Kite's thoughts on pergens: 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:

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2018-01-18 05:29:17 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2018-01-18 05:56:31 UTC</tt>.

: The original revision id was <tt>~~625029683~~</tt>.

: The original revision id was <tt>625030713</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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Some MOS scales are better understood using a pergen with a nonstandard prime subgroup. For example, 6L 1s can be roulette [7], with a 2.5.7 pergen (P8, (5/4)/2), where 5·G = 7/4.

A pergen

We can also examine which MOS scales are generated by a specific pergen. This depends on the size of the generator. In this table, the 5th is assumed to be between 4\7 and 3\5.

||~ pergen ||~ ||~ MOS scales 5-12 ||

||||~ pergen ||||~ MOS scales 5-12 ||~ ||~ ||

||= (P8, P5) ||= unsplit ||= 5, 7, 12~~, 17/19~~ ||

||= (P8, P5) ||= unsplit ||= 5 = 2L 3s ||= 7 = 5L 2s ||= 12 = 7L 5s __**or**__ 5L 7s ||= ||

||~ halves ||~ ||~ ||

||~ halves ||~ ||~ ||~ ||~ ||~ ||

||= (P8/2, P5) ||= half-8ve ||= 4, 6, 8, 10, 12 ||

||= (P8/2, P5) ||= half-8ve ||= 6 = 2L 4s ||= 8 = 2L 6s ||= 10 = 2L 8s ||= 12 = 2L 10s * ||

||= (P8, P4/2) ||= half-4th ||= 4, 5, 9~~, 14, 19~~ ||

||= (P8, P4/2) ||= half-4th ||= 5 = 4L 1s ||= 9 = 5L 4s ||= ||= ||

||= (P8, P5/2) ||= half-5th ||= 7, 10~~, 17~~ ||

||= (P8, P5/2) ||= half-5th ||= 7 = 3L 4s ||= 10 = 7L 3s ||= ||= ||

||= (P8/2, P4/2) ||= half-everything ||= 4, 6, 10~~, 14, 24~~ ||

||= (P8/2, P4/2) ||= half-everything ||= 6 = 4L 2s ||= 10 = 4L 6s ||= ||= ||

||~ thirds ||~ ||~ ||

||~ thirds ||~ ||~ ||~ ||~ ||~ ||

||= (P8/3, P5) ||= third-8ve ||= 6, 9, 12~~, 15/21~~ ||

||= (P8/3, P5) ||= third-8ve ||= 6 = 3L 3s ||= 9 = 3L 6s ||= 12 = 3L 9s * ||= ||

||= (P8, P4/3) ||= third-4th ||= ||

||= (P8, P4/3) ||= third-4th ||= 5 = 1L 4s ||= 6 = 1L 5s ||= 7 = 1L 6s ||= 8 = 7L 1s ||

||= (P8, P5/3) ||= third-5th ||= ||

||= (P8, P5/3) ||= third-5th ||= 5 = 1L 4s ||= 6 = 5L 1s ||= 11 = 5L 6s ||= ||

||= (P8, P11/3) ||= third-11th ||= ||

||= (P8, P11/3) ||= third-11th ||= 5 = 2L 3s ||= 7 = 2L 5s ||= 9 = 2L 7s ||= 11 = 2L 9s ||

