13/10: Difference between revisions

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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 = Barbados third, tridecimal semisixth

~~: This revision was by author [[User:Andrew_Heathwaite~~|~~Andrew_Heathwaite]] and made on <tt>2011-10-07 19:22:18 UTC</tt>.<br>~~

| Color name = 3og4, thogu 4th

~~: The original revision id was <tt>262737198</tt>.<br>~~

| Sound = jid_13_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>~~

~~<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 [[13-limit]] [[Just Intonation]], 13/10 is an [[interseptimal]] interval measuring about 454.2¢. It falls in an ambiguous zone between a wide major third ~~such as [[9_7|9/7]] and a flat perfect fourth such as [[21_16|21/16]]. The descriptor "interseptimal" comes from [[Margo Schulter]]~~, ~~and indicates its position between those two septimal (7-based) extremes. 13/10 appears between the 10th and 13th overtones of the [[OverToneSeries~~|~~harmonic series]] and appears in such chords as 8:10:13~~, ~~a quasi-augmented triad. 13/10 also appears in the relatively-simple 10:13:15 triad, which consists of an interseptimal ultramajor third (13/10) and an interseptimal inframinor third ([[15_13~~|~~15/13]]) which stack to make a [[3_2|3/2]] perfect fifth. It is well-approximated in [[24edo]], [[29edo]], [[37edo]], and of course, infinitely many other [[EDO]] systems~~.

~~See:~~ [[~~Gallery of Just Intervals~~]], [[~~List of root-3rd-P5 triads in JI~~]]~~</pre></div>~~

In [[13-limit]] [[just intonation]], '''13/10''', the '''tridecimal semisixth''' is an [[interseptimal]] interval measuring about 454.2¢. It falls in an ambiguous zone between a wide major third such as [[9/7]] and a flat perfect fourth such as [[21/16]]. The descriptor "interseptimal" comes from [[Margo Schulter]], and indicates its position between those two septimal (7-based) extremes. 13/10 appears between the 10th and 13th overtones of the [[harmonic series]] and appears in such chords as 8:10:13, a quasi-augmented triad. 13/10 also appears in the relatively-simple 10:13:15 triad, which consists of an interseptimal ultramajor third (13/10) and an interseptimal inframinor third ([[15/13]]) which stack to make a [[3/2]] perfect fifth. It is well-approximated in [[16edo]], [[21edo]], [[24edo]], [[29edo]], [[37edo]], and of course, infinitely many other [[EDO]] systems.

~~<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"><html><head><title>13_10</title></head><body>In <a class="wiki_link" href="/13-limit">13-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 13/10 is an ~~<a class="wiki_link" href="/~~interseptimal~~">interseptimal</a>~~ interval measuring about 454.2¢. It falls in an ambiguous zone between a wide major third such as ~~<a class="wiki_link" href="/9_7">~~9/7~~</a>~~ and a flat perfect fourth such as ~~<a class="wiki_link" href="/21_16">~~21/16~~</a>~~. The descriptor ~~&quot;~~interseptimal~~&quot;~~ comes from ~~<a class="wiki_link" href="/Margo%20Schulter">~~Margo Schulter~~</a>~~, and indicates its position between those two septimal (7-based) extremes. 13/10 appears between the 10th and 13th overtones of the ~~<a class="wiki_link" href="/OverToneSeries">~~harmonic series~~</a>~~ and appears in such chords as 8:10:13, a quasi-augmented triad. 13/10 also appears in the relatively-simple 10:13:15 triad, which consists of an interseptimal ultramajor third (13/10) and an interseptimal inframinor third (~~<a class="wiki_link" href="/15_13">~~15/13~~</a>~~) which stack to make a ~~<a class="wiki_link" href="/3_2">~~3/2~~</a>~~ perfect fifth. It is well-approximated in ~~<a class="wiki_link" href="/~~24edo~~">24edo</a>~~, ~~<a class="wiki_link" href="/~~29edo~~">29edo</a>~~, ~~<a class="wiki_link" href="/~~37edo~~">37edo</a>~~, and of course, infinitely many other ~~<~~a class="~~wiki_link" href=~~"/~~EDO">EDO<~~/~~a> systems~~.~~<~~br /~~>~~

== Interval chain ==

~~<~~br /~~>~~

Because 13/10 is an interseptimal interval, stacking it four times will result in a good approximation of a septimal interval. In this case, (13/10)<sup>4</sup> approximates 20/7 (compound [[10/7]]) remarkably well, with less than 1{{cent}} error.

