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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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-10-31 17:45:22 UTC</tt>.<br>
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-10-31 19:46:20 UTC</tt>.<br>
: The original revision id was <tt>270428564</tt>.<br>
: The original revision id was <tt>270457072</tt>.<br>
: The revision comment was: <tt></tt><br>
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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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...coming soon...
...coming soon...
Hm, try as I might, I can't get wikispaces to upload this image. Nevermind then.


==Modes of Porcupine[7]==  
==Modes of Porcupine[7]==  


The following modes are given in steps of 22edo. To generalize, 3 stands for the neutral third generating interval, and 4 stands for the wide major second. On the right is a contiguous chain of 7 tones separated by 6 iterations of the Porcupine generator.
The following modes are given in steps of 22edo. They are rotations of one moment of symmetry scale with two step sizes: a neutral tone (3\22) and a large whole tone (4\22). On the right is a contiguous chain of 7 tones separated by 6 iterations of the Porcupine generator. Modes in bold have a 3/2 approximation above the bass -- this can be verified easily by looking at the chain. The perfect fifth approximation is -3g, so every mode with a "-3" in the chain has a perfect fifth over the bass.


3 3 3 3 3 3 4 .. 0 1 2 3 4 5 6
3 3 3 3 3 3 4 .. 0 1 2 3 4 5 6
3 3 3 3 3 4 3 .. -1 0 1 2 3 4 5
3 3 3 3 3 4 3 .. -1 0 1 2 3 4 5
3 3 3 3 4 3 3 .. -2 -1 0 1 2 3 4
3 3 3 3 4 3 3 .. -2 -1 0 1 2 3 4
3 3 3 4 3 3 3 .. -3 -2 -1 0 1 2 3
**3 3 3 4 3 3 3 .. -3 -2 -1 0 1 2 3**
3 3 4 3 3 3 3 .. -4 -3 -2 -1 0 1 2
**3 3 4 3 3 3 3 .. -4 -3 -2 -1 0 1 2**
3 4 3 3 3 3 3 .. -5 -4 -3 -2 -1 0 1
**3 4 3 3 3 3 3 .. -5 -4 -3 -2 -1 0 1**
4 3 3 3 3 3 3 .. -6 -5 -4 -3 -2 -1 0
**4 3 3 3 3 3 3 .. -6 -5 -4 -3 -2 -1 0**


==Modes of Porcupine[7] that have one chromatic alteration==  
==Modes of Porcupine[7] that have one chromatic alteration==  


The following list includes all the modes (hopefully) that can be generated by shifting one tone of Porcupine[7] by one quartertone interval (chroma), which is one degree in 22edo. Underscores represent gaps in the chain of Porcupine generators. Note that lowering a tone by one chroma means sending it forward 7 spaces in the chain of generators, while raising a tone by one chroma means sending it backward 7 spaces in the chain of generators. This is how we wind up with such large gaps in the chain.
The following list includes all the modes (hopefully) that can be generated by shifting one tone of Porcupine[7] by one quartertone interval (chroma), which is one degree in 22edo. This produces scales with three step sizes -- in addition to a neutral tone (3\22) and large whole tone (4\22) there is now a semitone as well (2\22). In addition, two scales (and their rotations of course) have a 5-step subminor third. Underscores represent gaps in the chain of Porcupine generators. Note that lowering a tone by one quartertone interval (chroma) means sending it forward 7 spaces in the chain of generators, while raising a tone by one chroma means sending it backward 7 spaces in the chain of generators. This is how we wind up with such large gaps in the chain. Again, modes with perfect fifths from the bass are bolded.