||= (P8/3, P4/2) ||= third-8ve, half-4th ||= ||

||= (P8/3, P4/2) ||= third-8ve, half-4th ||= ||= ||= ||= ||

||= (P8/3, P5/2) ||= third-8ve, half-5th ||= ||

||= (P8/3, P5/2) ||= third-8ve, half-5th ||= ||= ||= ||= ||

||= (P8/2, P4/3) ||= half-8ve, third-4th ||= ||

||= (P8/2, P4/3) ||= half-8ve, third-4th ||= ||= ||= ||= ||

||= (P8/2, P5/3) ||= half-8ve, third-5th ||= ||

||= (P8/2, P5/3) ||= half-8ve, third-5th ||= ||= ||= ||= ||

||= (P8/2, P11/3) ||= half-8ve, third-11th ||= ||

||= (P8/2, P11/3) ||= half-8ve, third-11th ||= ||= ||= ||= ||

||= (P8/3, P4/3) ||= third-everything ||= ||

||= (P8/3, P4/3) ||= third-everything ||= ||= ||= ||= ||

||~ quarters ||~ ||~ ||

||~ quarters ||~ ||~ ||~ ||~ ||~ ||

||= (P8/4, P5) ||= ||= ||

||= (P8/4, P5) ||= ||= ||= ||= ||= ||

||= (P8, P4/4) ||= ||= ||

||= (P8, P4/4) ||= ||= ||= ||= ||= ||

||= (P8, P5/4) ||= ||= ||

||= (P8, P5/4) ||= ||= ||= ||= ||= ||

||= (P8, P11/4) ||= ||= ||

||= (P8, P11/4) ||= ||= ||= ||= ||= ||

||= (P8, P12/4) ||= ||= ||

||= (P8, P12/4) ||= ||= ||= ||= ||= ||

||= (P8/4, P4/2) ||= ||= ||

||= (P8/4, P4/2) ||= ||= ||= ||= ||= ||

||= (P8/2, M2/4) ||= ||= ||

||= (P8/2, M2/4) ||= ||= ||= ||= ||= ||

||= (P8/2, P4/4) ||= ||= ||

||= (P8/2, P4/4) ||= ||= ||= ||= ||= ||

||= (P8/2, P5/4) ||= ||= ||

||= (P8/2, P5/4) ||= ||= ||= ||= ||= ||

||= (P8/4, P4/3) ||= ||= ||

||= (P8/4, P4/3) ||= ||= ||= ||= ||= ||

||= (P8/4, P5/3) ||= ||= ||

||= (P8/4, P5/3) ||= ||= ||= ||= ||= ||

||= (P8/4, P11/3) ||= ||= ||

||= (P8/4, P11/3) ||= ||= ||= ||= ||= ||

||= (P8/3, P4/4) ||= ||= ||

||= (P8/3, P4/4) ||= ||= ||= ||= ||= ||

||= (P8/3, P5/4) ||= ||= ||

||= (P8/3, P5/4) ||= ||= ||= ||= ||= ||

||= (P8/3, P11/4) ||= ||= ||

||= (P8/3, P11/4) ||= ||= ||= ||= ||= ||

||= (P8/3, P12/4) ||= ||= ||

||= (P8/3, P12/4) ||= ||= ||= ||= ||= ||

||= (P8/4, P4/4) ||= ||= ||

||= (P8/4, P4/4) ||= ||= ||= ||= ||= ||

Line 2,956:

Some MOS scales are better understood using a pergen with a nonstandard prime subgroup. For example, 6L 1s can be roulette [7], with a 2.5.7 pergen (P8, (5/4)/2), where 5·G = 7/4.

A pergen

We can also examine which MOS scales are generated by a specific pergen. This depends on the size of the generator. In this table, the 5th is assumed to be between 4\7 and 3\5.

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<tr>

<th>pergen

<th colspan="2">pergen

</th>

<th colspan="2">MOS scales 5-12

</th>

<th>

</th>

<th>~~MOS scales 5-12~~

<th>

</th>

</tr>

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<td style="text-align: center;">unsplit

</td>

<td style="text-align: center;">5, 7, 12~~, 17~~/19

<td style="text-align: center;">5 = 2L 3s

</td>

<td style="text-align: center;">7 = 5L 2s

</td>

<td style="text-align: center;">12 = 7L 5s or 5L 7s

</td>

</td>

</tr>

<tr>

<th>halves

</th>

<th>

</th>

<th>

</th>

<th>

</th>

<th>

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<td style="text-align: center;">half-8ve

</td>

<td style="text-align: center;">4, 6, 8, 10, 12

<td style="text-align: center;">6 = 2L 4s

</td>

<td style="text-align: center;">8 = 2L 6s

</td>

<td style="text-align: center;">10 = 2L 8s

</td>

<td style="text-align: center;">12 = 2L 10s *

</td>

</tr>

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<td style="text-align: center;">half-4th

