7edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 278431640 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 288886385 - 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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-12-31 01:42:23 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>288886385</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> | ||
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==="neutral diatonic"=== | ==="neutral diatonic"=== | ||
7-edo divides the 1200-cent [[octave]] into 7 equal parts, making its smallest interval [[cent|171.428¢]], or the seventh root of 2. | 7-edo divides the 1200-cent [[octave]] into 7 equal parts, making its smallest interval [[cent|171.428¢]], or the seventh root of 2. It is the fourth [[prime numbers|prime]] edo, after [[2edo]], [[3edo]] and [[5edo]]. | ||
Equi-heptatonic scales are used in non-western music in African cultures and it has been speculated in "Indian music:history and structure", that the Indian three-sruti interval of 165 cents is close enough to be mistaken for 171 cents. (or 1.71 semitones). | Equi-heptatonic scales are used in non-western music in African cultures and it has been speculated in "Indian music:history and structure", that the Indian three-sruti interval of 165 cents is close enough to be mistaken for 171 cents. (or 1.71 semitones). | ||
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The step from seventh to octave is too large for the leading tone. | The step from seventh to octave is too large for the leading tone. | ||
==Relative tuning accuracy== | ==Relative tuning accuracy== | ||
7-edo is the third [[The Riemann Zeta Function and Tuning#Zeta | 7-edo is the third [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta integral edo]]. | ||
=== === | === === | ||
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<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x7 Equal Divisions of the Octave--&quot;neutral diatonic&quot;"></a><!-- ws:end:WikiTextHeadingRule:2 -->&quot;neutral diatonic&quot;</h3> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x7 Equal Divisions of the Octave--&quot;neutral diatonic&quot;"></a><!-- ws:end:WikiTextHeadingRule:2 -->&quot;neutral diatonic&quot;</h3> | ||
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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.<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 /> | ||
<br /> | <br /> | ||
Equi-heptatonic scales are used in non-western music in African cultures and it has been speculated in &quot;Indian music:history and structure&quot;, that the Indian three-sruti interval of 165 cents is close enough to be mistaken for 171 cents. (or 1.71 semitones).<br /> | Equi-heptatonic scales are used in non-western music in African cultures and it has been speculated in &quot;Indian music:history and structure&quot;, that the Indian three-sruti interval of 165 cents is close enough to be mistaken for 171 cents. (or 1.71 semitones).<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:664: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:664 -->&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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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:14:&lt;h2&gt; --><h2 id="toc7"><a name="x7 Equal Divisions of the Octave-Relative tuning accuracy"></a><!-- ws:end:WikiTextHeadingRule:14 -->Relative tuning accuracy</h2> | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x7 Equal Divisions of the Octave-Relative tuning accuracy"></a><!-- ws:end:WikiTextHeadingRule:14 -->Relative tuning accuracy</h2> | ||
7-edo is the third <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta | 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:16:&lt;h3&gt; --><h3 id="toc8"><!-- ws:end:WikiTextHeadingRule:16 --> </h3> | <!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><!-- ws:end:WikiTextHeadingRule:16 --> </h3> | ||