See~~: <a class~~=~~"wiki_link" href~~="/~~Gallery%20of%20Just%20Intervals">~~Gallery of ~~Just Intervals</a>, <a class="wiki_link" href="/List%20of%20root-3rd-P5%20triads%20in%20JI">~~List of root-3rd-P5 triads in JI~~</a></body></html></pre></div>~~

Additionally, while it may seem as though (13/10)<sup>2</sup> doesn't approximate 17/10 very well at first glance, it allows for an elegant interpretation of the tetrad formed by stacking 13/10 three times on top of itself: [[~]]10:13:17:22.

{| class="wikitable"

|+ [[Interval chain]] generated by 13/10

! #

! [[Cent]]s

! Approximated [[ratio]]s

! Associated [[comma]]s

|-

| 1

| 454.2

| 13/10<br>[[17/13]] (+10.2{{cent}})

| <br>[[170/169]] (major naiadma)

|-

| 2

| 908.4

| [[27/16]] (-2.6{{cent}})<br>[[22/13]] (+2.4{{cent}})<br>[[17/10]] (+10.2{{cent}})

| [[676/675]] (island comma)<br>[[2200/2197]] (petrma)<br>[[170/169]] (major naiadma)

|-

| 3

| 1362.6

| [[11/5]] (+2.4{{cent}})

| [[2200/2197]] (petrma)

|-

| 4

| 1816.9

| [[20/7]] (+0.6{{cent}})

| [[200000/199927]]

|-

| 5

| 2271.1

| [[26/7]] (+0.6{{cent}})

| [[200000/199927]]

|}

== See also ==

* [[20/13]] – its [[octave complement]]

* [[15/13]] – its [[fifth complement]]

* [[Gallery of just intervals]]

* [[List of root-3rd-P5 triads in JI]]

* [[The Archipelago]]

[[Category:Interseptimal intervals]]

[[Category:Naiadic]]

[[Category:Fourth]]

[[Category:Subfourth]]

[[Category:Third]]

[[Category:Supermajor third]]

[[Category:Over-5 intervals]]

