Kite's thoughts on pergens: Difference between revisions
Wikispaces>TallKite **Imported revision 630797843 - Original comment: ** |
Wikispaces>TallKite **Imported revision 630798459 - 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>2018-07-04 | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2018-07-04 03:38:31 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>630798459</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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||~ EDO ||~ Period ||||||||||||||||||~ Generator in edosteps ||~ ||~ ||~ ||~ ||~ ||~ || | ||~ EDO ||~ Period ||||||||||||||||||~ Generator in edosteps ||~ ||~ ||~ ||~ ||~ ||~ || | ||
||~ ||~ | ||~ ||~ in edosteps ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ ||~ ||~ ||~ ||~ || | ||
||~ 5 ||~ 5 = P8 ||= P4/2 ||= P5 ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||~ 5 ||~ 5 = P8 ||= P4/2 ||= P5 ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||
||~ 6 ||~ 6 = P8 ||= P4/2 ||= - ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||~ 6 ||~ 6 = P8 ||= P4/2 ||= - ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||
| Line 955: | Line 955: | ||
||~ 9 ||~ 9 = P8 ||= P4/4 ||= P4/2 ||= - ||= P5 ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||~ 9 ||~ 9 = P8 ||= P4/4 ||= P4/2 ||= - ||= P5 ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||
||~ " ||~ 3 = P8/3 ||= P5 ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||~ " ||~ 3 = P8/3 ||= P5 ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||
||~ 10 ||~ 10 = P8 ||= P4/4 ||= - ||= P5/2 ||= | ||~ 10 ||~ 10 = P8 ||= P4/4 ||= - ||= P5/2 ||= - ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||
||~ " ||~ 5 = P8/2 ||= P5 ||= P4/2 ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||~ " ||~ 5 = P8/2 ||= P5 ||= P4/2 ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||
||~ 11 ||~ 11 = P8 ||= P4/5 ||= P5/3 ||= P5/2 ||= P11/4 ||= P5 ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||~ 11 ||~ 11 = P8 ||= P4/5 ||= P5/3 ||= P5/2 ||= P11/4 ||= P5 ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||
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||~ " ||~ 3 = P8/4 ||= P5 ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||~ " ||~ 3 = P8/4 ||= P5 ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||
||~ 13b ||~ 13 = P8 ||= P4/6 ||= P4/3 ||= P4/2 ||= P12/5 ||= P12/4 ||= P5 ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||~ 13b ||~ 13 = P8 ||= P4/6 ||= P4/3 ||= P4/2 ||= P12/5 ||= P12/4 ||= P5 ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||
||~ 14 ||~ 14 = P8 ||= P4/6 ||= - ||= P4/2 ||= - ||= P11/4 ||= | ||~ 14 ||~ 14 = P8 ||= P4/6 ||= - ||= P4/2 ||= - ||= P11/4 ||= - ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||
||~ " ||~ 7 = P8/2 ||= P5 ||= P4/3 ||= P4/2 ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||~ " ||~ 7 = P8/2 ||= P5 ||= P4/3 ||= P4/2 ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||
||~ 15 ||~ 15 = P8 ||= P4/6 ||= P4/3 ||= - ||= P12/6 ||= - ||= - ||= P11/3 ||= ||= ||= ||= ||= ||= ||= ||= || | ||~ 15 ||~ 15 = P8 ||= P4/6 ||= P4/3 ||= - ||= P12/6 ||= - ||= - ||= P11/3 ||= ||= ||= ||= ||= ||= ||= ||= || | ||
||~ " ||~ 5 = P8/3 ||= P5 ||= P4/2 | ||~ " ||~ 5 = P8/3 ||= P5 ||= P4/2 ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||
||~ " ||~ 3 = P8/5 ||= P4/3 ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||~ " ||~ 3 = P8/5 ||= P4/3 ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||
||~ 16 ||~ 16 = P8 ||= P4/7 ||= - ||= P5/3 ||= - ||= P12/5 ||= - ||= P5 ||= ||= ||= ||= ||= ||= ||= ||= || | ||~ 16 ||~ 16 = P8 ||= P4/7 ||= - ||= P5/3 ||= - ||= P12/5 ||= - ||= P5 ||= ||= ||= ||= ||= ||= ||= ||= || | ||
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||~ 18b ||~ 18 = P8 ||= P4/8 ||= - ||= - ||= - ||= P5/2 ||= - ||= P12/4 ||= - ||= ||= ||= ||= ||= ||= ||= || | ||~ 18b ||~ 18 = P8 ||= P4/8 ||= - ||= - ||= - ||= P5/2 ||= - ||= P12/4 ||= - ||= ||= ||= ||= ||= ||= ||= || | ||
