Pergen names: Difference between revisions
Wikispaces>TallKite **Imported revision 622159045 - Original comment: ** |
Wikispaces>TallKite **Imported revision 622159279 - 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>2017-11-21 23: | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-21 23:48:49 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>622159279</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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P5/2 = ^m3 = vM3 | P5/2 = ^m3 = vM3 | ||
P8/2 = v/A4 = ^\d5 | P8/2 = v/A4 = ^\d5 | ||
= ^/P4 = v\P5 ||= \\m2, | =^/P4= | ||
v\P5 ||= \\m2, | |||
vvA1, | vvA1, | ||
^^\\d2, | ^^\\d2, | ||
| Line 190: | Line 191: | ||
/1 = 33/32 ||= " || | /1 = 33/32 ||= " || | ||
||~ thirds ||~ ||~ ||~ ||~ ||~ ||~ || | ||~ thirds ||~ ||~ ||~ ||~ ||~ ||~ || | ||
||= {P8/3, P5} ||= P8/3 = vM3 = ^^d4 ||= ^<span style="vertical-align: super;">3</span>d2 ||= C^<span style="vertical-align: super;">3</span> | ||= {P8/3, P5} ||= P8/3 = vM3 = ^^d4 ||= ^<span style="vertical-align: super;">3</span>d2 ||= C^<span style="vertical-align: super;">3</span>=B# || C - Ev - Ab^ - C ||= ||= 12, 15, 18b*, 21, | ||
=B# | |||
24*, 27, 30* || | 24*, 27, 30* || | ||
||= {P8, P4/3} ||= P4/3 = ^^m2 = vM2 ||= v<span style="vertical-align: super;">3</span>A1 ||= C^<span style="vertical-align: super;">3</span> | ||= {P8, P4/3} ||= P4/3 = ^^m2 = vM2 ||= v<span style="vertical-align: super;">3</span>A1 ||= C^<span style="vertical-align: super;">3</span> | ||
=C#= || C - Dv - Eb^ - F ||= porcupine ||= 13b, 14*, 15, 21*, | =C#= || C - Dv - Eb^ - F ||= porcupine ||= 13b, 14*, 15, 21*, | ||
22, 28*, 29, 30* || | 22, 28*, 29, 30* || | ||
||= {P8, P5/3} ||= P5/3 = ^M2 = vvm3 ||= v<span style="vertical-align: super;">3</span>m2 ||= C^<span style="vertical-align: super;">3</span> | ||= {P8, P5/3} ||= P5/3 = ^M2 = vvm3 ||= v<span style="vertical-align: super;">3</span>m2 ||= C^<span style="vertical-align: super;">3</span>=Db ||= C - D^ - Fv - G ||= slendric ||= 15*, 16, 20*, 21, | ||
=Db | |||
25*, 26, 30*, 31 || | 25*, 26, 30*, 31 || | ||
||= {P8, P11/3} ||= P11/3 = vA4 = ^^dd5 ||= ^<span style="vertical-align: super;">3</span>dd2 ||= C^<span style="vertical-align: super;">3</span> | ||= {P8, P11/3} ||= P11/3 = vA4 = ^^dd5 ||= ^<span style="vertical-align: super;">3</span>dd2 ||= C^<span style="vertical-align: super;">3</span> | ||
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(to be continued)</pre></div> | (to be continued)</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>pergen names</title></head><body><!-- ws:start:WikiTextTocRule: | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>pergen names</title></head><body><!-- ws:start:WikiTextTocRule:28:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><a href="#Definition">Definition</a><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#Derivation">Derivation</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | <a href="#Applications">Applications</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --> | <a href="#x^/P4">^/P4</a><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --> | <a href="#C#">C#</a><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --> | <a href="#B##">B##</a><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --> | <a href="#D">D</a><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --> | <a href="#B#3">B#3</a><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --> | <a href="#B#">B#</a><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --> | <a href="#B##">B##</a><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --> | <a href="#C#">C#</a><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --> | <a href="#Eb3">Eb3</a><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --> | <a href="#Db">Db</a><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --> | <a href="#B#3">B#3</a><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Definition"></a><!-- ws:end:WikiTextHeadingRule:0 --><u><strong>Definition</strong></u></h1> | ||
