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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 = septendecimal superfifth |
| : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-12-07 02:13:59 UTC</tt>.<br>
| | | Color name = 17u3o5, sutho 5th |
| : The original revision id was <tt>283163862</tt>.<br>
| | | Sound = jid_26_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>
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| <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">In [[17-limit]] [[Just Intonation]], 26/17 is the "septendecimal super-fifth," measuring about 735.572¢. It differs from a [[3_2|3/2]] perfect fifth by the [[comma]] 52/51, about 33.617¢. Although this difference is considerable, 26/17 may be used as a wide perfect fifth, thus allowing septendecimal versions of [[List of root-3rd-P5 triads in JI|root-3rd-P5]] chords -- in particular, 17:20:26, 17:21:26, 17:22:26.
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| 26/17 is the [[mediant]] between 3/2 and 23/15. Its inversion is [[17_13|17/13]], the "septendecimal sub-fourth". | | In [[17-limit]] [[just intonation]], '''26/17''' is the '''septendecimal superfifth'''. It differs from the [[3/2]] perfect fifth by the [[comma]] [[52/51]], about 33.6¢. Although this difference is considerable, 26/17 may be used as a wide perfect fifth, thus allowing septendecimal versions of [[List of root-3rd-P5 triads in JI|root-3rd-P5]] chords – in particular, 17:20:26, 17:21:26, 17:22:26. |
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| See: [[Gallery of Just Intervals]]</pre></div>
| | 26/17 is the [[mediant]] of 3/2 and [[23/15]]. |
| <h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>26_17</title></head><body>In <a class="wiki_link" href="/17-limit">17-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 26/17 is the &quot;septendecimal super-fifth,&quot; measuring about 735.572¢. It differs from a <a class="wiki_link" href="/3_2">3/2</a> perfect fifth by the <a class="wiki_link" href="/comma">comma</a> 52/51, about 33.617¢. Although this difference is considerable, 26/17 may be used as a wide perfect fifth, thus allowing septendecimal versions of <a class="wiki_link" href="/List%20of%20root-3rd-P5%20triads%20in%20JI">root-3rd-P5</a> chords -- in particular, 17:20:26, 17:21:26, 17:22:26.<br />
| | It is less than 0.2 cents sharp of [[31edo]]'s superfifth of 735.48¢ (19\31). |
| <br />
| | == Approximation == |
| 26/17 is the <a class="wiki_link" href="/mediant">mediant</a> between 3/2 and 23/15. Its inversion is <a class="wiki_link" href="/17_13">17/13</a>, the &quot;septendecimal sub-fourth&quot;.<br />
| | {{Interval edo approximation|26/17}} |
| <br />
| | == See also == |
| See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div>
| | * [[17/13]] – its [[octave complement]] |
| | * [[Gallery of just intervals]] |
| | |
| | [[Category:Fifth]] |
| | [[Category:Superfifth]] |
| | [[Category:Interseptimal intervals]] |
In 17-limit just intonation, 26/17 is the septendecimal superfifth. It differs from the 3/2 perfect fifth by the comma 52/51, about 33.6¢. Although this difference is considerable, 26/17 may be used as a wide perfect fifth, thus allowing septendecimal versions of root-3rd-P5 chords – in particular, 17:20:26, 17:21:26, 17:22:26.
26/17 is the mediant of 3/2 and 23/15.
It is less than 0.2 cents sharp of 31edo's superfifth of 735.48¢ (19\31).
Approximation
Edo approximations for 26/17 (735.57 ¢)
≤ 80edo, relative error ≤ 10%
| Edo |
Step size |
Cents (¢) |
Absolute error (¢) |
Relative error (%)
|
| 5 |
3\5 |
720.00 |
-15.57 |
-6.49
|
| 8 |
5\8 |
750.00 |
+14.43 |
+9.62
|
| 13 |
8\13 |
738.46 |
+2.89 |
+3.13
|
| 18 |
11\18 |
733.33 |
-2.24 |
-3.36
|
| 23 |
14\23 |
730.43 |
-5.14 |
-9.85
|
| 26 |
16\26 |
738.46 |
+2.89 |
+6.26
|
| 31 |
19\31 |
735.48 |
-0.09 |
-0.23
|
| 36 |
22\36 |
733.33 |
-2.24 |
-6.72
|
| 39 |
24\39 |
738.46 |
+2.89 |
+9.39
|
| 44 |
27\44 |
736.36 |
+0.79 |
+2.90
|
| 49 |
30\49 |
734.69 |
-0.88 |
-3.59
|
| 57 |
35\57 |
736.84 |
+1.27 |
+6.03
|
| 62 |
38\62 |
735.48 |
-0.09 |
-0.46
|
| 67 |
41\67 |
734.33 |
-1.24 |
-6.95
|
| 70 |
43\70 |
737.14 |
+1.57 |
+9.16
|
| 75 |
46\75 |
736.00 |
+0.43 |
+2.67
|
| 80 |
49\80 |
735.00 |
-0.57 |
-3.82
|
See also