32/21: Difference between revisions

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**Imported revision 513277558 - Original comment: **
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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 superfifth, wide fifth, octave-reduced 21st subharmonic
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-08 21:14:04 UTC</tt>.<br>
| Color name = r5, ru 5th
: The original revision id was <tt>513277558</tt>.<br>
| Sound = jid_32_21_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>
<h4>Original Wikitext content:</h4>
<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">**32/21**
|5 -1 0 -1&gt;
729.2191 cents
[[media type="file" key="jid_32_21_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_32_21_pluck_adu_dr220.mp3|sound sample]]


32/21, the septimal super-fifth, is the interval between [[9_8|9/8]] and [[12_7|12/7]]. It is [[64_63|64/63]] sharp of [[3_2|3/2]], and so is equated to 3/2 in temperaments such as [[pajara]], [[superpyth]] or [[augene]] which temper 64/63 out.</pre></div>
'''32/21''', the '''septimal superfifth''', is the interval between [[9/8]] and [[12/7]]. It is [[64/63]] sharp of [[3/2]], and so is equated to 3/2 in temperaments such as [[pajara]], [[superpyth]] or [[augene]] which tempers out 64/63.  
<h4>Original HTML content:</h4>
 
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;32_21&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;32/21&lt;/strong&gt;&lt;br /&gt;
In [[septimal meantone]], this interval is represented by the diminished sixth.  
|5 -1 0 -1&amp;gt;&lt;br /&gt;
== Approximation ==
729.2191 cents&lt;br /&gt;
{{Interval edo approximation|32/21}}
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== See also ==
&lt;br /&gt;
* [[Gallery of just intervals]]
32/21, the septimal super-fifth, is the interval between &lt;a class="wiki_link" href="/9_8"&gt;9/8&lt;/a&gt; and &lt;a class="wiki_link" href="/12_7"&gt;12/7&lt;/a&gt;. It is &lt;a class="wiki_link" href="/64_63"&gt;64/63&lt;/a&gt; sharp of &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt;, and so is equated to 3/2 in temperaments such as &lt;a class="wiki_link" href="/pajara"&gt;pajara&lt;/a&gt;, &lt;a class="wiki_link" href="/superpyth"&gt;superpyth&lt;/a&gt; or &lt;a class="wiki_link" href="/augene"&gt;augene&lt;/a&gt; which temper 64/63 out.&lt;/body&gt;&lt;/html&gt;</pre></div>
* [[21/16]], its [[inverse interval]]
 
[[Category:Fifth]]
[[Category:Superfifth]]

Latest revision as of 13:04, 3 November 2025

Interval information
Ratio 32/21
Factorization 25 × 3-1 × 7-1
Monzo [5 -1 0 -1
Size in cents 729.2191¢
Names septimal superfifth,
wide fifth,
octave-reduced 21st subharmonic
Color name r5, ru 5th
FJS name [math]\displaystyle{ \text{P5}_{7} }[/math]
Special properties reduced,
reduced subharmonic
Tenney norm (log2 nd) 9.39232
Weil norm (log2 max(n, d)) 10
Wilson norm (sopfr(nd)) 20

[sound info]
Open this interval in xen-calc

32/21, the septimal superfifth, is the interval between 9/8 and 12/7. It is 64/63 sharp of 3/2, and so is equated to 3/2 in temperaments such as pajara, superpyth or augene which tempers out 64/63.

In septimal meantone, this interval is represented by the diminished sixth.

Approximation

Edo approximations for 32/21 (729.22 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
5 3\5 720.00 -9.22 -3.84
10 6\10 720.00 -9.22 -7.68
18 11\18 733.33 +4.11 +6.17
23 14\23 730.43 +1.22 +2.33
28 17\28 728.57 -0.65 -1.51
33 20\33 727.27 -1.95 -5.35
38 23\38 726.32 -2.90 -9.19
41 25\41 731.71 +2.49 +8.50
46 28\46 730.43 +1.22 +4.66
51 31\51 729.41 +0.19 +0.82
56 34\56 728.57 -0.65 -3.02
61 37\61 727.87 -1.35 -6.86
69 42\69 730.43 +1.22 +6.99
74 45\74 729.73 +0.51 +3.15
79 48\79 729.11 -0.11 -0.69

See also