UDP: 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:mbattaglia1|mbattaglia1]] and made on <tt>2011-11-25 15:46:17 UTC</tt>.<br>

: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2011-11-25 15:49:14 UTC</tt>.<br>

: The original revision id was <tt>~~279063540~~</tt>.<br>

: The original revision id was <tt>279064020</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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=Examples=

For example, the proper generator for meantone[7] is the perfect fifth, because it's larger than the other specific interval it shares a class with, the diminished fifth. Consequentially, meantone[7]'s Ionian mode is 5|1(1), which is 5|1 for short, and Aeolian is 2|4. We can add accidentals as well, so that meantone's harmonic minor is 2|4 #7.

For example, the proper generator for meantone[7] is the perfect fifth, because it's larger than the other specific interval it shares a class with, the diminished fifth. Consequentially, meantone[7]'s Ionian mode is 5|1(1), which is 5|1 for short, because it contains five chroma-positive generators up from the root and one down, as in the diagram F-[C]-G-D-A-E-B for C ionian. This also means it has five "sharper" scale degrees - the second, third, fifth, sixth, and seventh - and one "flatter" scale degree - the fourth. If we want to sharpen the fourth to turn it into an augmented fourth, we arrive at 6|0 or [C]-G-D-A-E-B-F#. Conversely, Aeolian mode, with only two sharp scale degrees - the second and fifth - is 2|4. We can add accidentals as well, so that meantone's harmonic minor is 2|4 #7.

~~On the other hand, the~~ chroma-positive generator for porcupine[7] is the larger 7th, which is about ~11/6; as a consequence, porcupine[7]'s Lssssss mode is 6|0, and sssLsss is 3|3. Likewise, mavila[7]'s ssLsssL anti-Ionian is 1|5, and Mavila[9]'s LLsLLLsLL "Olympian" mode is 4|4.

The chroma-positive generator for porcupine[7] is the larger 7th, which is about ~11/6; as a consequence, porcupine[7]'s Lssssss mode is 6|0, and sssLsss is 3|3. Likewise, mavila[7]'s ssLsssL anti-Ionian is 1|5, and Mavila[9]'s LLsLLLsLL "Olympian" mode is 4|4.

It should be noted that the chroma-positive generator will vary from MOS to MOS even within the same temperament. For example, the chroma-positive generator for meantone[7] is the ~3/2, but is the ~4/3 for meantone[5].

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<h1 id="toc3"><a name="Examples"></a>Examples</h1>

<br />

For example, the proper generator for meantone[7] is the perfect fifth, because it's larger than the other specific interval it shares a class with, the diminished fifth. Consequentially, meantone[7]'s Ionian mode is 5|1(1), which is 5|1 for short, and Aeolian is 2|4. We can add accidentals as well, so that meantone's harmonic minor is 2|4 #7.<br />

For example, the proper generator for meantone[7] is the perfect fifth, because it's larger than the other specific interval it shares a class with, the diminished fifth. Consequentially, meantone[7]'s Ionian mode is 5|1(1), which is 5|1 for short, because it contains five chroma-positive generators up from the root and one down, as in the diagram F-[C]-G-D-A-E-B for C ionian. This also means it has five &quot;sharper&quot; scale degrees - the second, third, fifth, sixth, and seventh - and one &quot;flatter&quot; scale degree - the fourth. If we want to sharpen the fourth to turn it into an augmented fourth, we arrive at 6|0 or [C]-G-D-A-E-B-F#. Conversely, Aeolian mode, with only two sharp scale degrees - the second and fifth - is 2|4. We can add accidentals as well, so that meantone's harmonic minor is 2|4 #7.<br />

<br />

~~On the other hand, the~~ chroma-positive generator for porcupine[7] is the larger 7th, which is about ~11/6; as a consequence, porcupine[7]'s Lssssss mode is 6|0, and sssLsss is 3|3. Likewise, mavila[7]'s ssLsssL anti-Ionian is 1|5, and Mavila[9]'s LLsLLLsLL &quot;Olympian&quot; mode is 4|4.<br />

The chroma-positive generator for porcupine[7] is the larger 7th, which is about ~11/6; as a consequence, porcupine[7]'s Lssssss mode is 6|0, and sssLsss is 3|3. Likewise, mavila[7]'s ssLsssL anti-Ionian is 1|5, and Mavila[9]'s LLsLLLsLL &quot;Olympian&quot; mode is 4|4.<br />

<br />

It should be noted that the chroma-positive generator will vary from MOS to MOS even within the same temperament. For example, the chroma-positive generator for meantone[7] is the ~3/2, but is the ~4/3 for meantone[5].<br />

