2ed13/10: Difference between revisions
Jump to navigation
Jump to search
Wikispaces>Andrew_Heathwaite **Imported revision 111024881 - Original comment: ** |
Wikispaces>guest **Imported revision 284853356 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:guest|guest]] and made on <tt>2011-12-11 22:38:54 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>284853356</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : 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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
| Line 8: | Line 8: | ||
<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">=13:10= | <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">=13:10= | ||
13:10, as a frequency ratio, measures approximately 454.2 cents. It lies in the extremely xenharmonic and ambiguous territory between the perceptual category of a "third" and that of a "fourth". It appears in the [[OverToneSeries|overtone series]] between the tenth and thirteen overtones. | [[13_10|13:10]], as a frequency ratio, measures approximately 454.2 cents. It lies in the extremely xenharmonic and ambiguous territory between the perceptual category of a "third" and that of a "fourth" (see [[interseptimal]]). It appears in the [[OverToneSeries|overtone series]] between the tenth and thirteen overtones. | ||
=sqrt 13:10 as an interval= | =sqrt 13:10 as an interval= | ||
| Line 18: | Line 18: | ||
"The square root of 13:10" can also refer to the scale that is produced by repeatedly stacking the interval "the square root of 13:10". It is an [[EDONOI]], or "equal division of a nonoctave interval," and as such, it does not contain a perfect octave (2:1). It is also [[macrotonal]], since the smallest step, at 227.1 cents, is larger than a semitone. | "The square root of 13:10" can also refer to the scale that is produced by repeatedly stacking the interval "the square root of 13:10". It is an [[EDONOI]], or "equal division of a nonoctave interval," and as such, it does not contain a perfect octave (2:1). It is also [[macrotonal]], since the smallest step, at 227.1 cents, is larger than a semitone. | ||
In terms of equal | In terms of [[EDO|equal divisions of the octave]], it fits between [[5edo]] and [[6edo]] (about 5.284edo). Melodically, it can sound somewhat "pentatonic," but harmonically it is very different. | ||
==harmonic content== | ==harmonic content== | ||
| Line 24: | Line 24: | ||
Sqrt 13:10 (the scale) contains no octaves, and also no close approximation of the third harmonic (the perfect fifth). However, it comes very close to certain just intervals involving the numbers 5, 7, 11 and 13: in particular: 8/7, 13/10, 22/13, 11/5, 5/2, 20/7, 13/4, 26/7, 11/2, and 44/7. These near-just intervals can be combined so as to make available a set of 20 harmonic and subharmonic chords. | Sqrt 13:10 (the scale) contains no octaves, and also no close approximation of the third harmonic (the perfect fifth). However, it comes very close to certain just intervals involving the numbers 5, 7, 11 and 13: in particular: 8/7, 13/10, 22/13, 11/5, 5/2, 20/7, 13/4, 26/7, 11/2, and 44/7. These near-just intervals can be combined so as to make available a set of 20 harmonic and subharmonic chords. | ||
[[image:sqrt13_10_harmonic_contents.jpg]]</pre></div> | [[image:sqrt13_10_harmonic_contents.jpg]] | ||
=== === | |||
==Music:== | |||
[[http://soundcloud.com/andrew_heathwaite/truffles|Truffles?]] by Andrew Heathwaite and Michael Gaiuranos</pre></div> | |||
<h4>Original HTML content:</h4> | <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>square root of 13 over 10</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x13:10"></a><!-- ws:end:WikiTextHeadingRule:0 -->13:10</h1> | <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>square root of 13 over 10</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x13:10"></a><!-- ws:end:WikiTextHeadingRule:0 -->13:10</h1> | ||
<br /> | <br /> | ||