2 4 3 3 3 3 4 .. 0 _ 2 3 4 5 6 _ 8
2 4 3 3 3 3 4 .. 0 _ 2 3 4 5 6 _ 8
4 3 3 3 3 4 2 .. -8 _ -6 -5 -4 -3 -2 _ 0 === Mike Battaglia's Porcupine[7] 0|6 #7
**4 3 3 3 3 4 2 .. -8 _ -6 -5 -4 -3 -2 _ 0 === Mike Battaglia's Porcupine[7] 0|6 #7**
3 3 3 3 4 2 4 .. -2 _ 0 1 2 3 4 _ 6
3 3 3 3 4 2 4 .. -2 _ 0 1 2 3 4 _ 6
3 3 3 4 2 4 3 .. -3 _ -1 0 1 2 3 _ 5
**3 3 3 4 2 4 3 .. -3 _ -1 0 1 2 3 _ 5**
3 3 4 2 4 3 3 .. -4 _ -2 -1 0 1 2 _ 4
3 3 4 2 4 3 3 .. -4 _ -2 -1 0 1 2 _ 4
3 4 2 4 3 3 3 .. -5 _ -3 -2 -1 0 1 _ 3
**3 4 2 4 3 3 3 .. -5 _ -3 -2 -1 0 1 _ 3**
4 2 4 3 3 3 3 .. -6 _ -4 -3 -2 -1 0 _ 2
**4 2 4 3 3 3 3 .. -6 _ -4 -3 -2 -1 0 _ 2**


2 3 4 3 3 3 4 .. 0 _ _ 3 4 5 6 _ 8 9
2 3 4 3 3 3 4 .. 0 _ _ 3 4 5 6 _ 8 9
3 4 3 3 3 4 2 .. -8 _ _ -5 -4 -3 -2 _ 0 1
**3 4 3 3 3 4 2 .. -8 _ _ -5 -4 -3 -2 _ 0 1**
4 3 3 3 4 2 3 .. -9 _ _ -6 -5 -4 -3 _ -1 0
**4 3 3 3 4 2 3 .. -9 _ _ -6 -5 -4 -3 _ -1 0**
3 3 3 4 2 3 4 .. -3 _ _ 0 1 2 3 _ 5 6
3 3 3 4 2 3 4 .. -3 _ _ 0 1 2 3 _ 5 6
3 3 4 2 3 4 3 .. -4 _ _ -1 0 1 2 _ 4 5
3 3 4 2 3 4 3 .. -4 _ _ -1 0 1 2 _ 4 5
3 4 2 3 4 3 3 .. -5 _ _ -2 -1 0 1 _ 3 4
3 4 2 3 4 3 3 .. -5 _ _ -2 -1 0 1 _ 3 4
4 2 3 4 3 3 3 .. -6 _ _ -3 -2 -1 0 _ 1 2 === Mike Battaglia's&lt;span class="commentBody"&gt; Porcupine[7] 3|3 #2&lt;/span&gt;
**4 2 3 4 3 3 3 .. -6 _ _ -3 -2 -1 0 _ 1 2 === Mike Battaglia's&lt;span class="commentBody"&gt; Porcupine[7] 3|3 #2&lt;/span&gt;**


2 4 3 3 3 4 3 .. -1 0 _ 2 3 4 5 _ _ 8
2 4 3 3 3 4 3 .. -1 0 _ 2 3 4 5 _ _ 8
4 3 3 3 4 3 2 .. -9 -8 _ -6 -5 -4 -3 _ _ 0
**4 3 3 3 4 3 2 .. -9 -8 _ -6 -5 -4 -3 _ _ 0**
3 3 3 4 3 2 4 .. -3 -2 _ 0 1 2 3 _ _ 6
**3 3 3 4 3 2 4 .. -3 -2 _ 0 1 2 3 _ _ 6**
3 3 4 3 2 4 3 .. -4 -3 _ -1 0 1 2 _ _ 5 === one of Andrew's faves
**3 3 4 3 2 4 3 .. -4 -3 _ -1 0 1 2 _ _ 5 === one of Andrew's faves**
3 4 3 2 4 3 3 .. -5 -4 _ -2 -1 0 1 _ _ 4
3 4 3 2 4 3 3 .. -5 -4 _ -2 -1 0 1 _ _ 4
4 3 2 4 3 3 3 .. -6 -5 _ -3 -2 -1 0 _ _ 3 === Mike Battaglia's Porcupine[7] 0|6 b4
**4 3 2 4 3 3 3 .. -6 -5 _ -3 -2 -1 0 _ _ 3 === Mike Battaglia's Porcupine[7] 0|6 b4**
3 2 4 3 3 3 4 .. 0 1 _ 3 4 5 6 _ _ 9
3 2 4 3 3 3 4 .. 0 1 _ 3 4 5 6 _ _ 9


2 3 3 4 3 3 4 .. 0 _ _ _ 4 5 6 _ 8 9 10
2 3 3 4 3 3 4 .. 0 _ _ _ 4 5 6 _ 8 9 10
3 3 4 3 3 4 2 .. -8 _ _ _ -4 -3 -2 _ 0 1 2
**3 3 4 3 3 4 2 .. -8 _ _ _ -4 -3 -2 _ 0 1 2**
3 4 3 3 4 2 3 .. -9 _ _ _ -5 -4 -3 _ -1 0 1
**3 4 3 3 4 2 3 .. -9 _ _ _ -5 -4 -3 _ -1 0 1**
4 3 3 4 2 3 3 .. -10 _ _ _ -6 -5 -4 _ -2 -1 0
4 3 3 4 2 3 3 .. -10 _ _ _ -6 -5 -4 _ -2 -1 0
3 3 4 2 3 3 4 .. -4 _ _ _ 0 1 2 _ 4 5 6
3 3 4 2 3 3 4 .. -4 _ _ _ 0 1 2 _ 4 5 6
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2 4 3 3 4 3 3 .. -2 -1 0 _ 2 3 4 _ _ _ 8
2 4 3 3 4 3 3 .. -2 -1 0 _ 2 3 4 _ _ _ 8
4 3 3 4 3 3 2 .. -10 -9 -8 _ -6 -5 -4 _ _ _ 0
4 3 3 4 3 3 2 .. -10 -9 -8 _ -6 -5 -4 _ _ _ 0
3 3 4 3 3 2 4 .. -4 -3 -2 _ 0 1 2 _ _ _ 6
