| 23 |
6\23 |
313.04 |
-2.60 |
-4.98
|
| 34 |
9\34 |
317.65 |
+2.01 |
+5.68
|
| 38 |
10\38 |
315.79 |
+0.15 |
+0.47
|
| 42 |
11\42 |
314.29 |
-1.36 |
-4.74
|
| 46 |
12\46 |
313.04 |
-2.60 |
-9.96
|
| 53 |
14\53 |
316.98 |
+1.34 |
+5.92
|
| 57 |
15\57 |
315.79 |
+0.15 |
+0.70
|
| 61 |
16\61 |
314.75 |
-0.89 |
-4.51
|
| 65 |
17\65 |
313.85 |
-1.80 |
-9.72
|
| 72 |
19\72 |
316.67 |
+1.03 |
+6.15
|
| 76 |
20\76 |
315.79 |
+0.15 |
+0.94
|
| 80 |
21\80 |
315.00 |
-0.64 |
-4.28
|
See also
Notes
