7edo: Difference between revisions
Wikispaces>Cenobyte **Imported revision 370839812 - Original comment: ** |
Wikispaces>vaisvil **Imported revision 441269362 - Original comment: ** |
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<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:vaisvil|vaisvil]] and made on <tt>2013-07-13 23:17:53 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>441269362</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> | ||
<h4>Original Wikitext content:</h4> | <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">[[toc|flat]] | <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">[[toc|flat]] | ||
**7 Equal Divisions of the Octave** | **7 Equal Divisions of the Octave** | ||
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||= 243/242 || | -1 5 0 0 -2 > ||> 7.14 ||= Rastma ||= ||= || | ||= 243/242 || | -1 5 0 0 -2 > ||> 7.14 ||= Rastma ||= ||= || | ||
||= 385/384 || | -7 -1 1 1 1 > ||> 4.50 ||= Keenanisma ||= ||= || | ||= 385/384 || | -7 -1 1 1 1 > ||> 4.50 ||= Keenanisma ||= ||= || | ||
||= 4000/3993 || | 5 -1 3 0 -3 > ||> 3.03 ||= Wizardharry ||= ||= ||</pre></div> | ||= 4000/3993 || | 5 -1 3 0 -3 > ||> 3.03 ||= Wizardharry ||= ||= || | ||
[[media type="custom" key="23473438"]]</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>7edo</title></head><body><!-- ws:start:WikiTextTocRule: | <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>7edo</title></head><body><!-- ws:start:WikiTextTocRule:21:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --><a href="#x&quot;neutral diatonic&quot;">&quot;neutral diatonic&quot;</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --> | <a href="#Intervals in 7-edo">Intervals in 7-edo</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#Related scales">Related scales</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:32 --><strong>7 Equal Divisions of the Octave</strong><br /> | ||
<strong>7 Equal Divisions of the Octave</strong><br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:1:&lt;h1&gt; --><h1 id="toc0"><a name="x&quot;neutral diatonic&quot;"></a><!-- ws:end:WikiTextHeadingRule:1 -->&quot;neutral diatonic&quot;</h1> | ||
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7-edo divides the 1200-cent <a class="wiki_link" href="/octave">octave</a> into 7 equal parts, making its smallest interval <a class="wiki_link" href="/cent">171.428¢</a>, or the seventh root of 2. It is the fourth <a class="wiki_link" href="/prime%20numbers">prime</a> edo, after <a class="wiki_link" href="/2edo">2edo</a>, <a class="wiki_link" href="/3edo">3edo</a> and <a class="wiki_link" href="/5edo">5edo</a>.<br /> | 7-edo divides the 1200-cent <a class="wiki_link" href="/octave">octave</a> into 7 equal parts, making its smallest interval <a class="wiki_link" href="/cent">171.428¢</a>, or the seventh root of 2. It is the fourth <a class="wiki_link" href="/prime%20numbers">prime</a> edo, after <a class="wiki_link" href="/2edo">2edo</a>, <a class="wiki_link" href="/3edo">3edo</a> and <a class="wiki_link" href="/5edo">5edo</a>.<br /> | ||
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Similarly, in equi-heptatonic systems the desire for harmonic sound may dictate constant adjustments of intonation away from the theoretical interval of 171 cents. One of the most impressive areas in Africa in which a pen-equidistant heptatonic scale is combined with a distinctively harmonic style based on singing in intervals of thirds plus fifths, or thirds plus fourths, is the eastern Angolan culture area. This music is heptatonic and non-modal; i.e., there is no concept of major or minor thirds as distinctive intervals. In principle all the thirds are neutral, but in practice the thirds rendered by the singers often approximate natural major thirds (386 cents), especially at points of rest. In this manner, the principles of equidistance and harmonic euphony are accommodated within one tonal-harmonic system. For the notation of such music, a seven-line stave is most appropriate, with each horizontal line representing one pitch level.<br /> | Similarly, in equi-heptatonic systems the desire for harmonic sound may dictate constant adjustments of intonation away from the theoretical interval of 171 cents. One of the most impressive areas in Africa in which a pen-equidistant heptatonic scale is combined with a distinctively harmonic style based on singing in intervals of thirds plus fifths, or thirds plus fourths, is the eastern Angolan culture area. This music is heptatonic and non-modal; i.e., there is no concept of major or minor thirds as distinctive intervals. In principle all the thirds are neutral, but in practice the thirds rendered by the singers often approximate natural major thirds (386 cents), especially at points of rest. In this manner, the principles of equidistance and harmonic euphony are accommodated within one tonal-harmonic system. For the notation of such music, a seven-line stave is most appropriate, with each horizontal line representing one pitch level.<br /> | ||