||~ " ||~ 9 = P8/2 ||= P5 ||= P4/4 ||= - ||= P4/2 ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||~ " ||~ 9 = P8/2 ||= P5 ||= P4/4 ||= - ||= P4/2 ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||
||~ " ||~ 6 = P8/3 ||= | ||~ " ||~ 6 = P8/3 ||= P5/2 ||= - ||= - ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||
||~ " ||~ 3 = P8/6 ||= P5 ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||~ " ||~ 3 = P8/6 ||= P5 ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||
||~ 19 ||~ 19 = P8 ||= P4/8 ||= P4/4 ||= P11/9 ||= P4/2 ||= P12/6 ||= P12/5 ||= WWP5/7 ||= P5 ||= P11/3 ||= ||= ||= ||= ||= ||= || | ||~ 19 ||~ 19 = P8 ||= P4/8 ||= P4/4 ||= P11/9 ||= P4/2 ||= P12/6 ||= P12/5 ||= WWP5/7 ||= P5 ||= P11/3 ||= ||= ||= ||= ||= ||= || | ||
||~ 20 ||~ 20 = P8 ||= P4/8 ||= - ||= | ||~ 20 ||~ 20 = P8 ||= P4/8 ||= - ||= P5/4 ||= - ||= - ||= - ||= P11/4 ||= - ||= W<span style="vertical-align: super;">3</span>P5/8 ||= ||= ||= ||= ||= ||= || | ||
||~ " ||~ 10 = P8/2 ||= M2/4 ||= - ||= P5/4 ||= - ||= - ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||~ " ||~ 10 = P8/2 ||= M2/4 ||= - ||= P5/4 ||= - ||= - ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||
||~ " ||~ 5 = P8/4 ||= | ||~ " ||~ 5 = P8/4 ||= P4/2 ||= P5 ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||
||~ " ||~ 4 = P8/5 ||= P5/4 ||= - ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||~ " ||~ 4 = P8/5 ||= P5/4 ||= - ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||
||~ 21 ||~ 21 = P8 ||= P4/9 ||= P5/6 ||= - ||= P5/3 ||= P11/6 ||= - ||= - ||= W<span style="vertical-align: super;">3</span>P4/9 ||= - ||= P11/3 ||= ||= ||= ||= ||= || | ||~ 21 ||~ 21 = P8 ||= P4/9 ||= P5/6 ||= - ||= P5/3 ||= P11/6 ||= - ||= - ||= W<span style="vertical-align: super;">3</span>P4/9 ||= - ||= P11/3 ||= ||= ||= ||= ||= || | ||
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||~ " ||~ 4 = P8/6 ||= P4/2 ||= - ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||~ " ||~ 4 = P8/6 ||= P4/2 ||= - ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||
||~ " ||~ 3 = P8/8 ||= P5 ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||~ " ||~ 3 = P8/8 ||= P5 ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | ||
||~ 31 ||~ 31 = P8 ||= P4/13 ||= P5/9 ||= P5/6 ||= P11/11 ||= | ||~ 31 ||~ 31 = P8 ||= P4/13 ||= P5/9 ||= P5/6 ||= P11/11 ||= WWP4/15 ||= P5/3 ||= P12/7 ||= WWP5/10 ||= P5/2 ||= WWP5/8 ||= P11/4 ||= W<span style="vertical-align: super;">5</span>P4/14 ||= P5 ||= W<span style="vertical-align: super;">5</span> | ||
P4/14 ||= P5 ||= W<span style="vertical-align: super;">5</span> | |||
P4/12 ||= WW | P4/12 ||= WW | ||
P4/5 || | P4/5 || | ||
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<th><br /> | <th><br /> | ||
</th> | </th> | ||
<th><br /> | <th>in edosteps<br /> | ||
</th> | </th> | ||
<th>1<br /> | <th>1<br /> | ||
| Line 6,769: | Line 6,764: | ||
<td style="text-align: center;">P5/2<br /> | <td style="text-align: center;">P5/2<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">-<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 7,061: | Line 7,056: | ||
<td style="text-align: center;">P11/4<br /> | <td style="text-align: center;">P11/4<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">-<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 7,162: | Line 7,157: | ||
</td> | </td> | ||
<td style="text-align: center;">P4/2<br /> | <td style="text-align: center;">P4/2<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 7,484: | Line 7,478: | ||
<th>6 = P8/3<br /> | <th>6 = P8/3<br /> | ||
</th> | </th> | ||
<td style="text-align: center;"> | <td style="text-align: center;">P5/2<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">-<br /> | <td style="text-align: center;">-<br /> | ||
| Line 7,596: | Line 7,590: | ||
<td style="text-align: center;">-<br /> | <td style="text-align: center;">-<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">P5/4<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">-<br /> | <td style="text-align: center;">-<br /> | ||