</td>

<td style="text-align: center;">4, 5, 9~~, 14, 19~~

<td style="text-align: center;">5 = 4L 1s

</td>

<td style="text-align: center;">9 = 5L 4s

</td>

</td>

</td>

</tr>

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<td style="text-align: center;">half-5th

</td>

<td style="text-align: center;">7, 10~~, 17~~

<td style="text-align: center;">7 = 3L 4s

</td>

<td style="text-align: center;">10 = 7L 3s

</td>

</td>

</td>

</tr>

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<td style="text-align: center;">half-everything

</td>

<td style="text-align: center;">4, 6, 10~~, 14, 24~~

<td style="text-align: center;">6 = 4L 2s

</td>

<td style="text-align: center;">10 = 4L 6s

</td>

</td>

</td>

</tr>

<tr>

<th>thirds

</th>

<th>

</th>

<th>

</th>

<th>

</th>

<th>

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<td style="text-align: center;">third-8ve

</td>

<td style="text-align: center;">6, 9, 12~~, 15~~/21

<td style="text-align: center;">6 = 3L 3s

</td>

<td style="text-align: center;">9 = 3L 6s

</td>

<td style="text-align: center;">12 = 3L 9s *

</td>

</td>

</tr>

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<td style="text-align: center;">third-4th

</td>

<td style="text-align: center;">5 = 1L 4s

</td>

<td style="text-align: center;">6 = 1L 5s

</td>

<td style="text-align: center;">7 = 1L 6s

</td>

<td style="text-align: center;">8 = 7L 1s

</td>

</tr>

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</td>

<td style="text-align: center;">third-5th

</td>

<td style="text-align: center;">5 = 1L 4s

</td>

<td style="text-align: center;">6 = 5L 1s

</td>

<td style="text-align: center;">11 = 5L 6s

</td>

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<td style="text-align: center;">third-11th

</td>

<td style="text-align: center;">5 = 2L 3s

</td>

<td style="text-align: center;">7 = 2L 5s

</td>

<td style="text-align: center;">9 = 2L 7s

</td>

<td style="text-align: center;">11 = 2L 9s

</td>

</tr>

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</td>

<td style="text-align: center;">third-8ve, half-4th

</td>

</td>

</td>

</td>

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</td>

</tr>

</td>

</td>

</td>

</tr>

<tr>

<td style="text-align: center;">(P8/2, P4/3)

</td>

<td style="text-align: center;">half-8ve, third-4th

</td>

</td>

</td>

</td>

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</td>

<td style="text-align: center;">half-8ve, third-5th

</td>

</td>

</td>

</td>

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</td>

<td style="text-align: center;">half-8ve, third-11th

</td>

</td>

</td>

</td>

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</td>

<td style="text-align: center;">third-everything

</td>

</td>

</td>

</td>

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<tr>

<th>quarters

</th>

<th>

</th>

<th>

</th>

<th>

</th>

<th>

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</td>

~~</tr>~~

~~<tr>~~

<td style="text-align: center;">~~(P8, P4/4)~~

</td>

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</tr>

<tr>

<td style="text-align: center;">(P8, P5/4)

<td style="text-align: center;">(P8, P4/4)

</td>

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</td>

~~</tr>~~

~~<tr>~~

<td style="text-align: center;">~~(P8, P11/4)~~

</td>

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</tr>

<tr>

<td style="text-align: center;">(P8, ~~P12~~/4)

<td style="text-align: center;">(P8, P5/4)

</td>

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</td>

~~</tr>~~

~~<tr>~~

<td style="text-align: center;">~~(P8/4, P4/2)~~

</td>

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</tr>

<tr>

<td style="text-align: center;">(P8/2, M2/4)

<td style="text-align: center;">(P8, P11/4)

</td>

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</td>

~~</tr>~~

~~<tr>~~

<td style="text-align: center;">~~(P8/2, P4/4)~~

</td>

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Line 3,280:

