2ed13/10
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author Andrew_Heathwaite and made on 2009-12-24 18:29:31 UTC.
- The original revision id was 111024881.
- 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, 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. =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 equal scales, it fits between [[5edo]] and [[6edo]]. Each octave contains about 5.284 tones. 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]]
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 /> 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 <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 equal scales, it fits between <a class="wiki_link" href="/5edo">5edo</a> and <a class="wiki_link" href="/6edo">6edo</a>. Each octave contains about 5.284 tones. 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:8:<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:8 --></body></html>