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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 = diatismic minor seventh |
| : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-08 21:23:45 UTC</tt>.<br>
| | | Color name = 17uy6, suyo 6th |
| : The original revision id was <tt>513278288</tt>.<br>
| | | Sound = jid_30_17_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>
| | In [[17-limit]] [[just intonation]], '''30/17''' is the '''diatismic minor seventh''', measuring about 983.3{{cent}}. It falls short of the [[16/9|Pythagorean minor seventh (16/9)]] by a [[136/135|diatisma (136/135)]], hence the name. It is the [[mediant]] of [[7/4]] and [[23/13]]. Its inversion is [[17/15]], the "septendecimal whole tone"; both of these intervals are well approximated in [[22edo]] (18\22, 4\22). |
| <h4>Original Wikitext content:</h4>
| | == Approximation == |
| <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">**30/17**
| | {{Interval edo approximation|30/17}} |
| |1 1 1 0 0 0 -1>
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| 983.3133 cents
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| [[media type="file" key="jid_30_17_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_30_17_pluck_adu_dr220.mp3|sound sample]]
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| In [[17-limit]] [[Just Intonation]], 30/17 is the "septendecimal minor seventh," measuring about 983.3¢. It is the [[mediant]] between [[7_4|7/4]] and [[23_13|23/13]]. Its inversion is [[17_15|17/15]], the "septendecimal whole tone" -- both of these intervals are well-approximated in [[22edo]].
| | == See also == |
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| See: [[Gallery of Just Intervals]]</pre></div>
| | * [[17/15]] its [[octave complement]] |
| <h4>Original HTML content:</h4>
| | * [[Gallery of just intervals]] |
| <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>30_17</title></head><body><strong>30/17</strong><br />
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| |1 1 1 0 0 0 -1&gt;<br />
| | [[Category:Seventh]] |
| 983.3133 cents<br />
| | [[Category:Minor seventh]] |
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| | [[Category:Diatismic]] |
| <br />
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| In <a class="wiki_link" href="/17-limit">17-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 30/17 is the &quot;septendecimal minor seventh,&quot; measuring about 983.3¢. It is the <a class="wiki_link" href="/mediant">mediant</a> between <a class="wiki_link" href="/7_4">7/4</a> and <a class="wiki_link" href="/23_13">23/13</a>. Its inversion is <a class="wiki_link" href="/17_15">17/15</a>, the &quot;septendecimal whole tone&quot; -- both of these intervals are well-approximated in <a class="wiki_link" href="/22edo">22edo</a>.<br />
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| <br />
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| See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div>
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In 17-limit just intonation, 30/17 is the diatismic minor seventh, measuring about 983.3 ¢. It falls short of the Pythagorean minor seventh (16/9) by a diatisma (136/135), hence the name. It is the mediant of 7/4 and 23/13. Its inversion is 17/15, the "septendecimal whole tone"; both of these intervals are well approximated in 22edo (18\22, 4\22).
Approximation
Edo approximations for 30/17 (983.31 ¢)
≤ 80edo, relative error ≤ 10%
| Edo |
Step size |
Cents (¢) |
Absolute error (¢) |
Relative error (%)
|
| 5 |
4\5 |
960.00 |
-23.31 |
-9.71
|
| 6 |
5\6 |
1000.00 |
+16.69 |
+8.34
|
| 11 |
9\11 |
981.82 |
-1.50 |
-1.37
|
| 17 |
14\17 |
988.24 |
+4.92 |
+6.97
|
| 22 |
18\22 |
981.82 |
-1.50 |
-2.74
|
| 28 |
23\28 |
985.71 |
+2.40 |
+5.60
|
| 33 |
27\33 |
981.82 |
-1.50 |
-4.11
|
| 39 |
32\39 |
984.62 |
+1.30 |
+4.23
|
| 44 |
36\44 |
981.82 |
-1.50 |
-5.48
|
| 50 |
41\50 |
984.00 |
+0.69 |
+2.86
|
| 55 |
45\55 |
981.82 |
-1.50 |
-6.85
|
| 61 |
50\61 |
983.61 |
+0.29 |
+1.49
|
| 66 |
54\66 |
981.82 |
-1.50 |
-8.22
|
| 67 |
55\67 |
985.07 |
+1.76 |
+9.83
|
| 72 |
59\72 |
983.33 |
+0.02 |
+0.12
|
| 77 |
63\77 |
981.82 |
-1.50 |
-9.59
|
| 78 |
64\78 |
984.62 |
+1.30 |
+8.46
|
See also