7edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

: This revision was by author [[User:~~aum-milan~~|~~aum-milan~~]] and made on <tt>~~2009~~-08-~~26 15~~:58:18 UTC</tt>.<br>

: This revision was by author [[User:guest|guest]] and made on <tt>2010-02-19 05:56:39 UTC</tt>.<br>

: The original revision id was <tt>~~85725073~~</tt>.<br>

: The original revision id was <tt>121497415</tt>.<br>

: The revision comment was: <tt>~~links fix~~</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>

<h4>Original Wikitext content:</h4>

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7-edo divides the 1200-[[cents|cent]] octave into 7 equal parts, making its smallest interval [[171.428¢]], or the seventh root of 2.

Equi-heptitonic 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).

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.

"African music." Encyclopædia Britannica. 2009. Encyclopædia Britannica Online. 05 Jul. 2009 <http://www.britannica.com/EBchecked/topic/719112/African-music>.

==Intervals in 7-edo==

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<br />

7-edo divides the 1200-<a class="wiki_link" href="/cents">cent</a> octave into 7 equal parts, making its smallest interval <a class="wiki_link" href="/171.428%C2%A2">171.428¢</a>, or the seventh root of 2.<br />

<br />

Equi-heptitonic 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 />

<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 />

<br />

&quot;African music.&quot; Encyclopædia Britannica. 2009. Encyclopædia Britannica Online. 05 Jul. 2009 &lt;<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>&gt;.<br />

<br />

<h2 id="toc2"><a name="x7 Equal Divisions of the Octave-Intervals in 7-edo"></a>Intervals in 7-edo</h2>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:aum-milan|aum-milan]] and made on <tt>2009-08-26 15:58:18 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2010-02-19 05:56:39 UTC</tt>.<br>
-: The original revision id was <tt>85725073</tt>.<br>
+: The original revision id was <tt>121497415</tt>.<br>
-: The revision comment was: <tt>links fix</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>
 <h4>Original Wikitext content:</h4>
@@ Line 10: / Line 10: @@
 -edo divides the 1200-[[cents|cent]] octave into 7 equal parts, making its smallest interval [[171.428¢]], or the seventh root of 2.
+Equi-heptitonic 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).
+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.
+"African music." Encyclopædia Britannica. 2009. Encyclopædia Britannica Online. 05 Jul. 2009 &lt;http://www.britannica.com/EBchecked/topic/719112/African-music&gt;.
 ==Intervals in 7-edo==
@@ Line 64: / Line 70: @@
   &lt;br /&gt;
 -edo divides the 1200-&lt;a class="wiki_link" href="/cents"&gt;cent&lt;/a&gt; octave into 7 equal parts, making its smallest interval &lt;a class="wiki_link" href="/171.428%C2%A2"&gt;171.428¢&lt;/a&gt;, or the seventh root of 2.&lt;br /&gt;
+&lt;br /&gt;
+Equi-heptitonic scales are used in non-western music in African cultures and it has been speculated in &amp;quot;Indian music:history and structure&amp;quot;, that the Indian three-sruti interval of 165 cents is close enough to be mistaken for 171 cents. (or 1.71 semitones).&lt;br /&gt;
+&lt;br /&gt;
+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.&lt;br /&gt;
+&lt;br /&gt;
+&amp;quot;African music.&amp;quot; Encyclopædia Britannica. 2009. Encyclopædia Britannica Online. 05 Jul. 2009 &amp;lt;&lt;!-- ws:start:WikiTextUrlRule:201:http://www.britannica.com/EBchecked/topic/719112/African-music --&gt;&lt;a class="wiki_link_ext" href="http://www.britannica.com/EBchecked/topic/719112/African-music" rel="nofollow"&gt;http://www.britannica.com/EBchecked/topic/719112/African-music&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:201 --&gt;&amp;gt;.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x7 Equal Divisions of the Octave-Intervals in 7-edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Intervals in 7-edo&lt;/h2&gt;