19/10: Difference between revisions

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**Imported revision 513546938 - 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 = undeviceismal diminished octave, Eratosthenes' major seventh
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-10 21:50:13 UTC</tt>.<br>
| Color name = 19og8, nogu octave
: The original revision id was <tt>513546938</tt>.<br>
| Sound = jid_19_10_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>
In [[19-limit]] [[just intonation]], '''19/10''' is the '''undevicesimal diminished octave''', measuring about 1111.2¢. In the [[Functional Just System]] and [[Helmholtz-Ellis notation]], it is a ''diminished octave'', obtained by adding [[81/80]] and [[513/512]] to the [[4096/2187|Pythagorean diminished octave]], but it may be called the '''Eratosthenes' major seventh''' as it is sharp of the [[243/128|Pythagorean major seventh (243/128)]] by [[1216/1215]], the ''password'' aka ''Eratosthenes' comma''.  
<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">**19/10**
== Approximation ==
|-1 0 -1 0 0 0 0 1&gt;
{{Interval edo approximation|19/10}}
1111.1993 cents
 
[[media type="file" key="jid_19_10_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_19_10_pluck_adu_dr220.mp3|sound sample]]</pre></div>
[[Category:Octave]]
<h4>Original HTML content:</h4>
[[Category:Diminished octave]]
<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;19_10&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;19/10&lt;/strong&gt;&lt;br /&gt;
[[Category:Seventh]]
|-1 0 -1 0 0 0 0 1&amp;gt;&lt;br /&gt;
[[Category:Major seventh]]
1111.1993 cents&lt;br /&gt;
[[Category:Eratosthenes]]
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Latest revision as of 13:04, 3 November 2025

Interval information
Ratio 19/10
Subgroup monzo 2.5.19 [-1 -1 1⟩
Size in cents 1111.199¢
Names undeviceismal diminished octave,
Eratosthenes' major seventh
Color name 19og8, nogu octave
FJS name [math]\displaystyle{ \text{d8}^{19}_{5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 7.56986
Weil norm (log2 max(n, d)) 8.49586
Wilson norm (sopfr(nd)) 26

[sound info]
Open this interval in xen-calc

In 19-limit just intonation, 19/10 is the undevicesimal diminished octave, measuring about 1111.2¢. In the Functional Just System and Helmholtz-Ellis notation, it is a diminished octave, obtained by adding 81/80 and 513/512 to the Pythagorean diminished octave, but it may be called the Eratosthenes' major seventh as it is sharp of the Pythagorean major seventh (243/128) by 1216/1215, the password aka Eratosthenes' comma.

Approximation

Edo approximations for 19/10 (1111.20 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
13 12\13 1107.69 -3.51 -3.80
14 13\14 1114.29 +3.09 +3.60
26 24\26 1107.69 -3.51 -7.60
27 25\27 1111.11 -0.09 -0.20
28 26\28 1114.29 +3.09 +7.20
40 37\40 1110.00 -1.20 -4.00
41 38\41 1112.20 +1.00 +3.40
53 49\53 1109.43 -1.77 -7.80
54 50\54 1111.11 -0.09 -0.40
55 51\55 1112.73 +1.53 +7.00
67 62\67 1110.45 -0.75 -4.20
68 63\68 1111.76 +0.57 +3.20
80 74\80 1110.00 -1.20 -8.00
Retrieved from "https://en.xen.wiki/index.php?title=19/10&oldid=215986"