MODMOS scale: Difference between revisions
Wikispaces>genewardsmith **Imported revision 210336156 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 210370570 - 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:genewardsmith|genewardsmith]] and made on <tt>2011-03-14 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-14 14:58:27 UTC</tt>.<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#.) | 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. | |||
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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 /> | 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 /> | ||
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<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.<br /> | ||
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