<br /> | <br /> | ||
A <strong>pergen</strong> (pronounced &quot;peer-gen&quot;) is a way of identifying a rank-2 or rank-3 regular temperament solely by its period and generator(s). For any temperament, there are many possible periods and generators. For the pergen, they are chosen to use the fewest, and smallest, prime factors possible. Fractions are allowed, e.g. half-octave, but avoided if possible.<br /> | A <strong>pergen</strong> (pronounced &quot;peer-gen&quot;) is a way of identifying a rank-2 or rank-3 regular temperament solely by its period and generator(s). For any temperament, there are many possible periods and generators. For the pergen, they are chosen to use the fewest, and smallest, prime factors possible. Fractions are allowed, e.g. half-octave, but avoided if possible.<br /> | ||
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P5/2 = ^m3 = vM3<br /> | P5/2 = ^m3 = vM3<br /> | ||
P8/2 = v/A4 = ^\d5<br /> | P8/2 = v/A4 = ^\d5<br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="x^/P4"></a><!-- ws:end:WikiTextHeadingRule:6 --> ^/P4 </h1> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="x^/P4"></a><!-- ws:end:WikiTextHeadingRule:6 -->^/P4</h1> | ||
v\P5</td> | v\P5<br /> | ||
</td> | |||
<td style="text-align: center;">\\m2,<br /> | <td style="text-align: center;">\\m2,<br /> | ||
vvA1,<br /> | vvA1,<br /> | ||
| Line 1,105: | Line 1,105: | ||
<td style="text-align: center;">^<span style="vertical-align: super;">3</span>d2<br /> | <td style="text-align: center;">^<span style="vertical-align: super;">3</span>d2<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">C^<span style="vertical-align: super;">3</span> | <td style="text-align: center;">C^<span style="vertical-align: super;">3</span>=B#<br /> | ||
</td> | </td> | ||
<td | <td>C - Ev - Ab^ - C<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 1,124: | Line 1,123: | ||
</td> | </td> | ||
<td style="text-align: center;">C^<span style="vertical-align: super;">3</span><br /> | <td style="text-align: center;">C^<span style="vertical-align: super;">3</span><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="C#"></a><!-- ws:end:WikiTextHeadingRule:8 -->C#</h1> | ||
</td> | </td> | ||
<td>C - Dv - Eb^ - F<br /> | <td>C - Dv - Eb^ - F<br /> | ||
| Line 1,141: | Line 1,140: | ||
<td style="text-align: center;">v<span style="vertical-align: super;">3</span>m2<br /> | <td style="text-align: center;">v<span style="vertical-align: super;">3</span>m2<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">C^<span style="vertical-align: super;">3</span> | <td style="text-align: center;">C^<span style="vertical-align: super;">3</span>=Db<br /> | ||
</td> | </td> | ||
<td>C - D^ - Fv - G<br /> | <td style="text-align: center;">C - D^ - Fv - G<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">slendric<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">15*, 16, 20*, 21,<br /> | <td style="text-align: center;">15*, 16, 20*, 21,<br /> | ||
| Line 1,160: | Line 1,158: | ||
</td> | </td> | ||
<td style="text-align: center;">C^<span style="vertical-align: super;">3</span><br /> | <td style="text-align: center;">C^<span style="vertical-align: super;">3</span><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="B##"></a><!-- ws:end:WikiTextHeadingRule:10 -->B##</h1> | ||
</td> | </td> | ||
<td>C - F#v - Cb^ - F<br /> | <td>C - F#v - Cb^ - F<br /> | ||
| Line 1,177: | Line 1,175: | ||