</tr>

<tr>

<td style="text-align: center;">(P8/2, P5/4)

<td style="text-align: center;">(P8, P12/4)

</td>

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</td>

~~</tr>~~

~~<tr>~~

<td style="text-align: center;">~~(P8/4, P4/3)~~

</td>

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</tr>

<tr>

<td style="text-align: center;">(P8/4, P5/3)

<td style="text-align: center;">(P8/4, P4/2)

</td>

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</td>

~~</tr>~~

~~<tr>~~

<td style="text-align: center;">~~(P8/4, P11/3)~~

</td>

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</tr>

<tr>

<td style="text-align: center;">(P8/3, P4/4)

<td style="text-align: center;">(P8/2, M2/4)

</td>

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</td>

~~</tr>~~

~~<tr>~~

<td style="text-align: center;">~~(P8/3, P5/4)~~

</td>

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</tr>

<tr>

<td style="text-align: center;">(P8/3, ~~P11~~/4)

<td style="text-align: center;">(P8/2, P4/4)

</td>

</td>

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</td>

</tr>

</td>

</td>

</tr>

<tr>

<td style="text-align: center;">(P8/2, P5/4)

</td>

</td>

</td>

</td>

</td>

</td>

</tr>

<tr>

<td style="text-align: center;">(P8/3, P12/4)

<td style="text-align: center;">(P8/4, P4/3)

</td>

</td>

</td>

</td>

</td>

</td>

</tr>

<tr>

<td style="text-align: center;">(P8/4, P5/3)

</td>

</td>

</td>

</td>

</td>

</td>

</tr>

<tr>

<td style="text-align: center;">(P8/4, P11/3)

</td>

</td>

</td>

</td>

</td>

</td>

</tr>

<tr>

<td style="text-align: center;">(P8/3, P4/4)

</td>

</td>

</td>

</td>

</td>

</td>

</tr>

<tr>

<td style="text-align: center;">(P8/3, P5/4)

</td>

</td>

</td>

</td>

</td>

</td>

</tr>

<tr>

<td style="text-align: center;">(P8/3, P11/4)

</td>

</td>

</td>

</td>

</td>

</td>

</tr>

<tr>

<td style="text-align: center;">(P8/3, P12/4)

</td>

</td>

</td>

</td>

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<tr>

<td style="text-align: center;">(P8/4, P4/4)

</td>

</td>

</td>

</td>

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This PDF is a rank-2 notation guide that shows the full lattice for the first 15 pergens, up through the third-splits block.

<a class="wiki_link_ext" href="http://www.tallkite.com/misc_files/pergens.pdf" rel="nofollow">http://www.tallkite.com/misc_files/pergens.pdf</a>

<a class="wiki_link_ext" href="http://www.tallkite.com/misc_files/pergens.pdf" rel="nofollow">http://www.tallkite.com/misc_files/pergens.pdf</a>

Alt-pergenLister lists out thousands of pergens, and suggests periods, generators and enharmonics for each one. It can also list only those pergens supported by a specific edo. Written in Jesusonic, runs inside Reaper.

<a class="wiki_link_ext" href="http://www.tallkite.com/misc_files/alt-pergensLister.zip" rel="nofollow">http://www.tallkite.com/misc_files/alt-pergensLister.zip</a>

<a class="wiki_link_ext" href="http://www.tallkite.com/misc_files/alt-pergensLister.zip" rel="nofollow">http://www.tallkite.com/misc_files/alt-pergensLister.zip</a>

Screenshot of the first 38 pergens:

<img src="/file/view/alt-pergenLister.png/624838213/704x460/alt-pergenLister.png" alt="alt-pergenLister.png" title="alt-pergenLister.png" style="height: 460px; width: 704px;" />

<img src="/file/view/alt-pergenLister.png/624838213/704x460/alt-pergenLister.png" alt="alt-pergenLister.png" title="alt-pergenLister.png" style="height: 460px; width: 704px;" />