**3 3 4 3 3 2 4 .. -4 -3 -2 _ 0 1 2 _ _ _ 6**
3 4 3 3 2 4 3 .. -5 -4 -3 _ -1 0 1 _ _ _ 5
**3 4 3 3 2 4 3 .. -5 -4 -3 _ -1 0 1 _ _ _ 5**
4 3 3 2 4 3 3 .. -6 -5 -4 _ -2 -1 0 _ _ _ 4
4 3 3 2 4 3 3 .. -6 -5 -4 _ -2 -1 0 _ _ _ 4
3 3 2 4 3 3 4 .. 0 1 2 _ 4 5 6 _ _ _ 10
3 3 2 4 3 3 4 .. 0 1 2 _ 4 5 6 _ _ _ 10
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2 3 3 3 4 3 4 .. 0 _ _ _ _ 5 6 _ 8 9 10 11
2 3 3 3 4 3 4 .. 0 _ _ _ _ 5 6 _ 8 9 10 11
3 3 3 4 3 4 2 .. -8 _ _ _ _ -3 -2 _ 0 1 2 3
**3 3 3 4 3 4 2 .. -8 _ _ _ _ -3 -2 _ 0 1 2 3**
3 3 4 3 4 2 3 .. -9 _ _ _ _ -4 -3 _ -1 0 1 2
**3 3 4 3 4 2 3 .. -9 _ _ _ _ -4 -3 _ -1 0 1 2**
3 4 3 4 2 3 3 .. -10 _ _ _ _ -5 -4 _ -2 -1 0 1
3 4 3 4 2 3 3 .. -10 _ _ _ _ -5 -4 _ -2 -1 0 1
4 3 4 2 3 3 3 .. -11 _ _ _ _ -6 -5 _ -3 -2 -1 0
**4 3 4 2 3 3 3 .. -11 _ _ _ _ -6 -5 _ -3 -2 -1 0**
3 4 2 3 3 3 4 .. -5 _ _ _ _ 0 1 _ 3 4 5 6
3 4 2 3 3 3 4 .. -5 _ _ _ _ 0 1 _ 3 4 5 6
4 2 3 3 3 4 3 .. -6 _ _ _ _ -1 0 _ 2 3 4 5
4 2 3 3 3 4 3 .. -6 _ _ _ _ -1 0 _ 2 3 4 5


2 4 3 4 3 3 3 .. -3 -2 -1 0 _ 2 3 _ _ _ _ 8
**2 4 3 4 3 3 3 .. -3 -2 -1 0 _ 2 3 _ _ _ _ 8**
4 3 4 3 3 3 2 .. -11 -10 -9 -8 _ -6 -5 _ _ _ _ 0
4 3 4 3 3 3 2 .. -11 -10 -9 -8 _ -6 -5 _ _ _ _ 0
3 4 3 3 3 2 4 .. -5 -4 -3 -2 _ 0 1 _ _ _ _ 6 === one of Andrew's faves
**3 4 3 3 3 2 4 .. -5 -4 -3 -2 _ 0 1 _ _ _ _ 6 === one of Andrew's faves**
4 3 3 3 2 4 3 .. -6 -5 -4 -3 _ -1 0 _ _ _ _ 5
**4 3 3 3 2 4 3 .. -6 -5 -4 -3 _ -1 0 _ _ _ _ 5**
3 3 3 2 4 3 4 .. 0 1 2 3 _ 5 6 _ _ _ _ 11
3 3 3 2 4 3 4 .. 0 1 2 3 _ 5 6 _ _ _ _ 11
3 3 2 4 3 4 3 .. -1 0 1 2 _ 4 5 _ _ _ _ 10
3 3 2 4 3 4 3 .. -1 0 1 2 _ 4 5 _ _ _ _ 10
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2 3 3 3 3 4 4 .. 0 _ _ _ _ _ 6 _ 8 9 10 11 12
2 3 3 3 3 4 4 .. 0 _ _ _ _ _ 6 _ 8 9 10 11 12
3 3 3 3 4 4 2 .. -8 _ _ _ _ _ -2 _ 0 1 2 3 4
3 3 3 3 4 4 2 .. -8 _ _ _ _ _ -2 _ 0 1 2 3 4
3 3 3 4 4 2 3 .. -9 _ _ _ _ _ -3 _ -1 0 1 2 3
**3 3 3 4 4 2 3 .. -9 _ _ _ _ _ -3 _ -1 0 1 2 3**
3 3 4 4 2 3 3 .. -10 _ _ _ _ _ -4 _ -2 -1 0 1 2
3 3 4 4 2 3 3 .. -10 _ _ _ _ _ -4 _ -2 -1 0 1 2
3 4 4 2 3 3 3 .. -11 _ _ _ _ _ -5 _ -3 -2 -1 0 1
**3 4 4 2 3 3 3 .. -11 _ _ _ _ _ -5 _ -3 -2 -1 0 1**
4 4 2 3 3 3 3 .. -12 _ _ _ _ _ -6 _ -4 -3 -2 -1 0
**4 4 2 3 3 3 3 .. -12 _ _ _ _ _ -6 _ -4 -3 -2 -1 0**
4 2 3 3 3 3 4 .. -6 _ _ _ _ _ 0 _ 2 3 4 5 6
4 2 3 3 3 3 4 .. -6 _ _ _ _ _ 0 _ 2 3 4 5 6


2 4 4 3 3 3 3 .. -4 -3 -2 -1 0 _ 2 _ _ _ _ _ 8
**2 4 4 3 3 3 3 .. -4 -3 -2 -1 0 _ 2 _ _ _ _ _ 8**
4 4 3 3 3 3 2 .. -12 -11 -10 -9 -8 _ -6 _ _ _ _ _ 0
4 4 3 3 3 3 2 .. -12 -11 -10 -9 -8 _ -6 _ _ _ _ _ 0
4 3 3 3 3 2 4 .. -6 -5 -4 -3 -2 _ 0 _ _ _ _ _ 6 === Mike Battaglia's Porcupine[7] 0|6 b7
**4 3 3 3 3 2 4 .. -6 -5 -4 -3 -2 _ 0 _ _ _ _ _ 6 === Mike Battaglia's Porcupine[7] 0|6 b7**
3 3 3 3 2 4 4 .. 0 1 2 3 4 _ 6 _ _ _ _ _ 12
3 3 3 3 2 4 4 .. 0 1 2 3 4 _ 6 _ _ _ _ _ 12
3 3 3 2 4 4 3 .. -1 0 1 2 3 _ 5 _ _ _ _ _ 11
3 3 3 2 4 4 3 .. -1 0 1 2 3 _ 5 _ _ _ _ _ 11
3 3 2 4 4 3 3 .. -2 -1 0 1 2 _ 4 _ _ _ _ _ 10
3 3 2 4 4 3 3 .. -2 -1 0 1 2 _ 4 _ _ _ _ _ 10
3 2 4 4 3 3 3 .. -3 -2 -1 0 1 _ 3 _ _ _ _ _ 9
**3 2 4 4 3 3 3 .. -3 -2 -1 0 1 _ 3 _ _ _ _ _ 9**


2 3 3 3 3 3 5 .. 0 _ _ _ _ _ _ _ 8 9 10 11 12 13