<u><em>(&quot;African music.&quot; Encyclopædia Britannica. 2009. Encyclopædia Britannica Online. 05 Jul. 2009 &lt;<!-- ws:start:WikiTextUrlRule: | <u><em>(&quot;African music.&quot; Encyclopædia Britannica. 2009. Encyclopædia Britannica Online. 05 Jul. 2009 &lt;<!-- ws:start:WikiTextUrlRule:680:http://www.britannica.com/EBchecked/topic/719112/African-music --><a class="wiki_link_ext" href="http://www.britannica.com/EBchecked/topic/719112/African-music" rel="nofollow">http://www.britannica.com/EBchecked/topic/719112/African-music</a><!-- ws:end:WikiTextUrlRule:680 -->&gt;.</em></u>)<br /> | ||
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A Thai xylophone measured by Morton (1974) &quot;varied only plus or minus 5 cents,&quot; from 7-TET. A Ugandan Chopi xylophone measured by Haddon (1952) was also tuned to this system.<br /> | A Thai xylophone measured by Morton (1974) &quot;varied only plus or minus 5 cents,&quot; from 7-TET. A Ugandan Chopi xylophone measured by Haddon (1952) was also tuned to this system.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:3:&lt;h1&gt; --><h1 id="toc1"><a name="Intervals in 7-edo"></a><!-- ws:end:WikiTextHeadingRule:3 -->Intervals in 7-edo</h1> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:5:&lt;h1&gt; --><h1 id="toc2"><a name="Related scales"></a><!-- ws:end:WikiTextHeadingRule:5 -->Related scales</h1> | ||
<ul><li>Related in a lateral way to traditional Thai music.</li></ul><!-- ws:start:WikiTextHeadingRule: | <ul><li>Related in a lateral way to traditional Thai music.</li></ul><!-- ws:start:WikiTextHeadingRule:7:&lt;h2&gt; --><h2 id="toc3"><a name="Related scales-Notation"></a><!-- ws:end:WikiTextHeadingRule:7 -->Notation</h2> | ||
<ul><li>Notatable on a five-line staff without accidentals.</li></ul><!-- ws:start:WikiTextHeadingRule: | <ul><li>Notatable on a five-line staff without accidentals.</li></ul><!-- ws:start:WikiTextHeadingRule:9:&lt;h2&gt; --><h2 id="toc4"><a name="Related scales-Harmony"></a><!-- ws:end:WikiTextHeadingRule:9 -->Harmony</h2> | ||
There is no distinction between Major or Minor; each pitch class is unique.<br /> | There is no distinction between Major or Minor; each pitch class is unique.<br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:11:&lt;h2&gt; --><h2 id="toc5"><a name="Related scales-Melody"></a><!-- ws:end:WikiTextHeadingRule:11 -->Melody</h2> | ||
There is a neutral feel between whole tone scale and major/minor diatonic scale. The second 171,429 c works well as a basic step for melodic progression.<br /> | There is a neutral feel between whole tone scale and major/minor diatonic scale. The second 171,429 c works well as a basic step for melodic progression.<br /> | ||
The step from seventh to octave is too large for the leading tone.<br /> | The step from seventh to octave is too large for the leading tone.<br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:13:&lt;h2&gt; --><h2 id="toc6"><a name="Related scales-Relative tuning accuracy"></a><!-- ws:end:WikiTextHeadingRule:13 -->Relative tuning accuracy</h2> | ||
7-edo is the third <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta integral edo</a>.<br /> | 7-edo is the third <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta integral edo</a>.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:15:&lt;h3&gt; --><h3 id="toc7"><!-- ws:end:WikiTextHeadingRule:15 --> </h3> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:17:&lt;h1&gt; --><h1 id="toc8"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:17 -->Music</h1> | ||
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<a class="wiki_link_ext" href="http://sethares.engr.wisc.edu/mp3s/PagansRevenge.mp3" rel="nofollow">Pagan's Revenge</a> by Bill Sethares (synthetic gamelan)<br /> | <a class="wiki_link_ext" href="http://sethares.engr.wisc.edu/mp3s/PagansRevenge.mp3" rel="nofollow">Pagan's Revenge</a> by Bill Sethares (synthetic gamelan)<br /> | ||
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<a class="wiki_link_ext" href="http://media.soundcloud.com/stream/IUcgFYhtu3Rk?stream_token=4QIvd" rel="nofollow">Sävelmä</a> by <a class="wiki_link_ext" href="http://soundcloud.com/juhani-nuorvala/s-velm-long-version" rel="nofollow">Juhani Nuorvala</a><br /> | <a class="wiki_link_ext" href="http://media.soundcloud.com/stream/IUcgFYhtu3Rk?stream_token=4QIvd" rel="nofollow">Sävelmä</a> by <a class="wiki_link_ext" href="http://soundcloud.com/juhani-nuorvala/s-velm-long-version" rel="nofollow">Juhani Nuorvala</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:19:&lt;h1&gt; --><h1 id="toc9"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:19 -->Commas</h1> | ||
7 EDO tempers out the following commas. (Note: This assumes val &lt; 7 11 16 20 24 26 |.)<br /> | 7 EDO tempers out the following commas. (Note: This assumes val &lt; 7 11 16 20 24 26 |.)<br /> | ||
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</table> | </table> | ||
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