<h2 id="toc19"><a name="Further Discussion-Misc notes"></a>Misc notes</h2>

@@ 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:TallKite|TallKite]] and made on <tt>2018-01-18 05:29:17 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2018-01-18 05:56:31 UTC</tt>.<br>
-: The original revision id was <tt>625029683</tt>.<br>
+: The original revision id was <tt>625030713</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 542: / Line 542: @@
 Some MOS scales are better understood using a pergen with a nonstandard prime subgroup. For example, 6L 1s can be roulette [7], with a 2.5.7 pergen (P8, (5/4)/2), where 5·G = 7/4.
-A pergen
+We can also examine which MOS scales are generated by a specific pergen. This depends on the size of the generator. In this table, the 5th is assumed to be between 4\7 and 3\5.
-||~ pergen ||~   ||~ MOS scales 5-12 ||
+||||~ pergen ||||~ MOS scales 5-12 ||~   ||~   ||
-||= (P8, P5) ||= unsplit ||= 5, 7, 12, 17/19 ||
+||= (P8, P5) ||= unsplit ||= 5 = 2L 3s ||= 7 = 5L 2s ||= 12 = 7L 5s __**or**__ 5L 7s ||=   ||
-||~ halves ||~   ||~   ||
+||~ halves ||~   ||~   ||~   ||~   ||~   ||
-||= (P8/2, P5) ||= half-8ve ||= 4, 6, 8, 10, 12 ||
+||= (P8/2, P5) ||= half-8ve ||= 6 = 2L 4s ||= 8 = 2L 6s ||= 10 = 2L 8s ||= 12 = 2L 10s * ||
-||= (P8, P4/2) ||= half-4th ||= 4, 5, 9, 14, 19 ||
+||= (P8, P4/2) ||= half-4th ||= 5 = 4L 1s ||= 9 = 5L 4s ||=   ||=   ||
-||= (P8, P5/2) ||= half-5th ||= 7, 10, 17 ||
+||= (P8, P5/2) ||= half-5th ||= 7 = 3L 4s ||= 10 = 7L 3s ||=   ||=   ||
-||= (P8/2, P4/2) ||= half-everything ||= 4, 6, 10, 14, 24 ||
+||= (P8/2, P4/2) ||= half-everything ||= 6 = 4L 2s ||= 10 = 4L 6s ||=   ||=   ||
-||~ thirds ||~   ||~   ||
+||~ thirds ||~   ||~   ||~   ||~   ||~   ||
-||= (P8/3, P5) ||= third-8ve ||= 6, 9, 12, 15/21 ||
+||= (P8/3, P5) ||= third-8ve ||= 6 = 3L 3s ||= 9 = 3L 6s ||= 12 = 3L 9s * ||=   ||
-||= (P8, P4/3) ||= third-4th ||=   ||
+||= (P8, P4/3) ||= third-4th ||= 5 = 1L 4s ||= 6 = 1L 5s ||= 7 = 1L 6s ||= 8 = 7L 1s ||
-||= (P8, P5/3) ||= third-5th ||=   ||
+||= (P8, P5/3) ||= third-5th ||= 5 = 1L 4s ||= 6 = 5L 1s ||= 11 = 5L 6s ||=   ||
-||= (P8, P11/3) ||= third-11th ||=   ||
+||= (P8, P11/3) ||= third-11th ||= 5 = 2L 3s ||= 7 = 2L 5s ||= 9 = 2L 7s ||= 11 = 2L 9s ||
-||= (P8/3, P4/2) ||= third-8ve, half-4th ||=   ||
+||= (P8/3, P4/2) ||= third-8ve, half-4th ||=   ||=   ||=   ||=   ||
-||= (P8/3, P5/2) ||= third-8ve, half-5th ||=   ||
+||= (P8/3, P5/2) ||= third-8ve, half-5th ||=   ||=   ||=   ||=   ||
-||= (P8/2, P4/3) ||= half-8ve, third-4th ||=   ||
+||= (P8/2, P4/3) ||= half-8ve, third-4th ||=   ||=   ||=   ||=   ||
-||= (P8/2, P5/3) ||= half-8ve, third-5th ||=   ||
+||= (P8/2, P5/3) ||= half-8ve, third-5th ||=   ||=   ||=   ||=   ||
-||= (P8/2, P11/3) ||= half-8ve, third-11th ||=   ||
+||= (P8/2, P11/3) ||= half-8ve, third-11th ||=   ||=   ||=   ||=   ||
-||= (P8/3, P4/3) ||= third-everything ||=   ||
+||= (P8/3, P4/3) ||= third-everything ||=   ||=   ||=   ||=   ||
-||~ quarters ||~   ||~   ||
+||~ quarters ||~   ||~   ||~   ||~   ||~   ||
-||= (P8/4, P5) ||=   ||=   ||
+||= (P8/4, P5) ||=   ||=   ||=   ||=   ||=   ||
-||= (P8, P4/4) ||=   ||=   ||
+||= (P8, P4/4) ||=   ||=   ||=   ||=   ||=   ||
-||= (P8, P5/4) ||=   ||=   ||
+||= (P8, P5/4) ||=   ||=   ||=   ||=   ||=   ||
-||= (P8, P11/4) ||=   ||=   ||
+||= (P8, P11/4) ||=   ||=   ||=   ||=   ||=   ||
-||= (P8, P12/4) ||=   ||=   ||
+||= (P8, P12/4) ||=   ||=   ||=   ||=   ||=   ||
-||= (P8/4, P4/2) ||=   ||=   ||
+||= (P8/4, P4/2) ||=   ||=   ||=   ||=   ||=   ||
-||= (P8/2, M2/4) ||=   ||=   ||
+||= (P8/2, M2/4) ||=   ||=   ||=   ||=   ||=   ||
-||= (P8/2, P4/4) ||=   ||=   ||
+||= (P8/2, P4/4) ||=   ||=   ||=   ||=   ||=   ||
-||= (P8/2, P5/4) ||=   ||=   ||
+||= (P8/2, P5/4) ||=   ||=   ||=   ||=   ||=   ||
-||= (P8/4, P4/3) ||=   ||=   ||
+||= (P8/4, P4/3) ||=   ||=   ||=   ||=   ||=   ||
-||= (P8/4, P5/3) ||=   ||=   ||
+||= (P8/4, P5/3) ||=   ||=   ||=   ||=   ||=   ||
-||= (P8/4, P11/3) ||=   ||=   ||
+||= (P8/4, P11/3) ||=   ||=   ||=   ||=   ||=   ||
-||= (P8/3, P4/4) ||=   ||=   ||
+||= (P8/3, P4/4) ||=   ||=   ||=   ||=   ||=   ||
-||= (P8/3, P5/4) ||=   ||=   ||
+||= (P8/3, P5/4) ||=   ||=   ||=   ||=   ||=   ||
-||= (P8/3, P11/4) ||=   ||=   ||
+||= (P8/3, P11/4) ||=   ||=   ||=   ||=   ||=   ||
-||= (P8/3, P12/4) ||=   ||=   ||
+||= (P8/3, P12/4) ||=   ||=   ||=   ||=   ||=   ||