@@ 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:mbattaglia1|mbattaglia1]] and made on <tt>2011-11-25 15:46:17 UTC</tt>.<br>
+: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2011-11-25 15:49:14 UTC</tt>.<br>
-: The original revision id was <tt>279063540</tt>.<br>
+: The original revision id was <tt>279064020</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 35: / Line 35: @@
 =Examples=
-For example, the proper generator for meantone[7] is the perfect fifth, because it's larger than the other specific interval it shares a class with, the diminished fifth. Consequentially, meantone[7]'s Ionian mode is 5|1(1), which is 5|1 for short, and Aeolian is 2|4. We can add accidentals as well, so that meantone's harmonic minor is 2|4 #7.
+For example, the proper generator for meantone[7] is the perfect fifth, because it's larger than the other specific interval it shares a class with, the diminished fifth. Consequentially, meantone[7]'s Ionian mode is 5|1(1), which is 5|1 for short, because it contains five chroma-positive generators up from the root and one down, as in the diagram F-[C]-G-D-A-E-B for C ionian. This also means it has five "sharper" scale degrees - the second, third, fifth, sixth, and seventh - and one "flatter" scale degree - the fourth. If we want to sharpen the fourth to turn it into an augmented fourth, we arrive at 6|0 or [C]-G-D-A-E-B-F#. Conversely, Aeolian mode, with only two sharp scale degrees - the second and fifth - is 2|4. We can add accidentals as well, so that meantone's harmonic minor is 2|4 #7.
-On the other hand, the chroma-positive generator for porcupine[7] is the larger 7th, which is about ~11/6; as a consequence, porcupine[7]'s Lssssss mode is 6|0, and sssLsss is 3|3. Likewise, mavila[7]'s ssLsssL anti-Ionian is 1|5, and Mavila[9]'s LLsLLLsLL "Olympian" mode is 4|4.
+The chroma-positive generator for porcupine[7] is the larger 7th, which is about ~11/6; as a consequence, porcupine[7]'s Lssssss mode is 6|0, and sssLsss is 3|3. Likewise, mavila[7]'s ssLsssL anti-Ionian is 1|5, and Mavila[9]'s LLsLLLsLL "Olympian" mode is 4|4.
 It should be noted that the chroma-positive generator will vary from MOS to MOS even within the same temperament. For example, the chroma-positive generator for meantone[7] is the ~3/2, but is the ~4/3 for meantone[5].
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 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Examples"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Examples&lt;/h1&gt;
   &lt;br /&gt;
-For example, the proper generator for meantone[7] is the perfect fifth, because it's larger than the other specific interval it shares a class with, the diminished fifth. Consequentially, meantone[7]'s Ionian mode is 5|1(1), which is 5|1 for short, and Aeolian is 2|4. We can add accidentals as well, so that meantone's harmonic minor is 2|4 #7.&lt;br /&gt;
+For example, the proper generator for meantone[7] is the perfect fifth, because it's larger than the other specific interval it shares a class with, the diminished fifth. Consequentially, meantone[7]'s Ionian mode is 5|1(1), which is 5|1 for short, because it contains five chroma-positive generators up from the root and one down, as in the diagram F-[C]-G-D-A-E-B for C ionian. This also means it has five &amp;quot;sharper&amp;quot; scale degrees - the second, third, fifth, sixth, and seventh - and one &amp;quot;flatter&amp;quot; scale degree - the fourth. If we want to sharpen the fourth to turn it into an augmented fourth, we arrive at 6|0 or [C]-G-D-A-E-B-F#. Conversely, Aeolian mode, with only two sharp scale degrees - the second and fifth - is 2|4. We can add accidentals as well, so that meantone's harmonic minor is 2|4 #7.&lt;br /&gt;
 &lt;br /&gt;
-On the other hand, the chroma-positive generator for porcupine[7] is the larger 7th, which is about ~11/6; as a consequence, porcupine[7]'s Lssssss mode is 6|0, and sssLsss is 3|3. Likewise, mavila[7]'s ssLsssL anti-Ionian is 1|5, and Mavila[9]'s LLsLLLsLL &amp;quot;Olympian&amp;quot; mode is 4|4.&lt;br /&gt;
+The chroma-positive generator for porcupine[7] is the larger 7th, which is about ~11/6; as a consequence, porcupine[7]'s Lssssss mode is 6|0, and sssLsss is 3|3. Likewise, mavila[7]'s ssLsssL anti-Ionian is 1|5, and Mavila[9]'s LLsLLLsLL &amp;quot;Olympian&amp;quot; mode is 4|4.&lt;br /&gt;
 &lt;br /&gt;
 It should be noted that the chroma-positive generator will vary from MOS to MOS even within the same temperament. For example, the chroma-positive generator for meantone[7] is the ~3/2, but is the ~4/3 for meantone[5].&lt;br /&gt;