Kite's thoughts on pergens: Difference between revisions
Wikispaces>TallKite **Imported revision 625030713 - Original comment: ** |
Wikispaces>TallKite **Imported revision 625062379 - 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:TallKite|TallKite]] and made on <tt>2018-01-18 | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2018-01-18 15:22:52 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>625062379</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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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. | 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. | ||
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. | We can also examine which MOS scales are generated by a specific pergen. This of course depends on the exact size of the generator. In this table, the 5th is assumed to be between 4\7 and 3\5. | ||
||||~ pergen ||||~ | ||||~ pergen ||~ MOS scales ||~ from 5 to 12 ||~ ||~ || | ||
||= (P8, P5) ||= unsplit ||= 5 = 2L 3s ||= 7 = 5L 2s ||= 12 = 7L 5s __**or**__ 5L 7s ||= || | ||= (P8, P5) ||= unsplit ||= 5 = 2L 3s ||= 7 = 5L 2s ||= 12 = 7L 5s __**or**__ 5L 7s ||= || | ||
||~ halves ||~ ||~ ||~ ||~ ||~ || | ||~ halves ||~ ||~ ||~ ||~ ||~ || | ||
||= (P8/2, P5) ||= half-8ve ||= 6 = 2L 4s ||= 8 = 2L 6s ||= 10 = 2L 8s ||= 12 = 2L 10s * || | ||= (P8/2, P5) ||= half-8ve ||= 6 = 2L 4s ||= 8 = 2L 6s ||= 10 = 2L 8s ||= 12 = 2L 10s __**or**__ 10L 2s || | ||
||= (P8, P4/2) ||= half-4th ||= 5 = 4L 1s ||= 9 = 5L 4s ||= ||= || | ||= (P8, P4/2) ||= half-4th ||= 5 = 4L 1s ||= 9 = 5L 4s ||= ||= || | ||
||= (P8, P5/2) ||= half-5th ||= 7 = 3L 4s ||= 10 = 7L 3s ||= ||= || | ||= (P8, P5/2) ||= half-5th ||= 7 = 3L 4s ||= 10 = 7L 3s ||= ||= || | ||
||= (P8/2, P4/2) ||= half-everything ||= 6 = 4L 2s ||= 10 = 4L 6s ||= ||= || | ||= (P8/2, P4/2) ||= half-everything ||= 6 = 4L 2s ||= 10 = 4L 6s ||= ||= || | ||
||~ thirds ||~ ||~ ||~ ||~ ||~ || | ||~ thirds ||~ ||~ ||~ ||~ ||~ || | ||
||= (P8/3, P5) ||= third-8ve ||= 6 = 3L 3s ||= 9 = 3L 6s ||= 12 = 3L 9s * ||= || | ||= (P8/3, P5) ||= third-8ve ||= 6 = 3L 3s ||= 9 = 3L 6s ||= 12 = 3L 9s __**or**__ 9L 3s ||= || | ||
||= (P8, P4/3) ||= third-4th ||= 5 = 1L 4s ||= 6 = 1L 5s ||= 7 = 1L 6s ||= 8 = 7L 1s || | ||= (P8, P4/3) ||= third-4th ||= 5 = 1L 4s ||= 6 = 1L 5s ||= 7 = 1L 6s ||= 8 = 7L 1s || | ||
||= (P8, P5/3) ||= third-5th ||= 5 = 1L 4s ||= 6 = 5L 1s ||= 11 = 5L 6s ||= || | ||= (P8, P5/3) ||= third-5th ||= 5 = 1L 4s ||= 6 = 5L 1s ||= 11 = 5L 6s ||= || | ||
||= (P8, P11/3) ||= third-11th ||= 5 = 2L 3s ||= 7 = 2L 5s ||= 9 = 2L 7s ||= 11 = 2L 9s || | ||= (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 ||= 6 = 3L 3s ||= 9 = 6L 3s ||= ||= || | ||
||= (P8/3, P5/2) ||= third-8ve, half-5th ||= | ||= (P8/3, P5/2) ||= third-8ve, half-5th ||= 6 = 3L 3s ||= 9 = 3L 6s ||= 12 = 3L 9s ||= || | ||
||= (P8/2, P4/3) ||= half-8ve, third-4th ||= | ||= (P8/2, P4/3) ||= half-8ve, third-4th ||= 6 = 2L 4s ||= 8 = 6L 2s ||= ||= || | ||
||= (P8/2, P5/3) ||= half-8ve, third-5th ||= | ||= (P8/2, P5/3) ||= half-8ve, third-5th ||= 6 = 4L 2s ||= 10 = 6L 4s ||= ||= || | ||
||= (P8/2, P11/3) ||= half-8ve, third-11th ||= | ||= (P8/2, P11/3) ||= half-8ve, third-11th ||= 6 = 2L 4s ||= 8 = 2L 6s ||= 10 = 2L 8s ||= 12 = 2L 10s || | ||
||= (P8/3, P4/3) ||= third-everything ||= | ||= (P8/3, P4/3) ||= third-everything ||= 6 = 3L 3s ||= 9 = 6L 3s ||= ||= || | ||
||~ quarters ||~ ||~ ||~ ||~ ||~ || | ||~ quarters ||~ ||~ ||~ ||~ ||~ || | ||
||= (P8/4, P5) ||= ||= ||= ||= ||= || | ||= (P8/4, P5) ||= ||= ||= ||= ||= || | ||
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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.<br /> | 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.<br /> | ||
<br /> | <br /> | ||
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.<br /> | We can also examine which MOS scales are generated by a specific pergen. This of course depends on the exact size of the generator. In this table, the 5th is assumed to be between 4\7 and 3\5.<br /> | ||
<br /> | <br /> | ||
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<th colspan="2">pergen<br /> | <th colspan="2">pergen<br /> | ||
</th> | </th> | ||
<th | <th>MOS scales<br /> | ||
</th> | |||
<th>from 5 to 12<br /> | |||
</th> | </th> | ||
<th><br /> | <th><br /> | ||
