35/29: Difference between revisions

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**Imported revision 342213176 - Original comment: **
+ distance to the nearest simple pythagorean interval. Cleanup
 
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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 = doublewide minor third
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-06-03 13:51:55 UTC</tt>.<br>
| Color name = 29uzy3, twenuzoyo 3rd
: The original revision id was <tt>342213176</tt>.<br>
| Sound = jid_35_29_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>
'''35/29''', the '''doublewide minor third''', is a minor third in [[29-limit]] [[just intonation]]. It is sharp of [[32/27]], the Pythagorean minor third, by [[945/928]], and sharp of [[6/5]], the classical minor third, by [[175/174]]. It is flat by [[29/24]], another 29-limit minor third, by [[841/840]] ({{S|29}}), a comma 2.06{{C}} in size.
<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">35/29, the doublewide minor third, gives an excellent tuning for the [[Jubilismic clan#Doublewide|doublewide]] generator which is a sharp minor third. It lies between 16\59, the 118edo version of the generator, and 3\11, the 22edo version.</pre></div>
== Approximation ==
<h4>Original HTML content:</h4>
{{Interval edo approximation|35/29}}
<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_29&lt;/title&gt;&lt;/head&gt;&lt;body&gt;35/29, the doublewide minor third, gives an excellent tuning for the &lt;a class="wiki_link" href="/Jubilismic%20clan#Doublewide"&gt;doublewide&lt;/a&gt; generator which is a sharp minor third. It lies between 16\59, the 118edo version of the generator, and 3\11, the 22edo version.&lt;/body&gt;&lt;/html&gt;</pre></div>
 
== Temperaments ==
The 35/29 interval gives an excellent generator for the [[doublewide]] temperament with a half octave. It lies between [[59edo|16\59]] ([[118edo|32\118]]) and [[11edo|3\11]] ([[22edo|6\22]]), which may also serve as generators for doublewide.
 
[[Category:Third]]
[[Category:Minor third]]

Latest revision as of 12:03, 4 February 2026

Interval information
Ratio 35/29
Subgroup monzo 5.7.29 [1 1 -1⟩
Size in cents 325.5624¢
Name doublewide minor third
Color name 29uzy3, twenuzoyo 3rd
FJS name [math]\displaystyle{ \text{M3}^{5,7}_{29} }[/math]
Special properties reduced
Tenney norm (log2 nd) 9.98726
Weil norm (log2 max(n, d)) 10.2586
Wilson norm (sopfr(nd)) 41

[sound info]
Open this interval in xen-calc

35/29, the doublewide minor third, is a minor third in 29-limit just intonation. It is sharp of 32/27, the Pythagorean minor third, by 945/928, and sharp of 6/5, the classical minor third, by 175/174. It is flat by 29/24, another 29-limit minor third, by 841/840 (S29), a comma 2.06 ¢ in size.

Approximation

Edo approximations for 35/29 (325.56 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
4 1\4 300.00 -25.56 -8.52
11 3\11 327.27 +1.71 +1.57
15 4\15 320.00 -5.56 -6.95
22 6\22 327.27 +1.71 +3.14
26 7\26 323.08 -2.49 -5.39
33 9\33 327.27 +1.71 +4.70
37 10\37 324.32 -1.24 -3.82
44 12\44 327.27 +1.71 +6.27
48 13\48 325.00 -0.56 -2.25
55 15\55 327.27 +1.71 +7.84
59 16\59 325.42 -0.14 -0.68
63 17\63 323.81 -1.75 -9.20
66 18\66 327.27 +1.71 +9.41
70 19\70 325.71 +0.15 +0.89
74 20\74 324.32 -1.24 -7.63

Temperaments

The 35/29 interval gives an excellent generator for the doublewide temperament with a half octave. It lies between 16\59 (32\118) and 3\11 (6\22), which may also serve as generators for doublewide.

Retrieved from "https://en.xen.wiki/index.php?title=35/29&oldid=223213"