2 3 3 3 3 3 5 .. 0 _ _ _ _ _ _ _ 8 9 10 11 12 13
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3 3 3 3 5 2 3 .. -9 _ _ _ _ _ _ _ -1 0 1 2 3 4
3 3 3 3 5 2 3 .. -9 _ _ _ _ _ _ _ -1 0 1 2 3 4
3 3 3 5 2 3 3 .. -10 _ _ _ _ _ _ _ -2 -1 0 1 2 3
3 3 3 5 2 3 3 .. -10 _ _ _ _ _ _ _ -2 -1 0 1 2 3
3 3 5 2 3 3 3 .. -11 _ _ _ _ _ _ _ -3 -2 -1 0 1 2
**3 3 5 2 3 3 3 .. -11 _ _ _ _ _ _ _ -3 -2 -1 0 1 2**
3 5 2 3 3 3 3 .. -12 _ _ _ _ _ _ _ -4 -3 -2 -1 0 1
**3 5 2 3 3 3 3 .. -12 _ _ _ _ _ _ _ -4 -3 -2 -1 0 1**
5 2 3 3 3 3 3 .. -13 _ _ _ _ _ _ _ -5 -4 -3 -2 -1 0
**5 2 3 3 3 3 3 .. -13 _ _ _ _ _ _ _ -5 -4 -3 -2 -1 0**


2 5 3 3 3 3 3 .. -5 -4 -3 -2 -1 0 _ _ _ _ _ _ _ 8
**2 5 3 3 3 3 3 .. -5 -4 -3 -2 -1 0 _ _ _ _ _ _ _ 8**
5 3 3 3 3 3 2 .. -13 -12 -11 -10 -9 -8 _ _ _ _ _ _ _ 0
5 3 3 3 3 3 2 .. -13 -12 -11 -10 -9 -8 _ _ _ _ _ _ _ 0
3 3 3 3 3 2 5 .. 0 1 2 3 4 5 _ _ _ _ _ _ _ 13
3 3 3 3 3 2 5 .. 0 1 2 3 4 5 _ _ _ _ _ _ _ 13
3 3 3 3 2 5 3 .. -1 0 1 2 3 4 _ _ _ _ _ _ _ 12
3 3 3 3 2 5 3 .. -1 0 1 2 3 4 _ _ _ _ _ _ _ 12
3 3 3 2 5 3 3 .. -2 -1 0 1 2 3 _ _ _ _ _ _ _ 11
3 3 3 2 5 3 3 .. -2 -1 0 1 2 3 _ _ _ _ _ _ _ 11
3 3 2 5 3 3 3 .. -3 -2 -1 0 1 2 _ _ _ _ _ _ _ 10
**3 3 2 5 3 3 3 .. -3 -2 -1 0 1 2 _ _ _ _ _ _ _ 10**
3 2 5 3 3 3 3 .. -4 -3 -2 -1 0 1 _ _ _ _ _ _ _ 9
**3 2 5 3 3 3 3 .. -4 -3 -2 -1 0 1 _ _ _ _ _ _ _ 9**


Did I miss any???</pre></div>
Did I miss any???</pre></div>
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&lt;br /&gt;
&lt;br /&gt;
...coming soon...&lt;br /&gt;
...coming soon...&lt;br /&gt;
&lt;br /&gt;
Hm, try as I might, I can't get wikispaces to upload this image. Nevermind then.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Porcupine Chromaticism-Modes of Porcupine[7]"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Modes of Porcupine[7]&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Porcupine Chromaticism-Modes of Porcupine[7]"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Modes of Porcupine[7]&lt;/h2&gt;
  &lt;br /&gt;
  &lt;br /&gt;
The following modes are given in steps of 22edo. To generalize, 3 stands for the neutral third generating interval, and 4 stands for the wide major second. On the right is a contiguous chain of 7 tones separated by 6 iterations of the Porcupine generator.&lt;br /&gt;
The following modes are given in steps of 22edo. They are rotations of one moment of symmetry scale with two step sizes: a neutral tone (3\22) and a large whole tone (4\22). On the right is a contiguous chain of 7 tones separated by 6 iterations of the Porcupine generator. Modes in bold have a 3/2 approximation above the bass -- this can be verified easily by looking at the chain. The perfect fifth approximation is -3g, so every mode with a &amp;quot;-3&amp;quot; in the chain has a perfect fifth over the bass.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
3 3 3 3 3 3 4 .. 0 1 2 3 4 5 6&lt;br /&gt;
3 3 3 3 3 3 4 .. 0 1 2 3 4 5 6&lt;br /&gt;
3 3 3 3 3 4 3 .. -1 0 1 2 3 4 5&lt;br /&gt;
3 3 3 3 3 4 3 .. -1 0 1 2 3 4 5&lt;br /&gt;
3 3 3 3 4 3 3 .. -2 -1 0 1 2 3 4&lt;br /&gt;
3 3 3 3 4 3 3 .. -2 -1 0 1 2 3 4&lt;br /&gt;
3 3 3 4 3 3 3 .. -3 -2 -1 0 1 2 3&lt;br /&gt;