</td> | </td> | ||
<td style="text-align: center;">C^<span style="vertical-align: super;">3</span><br /> | <td style="text-align: center;">C^<span style="vertical-align: super;">3</span><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="D"></a><!-- ws:end:WikiTextHeadingRule:12 -->D</h1> | ||
</td> | </td> | ||
<td>C F^ Cv F<br /> | <td>C F^ Cv F<br /> | ||
| Line 1,243: | Line 1,241: | ||
</td> | </td> | ||
<td style="text-align: center;">C^<span style="vertical-align: super;">6</span><br /> | <td style="text-align: center;">C^<span style="vertical-align: super;">6</span><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="B#3"></a><!-- ws:end:WikiTextHeadingRule:14 -->B#<span style="vertical-align: super;">3</span></h1> | ||
</td> | </td> | ||
<td>C - F<span style="vertical-align: super;">x</span>v<span style="vertical-align: super;">3</span>=Gbb^<span style="vertical-align: super;">3</span> CC - D#vv - Fb^^ - G<br /> | <td>C - F<span style="vertical-align: super;">x</span>v<span style="vertical-align: super;">3</span>=Gbb^<span style="vertical-align: super;">3</span> CC - D#vv - Fb^^ - G<br /> | ||
| Line 1,328: | Line 1,326: | ||
</td> | </td> | ||
<td style="text-align: center;">C^<span style="vertical-align: super;">4</span><br /> | <td style="text-align: center;">C^<span style="vertical-align: super;">4</span><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="B#"></a><!-- ws:end:WikiTextHeadingRule:16 -->B#</h1> | ||
</td> | </td> | ||
<td>C Ebv Gbvv A^ C<br /> | <td>C Ebv Gbvv A^ C<br /> | ||
| Line 1,346: | Line 1,344: | ||
</td> | </td> | ||
<td style="text-align: center;">C^<span style="vertical-align: super;">4</span><br /> | <td style="text-align: center;">C^<span style="vertical-align: super;">4</span><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="B##"></a><!-- ws:end:WikiTextHeadingRule:18 -->B##</h1> | ||
</td> | </td> | ||
<td>C Db^ Ebb^^ Ev F<br /> | <td>C Db^ Ebb^^ Ev F<br /> | ||
| Line 1,363: | Line 1,361: | ||
</td> | </td> | ||
<td style="text-align: center;">C^<span style="vertical-align: super;">4</span><br /> | <td style="text-align: center;">C^<span style="vertical-align: super;">4</span><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="C#"></a><!-- ws:end:WikiTextHeadingRule:20 -->C#</h1> | ||
</td> | </td> | ||
<td>C Dv Evv F^ G^<br /> | <td>C Dv Evv F^ G^<br /> | ||
| Line 1,380: | Line 1,378: | ||
</td> | </td> | ||
<td style="text-align: center;">C^<span style="vertical-align: super;">4</span><br /> | <td style="text-align: center;">C^<span style="vertical-align: super;">4</span><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Eb3"></a><!-- ws:end:WikiTextHeadingRule:22 -->Eb<span style="vertical-align: super;">3</span></h1> | ||
</td> | </td> | ||
<td>C E^ G#^^ Dbv F<br /> | <td>C E^ G#^^ Dbv F<br /> | ||
| Line 1,397: | Line 1,395: | ||
</td> | </td> | ||
<td style="text-align: center;">C^<span style="vertical-align: super;">4</span><br /> | <td style="text-align: center;">C^<span style="vertical-align: super;">4</span><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="Db"></a><!-- ws:end:WikiTextHeadingRule:24 -->Db</h1> | ||
</td> | </td> | ||
<td>C Fv Bbvv D^ G<br /> | <td>C Fv Bbvv D^ G<br /> | ||
| Line 1,510: | Line 1,508: | ||
</td> | </td> | ||
<td style="text-align: center;">C^<span style="vertical-align: super;">5</span><br /> | <td style="text-align: center;">C^<span style="vertical-align: super;">5</span><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="B#3"></a><!-- ws:end:WikiTextHeadingRule:26 -->B#<span style="vertical-align: super;">3</span></h1> | ||
</td> | </td> | ||
<td>C - Db^ - Ebb^ -- E#vv - F#v - G<br /> | <td>C - Db^ - Ebb^ -- E#vv - F#v - G<br /> | ||