17/10: Difference between revisions

Interval information
Ratio	17/10
Factorization	2-1 × 5-1 × 17
Monzo	[-1 0 -1 0 0 0 1⟩
Size in cents	918.6417¢
Name	diatismic major sixth
Color name	17og7, sogu 7th
FJS name	[math]\displaystyle{ \text{d7}^{17}_{5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	7.40939
Weil norm (log2 max(n, d))	8.17493
Wilson norm (sopfr(nd))	24
	https://en.xen.wiki/w/File:Jid_17_10_pluck_adu_dr220.mp3; [sound info]
	Open this interval in xen-calc

VisualWikitext

Latest revision as of 13:14, 3 November 2025

In 17-limit just Intonation, 17/10 is the diatismic major sixth, measuring about 918.6¢. It exceeds the Pythagorean major sixth (27/16) by a diatisma (136/135), hence the name. It is the mediant of 5/3 and 12/7. Its octave complement is 20/17, the diatismic minor third.

Approximation

Edo approximations for 17/10 (918.64 ¢)
*≤ 80edo, relative error ≤ 10%*
Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
4	3\4	900.00	-18.64	-6.21
13	10\13	923.08	+4.44	+4.80
17	13\17	917.65	-0.99	-1.41
21	16\21	914.29	-4.36	-7.62
26	20\26	923.08	+4.44	+9.61
30	23\30	920.00	+1.36	+3.40
34	26\34	917.65	-0.99	-2.82
38	29\38	915.79	-2.85	-9.03
43	33\43	920.93	+2.29	+8.20
47	36\47	919.15	+0.51	+1.99
51	39\51	917.65	-0.99	-4.23
60	46\60	920.00	+1.36	+6.79
64	49\64	918.75	+0.11	+0.58
68	52\68	917.65	-0.99	-5.64
77	59\77	919.48	+0.84	+5.38

@@ Line 1: / Line 1: @@
-<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 = diatismic major sixth
-: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-12-07 02:25:32 UTC</tt>.<br>
+| Sound = jid_17_10_pluck_adu_dr220.mp3
-: The original revision id was <tt>283165060</tt>.<br>
+| Color name = 17og7, sogu 7th
-: 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">In [[17-limit]] [[Just Intonation]], 17/10 is the "septendecimal major sixth," measuring about 918.642¢. It is the [[mediant]] between [[5_3|5/3]] and [[12_7|12/7]]. Its inversion is [[20_17|20/17]], the "septendecimal minor third".
-See: [[Gallery of Just Intervals]]</pre></div>
+In [[17-limit]] [[just Intonation]], '''17/10''' is the '''diatismic major sixth''', measuring about 918.6¢. It exceeds the [[27/16|Pythagorean major sixth (27/16)]] by a [[136/135|diatisma (136/135)]], hence the name. It is the [[mediant]] of [[5/3]] and [[12/7]]. Its [[octave complement]] is [[20/17]], the diatismic minor third.
-<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;17_10&lt;/title&gt;&lt;/head&gt;&lt;body&gt;In &lt;a class="wiki_link" href="/17-limit"&gt;17-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt;, 17/10 is the &amp;quot;septendecimal major sixth,&amp;quot; measuring about 918.642¢. It is the &lt;a class="wiki_link" href="/mediant"&gt;mediant&lt;/a&gt; between &lt;a class="wiki_link" href="/5_3"&gt;5/3&lt;/a&gt; and &lt;a class="wiki_link" href="/12_7"&gt;12/7&lt;/a&gt;. Its inversion is &lt;a class="wiki_link" href="/20_17"&gt;20/17&lt;/a&gt;, the &amp;quot;septendecimal minor third&amp;quot;.&lt;br /&gt;
+{{Interval edo approximation|17/10}}
-&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>
+== See also ==
+* [[20/17]] – its [[octave complement]]
+* [[4edo|3\4]] or [[12edo|9\12]] (900 cents)
+* [[13edo|10\13]] (923.08 cents)
+* [[17edo|13\17]] (917.65 cents)
+* [[Gallery of just intervals]]
+[[Category:Sixth]]
+[[Category:Major sixth]]
+[[Category:Diatismic]]

17/10: Difference between revisions

Latest revision as of 13:14, 3 November 2025

Approximation

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