&lt;strong&gt;3 3 3 4 3 3 3 .. -3 -2 -1 0 1 2 3&lt;/strong&gt;&lt;br /&gt;
3 3 4 3 3 3 3 .. -4 -3 -2 -1 0 1 2&lt;br /&gt;
&lt;strong&gt;3 3 4 3 3 3 3 .. -4 -3 -2 -1 0 1 2&lt;/strong&gt;&lt;br /&gt;
3 4 3 3 3 3 3 .. -5 -4 -3 -2 -1 0 1&lt;br /&gt;
&lt;strong&gt;3 4 3 3 3 3 3 .. -5 -4 -3 -2 -1 0 1&lt;/strong&gt;&lt;br /&gt;
4 3 3 3 3 3 3 .. -6 -5 -4 -3 -2 -1 0&lt;br /&gt;
&lt;strong&gt;4 3 3 3 3 3 3 .. -6 -5 -4 -3 -2 -1 0&lt;/strong&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Porcupine Chromaticism-Modes of Porcupine[7] that have one chromatic alteration"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Modes of Porcupine[7] that have one chromatic alteration&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Porcupine Chromaticism-Modes of Porcupine[7] that have one chromatic alteration"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Modes of Porcupine[7] that have one chromatic alteration&lt;/h2&gt;
  &lt;br /&gt;
  &lt;br /&gt;
The following list includes all the modes (hopefully) that can be generated by shifting one tone of Porcupine[7] by one quartertone interval (chroma), which is one degree in 22edo. Underscores represent gaps in the chain of Porcupine generators. Note that lowering a tone by one chroma means sending it forward 7 spaces in the chain of generators, while raising a tone by one chroma means sending it backward 7 spaces in the chain of generators. This is how we wind up with such large gaps in the chain.&lt;br /&gt;
The following list includes all the modes (hopefully) that can be generated by shifting one tone of Porcupine[7] by one quartertone interval (chroma), which is one degree in 22edo. This produces scales with three step sizes -- in addition to a neutral tone (3\22) and large whole tone (4\22) there is now a semitone as well (2\22). In addition, two scales (and their rotations of course) have a 5-step subminor third. Underscores represent gaps in the chain of Porcupine generators. Note that lowering a tone by one quartertone interval (chroma) means sending it forward 7 spaces in the chain of generators, while raising a tone by one chroma means sending it backward 7 spaces in the chain of generators. This is how we wind up with such large gaps in the chain. Again, modes with perfect fifths from the bass are bolded.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2 4 3 3 3 3 4 .. 0 _ 2 3 4 5 6 _ 8&lt;br /&gt;
2 4 3 3 3 3 4 .. 0 _ 2 3 4 5 6 _ 8&lt;br /&gt;
4 3 3 3 3 4 2 .. -8 _ -6 -5 -4 -3 -2 _ 0 === Mike Battaglia's Porcupine[7] 0|6 #7&lt;br /&gt;
&lt;strong&gt;4 3 3 3 3 4 2 .. -8 _ -6 -5 -4 -3 -2 _ 0 === Mike Battaglia's Porcupine[7] 0|6 #7&lt;/strong&gt;&lt;br /&gt;
3 3 3 3 4 2 4 .. -2 _ 0 1 2 3 4 _ 6&lt;br /&gt;
3 3 3 3 4 2 4 .. -2 _ 0 1 2 3 4 _ 6&lt;br /&gt;
3 3 3 4 2 4 3 .. -3 _ -1 0 1 2 3 _ 5&lt;br /&gt;
&lt;strong&gt;3 3 3 4 2 4 3 .. -3 _ -1 0 1 2 3 _ 5&lt;/strong&gt;&lt;br /&gt;
3 3 4 2 4 3 3 .. -4 _ -2 -1 0 1 2 _ 4&lt;br /&gt;
3 3 4 2 4 3 3 .. -4 _ -2 -1 0 1 2 _ 4&lt;br /&gt;
3 4 2 4 3 3 3 .. -5 _ -3 -2 -1 0 1 _ 3&lt;br /&gt;
&lt;strong&gt;3 4 2 4 3 3 3 .. -5 _ -3 -2 -1 0 1 _ 3&lt;/strong&gt;&lt;br /&gt;
