78/71: Difference between revisions

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**Imported revision 513253542 - Original comment: **
m Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"
 
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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 = porcupine neutral second
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-08 15:05:19 UTC</tt>.<br>
| Color name = 71u3o2, <br>fitwewutho 2nd/seventy-wutho 2nd
: The original revision id was <tt>513253542</tt>.<br>
| Sound = jid_78_71_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">**78/71**
= 2 * 3 * 13 * 71&lt;span style="font-size: 80%; vertical-align: super;"&gt;-1&lt;/span&gt;
162.7861 cents
[[media type="file" key="jid_78_71_pluck_adu_dr220.mp3" width="240" height="20"]] [[file:xenharmonic/jid_78_71_pluck_adu_dr220.mp3|sound sample]]


The porcupine neutral second, 78/71, provides a good generator for [[Porcupine family#Porcupine|porcupine temperament]]. It is between 3\[[22edo|22]] and 8\[[59edo|59]], and leads to a fifth of 711.642 cents, which is 9.687 cents sharp of [[3_2|3/2]].</pre></div>
The '''porcupine neutral second''', '''78/71''' = 2 ⋅ 3 ⋅ 13 ⋅ 71<sup>−1</sup>, provides a good generator for [[Porcupine_family#Porcupine|porcupine temperament]]. It is between 3\[[22edo|22]] and 8\[[59edo|59]], and leads to a fifth of 711.642 cents, which is 9.687 cents sharp of [[3/2]].
<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;78_71&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;78/71&lt;/strong&gt;&lt;br /&gt;
[[Category:Second]]
= 2 * 3 * 13 * 71&lt;span style="font-size: 80%; vertical-align: super;"&gt;-1&lt;/span&gt;&lt;br /&gt;
[[Category:Neutral second]]
162.7861 cents&lt;br /&gt;
[[Category:Porcupine]]
&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_78_71_pluck_adu_dr220.mp3?h=20&amp;amp;w=240&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;jid_78_71_pluck_adu_dr220.mp3&amp;amp;quot; width=&amp;amp;quot;240&amp;amp;quot; height=&amp;amp;quot;20&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;20&amp;quot; width=&amp;quot;240&amp;quot;/&amp;gt; --&gt;&lt;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_78_71_pluck_adu_dr220.mp3?file_extension=mp3&amp;autostart=false&amp;repeat=false&amp;showdigits=true&amp;showfsbutton=false&amp;width=240&amp;height=20"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt; &lt;a href="http://xenharmonic.wikispaces.com/file/view/jid_78_71_pluck_adu_dr220.mp3/513250454/jid_78_71_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_78_71_pluck_adu_dr220.mp3/513250454/jid_78_71_pluck_adu_dr220.mp3');"&gt;sound sample&lt;/a&gt;&lt;br /&gt;
== Approximation ==
&lt;br /&gt;
{{Interval edo approximation|78/71}}
The porcupine neutral second, 78/71, provides a good generator for &lt;a class="wiki_link" href="/Porcupine%20family#Porcupine"&gt;porcupine temperament&lt;/a&gt;. It is between 3\&lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt; and 8\&lt;a class="wiki_link" href="/59edo"&gt;59&lt;/a&gt;, and leads to a fifth of 711.642 cents, which is 9.687 cents sharp of &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 13:06, 3 November 2025

Interval information
Ratio 78/71
Subgroup monzo 2.3.13.71 [1 1 1 -1⟩
Size in cents 162.7861¢
Name porcupine neutral second
Color name 71u3o2,
fitwewutho 2nd/seventy-wutho 2nd
FJS name [math]\displaystyle{ \text{m2}^{13}_{71} }[/math]
Special properties reduced
Tenney norm (log2 nd) 12.4351
Weil norm (log2 max(n, d)) 12.5708
Wilson norm (sopfr(nd)) 89

[sound info]
Open this interval in xen-calc

The porcupine neutral second, 78/71 = 2 ⋅ 3 ⋅ 13 ⋅ 71−1, provides a good generator for porcupine temperament. It is between 3\22 and 8\59, and leads to a fifth of 711.642 cents, which is 9.687 cents sharp of 3/2.

Approximation

Edo approximations for 78/71 (162.79 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
7 1\7 171.43 +8.64 +5.04
8 1\8 150.00 -12.79 -8.52
15 2\15 160.00 -2.79 -3.48
22 3\22 163.64 +0.85 +1.56
29 4\29 165.52 +2.73 +6.60
30 4\30 160.00 -2.79 -6.97
37 5\37 162.16 -0.62 -1.92
44 6\44 163.64 +0.85 +3.12
51 7\51 164.71 +1.92 +8.16
52 7\52 161.54 -1.25 -5.41
59 8\59 162.71 -0.07 -0.37
66 9\66 163.64 +0.85 +4.68
67 9\67 161.19 -1.59 -8.89
73 10\73 164.38 +1.60 +9.72
74 10\74 162.16 -0.62 -3.85
Retrieved from "https://en.xen.wiki/index.php?title=78/71&oldid=216011"