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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 major sixth, classic(al) major sixth, ptolemaic major sixth |
| : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-07 11:46:39 UTC</tt>.<br>
| | | Color name = y6, yo 6th |
| : The original revision id was <tt>513182402</tt>.<br>
| | | Sound = jid_5_3_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|Major sixth}} |
| <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">**5/3**
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| |0 -1 1> | |
| 884.35871 cents
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| [[media type="file" key="jid_5_3_pluck_adu_dr220.mp3"]]
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| In [[5-limit]] [[Just Intonation]], 5/3 is a major sixth of about 884.4¢. It represents the difference between the 5th and 3rd overtones of the [[OverToneSeries|harmonic series]], and appears in just chords such as 3:4:5 (a 2nd inversion major triad). Its inversion is [[6_5|6/5]], the 5-limit minor third. It differs from the Pythagorean major sixth of [[27_16|27/16]] (about 905.9¢) by the syntonic comma of [[81_80|81/80]] (about 21.5¢). This means that in systems which temper out the syntonic comma, such as [[12edo]] and [[meantone]] systems, 5/3 and 27/16 are conflated. | | In [[5-limit]] [[just intonation]], '''5/3''' is the '''just major sixth''', '''classic(al) major sixth''', or '''ptolemaic major sixth'''<ref>For reference, see [[5-limit]]. </ref> of about 884.4¢. It represents the difference between the 5th and 3rd [[harmonic]]s, and appears in just chords such as 3:4:5 (a 2nd inversion major triad). Its inversion is [[6/5]], the 5-limit minor third. It differs from the Pythagorean major sixth of [[27/16]] (about 905.9¢) by the syntonic comma of [[81/80]] (about 21.5¢). This means that in systems which temper out the syntonic comma, such as [[12edo]] and [[meantone]] systems, 5/3 and [[27/16]] are conflated. |
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| 5/3 has a more mellow sound than 27/16, owing to its relative smallness. | | 5/3 has a more mellow sound than 27/16, owing to its simpler beating pattern as well as its smaller size. |
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| See: [[Gallery of Just Intervals]]</pre></div>
| | == Approximation == |
| <h4>Original HTML content:</h4>
| | 5/3 is very accurately approximated by [[19edo]] (14\19), and hence the [[enneadecal]] temperament. |
| <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>5_3</title></head><body><strong>5/3</strong><br />
| | {{Interval edo approximation|5/3}} |
| |0 -1 1&gt;<br /> | | |
| 884.35871 cents<br />
| | == See also == |
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| | * [[6/5]] – its [[octave complement]] |
| <br />
| | * [[9/5]] – its [[twelfth complement]] |
| In <a class="wiki_link" href="/5-limit">5-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 5/3 is a major sixth of about 884.4¢. It represents the difference between the 5th and 3rd overtones of the <a class="wiki_link" href="/OverToneSeries">harmonic series</a>, and appears in just chords such as 3:4:5 (a 2nd inversion major triad). Its inversion is <a class="wiki_link" href="/6_5">6/5</a>, the 5-limit minor third. It differs from the Pythagorean major sixth of <a class="wiki_link" href="/27_16">27/16</a> (about 905.9¢) by the syntonic comma of <a class="wiki_link" href="/81_80">81/80</a> (about 21.5¢). This means that in systems which temper out the syntonic comma, such as <a class="wiki_link" href="/12edo">12edo</a> and <a class="wiki_link" href="/meantone">meantone</a> systems, 5/3 and 27/16 are conflated.<br />
| | * [[Ed5/3]] |
| <br />
| | * [[Gallery of just intervals]] |
| 5/3 has a more mellow sound than 27/16, owing to its relative smallness.<br />
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| <br />
| | == Notes == |
| See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div>
| | <references/> |
| | |
| | [[Category:Sixth]] |
| | [[Category:Major sixth]] |
| | [[Category:Over-3 intervals]] |
| | [[Category:Tritave-reduced harmonics]] |
| | [[Category:Taxicab-2 intervals]] |
In 5-limit just intonation, 5/3 is the just major sixth, classic(al) major sixth, or ptolemaic major sixth[1] of about 884.4¢. It represents the difference between the 5th and 3rd harmonics, and appears in just chords such as 3:4:5 (a 2nd inversion major triad). Its inversion is 6/5, the 5-limit minor third. It differs from the Pythagorean major sixth of 27/16 (about 905.9¢) by the syntonic comma of 81/80 (about 21.5¢). This means that in systems which temper out the syntonic comma, such as 12edo and meantone systems, 5/3 and 27/16 are conflated.
5/3 has a more mellow sound than 27/16, owing to its simpler beating pattern as well as its smaller size.
Approximation
5/3 is very accurately approximated by 19edo (14\19), and hence the enneadecal temperament.
Edo approximations for 5/3 (884.36 ¢)
≤ 80edo, relative error ≤ 10%
| Edo |
Step size |
Cents (¢) |
Absolute error (¢) |
Relative error (%)
|
| 4 |
3\4 |
900.00 |
+15.64 |
+5.21
|
| 15 |
11\15 |
880.00 |
-4.36 |
-5.45
|
| 19 |
14\19 |
884.21 |
-0.15 |
-0.23
|
| 23 |
17\23 |
886.96 |
+2.60 |
+4.98
|
| 34 |
25\34 |
882.35 |
-2.01 |
-5.68
|
| 38 |
28\38 |
884.21 |
-0.15 |
-0.47
|
| 42 |
31\42 |
885.71 |
+1.36 |
+4.74
|
| 46 |
34\46 |
886.96 |
+2.60 |
+9.96
|
| 53 |
39\53 |
883.02 |
-1.34 |
-5.92
|
| 57 |
42\57 |
884.21 |
-0.15 |
-0.70
|
| 61 |
45\61 |
885.25 |
+0.89 |
+4.51
|
| 65 |
48\65 |
886.15 |
+1.80 |
+9.72
|
| 72 |
53\72 |
883.33 |
-1.03 |
-6.15
|
| 76 |
56\76 |
884.21 |
-0.15 |
-0.94
|
| 80 |
59\80 |
885.00 |
+0.64 |
+4.28
|
See also
Notes
