10/7: Difference between revisions

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Hemifamity 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 = high tritone, greater septimal tritone, Euler's tritone
: This revision was by author [[User:k9assassin|k9assassin]] and made on <tt>2015-03-24 20:46:11 UTC</tt>.<br>
| Color name = ry4, ruyo 4th
: The original revision id was <tt>545215048</tt>.<br>
| Sound = jid_10_7_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>
{{Wikipedia|Septimal tritone}}
<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">[[image:ji glyph 10 7.png width="148" height="118" caption="JI Glyph for 10/7
"]]


**10/7**
In [[7-limit]] [[just intonation]], '''10/7''' is a '''high [[tritone]]''' (or '''Euler's tritone''') measuring about 617.5¢. It has a similar sound to its inversion, [[7/5]], but may sound a little edgier, less relaxed. Nonetheless, it is considered a septimal consonance. It appears in chords where a major third ([[5/4]]) appears above the harmonic seventh ([[7/4]]), such as 4:6:7:10 – This particular chord is well-approximated in [[88cET]], which has a good approximation of 10/7, but no 7/5. It's well approximated by the Pythagorean augmented fourth [[729/512]], differing by [[5120/5103]].
|1 0 1 -1&gt;
617.48781 cents
Type: Utonal
[[media type="file" key="jid_10_7_pluck_adu_dr220.mp3" width="240" height="20"]] [[file:xenharmonic/jid_10_7_pluck_adu_dr220.mp3|sound sample]]


In [[7-limit]] [[Just Intonation]], 10/7 is a high tritone measuring about 617.5¢. It has a similar sound to its inversion, [[7_5|7/5]], but may sound a little edgier, less relaxed. Nonetheless, it is considered a septimal consonance. It appears in chords where a major third ([[5_4|5/4]]) appears above the harmonic seventh ([[7_4|7/4]]), such as 4:6:7:10. (This particular chord is well-approximated in [[88cET]], which has a good approximation of 10/7 -- but no 7/5.)
While in the context of the [[harmonic seventh chord]], it is rightly recognized as a type of augmented fourth, it can also be argued on the basis of the fact that 10/7 interval is larger than 600 cents that it acts more as a type of diminished fifth than an augmented fourth – an analysis that is required in cases where this interval occurs in a [[5L 2s|diatonic scale]] that demonstrates [[Rothenberg propriety]].
== Approximation ==
{{Interval edo approximation|10/7}}
== See also ==
* [[7/5]] – its [[octave complement]]
* [[21/20]] – its [[fifth complement]]
* [[Gallery of just intervals]]


See: [[Gallery of Just Intervals]]</pre></div>
[[Category:Tritone]]
<h4>Original HTML content:</h4>
[[Category:Over-7 intervals]]
<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;10_7&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextLocalImageRule:1:&amp;lt;img src=&amp;quot;/file/view/ji%20glyph%2010%207.png/545214478/148x118/ji%20glyph%2010%207.png&amp;quot; alt=&amp;quot;JI Glyph for 10/7&amp;quot; title=&amp;quot;JI Glyph for 10/7&amp;quot; style=&amp;quot;height: 118px; width: 148px;&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="/file/view/ji%20glyph%2010%207.png/545214478/148x118/ji%20glyph%2010%207.png" alt="ji glyph 10 7.png" title="ji glyph 10 7.png" style="height: 118px; width: 148px;" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;JI Glyph for 10/7&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextLocalImageRule:1 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;10/7&lt;/strong&gt;&lt;br /&gt;
|1 0 1 -1&amp;gt;&lt;br /&gt;
617.48781 cents&lt;br /&gt;
Type: Utonal &lt;br /&gt;
&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_10_7_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_10_7_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_10_7_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_10_7_pluck_adu_dr220.mp3/513184772/jid_10_7_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_10_7_pluck_adu_dr220.mp3/513184772/jid_10_7_pluck_adu_dr220.mp3');"&gt;sound sample&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
In &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt;, 10/7 is a high tritone measuring about 617.5¢. It has a similar sound to its inversion, &lt;a class="wiki_link" href="/7_5"&gt;7/5&lt;/a&gt;, but may sound a little edgier, less relaxed. Nonetheless, it is considered a septimal consonance. It appears in chords where a major third (&lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt;) appears above the harmonic seventh (&lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt;), such as 4:6:7:10. (This particular chord is well-approximated in &lt;a class="wiki_link" href="/88cET"&gt;88cET&lt;/a&gt;, which has a good approximation of 10/7 -- but no 7/5.)&lt;br /&gt;
&lt;br /&gt;
See: &lt;a class="wiki_link" href="/Gallery%20of%20Just%20Intervals"&gt;Gallery of Just Intervals&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 15:32, 12 December 2025

Interval information
Ratio 10/7
Factorization 2 × 5 × 7-1
Monzo [1 0 1 -1⟩
Size in cents 617.4878¢
Names high tritone,
greater septimal tritone,
Euler's tritone
Color name ry4, ruyo 4th
FJS name [math]\displaystyle{ \text{A4}^{5}_{7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 6.12928
Weil norm (log2 max(n, d)) 6.64386
Wilson norm (sopfr(nd)) 14

[sound info]
Open this interval in xen-calc
English Wikipedia has an article on:

In 7-limit just intonation, 10/7 is a high tritone (or Euler's tritone) measuring about 617.5¢. It has a similar sound to its inversion, 7/5, but may sound a little edgier, less relaxed. Nonetheless, it is considered a septimal consonance. It appears in chords where a major third (5/4) appears above the harmonic seventh (7/4), such as 4:6:7:10 – This particular chord is well-approximated in 88cET, which has a good approximation of 10/7, but no 7/5. It's well approximated by the Pythagorean augmented fourth 729/512, differing by 5120/5103.

While in the context of the harmonic seventh chord, it is rightly recognized as a type of augmented fourth, it can also be argued on the basis of the fact that 10/7 interval is larger than 600 cents that it acts more as a type of diminished fifth than an augmented fourth – an analysis that is required in cases where this interval occurs in a diatonic scale that demonstrates Rothenberg propriety.

Approximation

Edo approximations for 10/7 (617.49 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
2 1\2 600.00 -17.49 -2.91
4 2\4 600.00 -17.49 -5.83
6 3\6 600.00 -17.49 -8.74
29 15\29 620.69 +3.20 +7.74
31 16\31 619.35 +1.87 +4.82
33 17\33 618.18 +0.69 +1.91
35 18\35 617.14 -0.34 -1.01
37 19\37 616.22 -1.27 -3.92
39 20\39 615.38 -2.10 -6.84
41 21\41 614.63 -2.85 -9.75
62 32\62 619.35 +1.87 +9.65
64 33\64 618.75 +1.26 +6.73
66 34\66 618.18 +0.69 +3.82
68 35\68 617.65 +0.16 +0.90
70 36\70 617.14 -0.34 -2.01
72 37\72 616.67 -0.82 -4.93
74 38\74 616.22 -1.27 -7.84

See also

Retrieved from "https://en.xen.wiki/index.php?title=10/7&oldid=218871"