35/32: Difference between revisions

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**Imported revision 300949110 - 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 neutral second
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-12 13:16:46 UTC</tt>.<br>
| Color name = zy2, zoyo 2nd
: The original revision id was <tt>300949110</tt>.<br>
| Sound = jid_35_32_pluck_adu_dr220.mp3
: The revision comment was: <tt></tt><br>
| Comma = no
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">**35/32**, the **septimal neutral second**, is approximately half of a [[6_5|6/5]] just minor third; (6/5)/(35/32)^2 = 6144/6125, the [[porwell comma]]. It is the interval between [[8_7|8/7]] and [[5_4|5/4]]. It is 385/384 sharp of 12/11, and tempering it out makes the interval from 8/7 to 5/4 a 12/11, and leads to [[keenanismic chords]], interpreting [[48_35|48/35]] as [[11_8|11/8]]. It is also 176/175 flat of 11/10, and tempering that out instead leads to [[valinorsmic chords]] and interprets 48/35 as [[15_11|15/11]].</pre></div>
'''35/32''', the '''septimal neutral second''', is approximately half of a [[6/5]] just minor third; (6/5)/(35/32)<sup>2</sup> = [[6144/6125]], the porwell comma. It is the interval between [[8/7]] and [[5/4]]. It is 385/384 sharp of [[12/11]], and tempering it out makes the interval from 8/7 to 5/4 a 12/11, and leads to [[keenanismic chords]], interpreting [[48/35]] as [[11/8]]. It is also [[176/175]] flat of [[11/10]], and tempering that out instead leads to [[valinorsmic chords]] and interprets 48/35 as [[15/11]].
<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;35_32&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;35/32&lt;/strong&gt;, the &lt;strong&gt;septimal neutral second&lt;/strong&gt;, is approximately half of a &lt;a class="wiki_link" href="/6_5"&gt;6/5&lt;/a&gt; just minor third; (6/5)/(35/32)^2 = 6144/6125, the &lt;a class="wiki_link" href="/porwell%20comma"&gt;porwell comma&lt;/a&gt;. It is the interval between &lt;a class="wiki_link" href="/8_7"&gt;8/7&lt;/a&gt; and &lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt;. It is 385/384 sharp of 12/11, and tempering it out makes the interval from 8/7 to 5/4 a 12/11, and leads to &lt;a class="wiki_link" href="/keenanismic%20chords"&gt;keenanismic chords&lt;/a&gt;, interpreting &lt;a class="wiki_link" href="/48_35"&gt;48/35&lt;/a&gt; as &lt;a class="wiki_link" href="/11_8"&gt;11/8&lt;/a&gt;. It is also 176/175 flat of 11/10, and tempering that out instead leads to &lt;a class="wiki_link" href="/valinorsmic%20chords"&gt;valinorsmic chords&lt;/a&gt; and interprets 48/35 as &lt;a class="wiki_link" href="/15_11"&gt;15/11&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
It is very closely approximated by [[31edo|4\31]], being just 0.3 [[cents]] sharp of that interval.
 
== See also ==
* [[64/35]] – its [[octave complement]]
* [[Gallery of just intervals]]
 
[[Category:Second]]
[[Category:Neutral second]]
[[Category:Mint]]

Latest revision as of 22:17, 31 March 2025

Interval information
Ratio 35/32
Factorization 2-5 × 5 × 7
Monzo [-5 0 1 1
Size in cents 155.1396¢
Name septimal neutral second
Color name zy2, zoyo 2nd
FJS name [math]\displaystyle{ \text{M2}^{5,7} }[/math]
Special properties reduced,
reduced harmonic
Tenney height (log2 nd) 10.1293
Weil height (log2 max(n, d)) 10.2586
Wilson height (sopfr(nd)) 22
Comma size large
S-expression S5 × S6 × S7

[sound info]
Open this interval in xen-calc

35/32, the septimal neutral second, is approximately half of a 6/5 just minor third; (6/5)/(35/32)2 = 6144/6125, the porwell comma. It is the interval between 8/7 and 5/4. It is 385/384 sharp of 12/11, and tempering it out makes the interval from 8/7 to 5/4 a 12/11, and leads to keenanismic chords, interpreting 48/35 as 11/8. It is also 176/175 flat of 11/10, and tempering that out instead leads to valinorsmic chords and interprets 48/35 as 15/11.

It is very closely approximated by 4\31, being just 0.3 cents sharp of that interval.

See also