MODMOS scale: 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:genewardsmith|genewardsmith]] and made on <tt>2011-03-~~14 22~~:57:31 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-15 11:15:46 UTC</tt>.<br>

: The original revision id was <tt>~~210530082~~</tt>.<br>

: The original revision id was <tt>210673034</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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If we take the 12 note MOS rather than the seven notes of the diatonic scale, then the chroma is a diesis, which in 1/4 comma meantone is exactly 128/125, or 41.059 cents. However, other meantone tunings will give it a different size, and in [[50edo|50et]], for example, it is exactly 48 cents in size. Subtracting this adjusts a note twelve fifths up on the chain of fifths, and adding it adjusts it twelve notes down. If we take a chain of eleven 50et fifths up from the unison to create a 12-note MOS, so that we have a generator chain from 0 to 11, we may adjust the 3 up to 15 and the 7 up to 19. This leads to the scale called "smithgw_modmos12a.scl" in the [[http://www.huygens-fokker.org/docs/scales.zip|Scala Scale Archive]]. Another MODMOS of Meantone[12] in the archive is wreckpop, "smithgw_wreckpop.scl". This takes a gamut of Meantone[12] from -4 to 7, which we may call from Ab to F#, and adjusts the 5 (B) up a 48 cent diesis, and so down to -7 fifths, or Cb, and the -2 (Bb) down a diesis, and so up the chain of fifths to 10 (A#.)

Of course, MODMOS are not confined to scales of meantone. If we take the [[Hobbits|hobbit scale]] [[prodigy11]] and tune it in a miracle tuning such as [[72edo|72et]], we obtain a MODMOS of Miracle[11]. In general, ~~choosing~~ a rank three ~~hobbit~~ with a tuning very close to a rank two temperament and ~~tuning~~ a hobbit for it in ~~a tuning for~~ that rank two temperament is an ~~excellent method of constructing~~ interesting MODMOS ~~scales~~. It is particularly useful in connection with MODMOS of temperaments where the basic MOS doesn't contain a lot of consonant chords such as Miracle[11].

Of course, MODMOS are not confined to scales of meantone. If we take the [[Hobbits|hobbit scale]] [[prodigy11]] and tune it in a miracle tuning such as [[72edo|72et]], we obtain a MODMOS of Miracle[11]. In general, if we choose a rank three temperament with an optimal tuning very close to an optimal tuning for a rank two temperament and then tune a hobbit for it in that optimal rank two temperament tuning, we are very likely to construct an interesting MODMOS scale. It is particularly useful in connection with MODMOS of temperaments where the basic MOS doesn't contain a lot of consonant chords, such as Miracle[11].

=MODMOS in Jazz=

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If we take the 12 note MOS rather than the seven notes of the diatonic scale, then the chroma is a diesis, which in 1/4 comma meantone is exactly 128/125, or 41.059 cents. However, other meantone tunings will give it a different size, and in <a class="wiki_link" href="/50edo">50et</a>, for example, it is exactly 48 cents in size. Subtracting this adjusts a note twelve fifths up on the chain of fifths, and adding it adjusts it twelve notes down. If we take a chain of eleven 50et fifths up from the unison to create a 12-note MOS, so that we have a generator chain from 0 to 11, we may adjust the 3 up to 15 and the 7 up to 19. This leads to the scale called &quot;smithgw_modmos12a.scl&quot; in the <a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/scales.zip" rel="nofollow">Scala Scale Archive</a>. Another MODMOS of Meantone[12] in the archive is wreckpop, &quot;smithgw_wreckpop.scl&quot;. This takes a gamut of Meantone[12] from -4 to 7, which we may call from Ab to F#, and adjusts the 5 (B) up a 48 cent diesis, and so down to -7 fifths, or Cb, and the -2 (Bb) down a diesis, and so up the chain of fifths to 10 (A#.)<br />

<br />

Of course, MODMOS are not confined to scales of meantone. If we take the <a class="wiki_link" href="/Hobbits">hobbit scale</a> <a class="wiki_link" href="/prodigy11">prodigy11</a> and tune it in a miracle tuning such as <a class="wiki_link" href="/72edo">72et</a>, we obtain a MODMOS of Miracle[11]. In general, ~~choosing~~ a rank three ~~hobbit~~ with a tuning very close to a rank two temperament and ~~tuning~~ a hobbit for it in ~~a tuning for~~ that rank two temperament is an ~~excellent method of constructing~~ interesting MODMOS ~~scales~~. It is particularly useful in connection with MODMOS of temperaments where the basic MOS doesn't contain a lot of consonant chords such as Miracle[11].<br />

Of course, MODMOS are not confined to scales of meantone. If we take the <a class="wiki_link" href="/Hobbits">hobbit scale</a> <a class="wiki_link" href="/prodigy11">prodigy11</a> and tune it in a miracle tuning such as <a class="wiki_link" href="/72edo">72et</a>, we obtain a MODMOS of Miracle[11]. In general, if we choose a rank three temperament with an optimal tuning very close to an optimal tuning for a rank two temperament and then tune a hobbit for it in that optimal rank two temperament tuning, we are very likely to construct an interesting MODMOS scale. It is particularly useful in connection with MODMOS of temperaments where the basic MOS doesn't contain a lot of consonant chords, such as Miracle[11].<br />

