Kite's thoughts on pergens: Difference between revisions
Wikispaces>TallKite **Imported revision 626613657 - Original comment: ** |
Wikispaces>TallKite **Imported revision 626629395 - 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>2018-02-19 | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2018-02-19 18:44:56 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>626629395</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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For a pergen (P8/m, M/n), let x be any number that divides m, R be any 3-limit ratio, and z be any integer. The interval z·P8 ± x·R splits into x parts. Let y be any number that divides n, the interval z·M ± y·R splits into y parts. If x divides both m and n, the interval z·P8 + z'·M ± x·R splits into x parts (z' is any integer). | For a pergen (P8/m, M/n), let x be any number that divides m, R be any 3-limit ratio, and z be any integer. The interval z·P8 ± x·R splits into x parts. Let y be any number that divides n, the interval z·M ± y·R splits into y parts. If x divides both m and n, the interval z·P8 + z'·M ± x·R splits into x parts (z' is any integer). | ||
||~ | ||~ block ||||~ pergen ||~ secondary splits <= 12th || | ||
||~ halves ||||= all pergens ||= M3/2, d5/2, A5/ | ||~ halves ||||= all pergens ||= M3/2, d5/2, A5/4, m7/2, M9/2, A11/2 || | ||
|| ||= (P8/2, P5) ||= half-8ve ||= M2/2, A4/ | || ||= (P8/2, P5) ||= half-8ve ||= M2/2, M3/4, A4/6, m6/2, M10/2, d12/2 || | ||
|| ||= (P8, P4/2) ||= half-4th ||= m2/2, M6/2, A8/2, m10/2, P12/2 || | || ||= (P8, P4/2) ||= half-4th ||= m2/2, M6/2, A8/2, m10/2, P12/2 || | ||
|| ||= (P8, P5/2) ||= half-5th ||= A1/2, m3/2, M7/2, m9/2, P11/2 || | || ||= (P8, P5/2) ||= half-5th ||= A1/2, m3/2, M7/2, m9/2, P11/2 || | ||
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||~ thirds ||||= all pergens ||= A4/3, m10/3 || | ||~ thirds ||||= all pergens ||= A4/3, m10/3 || | ||
|| ||= (P8/3, P5) ||= third-8ve ||= m3/3, M6/3, A11/3, d12/3 || | || ||= (P8/3, P5) ||= third-8ve ||= m3/3, M6/3, A11/3, d12/3 || | ||
|| ||= (P8, P4/3) ||= third-4th ||= A1/3, m7/ | || ||= (P8, P4/3) ||= third-4th ||= A1/3, m7/6, M7/3, M10/3 || | ||
|| ||= (P8, P5/3) ||= third-5th ||= m2/3, m6/3, M9/3, A8/3 || | || ||= (P8, P5/3) ||= third-5th ||= m2/3, m6/3, M9/3, A8/3 || | ||
|| ||= (P8, P11/3) ||= third-11th ||= M2/3, M3/3, m9/3, P12/3 || | || ||= (P8, P11/3) ||= third-11th ||= M2/3, M3/3, m9/3, P12/3 || | ||
|| ||= (P8/3, P4/2) ||= third-8ve half-4th ||= | || ||= (P8/3, P4/2) ||= third-8ve half-4th ||= half-4th + third-8ve + M6/6, m10/6, A11/12 || | ||
|| ||= | || ||= (P8/3, P5/2) ||= third-8ve half-5th ||= half-5th + third-8ve + m3/6, d5/12 || | ||
|| ||= | || ||= (P8/2, P4/3) ||= half-8ve third-4th ||= half-8ve + third-4th + A4/6, M10/6 || | ||
|| ||= | || ||= (P8/2, P5/3) ||= half-8ve third-5th ||= half-8ve + third-5th + m6/6, M9/6 || | ||
|| ||= | || ||= (P8/2, P11/3) ||= half-8ve third-11th ||= half-8ve + third-11th + M2/6, M3/12, A4/18 || | ||
|| ||= | || ||= (P83, P4/3) ||= third-everything ||= (every 3-limit interval)/3 || | ||
|| ||= ||= ||= || | || ||= ||= ||= || | ||
|| ||= ||= ||= || | || ||= ||= ||= || | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<th> | <th>block<br /> | ||
</th> | </th> | ||
<th colspan="2" | <th colspan="2">pergen<br /> | ||
</th> | </th> | ||
<th>secondary splits &lt;= | <th>secondary splits &lt;= 12th<br /> | ||
</th> | </th> | ||
</tr> | </tr> | ||
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<td colspan="2" style="text-align: center;">all pergens<br /> | <td colspan="2" style="text-align: center;">all pergens<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">M3/2, d5/2, A5/ | <td style="text-align: center;">M3/2, d5/2, A5/4, m7/2, M9/2, A11/2<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td style="text-align: center;">half-8ve<br /> | <td style="text-align: center;">half-8ve<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">M2/2, A4/ | <td style="text-align: center;">M2/2, M3/4, A4/6, m6/2, M10/2, d12/2<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td style="text-align: center;">third-4th<br /> | <td style="text-align: center;">third-4th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">A1/3, m7/ | <td style="text-align: center;">A1/3, m7/6, M7/3, M10/3<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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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;">half-4th + third-8ve + M6/6, m10/6, A11/12<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">(P8/3, P5/2)<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">third-8ve half-5th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">half-5th + third-8ve + m3/6, d5/12<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">(P8/2, P4/3)<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">half-8ve third-4th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">half-8ve + third-4th + A4/6, M10/6<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">(P8/2, P5/3)<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">half-8ve third-5th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">half-8ve + third-5th + m6/6, M9/6<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">(P8/2, P11/3)<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">half-8ve third-11th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">half-8ve + third-11th + M2/6, M3/12, A4/18<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">(P83, P4/3)<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">third-everything<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">(every 3-limit interval)/3<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||