4 2 4 3 3 3 3 .. -6 _ -4 -3 -2 -1 0 _ 2&lt;br /&gt;
&lt;strong&gt;4 2 4 3 3 3 3 .. -6 _ -4 -3 -2 -1 0 _ 2&lt;/strong&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2 3 4 3 3 3 4 .. 0 _ _ 3 4 5 6 _ 8 9&lt;br /&gt;
2 3 4 3 3 3 4 .. 0 _ _ 3 4 5 6 _ 8 9&lt;br /&gt;
3 4 3 3 3 4 2 .. -8 _ _ -5 -4 -3 -2 _ 0 1&lt;br /&gt;
&lt;strong&gt;3 4 3 3 3 4 2 .. -8 _ _ -5 -4 -3 -2 _ 0 1&lt;/strong&gt;&lt;br /&gt;
4 3 3 3 4 2 3 .. -9 _ _ -6 -5 -4 -3 _ -1 0&lt;br /&gt;
&lt;strong&gt;4 3 3 3 4 2 3 .. -9 _ _ -6 -5 -4 -3 _ -1 0&lt;/strong&gt;&lt;br /&gt;
3 3 3 4 2 3 4 .. -3 _ _ 0 1 2 3 _ 5 6&lt;br /&gt;
3 3 3 4 2 3 4 .. -3 _ _ 0 1 2 3 _ 5 6&lt;br /&gt;
3 3 4 2 3 4 3 .. -4 _ _ -1 0 1 2 _ 4 5&lt;br /&gt;
3 3 4 2 3 4 3 .. -4 _ _ -1 0 1 2 _ 4 5&lt;br /&gt;
3 4 2 3 4 3 3 .. -5 _ _ -2 -1 0 1 _ 3 4&lt;br /&gt;
3 4 2 3 4 3 3 .. -5 _ _ -2 -1 0 1 _ 3 4&lt;br /&gt;
4 2 3 4 3 3 3 .. -6 _ _ -3 -2 -1 0 _ 1 2 === Mike Battaglia's&lt;span class="commentBody"&gt; Porcupine[7] 3|3 #2&lt;/span&gt;&lt;br /&gt;
&lt;strong&gt;4 2 3 4 3 3 3 .. -6 _ _ -3 -2 -1 0 _ 1 2 === Mike Battaglia's&lt;span class="commentBody"&gt; Porcupine[7] 3|3 #2&lt;/span&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2 4 3 3 3 4 3 .. -1 0 _ 2 3 4 5 _ _ 8&lt;br /&gt;
2 4 3 3 3 4 3 .. -1 0 _ 2 3 4 5 _ _ 8&lt;br /&gt;
4 3 3 3 4 3 2 .. -9 -8 _ -6 -5 -4 -3 _ _ 0&lt;br /&gt;
&lt;strong&gt;4 3 3 3 4 3 2 .. -9 -8 _ -6 -5 -4 -3 _ _ 0&lt;/strong&gt;&lt;br /&gt;
3 3 3 4 3 2 4 .. -3 -2 _ 0 1 2 3 _ _ 6&lt;br /&gt;
&lt;strong&gt;3 3 3 4 3 2 4 .. -3 -2 _ 0 1 2 3 _ _ 6&lt;/strong&gt;&lt;br /&gt;
3 3 4 3 2 4 3 .. -4 -3 _ -1 0 1 2 _ _ 5 === one of Andrew's faves&lt;br /&gt;
&lt;strong&gt;3 3 4 3 2 4 3 .. -4 -3 _ -1 0 1 2 _ _ 5 === one of Andrew's faves&lt;/strong&gt;&lt;br /&gt;
3 4 3 2 4 3 3 .. -5 -4 _ -2 -1 0 1 _ _ 4&lt;br /&gt;
3 4 3 2 4 3 3 .. -5 -4 _ -2 -1 0 1 _ _ 4&lt;br /&gt;
4 3 2 4 3 3 3 .. -6 -5 _ -3 -2 -1 0 _ _ 3 === Mike Battaglia's Porcupine[7] 0|6 b4&lt;br /&gt;
&lt;strong&gt;4 3 2 4 3 3 3 .. -6 -5 _ -3 -2 -1 0 _ _ 3 === Mike Battaglia's Porcupine[7] 0|6 b4&lt;/strong&gt;&lt;br /&gt;
3 2 4 3 3 3 4 .. 0 1 _ 3 4 5 6 _ _ 9&lt;br /&gt;
3 2 4 3 3 3 4 .. 0 1 _ 3 4 5 6 _ _ 9&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2 3 3 4 3 3 4 .. 0 _ _ _ 4 5 6 _ 8 9 10&lt;br /&gt;
2 3 3 4 3 3 4 .. 0 _ _ _ 4 5 6 _ 8 9 10&lt;br /&gt;
3 3 4 3 3 4 2 .. -8 _ _ _ -4 -3 -2 _ 0 1 2&lt;br /&gt;
&lt;strong&gt;3 3 4 3 3 4 2 .. -8 _ _ _ -4 -3 -2 _ 0 1 2&lt;/strong&gt;&lt;br /&gt;
3 4 3 3 4 2 3 .. -9 _ _ _ -5 -4 -3 _ -1 0 1&lt;br /&gt;
&lt;strong&gt;3 4 3 3 4 2 3 .. -9 _ _ _ -5 -4 -3 _ -1 0 1&lt;/strong&gt;&lt;br /&gt;
4 3 3 4 2 3 3 .. -10 _ _ _ -6 -5 -4 _ -2 -1 0&lt;br /&gt;
4 3 3 4 2 3 3 .. -10 _ _ _ -6 -5 -4 _ -2 -1 0&lt;br /&gt;
3 3 4 2 3 3 4 .. -4 _ _ _ 0 1 2 _ 4 5 6&lt;br /&gt;
3 3 4 2 3 3 4 .. -4 _ _ _ 0 1 2 _ 4 5 6&lt;br /&gt;
Line 195: Line 199:
2 4 3 3 4 3 3 .. -2 -1 0 _ 2 3 4 _ _ _ 8&lt;br /&gt;
2 4 3 3 4 3 3 .. -2 -1 0 _ 2 3 4 _ _ _ 8&lt;br /&gt;
4 3 3 4 3 3 2 .. -10 -9 -8 _ -6 -5 -4 _ _ _ 0&lt;br /&gt;
4 3 3 4 3 3 2 .. -10 -9 -8 _ -6 -5 -4 _ _ _ 0&lt;br /&gt;
3 3 4 3 3 2 4 .. -4 -3 -2 _ 0 1 2 _ _ _ 6&lt;br /&gt;
