UDP: Difference between revisions
Wikispaces>mbattaglia1 **Imported revision 270590048 - Original comment: ** |
Wikispaces>mbattaglia1 **Imported revision 275514280 - 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>2011-11- | : This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2011-11-15 03:16:22 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>275514280</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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=Definition= | =Definition= | ||
The UDP notation for any mode is U|D | The UDP notation for any mode is U|D(P), where "u" specifies the number of chroma-aligned generators "up," d specifies the number of chroma-aligned generators "down," and p specifies the number of periods per equivalence interval. The chroma-aligned generator is the one such that more generators "up" also means more "major" scale degrees, or more generally, more "large" intervals that contain the root of the scale. | ||
When the period is one, the (p) can be left off by convention for the short form of UDP notation, such that meantone's Ionian mode can simply be stated 5|1 instead of 5|1(1). | When the period is one, the (p) can be left off by convention for the short form of UDP notation, such that meantone's Ionian mode can simply be stated 5|1 instead of 5|1(1). | ||
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<ul><li>Meantone[7]'s ionian mode is 5|1(1), abbreviated 5|1 for short.</li><li>Melodic minor is 5|1(1) b3, abbreviated 5|1 b3 for short, but could also be 3|3(1) #7, abbreviated 3|3 #7 for short.</li><li>Paul Erlich's standard pentachordal major is 4|4(2) #8, or alternatively 6|2(2) b3.</li></ul><br /> | <ul><li>Meantone[7]'s ionian mode is 5|1(1), abbreviated 5|1 for short.</li><li>Melodic minor is 5|1(1) b3, abbreviated 5|1 b3 for short, but could also be 3|3(1) #7, abbreviated 3|3 #7 for short.</li><li>Paul Erlich's standard pentachordal major is 4|4(2) #8, or alternatively 6|2(2) b3.</li></ul><br /> | ||
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The UDP notation for any mode is U|D | The UDP notation for any mode is U|D(P), where &quot;u&quot; specifies the number of chroma-aligned generators &quot;up,&quot; d specifies the number of chroma-aligned generators &quot;down,&quot; and p specifies the number of periods per equivalence interval. The chroma-aligned generator is the one such that more generators &quot;up&quot; also means more &quot;major&quot; scale degrees, or more generally, more &quot;large&quot; intervals that contain the root of the scale.<br /> | ||
<br /> | <br /> | ||
When the period is one, the (p) can be left off by convention for the short form of UDP notation, such that meantone's Ionian mode can simply be stated 5|1 instead of 5|1(1).<br /> | When the period is one, the (p) can be left off by convention for the short form of UDP notation, such that meantone's Ionian mode can simply be stated 5|1 instead of 5|1(1).<br /> | ||