-||= (P8/4, P4/4) ||=   ||=   ||
+||= (P8/4, P4/4) ||=   ||=   ||=   ||=   ||=   ||
@@ Line 2,956: / Line 2,956: @@
 Some MOS scales are better understood using a pergen with a nonstandard prime subgroup. For example, 6L 1s can be roulette [7], with a 2.5.7 pergen (P8, (5/4)/2), where 5·G = 7/4.&lt;br /&gt;
 &lt;br /&gt;
-A pergen&lt;br /&gt;
+We can also examine which MOS scales are generated by a specific pergen. This depends on the size of the generator. In this table, the 5th is assumed to be between 4\7 and 3\5.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 2,962: / Line 2,962: @@
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;th&gt;pergen&lt;br /&gt;
+         &lt;th colspan="2"&gt;pergen&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th colspan="2"&gt;MOS scales 5-12&lt;br /&gt;
 &lt;/th&gt;
          &lt;th&gt;&lt;br /&gt;
 &lt;/th&gt;
-         &lt;th&gt;MOS scales 5-12&lt;br /&gt;
+         &lt;th&gt;&lt;br /&gt;
 &lt;/th&gt;
      &lt;/tr&gt;
@@ Line 2,974: / Line 2,976: @@
          &lt;td style="text-align: center;"&gt;unsplit&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;5, 7, 12, 17/19&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;5 = 2L 3s&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;7 = 5L 2s&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;12 = 7L 5s &lt;u&gt;&lt;strong&gt;or&lt;/strong&gt;&lt;/u&gt; 5L 7s&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;th&gt;halves&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;&lt;br /&gt;
 &lt;/th&gt;
          &lt;th&gt;&lt;br /&gt;
@@ Line 2,990: / Line 3,004: @@
          &lt;td style="text-align: center;"&gt;half-8ve&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;4, 6, 8, 10, 12&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;6 = 2L 4s&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;8 = 2L 6s&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;10 = 2L 8s&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;12 = 2L 10s *&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 2,998: / Line 3,018: @@
          &lt;td style="text-align: center;"&gt;half-4th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;4, 5, 9, 14, 19&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;5 = 4L 1s&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;9 = 5L 4s&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 3,006: / Line 3,032: @@
          &lt;td style="text-align: center;"&gt;half-5th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;7, 10, 17&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;7 = 3L 4s&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;10 = 7L 3s&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 3,014: / Line 3,046: @@
          &lt;td style="text-align: center;"&gt;half-everything&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;4, 6, 10, 14, 24&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;6 = 4L 2s&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;10 = 4L 6s&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;th&gt;thirds&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;&lt;br /&gt;
 &lt;/th&gt;
          &lt;th&gt;&lt;br /&gt;
@@ Line 3,030: / Line 3,074: @@
          &lt;td style="text-align: center;"&gt;third-8ve&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;6, 9, 12, 15/21&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;6 = 3L 3s&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;9 = 3L 6s&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;12 = 3L 9s *&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 3,038: / Line 3,088: @@
          &lt;td style="text-align: center;"&gt;third-4th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;5 = 1L 4s&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;6 = 1L 5s&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;7 = 1L 6s&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;8 = 7L 1s&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 3,045: / Line 3,101: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;third-5th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;5 = 1L 4s&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;6 = 5L 1s&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;11 = 5L 6s&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,054: / Line 3,116: @@
