UDP: Difference between revisions

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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Then Ionian[i] = Lydian[i+4]-Lydian[4], Mixolydian[i] = Lydian[i+8]-Lydian[8], Dorian[i]=Lydian[i+12]-Lydian[12], Aeolian[i] = Lydian[i+16]-Lydian[16], Phrygian[i] = Lydian[i+20]-Lydian[20], Locrian[i] = Lydian[i+24]-Lydian[24]. Lydian is the bottom mode, and Locrian is the top mode; if we attempt to go higher than Locrian by considering Locrian[i+4]-Locrian[4] = Lydian[i+28]-Lydian[28] we jump down the stack of modes to Lydian again. The "up" generator is Lydian[4] = 18, or in other words the meantone fifth. The Lydian mode takes the bottommost note of the chain of generators, choosing the "up" generator, and stacking notes, reducing modulo octaves, to obtain the scale. Starting with F, we go up the chain of fifths and get F-C-G-D-A-E-B, with F the tonic note, or 1/1 of the scale. Lydian, the bottom mode, has 6 modes above it and none below it, so that it is denoted 6|0. It is obtained by stacking six fifths (the "up" generator) above the tonic, and none below it, which is another way to get to 6|0. Ionian, with fives modes above and one below, is 5|1; this can also be seen as starting from C and going five fifths up to B, or one down to F.

=The Chroma-Aligned Generator=  

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Then Ionian[i] = Lydian[i+4]-Lydian[4], Mixolydian[i] = Lydian[i+8]-Lydian[8], Dorian[i]=Lydian[i+12]-Lydian[12], Aeolian[i] = Lydian[i+16]-Lydian[16], Phrygian[i] = Lydian[i+20]-Lydian[20], Locrian[i] = Lydian[i+24]-Lydian[24]. Lydian is the bottom mode, and Locrian is the top mode; if we attempt to go higher than Locrian by considering Locrian[i+4]-Locrian[4] = Lydian[i+28]-Lydian[28] we jump down the stack of modes to Lydian again. The &amp;quot;up&amp;quot; generator is Lydian[4] = 18, or in other words the meantone fifth. The Lydian mode takes the bottommost note of the chain of generators, choosing the &amp;quot;up&amp;quot; generator, and stacking notes, reducing modulo octaves, to obtain the scale. Starting with F, we go up the chain of fifths and get F-C-G-D-A-E-B, with F the tonic note, or 1/1 of the scale. Lydian, the bottom mode, has 6 modes above it and none below it, so that it is denoted 6|0. It is obtained by stacking six fifths (the &amp;quot;up&amp;quot; generator) above the tonic, and none below it, which is another way to get to 6|0. Ionian, with fives modes above and one below, is 5|1; this can also be seen as starting from C and going five fifths up to B, or one down to F.&lt;br /&gt;

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&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="The Chroma-Aligned Generator"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;The Chroma-Aligned Generator&lt;/h1&gt;