31edo: 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:guest|guest]] and made on <tt>2012-03-28 09:21:01 UTC</tt>.<br>

: This revision was by author [[User:guest|guest]] and made on <tt>2012-03-28 09:42:37 UTC</tt>.<br>

: The original revision id was <tt>~~315405798~~</tt>.<br>

: The original revision id was <tt>315414420</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>

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=Harmonic Scale=

31edo approximates Mode 8 of the [[OverToneSeries|harmonic series]] O.K., but many intervals between the harmonics aren't distinguished, most importantly 9/8 (major tone) and 10/9 (minor tone), as 31EDO is a meantone temperament. The interval between the 8th and 11th harmonics is approximated O.K., but the intervals between the 11th harmonic and closer harmonics such as the 12th and 9th harmonics are approximated even better~~. 13/8 isn't distinguished from the 11-limit 18/11, as 144/143 is tempered out, so 13-limit intervals can't be distinguished from 11-limit ones~~.

31edo approximates Mode 8 of the [[OverToneSeries|harmonic series]] O.K., but many intervals between the harmonics aren't distinguished, most importantly 9/8 (major tone) and 10/9 (minor tone), as 31EDO is a meantone temperament. The interval between the 8th and 11th harmonics is approximated O.K., but the intervals between the 11th harmonic and closer harmonics such as the 12th and 9th harmonics are approximated even better.

|| Overtones in "Mode 8": || 8 || 9 || 10 || 11 || 12 || 13 || 14 || 15 || 16 ||

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<br />

<h1 id="toc32"><a name="Harmonic Scale"></a>Harmonic Scale</h1>

31edo approximates Mode 8 of the <a class="wiki_link" href="/OverToneSeries">harmonic series</a> O.K., but many intervals between the harmonics aren't distinguished, most importantly 9/8 (major tone) and 10/9 (minor tone), as 31EDO is a meantone temperament. The interval between the 8th and 11th harmonics is approximated O.K., but the intervals between the 11th harmonic and closer harmonics such as the 12th and 9th harmonics are approximated even better~~. 13/8 isn't distinguished from the 11-limit 18/11, as 144/143 is tempered out, so 13-limit intervals can't be distinguished from 11-limit ones~~.<br />

31edo approximates Mode 8 of the <a class="wiki_link" href="/OverToneSeries">harmonic series</a> O.K., but many intervals between the harmonics aren't distinguished, most importantly 9/8 (major tone) and 10/9 (minor tone), as 31EDO is a meantone temperament. The interval between the 8th and 11th harmonics is approximated O.K., but the intervals between the 11th harmonic and closer harmonics such as the 12th and 9th harmonics are approximated even better.<br />

<br />

@@ 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:guest|guest]] and made on <tt>2012-03-28 09:21:01 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2012-03-28 09:42:37 UTC</tt>.<br>
-: The original revision id was <tt>315405798</tt>.<br>
+: The original revision id was <tt>315414420</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>
@@ Line 200: / Line 200: @@
 =Harmonic Scale=
-edo approximates Mode 8 of the [[OverToneSeries|harmonic series]] O.K., but many intervals between the harmonics aren't distinguished, most importantly 9/8 (major tone) and 10/9 (minor tone), as 31EDO is a meantone temperament. The interval between the 8th and 11th harmonics is approximated O.K., but the intervals between the 11th harmonic and closer harmonics such as the 12th and 9th harmonics are approximated even better. 13/8 isn't distinguished from the 11-limit 18/11, as 144/143 is tempered out, so 13-limit intervals can't be distinguished from 11-limit ones.
+edo approximates Mode 8 of the [[OverToneSeries|harmonic series]] O.K., but many intervals between the harmonics aren't distinguished, most importantly 9/8 (major tone) and 10/9 (minor tone), as 31EDO is a meantone temperament. The interval between the 8th and 11th harmonics is approximated O.K., but the intervals between the 11th harmonic and closer harmonics such as the 12th and 9th harmonics are approximated even better.
 || Overtones in "Mode 8": || 8 || 9 || 10 || 11 || 12 || 13 || 14 || 15 || 16 ||
@@ Line 7,233: / Line 7,233: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:64:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc32"&gt;&lt;a name="Harmonic Scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:64 --&gt;Harmonic Scale&lt;/h1&gt;
-edo approximates Mode 8 of the &lt;a class="wiki_link" href="/OverToneSeries"&gt;harmonic series&lt;/a&gt; O.K., but many intervals between the harmonics aren't distinguished, most importantly 9/8 (major tone) and 10/9 (minor tone), as 31EDO is a meantone temperament. The interval between the 8th and 11th harmonics is approximated O.K., but the intervals between the 11th harmonic and closer harmonics such as the 12th and 9th harmonics are approximated even better. 13/8 isn't distinguished from the 11-limit 18/11, as 144/143 is tempered out, so 13-limit intervals can't be distinguished from 11-limit ones.&lt;br /&gt;
+edo approximates Mode 8 of the &lt;a class="wiki_link" href="/OverToneSeries"&gt;harmonic series&lt;/a&gt; O.K., but many intervals between the harmonics aren't distinguished, most importantly 9/8 (major tone) and 10/9 (minor tone), as 31EDO is a meantone temperament. The interval between the 8th and 11th harmonics is approximated O.K., but the intervals between the 11th harmonic and closer harmonics such as the 12th and 9th harmonics are approximated even better.&lt;br /&gt;
 &lt;br /&gt;