          &lt;td style="text-align: center;"&gt;third-11th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;5 = 2L 3s&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;7 = 2L 5s&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;9 = 2L 7s&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;11 = 2L 9s&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 3,061: / Line 3,129: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;third-8ve, half-4th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,072: / Line 3,146: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-     &lt;/tr&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+     &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td style="text-align: center;"&gt;(P8/2, P4/3)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;half-8ve, third-4th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,085: / Line 3,171: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;half-8ve, third-5th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,093: / Line 3,185: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;half-8ve, third-11th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,101: / Line 3,199: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;third-everything&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,107: / Line 3,211: @@
      &lt;tr&gt;
          &lt;th&gt;quarters&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;&lt;br /&gt;
 &lt;/th&gt;
          &lt;th&gt;&lt;br /&gt;
@@ Line 3,120: / Line 3,230: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-    &lt;/tr&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
-    &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;(P8, P4/4)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,130: / Line 3,238: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;(P8, P5/4)&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;(P8, P4/4)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,136: / Line 3,244: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-    &lt;/tr&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
-    &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;(P8, P11/4)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,146: / Line 3,252: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;(P8, P12/4)&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;(P8, P5/4)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,152: / Line 3,258: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-    &lt;/tr&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
-    &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;(P8/4, P4/2)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,162: / Line 3,266: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;(P8/2, M2/4)&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;(P8, P11/4)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,168: / Line 3,272: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-    &lt;/tr&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
-    &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;(P8/2, P4/4)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,178: / Line 3,280: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;(P8/2, P5/4)&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;(P8, P12/4)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,184: / Line 3,286: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-    &lt;/tr&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
-    &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;(P8/4, P4/3)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,194: / Line 3,294: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;(P8/4, P5/3)&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;(P8/4, P4/2)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,200: / Line 3,300: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-    &lt;/tr&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
-    &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;(P8/4, P11/3)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,210: / Line 3,308: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;(P8/3, P4/4)&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;(P8/2, M2/4)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,216: / Line 3,314: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-    &lt;/tr&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