13:10, as a frequency ratio, measures approximately 454.2 cents. It lies in the extremely xenharmonic and ambiguous territory between the perceptual category of a &quot;third&quot; and that of a &quot;fourth&quot;. It appears in the <a class="wiki_link" href="/OverToneSeries">overtone series</a> between the tenth and thirteen overtones.<br /> | <a class="wiki_link" href="/13_10">13:10</a>, as a frequency ratio, measures approximately 454.2 cents. It lies in the extremely xenharmonic and ambiguous territory between the perceptual category of a &quot;third&quot; and that of a &quot;fourth&quot; (see <a class="wiki_link" href="/interseptimal">interseptimal</a>). It appears in the <a class="wiki_link" href="/OverToneSeries">overtone series</a> between the tenth and thirteen overtones.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="sqrt 13:10 as an interval"></a><!-- ws:end:WikiTextHeadingRule:2 -->sqrt 13:10 as an interval</h1> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="sqrt 13:10 as an interval"></a><!-- ws:end:WikiTextHeadingRule:2 -->sqrt 13:10 as an interval</h1> | ||
| Line 38: | Line 43: | ||
&quot;The square root of 13:10&quot; can also refer to the scale that is produced by repeatedly stacking the interval &quot;the square root of 13:10&quot;. It is an <a class="wiki_link" href="/EDONOI">EDONOI</a>, or &quot;equal division of a nonoctave interval,&quot; and as such, it does not contain a perfect octave (2:1). It is also <a class="wiki_link" href="/macrotonal">macrotonal</a>, since the smallest step, at 227.1 cents, is larger than a semitone.<br /> | &quot;The square root of 13:10&quot; can also refer to the scale that is produced by repeatedly stacking the interval &quot;the square root of 13:10&quot;. It is an <a class="wiki_link" href="/EDONOI">EDONOI</a>, or &quot;equal division of a nonoctave interval,&quot; and as such, it does not contain a perfect octave (2:1). It is also <a class="wiki_link" href="/macrotonal">macrotonal</a>, since the smallest step, at 227.1 cents, is larger than a semitone.<br /> | ||
<br /> | <br /> | ||
In terms of equal | In terms of <a class="wiki_link" href="/EDO">equal divisions of the octave</a>, it fits between <a class="wiki_link" href="/5edo">5edo</a> and <a class="wiki_link" href="/6edo">6edo</a> (about 5.284edo). Melodically, it can sound somewhat &quot;pentatonic,&quot; but harmonically it is very different.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="sqrt 13:10 as a scale-harmonic content"></a><!-- ws:end:WikiTextHeadingRule:6 -->harmonic content</h2> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="sqrt 13:10 as a scale-harmonic content"></a><!-- ws:end:WikiTextHeadingRule:6 -->harmonic content</h2> | ||
| Line 44: | Line 49: | ||
Sqrt 13:10 (the scale) contains no octaves, and also no close approximation of the third harmonic (the perfect fifth). However, it comes very close to certain just intervals involving the numbers 5, 7, 11 and 13: in particular: 8/7, 13/10, 22/13, 11/5, 5/2, 20/7, 13/4, 26/7, 11/2, and 44/7. These near-just intervals can be combined so as to make available a set of 20 harmonic and subharmonic chords.<br /> | Sqrt 13:10 (the scale) contains no octaves, and also no close approximation of the third harmonic (the perfect fifth). However, it comes very close to certain just intervals involving the numbers 5, 7, 11 and 13: in particular: 8/7, 13/10, 22/13, 11/5, 5/2, 20/7, 13/4, 26/7, 11/2, and 44/7. These near-just intervals can be combined so as to make available a set of 20 harmonic and subharmonic chords.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:12:&lt;img src=&quot;/file/view/sqrt13_10_harmonic_contents.jpg/111024861/sqrt13_10_harmonic_contents.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/sqrt13_10_harmonic_contents.jpg/111024861/sqrt13_10_harmonic_contents.jpg" alt="sqrt13_10_harmonic_contents.jpg" title="sqrt13_10_harmonic_contents.jpg" /><!-- ws:end:WikiTextLocalImageRule:12 --><br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><!-- ws:end:WikiTextHeadingRule:8 --> </h3> | |||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="sqrt 13:10 as a scale-Music:"></a><!-- ws:end:WikiTextHeadingRule:10 -->Music:</h2> | |||
<br /> | |||
<a class="wiki_link_ext" href="http://soundcloud.com/andrew_heathwaite/truffles" rel="nofollow">Truffles?</a> by Andrew Heathwaite and Michael Gaiuranos</body></html></pre></div> | |||
Revision as of 22:38, 11 December 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author guest and made on 2011-12-11 22:38:54 UTC.
