MODMOS scale: Difference between revisions
Wikispaces>mbattaglia1 **Imported revision 210413818 - Original comment: ** |
Wikispaces>mbattaglia1 **Imported revision 210508644 - 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:mbattaglia1|mbattaglia1]] and made on <tt>2011-03-14 | : This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2011-03-14 21:27:06 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>210508644</tt>.<br> | ||
: The revision comment was: <tt></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> | 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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=Examples= | =Examples= | ||
Consider the MOS of 1/4-comma meantone, where the generator g is log2(5)/4 = 0.58048 octaves, or 696.578 cents. The seven note MOS is the diatonic scale tuned in 1/4 comma tuning, with large step L a whole tone of 193.157 cents and small step s a diatonic semitone of 117.108 cents. L-s is the chromatic semitone, 78.049 cents. This is the interval whose adjustment of a note up or down is represented by a sharp # or flat b symbol. The diatonic scale has steps LLsLLLs, which in the key of C can be written CDEFGABC'. From the definition of a MODMOS, if we add sharps and flats to this, and | Consider the MOS of 1/4-comma meantone, where the generator g is log2(5)/4 = 0.58048 octaves, or 696.578 cents. The seven note MOS is the diatonic scale tuned in 1/4 comma tuning, with large step L a whole tone of 193.157 cents and small step s a diatonic semitone of 117.108 cents. L-s is the chromatic semitone, 78.049 cents. This is the interval whose adjustment of a note up or down is represented by a sharp # or flat b symbol. The diatonic scale has steps LLsLLLs, which in the key of C can be written CDEFGABC'. From the definition of a MODMOS, if we add sharps and flats to this, and do not get another diatonic scale, then we have a MODMOS. For example LsLLLLs, which is CDEbFGABC', is the melodic minor scale, which is therefore a MODMOS. The harmonic minor scale is CDEbFGAbBC', and is therefore also a MODMOS. However, the natural minor, CDEbFGAbBbC' is a mode of the diatonic scale, and a MOS rather than a MODMOS. | ||
do not get another diatonic scale, then we have a MODMOS. For example LsLLLLs, which is CDEbFGABC', is the melodic minor scale, which is therefore a MODMOS. The harmonic minor scale is CDEbFGAbBC', and is therefore also a MODMOS. However, the natural minor, CDEbFGAbBbC' is a mode of the diatonic scale, and a MOS rather than a MODMOS. | |||
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#.) | ||
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=Proper MODMOS= | =Proper MODMOS= | ||
By confining attention to MODMOS which are [[http://en.wikipedia.org/wiki/Rothenberg_propriety|Rothenberg proper]], one may survey all of the proper MODMOS for a particular proper MOS, which are of | By confining attention to MODMOS which are [[http://en.wikipedia.org/wiki/Rothenberg_propriety|Rothenberg proper]], one may survey all of the proper MODMOS for a particular proper MOS, which are of special interest. | ||
In keeping with tradition, we will may the # sign to denote sharpening by a chroma, b to denote flatening, and numbers to denote scale degrees of the base MOS, where the first note is scale degree 1. | In keeping with tradition, we will may the # sign to denote sharpening by a chroma, b to denote flatening, and numbers to denote scale degrees of the base MOS, where the first note is scale degree 1. | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Examples"></a><!-- ws:end:WikiTextHeadingRule:2 -->Examples</h1> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Examples"></a><!-- ws:end:WikiTextHeadingRule:2 -->Examples</h1> | ||
Consider the MOS of 1/4-comma meantone, where the generator g is log2(5)/4 = 0.58048 octaves, or 696.578 cents. The seven note MOS is the diatonic scale tuned in 1/4 comma tuning, with large step L a whole tone of 193.157 cents and small step s a diatonic semitone of 117.108 cents. L-s is the chromatic semitone, 78.049 cents. This is the interval whose adjustment of a note up or down is represented by a sharp # or flat b symbol. The diatonic scale has steps LLsLLLs, which in the key of C can be written CDEFGABC'. From the definition of a MODMOS, if we add sharps and flats to this, and | Consider the MOS of 1/4-comma meantone, where the generator g is log2(5)/4 = 0.58048 octaves, or 696.578 cents. The seven note MOS is the diatonic scale tuned in 1/4 comma tuning, with large step L a whole tone of 193.157 cents and small step s a diatonic semitone of 117.108 cents. L-s is the chromatic semitone, 78.049 cents. This is the interval whose adjustment of a note up or down is represented by a sharp # or flat b symbol. The diatonic scale has steps LLsLLLs, which in the key of C can be written CDEFGABC'. From the definition of a MODMOS, if we add sharps and flats to this, and do not get another diatonic scale, then we have a MODMOS. For example LsLLLLs, which is CDEbFGABC', is the melodic minor scale, which is therefore a MODMOS. The harmonic minor scale is CDEbFGAbBC', and is therefore also a MODMOS. However, the natural minor, CDEbFGAbBbC' is a mode of the diatonic scale, and a MOS rather than a MODMOS.<br /> | ||
do not get another diatonic scale, then we have a MODMOS. For example LsLLLLs, which is CDEbFGABC', is the melodic minor scale, which is therefore a MODMOS. The harmonic minor scale is CDEbFGAbBC', and is therefore also a MODMOS. However, the natural minor, CDEbFGAbBbC' is a mode of the diatonic scale, and a MOS rather than a MODMOS.<br /> | |||
<br /> | <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 /> | 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 /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Proper MODMOS"></a><!-- ws:end:WikiTextHeadingRule:6 -->Proper MODMOS</h1> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Proper MODMOS"></a><!-- ws:end:WikiTextHeadingRule:6 -->Proper MODMOS</h1> | ||
By confining attention to MODMOS which are <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Rothenberg_propriety" rel="nofollow">Rothenberg proper</a>, one may survey all of the proper MODMOS for a particular proper MOS, which are of | By confining attention to MODMOS which are <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Rothenberg_propriety" rel="nofollow">Rothenberg proper</a>, one may survey all of the proper MODMOS for a particular proper MOS, which are of special interest.<br /> | ||
<br /> | <br /> | ||
In keeping with tradition, we will may the # sign to denote sharpening by a chroma, b to denote flatening, and numbers to denote scale degrees of the base MOS, where the first note is scale degree 1. <br /> | In keeping with tradition, we will may the # sign to denote sharpening by a chroma, b to denote flatening, and numbers to denote scale degrees of the base MOS, where the first note is scale degree 1. <br /> | ||