-    &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;(P8/3, P5/4)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,226: / Line 3,322: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;(P8/3, P11/4)&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;(P8/2, P4/4)&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,232: / Line 3,330: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-     &lt;/tr&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;(P8/2, P5/4)&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+     &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;(P8/3, P12/4)&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;(P8/4, P4/3)&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;(P8/4, P5/3)&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;(P8/4, P11/3)&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;(P8/3, P4/4)&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;(P8/3, P5/4)&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;(P8/3, P11/4)&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+         &lt;td style="text-align: center;"&gt;(P8/3, P12/4)&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,243: / Line 3,449: @@
      &lt;tr&gt;
          &lt;td style="text-align: center;"&gt;(P8/4, P4/4)&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,574: / Line 3,786: @@
   &lt;br /&gt;
 This PDF is a rank-2 notation guide that shows the full lattice for the first 15 pergens, up through the third-splits block.&lt;br /&gt;
-&lt;!-- ws:start:WikiTextUrlRule:4378:http://www.tallkite.com/misc_files/pergens.pdf --&gt;&lt;a class="wiki_link_ext" href="http://www.tallkite.com/misc_files/pergens.pdf" rel="nofollow"&gt;http://www.tallkite.com/misc_files/pergens.pdf&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:4378 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextUrlRule:4696:http://www.tallkite.com/misc_files/pergens.pdf --&gt;&lt;a class="wiki_link_ext" href="http://www.tallkite.com/misc_files/pergens.pdf" rel="nofollow"&gt;http://www.tallkite.com/misc_files/pergens.pdf&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:4696 --&gt;&lt;br /&gt;
 &lt;br /&gt;
 Alt-pergenLister lists out thousands of pergens, and suggests periods, generators and enharmonics for each one. It can also list only those pergens supported by a specific edo. Written in Jesusonic, runs inside Reaper.&lt;br /&gt;
-&lt;!-- ws:start:WikiTextUrlRule:4379:http://www.tallkite.com/misc_files/alt-pergensLister.zip --&gt;&lt;a class="wiki_link_ext" href="http://www.tallkite.com/misc_files/alt-pergensLister.zip" rel="nofollow"&gt;http://www.tallkite.com/misc_files/alt-pergensLister.zip&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:4379 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextUrlRule:4697:http://www.tallkite.com/misc_files/alt-pergensLister.zip --&gt;&lt;a class="wiki_link_ext" href="http://www.tallkite.com/misc_files/alt-pergensLister.zip" rel="nofollow"&gt;http://www.tallkite.com/misc_files/alt-pergensLister.zip&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:4697 --&gt;&lt;br /&gt;
 &lt;br /&gt;
 Screenshot of the first 38 pergens:&lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:2534:&amp;lt;img src=&amp;quot;/file/view/alt-pergenLister.png/624838213/704x460/alt-pergenLister.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 460px; width: 704px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/alt-pergenLister.png/624838213/704x460/alt-pergenLister.png" alt="alt-pergenLister.png" title="alt-pergenLister.png" style="height: 460px; width: 704px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:2534 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:2746:&amp;lt;img src=&amp;quot;/file/view/alt-pergenLister.png/624838213/704x460/alt-pergenLister.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 460px; width: 704px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/alt-pergenLister.png/624838213/704x460/alt-pergenLister.png" alt="alt-pergenLister.png" title="alt-pergenLister.png" style="height: 460px; width: 704px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:2746 --&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:90:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Further Discussion-Misc notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:90 --&gt;Misc notes&lt;/h2&gt;