88/81: Difference between revisions

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**Imported revision 515457298 - 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 = 2nd undecimal neutral second, Alpharabian artoneutral second
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-07-02 15:33:45 UTC</tt>.<br>
| Color name = 1o2, ilo second
: The original revision id was <tt>515457298</tt>.<br>
}}
: 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">**88/81**
|3 -4 0 0 1&gt;
143.497939


**88/81** is 352/351 (4.9 cents) sharp of [[13_12|13/12]] and 243/242 (7.1 cents) flat of [[12_11|12/11]]. It is the interval between [[9_8|9/8]] and [[11_9|11/9]].</pre></div>
'''88/81''', the '''2nd undecimal neutral second'''<ref>http://www.huygens-fokker.org/docs/intervals.html</ref>, is an interval of about 143.5 cents. It is 352/351 (4.9 cents) sharp of [[13/12]] and 243/242 (7.1 cents) flat of [[12/11]]. It is also the interval between [[9/8]] and [[11/9]]. In [[Alpharabian tuning]] it is known as the '''Alpharabian artoneutral second'''.
<h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;88_81&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;88/81&lt;/strong&gt;&lt;br /&gt;
{{Interval edo approximation|88/81}}
|3 -4 0 0 1&amp;gt;&lt;br /&gt;
== See also ==
143.497939&lt;br /&gt;
* [[81/44]] – its [[octave complement]]
&lt;br /&gt;
* [[Gallery of just intervals]]
&lt;strong&gt;88/81&lt;/strong&gt; is 352/351 (4.9 cents) sharp of &lt;a class="wiki_link" href="/13_12"&gt;13/12&lt;/a&gt; and 243/242 (7.1 cents) flat of &lt;a class="wiki_link" href="/12_11"&gt;12/11&lt;/a&gt;. It 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="/11_9"&gt;11/9&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
 
== References ==
<references/>
 
[[Category:Second]]
[[Category:Neutral second]]

Latest revision as of 13:04, 3 November 2025

Interval information
Ratio 88/81
Factorization 23 × 3-4 × 11
Monzo [3 -4 0 0 1⟩
Size in cents 143.4979¢
Names 2nd undecimal neutral second,
Alpharabian artoneutral second
Color name 1o2, ilo second
FJS name [math]\displaystyle{ \text{m2}^{11} }[/math]
Special properties reduced
Tenney norm (log2 nd) 12.7993
Weil norm (log2 max(n, d)) 12.9189
Wilson norm (sopfr(nd)) 29
Open this interval in xen-calc

88/81, the 2nd undecimal neutral second[1], is an interval of about 143.5 cents. It is 352/351 (4.9 cents) sharp of 13/12 and 243/242 (7.1 cents) flat of 12/11. It is also the interval between 9/8 and 11/9. In Alpharabian tuning it is known as the Alpharabian artoneutral second.

Approximation

Edo approximations for 88/81 (143.50 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
8 1\8 150.00 +6.50 +4.33
9 1\9 133.33 -10.16 -7.62
16 2\16 150.00 +6.50 +8.67
17 2\17 141.18 -2.32 -3.29
25 3\25 144.00 +0.50 +1.05
33 4\33 145.45 +1.96 +5.38
34 4\34 141.18 -2.32 -6.58
41 5\41 146.34 +2.84 +9.72
42 5\42 142.86 -0.64 -2.24
50 6\50 144.00 +0.50 +2.09
51 6\51 141.18 -2.32 -9.87
58 7\58 144.83 +1.33 +6.43
59 7\59 142.37 -1.13 -5.53
67 8\67 143.28 -0.21 -1.20
75 9\75 144.00 +0.50 +3.14
76 9\76 142.11 -1.39 -8.82

See also

References

  1. ↑ http://www.huygens-fokker.org/docs/intervals.html
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