@@ 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 = Barbados third, tridecimal semisixth
-: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-10-07 19:22:18 UTC</tt>.<br>
+| Color name = 3og4, thogu 4th
-: The original revision id was <tt>262737198</tt>.<br>
+| Sound = jid_13_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>
-<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 [[13-limit]] [[Just Intonation]], 13/10 is an [[interseptimal]] interval measuring about 454.2¢. It falls in an ambiguous zone between a wide major third such as [[9_7|9/7]] and a flat perfect fourth such as [[21_16|21/16]]. The descriptor "interseptimal" comes from [[Margo Schulter]], and indicates its position between those two septimal (7-based) extremes. 13/10 appears between the 10th and 13th overtones of the [[OverToneSeries|harmonic series]] and appears in such chords as 8:10:13, a quasi-augmented triad. 13/10 also appears in the relatively-simple 10:13:15 triad, which consists of an interseptimal ultramajor third (13/10) and an interseptimal inframinor third ([[15_13|15/13]]) which stack to make a [[3_2|3/2]] perfect fifth. It is well-approximated in [[24edo]], [[29edo]], [[37edo]], and of course, infinitely many other [[EDO]] systems.
-See: [[Gallery of Just Intervals]], [[List of root-3rd-P5 triads in JI]]</pre></div>
+In [[13-limit]] [[just intonation]], '''13/10''', the '''tridecimal semisixth''' is an [[interseptimal]] interval measuring about 454.2¢. It falls in an ambiguous zone between a wide major third such as [[9/7]] and a flat perfect fourth such as [[21/16]]. The descriptor "interseptimal" comes from [[Margo Schulter]], and indicates its position between those two septimal (7-based) extremes. 13/10 appears between the 10th and 13th overtones of the [[harmonic series]] and appears in such chords as 8:10:13, a quasi-augmented triad. 13/10 also appears in the relatively-simple 10:13:15 triad, which consists of an interseptimal ultramajor third (13/10) and an interseptimal inframinor third ([[15/13]]) which stack to make a [[3/2]] perfect fifth. It is well-approximated in [[16edo]], [[21edo]], [[24edo]], [[29edo]], [[37edo]], and of course, infinitely many other [[EDO]] systems.
-<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;13_10&lt;/title&gt;&lt;/head&gt;&lt;body&gt;In &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt;, 13/10 is an &lt;a class="wiki_link" href="/interseptimal"&gt;interseptimal&lt;/a&gt; interval measuring about 454.2¢. It falls in an ambiguous zone between a wide major third such as &lt;a class="wiki_link" href="/9_7"&gt;9/7&lt;/a&gt; and a flat perfect fourth such as &lt;a class="wiki_link" href="/21_16"&gt;21/16&lt;/a&gt;. The descriptor &amp;quot;interseptimal&amp;quot; comes from &lt;a class="wiki_link" href="/Margo%20Schulter"&gt;Margo Schulter&lt;/a&gt;, and indicates its position between those two septimal (7-based) extremes. 13/10 appears between the 10th and 13th overtones of the &lt;a class="wiki_link" href="/OverToneSeries"&gt;harmonic series&lt;/a&gt; and appears in such chords as 8:10:13, a quasi-augmented triad. 13/10 also appears in the relatively-simple 10:13:15 triad, which consists of an interseptimal ultramajor third (13/10) and an interseptimal inframinor third (&lt;a class="wiki_link" href="/15_13"&gt;15/13&lt;/a&gt;) which stack to make a &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt; perfect fifth. It is well-approximated in &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt;, &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt;, &lt;a class="wiki_link" href="/37edo"&gt;37edo&lt;/a&gt;, and of course, infinitely many other &lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt; systems.&lt;br /&gt;
+== Interval chain ==
-&lt;br /&gt;
+Because 13/10 is an interseptimal interval, stacking it four times will result in a good approximation of a septimal interval. In this case, (13/10)<sup>4</sup> approximates 20/7 (compound [[10/7]]) remarkably well, with less than 1{{cent}} error.
-See: &lt;a class="wiki_link" href="/Gallery%20of%20Just%20Intervals"&gt;Gallery of Just Intervals&lt;/a&gt;, &lt;a class="wiki_link" href="/List%20of%20root-3rd-P5%20triads%20in%20JI"&gt;List of root-3rd-P5 triads in JI&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
+Additionally, while it may seem as though (13/10)<sup>2</sup> doesn't approximate 17/10 very well at first glance, it allows for an elegant interpretation of the tetrad formed by stacking 13/10 three times on top of itself: [[~]]10:13:17:22.
+{| class="wikitable"
+|+ [[Interval chain]] generated by 13/10
+! #
+! [[Cent]]s
+! Approximated [[ratio]]s
+! Associated [[comma]]s
+|-
+| 1
+| 454.2
+| 13/10<br>[[17/13]] (+10.2{{cent}})
+| <br>[[170/169]] (major naiadma)
+|-
+| 2
+| 908.4
+| [[27/16]] (-2.6{{cent}})<br>[[22/13]] (+2.4{{cent}})<br>[[17/10]] (+10.2{{cent}})
+| [[676/675]] (island comma)<br>[[2200/2197]] (petrma)<br>[[170/169]] (major naiadma)
+|-
+| 3
+| 1362.6
+| [[11/5]] (+2.4{{cent}})
+| [[2200/2197]] (petrma)
+|-
+| 4
+| 1816.9
+| [[20/7]] (+0.6{{cent}})
+| [[200000/199927]]
+|-
+| 5
+| 2271.1
+| [[26/7]] (+0.6{{cent}})
+| [[200000/199927]]
+|}
+== See also ==
+* [[20/13]] – its [[octave complement]]
+* [[15/13]] – its [[fifth complement]]
+* [[Gallery of just intervals]]
+* [[List of root-3rd-P5 triads in JI]]
+* [[The Archipelago]]
+[[Category:Interseptimal intervals]]
+[[Category:Naiadic]]
+[[Category:Fourth]]
+[[Category:Subfourth]]
+[[Category:Third]]
+[[Category:Supermajor third]]
+[[Category:Over-5 intervals]]