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<td style="text-align: center;">10 = 2L 8s<br /> | <td style="text-align: center;">10 = 2L 8s<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">12 = 2L 10s | <td style="text-align: center;">12 = 2L 10s <u><strong>or</strong></u> 10L 2s<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td style="text-align: center;">9 = 3L 6s<br /> | <td style="text-align: center;">9 = 3L 6s<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">12 = 3L 9s | <td style="text-align: center;">12 = 3L 9s <u><strong>or</strong></u> 9L 3s<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
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<td style="text-align: center;">third-8ve, half-4th<br /> | <td style="text-align: center;">third-8ve, half-4th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">6 = 3L 3s<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">9 = 6L 3s<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
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<td style="text-align: center;">third-8ve, half-5th<br /> | <td style="text-align: center;">third-8ve, half-5th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">6 = 3L 3s<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">9 = 3L 6s<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">12 = 3L 9s<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
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<td style="text-align: center;">half-8ve, third-4th<br /> | <td style="text-align: center;">half-8ve, third-4th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">6 = 2L 4s<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">8 = 6L 2s<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
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<td style="text-align: center;">half-8ve, third-5th<br /> | <td style="text-align: center;">half-8ve, third-5th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">6 = 4L 2s<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">10 = 6L 4s<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
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<td style="text-align: center;">half-8ve, third-11th<br /> | <td style="text-align: center;">half-8ve, third-11th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">6 = 2L 4s<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">8 = 2L 6s<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">10 = 2L 8s<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">12 = 2L 10s<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td style="text-align: center;">third-everything<br /> | <td style="text-align: center;">third-everything<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">6 = 3L 3s<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">9 = 6L 3s<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
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<br /> | <br /> | ||
This PDF is a rank-2 notation guide that shows the full lattice for the first 15 pergens, up through the third-splits block.<br /> | This PDF is a rank-2 notation guide that shows the full lattice for the first 15 pergens, up through the third-splits block.<br /> | ||
<!-- ws:start:WikiTextUrlRule: | <!-- ws:start:WikiTextUrlRule:4699:http://www.tallkite.com/misc_files/pergens.pdf --><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><!-- ws:end:WikiTextUrlRule:4699 --><br /> | ||
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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.<br /> | 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.<br /> | ||
<!-- ws:start:WikiTextUrlRule: | <!-- ws:start:WikiTextUrlRule:4700:http://www.tallkite.com/misc_files/alt-pergensLister.zip --><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><!-- ws:end:WikiTextUrlRule:4700 --><br /> | ||
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Screenshot of the first 38 pergens:<br /> | Screenshot of the first 38 pergens:<br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:2748:&lt;img src=&quot;/file/view/alt-pergenLister.png/624838213/704x460/alt-pergenLister.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 460px; width: 704px;&quot; /&gt; --><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;" /><!-- ws:end:WikiTextLocalImageRule:2748 --><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:90:&lt;h2&gt; --><h2 id="toc19"><a name="Further Discussion-Misc notes"></a><!-- ws:end:WikiTextHeadingRule:90 -->Misc notes</h2> | <!-- ws:start:WikiTextHeadingRule:90:&lt;h2&gt; --><h2 id="toc19"><a name="Further Discussion-Misc notes"></a><!-- ws:end:WikiTextHeadingRule:90 -->Misc notes</h2> | ||