| Line 7,604: | Line 7,598: | ||
<td style="text-align: center;">-<br /> | <td style="text-align: center;">-<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">P11/4<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">-<br /> | <td style="text-align: center;">-<br /> | ||
| Line 7,664: | Line 7,658: | ||
<th>5 = P8/4<br /> | <th>5 = P8/4<br /> | ||
</th> | </th> | ||
<td style="text-align: center;"> | <td style="text-align: center;">P4/2<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">P5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 8,176: | Line 8,170: | ||
<td style="text-align: center;">P11/11<br /> | <td style="text-align: center;">P11/11<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">WWP4/15<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P5/3<br /> | <td style="text-align: center;">P5/3<br /> | ||
| Line 8,183: | Line 8,176: | ||
<td style="text-align: center;">P12/7<br /> | <td style="text-align: center;">P12/7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">WWP5/10<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P5/2<br /> | <td style="text-align: center;">P5/2<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">WWP5/8<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P11/4<br /> | <td style="text-align: center;">P11/4<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">W<span style="vertical-align: super;">5</span> | <td style="text-align: center;">W<span style="vertical-align: super;">5</span>P4/14<br /> | ||
P4/14<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">P5<br /> | <td style="text-align: center;">P5<br /> | ||
| Line 8,760: | Line 8,750: | ||
<br /> | <br /> | ||
Alt-pergenLister lists out thousands of rank-2 pergens, and suggests periods, generators and enharmonics for each one. Alternate enharmonics are not listed, but single-pair notation for false-double pergens is. It can also list only those pergens supported by a specific edo or edo pair. Written in Jesusonic, runs inside Reaper.<br /> | Alt-pergenLister lists out thousands of rank-2 pergens, and suggests periods, generators and enharmonics for each one. Alternate enharmonics are not listed, but single-pair notation for false-double pergens is. It can also list only those pergens supported by a specific edo or edo pair. Written in Jesusonic, runs inside Reaper.<br /> | ||
<!-- ws:start:WikiTextUrlRule: | <!-- ws:start:WikiTextUrlRule:11208:http://www.tallkite.com/misc_files/alt-pergenLister.zip --><a class="wiki_link_ext" href="http://www.tallkite.com/misc_files/alt-pergenLister.zip" rel="nofollow">http://www.tallkite.com/misc_files/alt-pergenLister.zip</a><!-- ws:end:WikiTextUrlRule:11208 --><br /> | ||
<br /> | <br /> | ||
The first section (PERGEN and Per/Gen cents) describes each pergen without regard to notational issues. The period and generator's cents are given, assuming a 5th of 700¢ + c. The generator is reduced, e.g. (P8/2, P5) has a generator of 100¢ + c, not 700¢ + c. The next two sections show a possible notation for P and G. The last section shows the unreduced pergen, and for false doubles, a possible single-pair notation. Horizontal lines group the pergens into blocks (half-splits, third-splits, etc). Red indicates problems. Generators of 50¢ or less are in red. Enharmonics of a 3rd or more are in red.<br /> | The first section (PERGEN and Per/Gen cents) describes each pergen without regard to notational issues. The period and generator's cents are given, assuming a 5th of 700¢ + c. The generator is reduced, e.g. (P8/2, P5) has a generator of 100¢ + c, not 700¢ + c. The next two sections show a possible notation for P and G. The last section shows the unreduced pergen, and for false doubles, a possible single-pair notation. Horizontal lines group the pergens into blocks (half-splits, third-splits, etc). Red indicates problems. Generators of 50¢ or less are in red. Enharmonics of a 3rd or more are in red.<br /> | ||