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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2012-08-26 10:38~~:23~~ UTC</tt>.<br>

: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2012-08-26 10:45:38 UTC</tt>.<br>

: The original revision id was <tt>~~359972233~~</tt>.<br>

: The original revision id was <tt>359972909</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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===5\31 octave - approx. 193.55¢ - Whole Tone or Major Second===

A rather smallish whole tone. Sometimes called melodically dull. As it falls between (and functions as) just whole tones 9:8 and 10:9, 5\31 is considered a "meantone". Two meantones make a near-just major third. Perhaps it is worth noting that its relative narrowness (to JI 9/8) makes it easier to distinguish from the 8/7 approximation. And although it is over 10¢ flat of 9/8, 5\31 can function as a somewhat "active" (as opposed to perfectly stable) harmonic ninth, and it effective in combination with the also-narrow 11th harmonic. Indeed, the 11/9 approximation is excellent. Generates [[Gamelismic clan|hemithirds temperament]] and [[Wuerschmidt family|hermiwuerschmidt temperament]].

A rather smallish whole tone. Sometimes called melodically dull. As it falls between (and functions as) just whole tones 9:8 and 10:9, 5\31 is considered a "meantone". Two meantones make a near-just major third. Perhaps it is worth noting that its relative narrowness (to JI 9/8) makes it easier to distinguish from the 8/7 approximation. And although it is over 10¢ flat of 9/8, 5\31 can function as a somewhat "active" (as opposed to perfectly stable) harmonic ninth, and it can be effective in combination with the also-narrow 11th harmonic. Indeed, the 11/9 approximation is excellent. Try, for instance 31's version of a 4:6:9:11 chord (steps 0-18-36-45). Generates [[Gamelismic clan|hemithirds temperament]] and [[Wuerschmidt family|hermiwuerschmidt temperament]].

====MOS Scales generated by 5\31:====

||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||

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===11\31 octave - approx. 425.806¢ - Supermajor Third===

11\31 functions as 14:11 (417.51¢), 23:18 (424.36¢), 32:25 (427.37¢), 9:7 (435.08¢) and others. Generates [[Meantone family|squares temperament]].

11\31 functions as 14:11 (417.51¢), 23:18 (424.36¢), 32:25 (427.37¢), 9:7 (435.08¢) and others. In meantone temperament, it is a diminished fourth, eg. C to Fb. Generates [[Meantone family|squares temperament]].

====MOS Scales generated by 11\31:====

||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||

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<br />

<h3 id="toc9"><a name="Intervals--5\31 octave - approx. 193.55¢ - Whole Tone or Major Second"></a>5\31 octave - approx. 193.55¢ - Whole Tone or Major Second</h3>

A rather smallish whole tone. Sometimes called melodically dull. As it falls between (and functions as) just whole tones 9:8 and 10:9, 5\31 is considered a &quot;meantone&quot;. Two meantones make a near-just major third. Perhaps it is worth noting that its relative narrowness (to JI 9/8) makes it easier to distinguish from the 8/7 approximation. And although it is over 10¢ flat of 9/8, 5\31 can function as a somewhat &quot;active&quot; (as opposed to perfectly stable) harmonic ninth, and it effective in combination with the also-narrow 11th harmonic. Indeed, the 11/9 approximation is excellent. Generates <a class="wiki_link" href="/Gamelismic%20clan">hemithirds temperament</a> and <a class="wiki_link" href="/Wuerschmidt%20family">hermiwuerschmidt temperament</a>.<br />