<br />

<h1 id="toc2"><a name="MODMOS in Jazz"></a>MODMOS in Jazz</h1>

@@ 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:genewardsmith|genewardsmith]] and made on <tt>2011-03-14 22:57:31 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-15 11:15:46 UTC</tt>.<br>
-: The original revision id was <tt>210530082</tt>.<br>
+: The original revision id was <tt>210673034</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 17: / Line 17: @@
 If we take the 12 note MOS rather than the seven notes of the diatonic scale, then the chroma is a diesis, which in 1/4 comma meantone is exactly 128/125, or 41.059 cents. However, other meantone tunings will give it a different size, and in [[50edo|50et]], for example, it is exactly 48 cents in size. Subtracting this adjusts a note twelve fifths up on the chain of fifths, and adding it adjusts it twelve notes down. If we take a chain of eleven 50et fifths up from the unison to create a 12-note MOS, so that we have a generator chain from 0 to 11, we may adjust the 3 up to 15 and the 7 up to 19. This leads to the scale called "smithgw_modmos12a.scl" in the [[http://www.huygens-fokker.org/docs/scales.zip|Scala Scale Archive]]. Another MODMOS of Meantone[12] in the archive is wreckpop, "smithgw_wreckpop.scl". This takes a gamut of Meantone[12] from -4 to 7, which we may call from Ab to F#, and adjusts the 5 (B) up a 48 cent diesis, and so down to -7 fifths, or Cb, and the -2 (Bb) down a diesis, and so up the chain of fifths to 10 (A#.)
-Of course, MODMOS are not confined to scales of meantone. If we take the [[Hobbits|hobbit scale]] [[prodigy11]] and tune it in a miracle tuning such as [[72edo|72et]], we obtain a MODMOS of Miracle[11]. In general, choosing a rank three hobbit with a tuning very close to a rank two temperament and tuning a hobbit for it in a tuning for that rank two temperament is an excellent method of constructing interesting MODMOS scales. It is particularly useful in connection with MODMOS of temperaments where the basic MOS doesn't contain a lot of consonant chords such as Miracle[11].
+Of course, MODMOS are not confined to scales of meantone. If we take the [[Hobbits|hobbit scale]] [[prodigy11]] and tune it in a miracle tuning such as [[72edo|72et]], we obtain a MODMOS of Miracle[11]. In general, if we choose a rank three temperament with an optimal tuning very close to an optimal tuning for a rank two temperament and then tune a hobbit for it in that optimal rank two temperament tuning, we are very likely to construct an interesting MODMOS scale. It is particularly useful in connection with MODMOS of temperaments where the basic MOS doesn't contain a lot of consonant chords, such as Miracle[11].
 =MODMOS in Jazz=
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 If we take the 12 note MOS rather than the seven notes of the diatonic scale, then the chroma is a diesis, which in 1/4 comma meantone is exactly 128/125, or 41.059 cents. However, other meantone tunings will give it a different size, and in &lt;a class="wiki_link" href="/50edo"&gt;50et&lt;/a&gt;, for example, it is exactly 48 cents in size. Subtracting this adjusts a note twelve fifths up on the chain of fifths, and adding it adjusts it twelve notes down. If we take a chain of eleven 50et fifths up from the unison to create a 12-note MOS, so that we have a generator chain from 0 to 11, we may adjust the 3 up to 15 and the 7 up to 19. This leads to the scale called &amp;quot;smithgw_modmos12a.scl&amp;quot; in the &lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/scales.zip" rel="nofollow"&gt;Scala Scale Archive&lt;/a&gt;. Another MODMOS of Meantone[12] in the archive is wreckpop, &amp;quot;smithgw_wreckpop.scl&amp;quot;. This takes a gamut of Meantone[12] from -4 to 7, which we may call from Ab to F#, and adjusts the 5 (B) up a 48 cent diesis, and so down to -7 fifths, or Cb, and the -2 (Bb) down a diesis, and so up the chain of fifths to 10 (A#.)&lt;br /&gt;
 &lt;br /&gt;
-Of course, MODMOS are not confined to scales of meantone. If we take the &lt;a class="wiki_link" href="/Hobbits"&gt;hobbit scale&lt;/a&gt; &lt;a class="wiki_link" href="/prodigy11"&gt;prodigy11&lt;/a&gt; and tune it in a miracle tuning such as &lt;a class="wiki_link" href="/72edo"&gt;72et&lt;/a&gt;, we obtain a MODMOS of Miracle[11]. In general, choosing a rank three hobbit with a tuning very close to a rank two temperament and tuning a hobbit for it in a tuning for that rank two temperament is an excellent method of constructing interesting MODMOS scales. It is particularly useful in connection with MODMOS of temperaments where the basic MOS doesn't contain a lot of consonant chords such as Miracle[11].&lt;br /&gt;
+Of course, MODMOS are not confined to scales of meantone. If we take the &lt;a class="wiki_link" href="/Hobbits"&gt;hobbit scale&lt;/a&gt; &lt;a class="wiki_link" href="/prodigy11"&gt;prodigy11&lt;/a&gt; and tune it in a miracle tuning such as &lt;a class="wiki_link" href="/72edo"&gt;72et&lt;/a&gt;, we obtain a MODMOS of Miracle[11]. In general, if we choose a rank three temperament with an optimal tuning very close to an optimal tuning for a rank two temperament and then tune a hobbit for it in that optimal rank two temperament tuning, we are very likely to construct an interesting MODMOS scale. It is particularly useful in connection with MODMOS of temperaments where the basic MOS doesn't contain a lot of consonant chords, such as Miracle[11].&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="MODMOS in Jazz"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;MODMOS in Jazz&lt;/h1&gt;