- The original revision id was 284853356.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
=13:10= [[13_10|13:10]], as a frequency ratio, measures approximately 454.2 cents. It lies in the extremely xenharmonic and ambiguous territory between the perceptual category of a "third" and that of a "fourth" (see [[interseptimal]]). It appears in the [[OverToneSeries|overtone series]] between the tenth and thirteen overtones. =sqrt 13:10 as an interval= The "square root of 13:10", then, means an interval which logarithmically bisects 13:10. It's an irrational number which measures, in cents, about 227.1. =sqrt 13:10 as a scale= "The square root of 13:10" can also refer to the scale that is produced by repeatedly stacking the interval "the square root of 13:10". It is an [[EDONOI]], or "equal division of a nonoctave interval," and as such, it does not contain a perfect octave (2:1). It is also [[macrotonal]], since the smallest step, at 227.1 cents, is larger than a semitone. In terms of [[EDO|equal divisions of the octave]], it fits between [[5edo]] and [[6edo]] (about 5.284edo). Melodically, it can sound somewhat "pentatonic," but harmonically it is very different. ==harmonic content== Sqrt 13:10 (the scale) contains no octaves, and also no close approximation of the third harmonic (the perfect fifth). However, it comes very close to certain just intervals involving the numbers 5, 7, 11 and 13: in particular: 8/7, 13/10, 22/13, 11/5, 5/2, 20/7, 13/4, 26/7, 11/2, and 44/7. These near-just intervals can be combined so as to make available a set of 20 harmonic and subharmonic chords. [[image:sqrt13_10_harmonic_contents.jpg]] === === ==Music:== [[http://soundcloud.com/andrew_heathwaite/truffles|Truffles?]] by Andrew Heathwaite and Michael Gaiuranos
Original HTML content:
<html><head><title>square root of 13 over 10</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x13:10"></a><!-- ws:end:WikiTextHeadingRule:0 -->13:10</h1> <br /> <a class="wiki_link" href="/13_10">13:10</a>, as a frequency ratio, measures approximately 454.2 cents. It lies in the extremely xenharmonic and ambiguous territory between the perceptual category of a "third" and that of a "fourth" (see <a class="wiki_link" href="/interseptimal">interseptimal</a>). It appears in the <a class="wiki_link" href="/OverToneSeries">overtone series</a> between the tenth and thirteen overtones.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="sqrt 13:10 as an interval"></a><!-- ws:end:WikiTextHeadingRule:2 -->sqrt 13:10 as an interval</h1> <br /> The "square root of 13:10", then, means an interval which logarithmically bisects 13:10. It's an irrational number which measures, in cents, about 227.1.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="sqrt 13:10 as a scale"></a><!-- ws:end:WikiTextHeadingRule:4 -->sqrt 13:10 as a scale</h1> <br /> "The square root of 13:10" can also refer to the scale that is produced by repeatedly stacking the interval "the square root of 13:10". It is an <a class="wiki_link" href="/EDONOI">EDONOI</a>, or "equal division of a nonoctave interval," and as such, it does not contain a perfect octave (2:1). It is also <a class="wiki_link" href="/macrotonal">macrotonal</a>, since the smallest step, at 227.1 cents, is larger than a semitone.<br /> <br /> In terms of <a class="wiki_link" href="/EDO">equal divisions of the octave</a>, it fits between <a class="wiki_link" href="/5edo">5edo</a> and <a class="wiki_link" href="/6edo">6edo</a> (about 5.284edo). Melodically, it can sound somewhat "pentatonic," but harmonically it is very different.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="sqrt 13:10 as a scale-harmonic content"></a><!-- ws:end:WikiTextHeadingRule:6 -->harmonic content</h2> <br /> Sqrt 13:10 (the scale) contains no octaves, and also no close approximation of the third harmonic (the perfect fifth). However, it comes very close to certain just intervals involving the numbers 5, 7, 11 and 13: in particular: 8/7, 13/10, 22/13, 11/5, 5/2, 20/7, 13/4, 26/7, 11/2, and 44/7. These near-just intervals can be combined so as to make available a set of 20 harmonic and subharmonic chords.<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:12:<img src="/file/view/sqrt13_10_harmonic_contents.jpg/111024861/sqrt13_10_harmonic_contents.jpg" alt="" title="" /> --><img src="/file/view/sqrt13_10_harmonic_contents.jpg/111024861/sqrt13_10_harmonic_contents.jpg" alt="sqrt13_10_harmonic_contents.jpg" title="sqrt13_10_harmonic_contents.jpg" /><!-- ws:end:WikiTextLocalImageRule:12 --><br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h3> --><h3 id="toc4"><!-- ws:end:WikiTextHeadingRule:8 --> </h3> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="sqrt 13:10 as a scale-Music:"></a><!-- ws:end:WikiTextHeadingRule:10 -->Music:</h2> <br /> <a class="wiki_link_ext" href="http://soundcloud.com/andrew_heathwaite/truffles" rel="nofollow">Truffles?</a> by Andrew Heathwaite and Michael Gaiuranos</body></html>