A rather smallish whole tone. Sometimes called melodically dull. As it falls between (and functions as) just whole tones 9:8 and 10:9, 5\31 is considered a &quot;meantone&quot;. Two meantones make a near-just major third. Perhaps it is worth noting that its relative narrowness (to JI 9/8) makes it easier to distinguish from the 8/7 approximation. And although it is over 10¢ flat of 9/8, 5\31 can function as a somewhat &quot;active&quot; (as opposed to perfectly stable) harmonic ninth, and it can be effective in combination with the also-narrow 11th harmonic. Indeed, the 11/9 approximation is excellent. Try, for instance 31's version of a 4:6:9:11 chord (steps 0-18-36-45). Generates <a class="wiki_link" href="/Gamelismic%20clan">hemithirds temperament</a> and <a class="wiki_link" href="/Wuerschmidt%20family">hermiwuerschmidt temperament</a>.<br />

<h4 id="toc10"><a name="Intervals--5\31 octave - approx. 193.55¢ - Whole Tone or Major Second-MOS Scales generated by 5\31:"></a>MOS Scales generated by 5\31:</h4>

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<br />

<h3 id="toc21"><a name="Intervals--11\31 octave - approx. 425.806¢ - Supermajor Third"></a>11\31 octave - approx. 425.806¢ - Supermajor Third</h3>

11\31 functions as 14:11 (417.51¢), 23:18 (424.36¢), 32:25 (427.37¢), 9:7 (435.08¢) and others. Generates <a class="wiki_link" href="/Meantone%20family">squares temperament</a>.<br />

11\31 functions as 14:11 (417.51¢), 23:18 (424.36¢), 32:25 (427.37¢), 9:7 (435.08¢) and others. In meantone temperament, it is a diminished fourth, eg. C to Fb. Generates <a class="wiki_link" href="/Meantone%20family">squares temperament</a>.<br />

<h4 id="toc22"><a name="Intervals--11\31 octave - approx. 425.806¢ - Supermajor Third-MOS Scales generated by 11\31:"></a>MOS Scales generated by 11\31:</h4>