&lt;strong&gt;3 3 4 3 3 2 4 .. -4 -3 -2 _ 0 1 2 _ _ _ 6&lt;/strong&gt;&lt;br /&gt;
3 4 3 3 2 4 3 .. -5 -4 -3 _ -1 0 1 _ _ _ 5&lt;br /&gt;
&lt;strong&gt;3 4 3 3 2 4 3 .. -5 -4 -3 _ -1 0 1 _ _ _ 5&lt;/strong&gt;&lt;br /&gt;
4 3 3 2 4 3 3 .. -6 -5 -4 _ -2 -1 0 _ _ _ 4&lt;br /&gt;
4 3 3 2 4 3 3 .. -6 -5 -4 _ -2 -1 0 _ _ _ 4&lt;br /&gt;
3 3 2 4 3 3 4 .. 0 1 2 _ 4 5 6 _ _ _ 10&lt;br /&gt;
3 3 2 4 3 3 4 .. 0 1 2 _ 4 5 6 _ _ _ 10&lt;br /&gt;
Line 202: Line 206:
&lt;br /&gt;
&lt;br /&gt;
2 3 3 3 4 3 4 .. 0 _ _ _ _ 5 6 _ 8 9 10 11&lt;br /&gt;
2 3 3 3 4 3 4 .. 0 _ _ _ _ 5 6 _ 8 9 10 11&lt;br /&gt;
3 3 3 4 3 4 2 .. -8 _ _ _ _ -3 -2 _ 0 1 2 3&lt;br /&gt;
&lt;strong&gt;3 3 3 4 3 4 2 .. -8 _ _ _ _ -3 -2 _ 0 1 2 3&lt;/strong&gt;&lt;br /&gt;
3 3 4 3 4 2 3 .. -9 _ _ _ _ -4 -3 _ -1 0 1 2&lt;br /&gt;
&lt;strong&gt;3 3 4 3 4 2 3 .. -9 _ _ _ _ -4 -3 _ -1 0 1 2&lt;/strong&gt;&lt;br /&gt;
3 4 3 4 2 3 3 .. -10 _ _ _ _ -5 -4 _ -2 -1 0 1&lt;br /&gt;
3 4 3 4 2 3 3 .. -10 _ _ _ _ -5 -4 _ -2 -1 0 1&lt;br /&gt;
4 3 4 2 3 3 3 .. -11 _ _ _ _ -6 -5 _ -3 -2 -1 0&lt;br /&gt;
&lt;strong&gt;4 3 4 2 3 3 3 .. -11 _ _ _ _ -6 -5 _ -3 -2 -1 0&lt;/strong&gt;&lt;br /&gt;
3 4 2 3 3 3 4 .. -5 _ _ _ _ 0 1 _ 3 4 5 6&lt;br /&gt;
3 4 2 3 3 3 4 .. -5 _ _ _ _ 0 1 _ 3 4 5 6&lt;br /&gt;
4 2 3 3 3 4 3 .. -6 _ _ _ _ -1 0 _ 2 3 4 5&lt;br /&gt;
4 2 3 3 3 4 3 .. -6 _ _ _ _ -1 0 _ 2 3 4 5&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2 4 3 4 3 3 3 .. -3 -2 -1 0 _ 2 3 _ _ _ _ 8&lt;br /&gt;
&lt;strong&gt;2 4 3 4 3 3 3 .. -3 -2 -1 0 _ 2 3 _ _ _ _ 8&lt;/strong&gt;&lt;br /&gt;
4 3 4 3 3 3 2 .. -11 -10 -9 -8 _ -6 -5 _ _ _ _ 0&lt;br /&gt;
4 3 4 3 3 3 2 .. -11 -10 -9 -8 _ -6 -5 _ _ _ _ 0&lt;br /&gt;
3 4 3 3 3 2 4 .. -5 -4 -3 -2 _ 0 1 _ _ _ _ 6 === one of Andrew's faves&lt;br /&gt;
&lt;strong&gt;3 4 3 3 3 2 4 .. -5 -4 -3 -2 _ 0 1 _ _ _ _ 6 === one of Andrew's faves&lt;/strong&gt;&lt;br /&gt;
4 3 3 3 2 4 3 .. -6 -5 -4 -3 _ -1 0 _ _ _ _ 5&lt;br /&gt;
&lt;strong&gt;4 3 3 3 2 4 3 .. -6 -5 -4 -3 _ -1 0 _ _ _ _ 5&lt;/strong&gt;&lt;br /&gt;
3 3 3 2 4 3 4 .. 0 1 2 3 _ 5 6 _ _ _ _ 11&lt;br /&gt;
3 3 3 2 4 3 4 .. 0 1 2 3 _ 5 6 _ _ _ _ 11&lt;br /&gt;
3 3 2 4 3 4 3 .. -1 0 1 2 _ 4 5 _ _ _ _ 10&lt;br /&gt;
3 3 2 4 3 4 3 .. -1 0 1 2 _ 4 5 _ _ _ _ 10&lt;br /&gt;
Line 219: Line 223:
2 3 3 3 3 4 4 .. 0 _ _ _ _ _ 6 _ 8 9 10 11 12&lt;br /&gt;
2 3 3 3 3 4 4 .. 0 _ _ _ _ _ 6 _ 8 9 10 11 12&lt;br /&gt;
3 3 3 3 4 4 2 .. -8 _ _ _ _ _ -2 _ 0 1 2 3 4&lt;br /&gt;
3 3 3 3 4 4 2 .. -8 _ _ _ _ _ -2 _ 0 1 2 3 4&lt;br /&gt;
3 3 3 4 4 2 3 .. -9 _ _ _ _ _ -3 _ -1 0 1 2 3&lt;br /&gt;
&lt;strong&gt;3 3 3 4 4 2 3 .. -9 _ _ _ _ _ -3 _ -1 0 1 2 3&lt;/strong&gt;&lt;br /&gt;
3 3 4 4 2 3 3 .. -10 _ _ _ _ _ -4 _ -2 -1 0 1 2&lt;br /&gt;
3 3 4 4 2 3 3 .. -10 _ _ _ _ _ -4 _ -2 -1 0 1 2&lt;br /&gt;
3 4 4 2 3 3 3 .. -11 _ _ _ _ _ -5 _ -3 -2 -1 0 1&lt;br /&gt;
&lt;strong&gt;3 4 4 2 3 3 3 .. -11 _ _ _ _ _ -5 _ -3 -2 -1 0 1&lt;/strong&gt;&lt;br /&gt;
4 4 2 3 3 3 3 .. -12 _ _ _ _ _ -6 _ -4 -3 -2 -1 0&lt;br /&gt;
&lt;strong&gt;4 4 2 3 3 3 3 .. -12 _ _ _ _ _ -6 _ -4 -3 -2 -1 0&lt;/strong&gt;&lt;br /&gt;
4 2 3 3 3 3 4 .. -6 _ _ _ _ _ 0 _ 2 3 4 5 6&lt;br /&gt;