@@ 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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2012-08-26 10:38:23 UTC</tt>.<br>
+: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2012-08-26 10:45:38 UTC</tt>.<br>
-: The original revision id was <tt>359972233</tt>.<br>
+: The original revision id was <tt>359972909</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 64: / Line 64: @@
 ===5\31 octave - approx. 193.55¢ - Whole Tone or Major Second===
-A rather smallish whole tone. Sometimes called melodically dull. As it falls between (and functions as) just whole tones 9:8 and 10:9, 5\31 is considered a "meantone". Two meantones make a near-just major third. Perhaps it is worth noting that its relative narrowness (to JI 9/8) makes it easier to distinguish from the 8/7 approximation. And although it is over 10¢ flat of 9/8, 5\31 can function as a somewhat "active" (as opposed to perfectly stable) harmonic ninth, and it effective in combination with the also-narrow 11th harmonic. Indeed, the 11/9 approximation is excellent. Generates [[Gamelismic clan|hemithirds temperament]] and [[Wuerschmidt family|hermiwuerschmidt temperament]].
+A rather smallish whole tone. Sometimes called melodically dull. As it falls between (and functions as) just whole tones 9:8 and 10:9, 5\31 is considered a "meantone". Two meantones make a near-just major third. Perhaps it is worth noting that its relative narrowness (to JI 9/8) makes it easier to distinguish from the 8/7 approximation. And although it is over 10¢ flat of 9/8, 5\31 can function as a somewhat "active" (as opposed to perfectly stable) harmonic ninth, and it can be effective in combination with the also-narrow 11th harmonic. Indeed, the 11/9 approximation is excellent. Try, for instance 31's version of a 4:6:9:11 chord (steps 0-18-36-45). Generates [[Gamelismic clan|hemithirds temperament]] and [[Wuerschmidt family|hermiwuerschmidt temperament]].
 ====MOS Scales generated by 5\31:====
 ||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||
@@ Line 134: / Line 134: @@
 ===11\31 octave - approx. 425.806¢ - Supermajor Third===
-\31 functions as 14:11 (417.51¢), 23:18 (424.36¢), 32:25 (427.37¢), 9:7 (435.08¢) and others. Generates [[Meantone family|squares temperament]].
+\31 functions as 14:11 (417.51¢), 23:18 (424.36¢), 32:25 (427.37¢), 9:7 (435.08¢) and others. In meantone temperament, it is a diminished fourth, eg. C to Fb. Generates [[Meantone family|squares temperament]].
 ====MOS Scales generated by 11\31:====
 ||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||
@@ Line 1,425: / Line 1,425: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc9"&gt;&lt;a name="Intervals--5\31 octave - approx. 193.55¢ - Whole Tone or Major Second"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;5\31 octave - approx. 193.55¢ - Whole Tone or Major Second&lt;/h3&gt;
-  A rather smallish whole tone. Sometimes called melodically dull. As it falls between (and functions as) just whole tones 9:8 and 10:9, 5\31 is considered a &amp;quot;meantone&amp;quot;. Two meantones make a near-just major third. Perhaps it is worth noting that its relative narrowness (to JI 9/8) makes it easier to distinguish from the 8/7 approximation. And although it is over 10¢ flat of 9/8, 5\31 can function as a somewhat &amp;quot;active&amp;quot; (as opposed to perfectly stable) harmonic ninth, and it effective in combination with the also-narrow 11th harmonic. Indeed, the 11/9 approximation is excellent. Generates &lt;a class="wiki_link" href="/Gamelismic%20clan"&gt;hemithirds temperament&lt;/a&gt; and &lt;a class="wiki_link" href="/Wuerschmidt%20family"&gt;hermiwuerschmidt temperament&lt;/a&gt;.&lt;br /&gt;
+  A rather smallish whole tone. Sometimes called melodically dull. As it falls between (and functions as) just whole tones 9:8 and 10:9, 5\31 is considered a &amp;quot;meantone&amp;quot;. Two meantones make a near-just major third. Perhaps it is worth noting that its relative narrowness (to JI 9/8) makes it easier to distinguish from the 8/7 approximation. And although it is over 10¢ flat of 9/8, 5\31 can function as a somewhat &amp;quot;active&amp;quot; (as opposed to perfectly stable) harmonic ninth, and it can be effective in combination with the also-narrow 11th harmonic. Indeed, the 11/9 approximation is excellent. Try, for instance 31's version of a 4:6:9:11 chord (steps 0-18-36-45). Generates &lt;a class="wiki_link" href="/Gamelismic%20clan"&gt;hemithirds temperament&lt;/a&gt; and &lt;a class="wiki_link" href="/Wuerschmidt%20family"&gt;hermiwuerschmidt temperament&lt;/a&gt;.&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc10"&gt;&lt;a name="Intervals--5\31 octave - approx. 193.55¢ - Whole Tone or Major Second-MOS Scales generated by 5\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;MOS Scales generated by 5\31:&lt;/h4&gt;
@@ Line 4,406: / Line 4,406: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc21"&gt;&lt;a name="Intervals--11\31 octave - approx. 425.806¢ - Supermajor Third"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;11\31 octave - approx. 425.806¢ - Supermajor Third&lt;/h3&gt;
-\31 functions as 14:11 (417.51¢), 23:18 (424.36¢), 32:25 (427.37¢), 9:7 (435.08¢) and others. Generates &lt;a class="wiki_link" href="/Meantone%20family"&gt;squares temperament&lt;/a&gt;.&lt;br /&gt;
+\31 functions as 14:11 (417.51¢), 23:18 (424.36¢), 32:25 (427.37¢), 9:7 (435.08¢) and others. In meantone temperament, it is a diminished fourth, eg. C to Fb. Generates &lt;a class="wiki_link" href="/Meantone%20family"&gt;squares temperament&lt;/a&gt;.&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc22"&gt;&lt;a name="Intervals--11\31 octave - approx. 425.806¢ - Supermajor Third-MOS Scales generated by 11\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;MOS Scales generated by 11\31:&lt;/h4&gt;

31edo: Difference between revisions

Wikispaces>Andrew_Heathwaite