4 2 3 3 3 3 4 .. -6 _ _ _ _ _ 0 _ 2 3 4 5 6&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2 4 4 3 3 3 3 .. -4 -3 -2 -1 0 _ 2 _ _ _ _ _ 8&lt;br /&gt;
&lt;strong&gt;2 4 4 3 3 3 3 .. -4 -3 -2 -1 0 _ 2 _ _ _ _ _ 8&lt;/strong&gt;&lt;br /&gt;
4 4 3 3 3 3 2 .. -12 -11 -10 -9 -8 _ -6 _ _ _ _ _ 0&lt;br /&gt;
4 4 3 3 3 3 2 .. -12 -11 -10 -9 -8 _ -6 _ _ _ _ _ 0&lt;br /&gt;
4 3 3 3 3 2 4 .. -6 -5 -4 -3 -2 _ 0 _ _ _ _ _ 6 === Mike Battaglia's Porcupine[7] 0|6 b7&lt;br /&gt;
&lt;strong&gt;4 3 3 3 3 2 4 .. -6 -5 -4 -3 -2 _ 0 _ _ _ _ _ 6 === Mike Battaglia's Porcupine[7] 0|6 b7&lt;/strong&gt;&lt;br /&gt;
3 3 3 3 2 4 4 .. 0 1 2 3 4 _ 6 _ _ _ _ _ 12&lt;br /&gt;
3 3 3 3 2 4 4 .. 0 1 2 3 4 _ 6 _ _ _ _ _ 12&lt;br /&gt;
3 3 3 2 4 4 3 .. -1 0 1 2 3 _ 5 _ _ _ _ _ 11&lt;br /&gt;
3 3 3 2 4 4 3 .. -1 0 1 2 3 _ 5 _ _ _ _ _ 11&lt;br /&gt;
3 3 2 4 4 3 3 .. -2 -1 0 1 2 _ 4 _ _ _ _ _ 10&lt;br /&gt;
3 3 2 4 4 3 3 .. -2 -1 0 1 2 _ 4 _ _ _ _ _ 10&lt;br /&gt;
3 2 4 4 3 3 3 .. -3 -2 -1 0 1 _ 3 _ _ _ _ _ 9&lt;br /&gt;
&lt;strong&gt;3 2 4 4 3 3 3 .. -3 -2 -1 0 1 _ 3 _ _ _ _ _ 9&lt;/strong&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2 3 3 3 3 3 5 .. 0 _ _ _ _ _ _ _ 8 9 10 11 12 13&lt;br /&gt;
2 3 3 3 3 3 5 .. 0 _ _ _ _ _ _ _ 8 9 10 11 12 13&lt;br /&gt;
Line 237: Line 241:
3 3 3 3 5 2 3 .. -9 _ _ _ _ _ _ _ -1 0 1 2 3 4&lt;br /&gt;
3 3 3 3 5 2 3 .. -9 _ _ _ _ _ _ _ -1 0 1 2 3 4&lt;br /&gt;
3 3 3 5 2 3 3 .. -10 _ _ _ _ _ _ _ -2 -1 0 1 2 3&lt;br /&gt;
3 3 3 5 2 3 3 .. -10 _ _ _ _ _ _ _ -2 -1 0 1 2 3&lt;br /&gt;
3 3 5 2 3 3 3 .. -11 _ _ _ _ _ _ _ -3 -2 -1 0 1 2&lt;br /&gt;
&lt;strong&gt;3 3 5 2 3 3 3 .. -11 _ _ _ _ _ _ _ -3 -2 -1 0 1 2&lt;/strong&gt;&lt;br /&gt;
3 5 2 3 3 3 3 .. -12 _ _ _ _ _ _ _ -4 -3 -2 -1 0 1&lt;br /&gt;
&lt;strong&gt;3 5 2 3 3 3 3 .. -12 _ _ _ _ _ _ _ -4 -3 -2 -1 0 1&lt;/strong&gt;&lt;br /&gt;
5 2 3 3 3 3 3 .. -13 _ _ _ _ _ _ _ -5 -4 -3 -2 -1 0&lt;br /&gt;
&lt;strong&gt;5 2 3 3 3 3 3 .. -13 _ _ _ _ _ _ _ -5 -4 -3 -2 -1 0&lt;/strong&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2 5 3 3 3 3 3 .. -5 -4 -3 -2 -1 0 _ _ _ _ _ _ _ 8&lt;br /&gt;
&lt;strong&gt;2 5 3 3 3 3 3 .. -5 -4 -3 -2 -1 0 _ _ _ _ _ _ _ 8&lt;/strong&gt;&lt;br /&gt;
5 3 3 3 3 3 2 .. -13 -12 -11 -10 -9 -8 _ _ _ _ _ _ _ 0&lt;br /&gt;
5 3 3 3 3 3 2 .. -13 -12 -11 -10 -9 -8 _ _ _ _ _ _ _ 0&lt;br /&gt;
3 3 3 3 3 2 5 .. 0 1 2 3 4 5 _ _ _ _ _ _ _ 13&lt;br /&gt;
3 3 3 3 3 2 5 .. 0 1 2 3 4 5 _ _ _ _ _ _ _ 13&lt;br /&gt;
3 3 3 3 2 5 3 .. -1 0 1 2 3 4 _ _ _ _ _ _ _ 12&lt;br /&gt;
3 3 3 3 2 5 3 .. -1 0 1 2 3 4 _ _ _ _ _ _ _ 12&lt;br /&gt;
3 3 3 2 5 3 3 .. -2 -1 0 1 2 3 _ _ _ _ _ _ _ 11&lt;br /&gt;
3 3 3 2 5 3 3 .. -2 -1 0 1 2 3 _ _ _ _ _ _ _ 11&lt;br /&gt;
3 3 2 5 3 3 3 .. -3 -2 -1 0 1 2 _ _ _ _ _ _ _ 10&lt;br /&gt;
&lt;strong&gt;3 3 2 5 3 3 3 .. -3 -2 -1 0 1 2 _ _ _ _ _ _ _ 10&lt;/strong&gt;&lt;br /&gt;
3 2 5 3 3 3 3 .. -4 -3 -2 -1 0 1 _ _ _ _ _ _ _ 9&lt;br /&gt;
&lt;strong&gt;3 2 5 3 3 3 3 .. -4 -3 -2 -1 0 1 _ _ _ _ _ _ _ 9&lt;/strong&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Did I miss any???&lt;/body&gt;&lt;/html&gt;</pre></div>
Did I miss any???&lt;/body&gt;&lt;/html&gt;</pre></div>
Retrieved from "https://en.xen.wiki/w/Andrew_Heathwaite%27s_MOS_Investigations"