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Pergen names: Difference between revisions

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Wikispaces>TallKite
**Imported revision 621997883 - Original comment: **
Wikispaces>TallKite
**Imported revision 621999693 - 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>2017-11-20 04:23:35 UTC</tt>.<br>
: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-20 04:57:28 UTC</tt>.<br>
: The original revision id was <tt>621997883</tt>.<br>
: The original revision id was <tt>621999693</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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||~ pergen set ||~ valid range
||~ pergen set ||~ valid range
of the 5th ||~ split intervals ||~ enharmonic
of the 5th ||~ split interval(s) ||~ enharmonic
interval(s) ||~ genchain(s) ||~ example
interval(s) ||~ genchain(s) ||~ example
temperament ||~ compatible edos  
temperament ||~ compatible edos  
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||= " ||= ? ||= P4/2 = ^A2 = vd3 ||= vvdd2 ||= C - D#^=Ebv - F ||=  ||=  ||
||= " ||= ? ||= P4/2 = ^A2 = vd3 ||= vvdd2 ||= C - D#^=Ebv - F ||=  ||=  ||
||= {P8, P5/2} ||= 4\7 - 720¢ ||= P5/2 = ^m3 = vM3 ||= vvA1 ||= C - Eb^=Ev - G ||= mohajira,
||= {P8, P5/2} ||= 4\7 - 720¢ ||= P5/2 = ^m3 = vM3 ||= vvA1 ||= C - Eb^=Ev - G ||= mohajira,
^1 = 33/32 ||= 14*, 17, 20*, 21*, 24  
^1 = j1 = 33/32 ||= 14*, 17, 20*, 21*, 24  
27, 28*, 30*, 31 ||
27, 28*, 30*, 31 ||
||= " ||= 600¢ - 4\7 ||= P5/2 = ^M3 = vm3 ||= vvd1 ||= C - E^=Ebv - G ||=  ||= 14*, 18b, 21*, 28* ||
||= " ||= 600¢ - 4\7 ||= P5/2 = ^M3 = vm3 ||= vvd1 ||= C - E^=Ebv - G ||=  ||= 14*, 18b, 21*, 28* ||
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C - F#v/=Gb^\ - C,
C - F#v/=Gb^\ - C,
C - F^/=Gv\ - C ||= bb&amp;aaT,
C - F^/=Gv\ - C ||= bb&amp;aaT,
^1 = 33/32,
^1 = j1 = 33/32,
/1 = 64/63 ||=   ||
/1 = r1 = 64/63 ||= 14, 18b, 20*,
24, 28*, 30* ||
||= " ||=  ||= P8/2 = vA4 = ^d5,
||= " ||=  ||= P8/2 = vA4 = ^d5,
P4/2 = /M2 = \m3,
P4/2 = /M2 = \m3,
P5/2 = ^/m3 = v\M3
P5/2 = ^/m3 = v\M3 ||= ^^d2,
= v/A2 = ^\d4 ||= ^^d2,
\\m2,
\\m2,
vv\\A1,
vv\\A1 ||= C - F#v=Gb^ - C,
^^\\dd3 ||= C - F#v=Gb^ - C,
C - D/=Eb\ - F,
C - D/=Eb\ - F,
C - Eb^/=Ev\ - G,
C - Eb^/=Ev\ - G ||= sgg&amp;bbT,
C - D#v/=Fb^\ - G ||= sgg&amp;bbT,
^1 = g1 = 81/80,
^1 = 81/80,
/1 = r1 = 64/63 ||= " ||
/1 = 64/63 ||=   ||
||= " ||=  ||= P8/2 = vA4 = ^d5,
||= " ||=  ||= P8/2 = ^A4 = vd5,
P5/2 = /m3 = \M3,
P5/2 = /m3 = \M3,
P4/2 =^/M2 = v\m3
P4/2 =v/M2 = ^\m3 ||= ^^d2,
= ^\A2 = v/d3 ||= vvd2,
\\A1,
\\A1,
vv\\m2,
^^\\m2 ||= C - F#v=Gb^ - C,
vv//dd2 ||= C - F#^=Gbv - C,
C - Eb/=E\ - G,
C - Eb/=E\ - G,
C - D^/=Ebv\ - F,
C - Dv/=Eb^\ - F ||= sgg&amp;aaT,
C - D#^\=Ebbv/ - F ||= sgg&amp;aaT,
^1 = g1 = 81/80,
^1 = jr1
/1 = j1 = 33/32 ||= " ||
^/1 = 64/63
/1 = 33/32 ||=   ||
||~ thirds ||~  ||~  ||~  ||~  ||~  ||~  ||
||~ thirds ||~  ||~  ||~  ||~  ||~  ||~  ||
||= {P8/3, P5} ||=  ||=  ||=  ||=  ||=  ||= 12, 15, 18b*, 21, 24*,  
||= {P8/3, P5} ||=  ||=  ||=  ||=  ||=  ||= 12, 15, 18b*, 21, 24*,  
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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">&lt;html&gt;&lt;head&gt;&lt;title&gt;pergen names&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:12:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;&lt;a href="#Definition"&gt;Definition&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt; | &lt;a href="#Derivation"&gt;Derivation&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt; | &lt;a href="#Applications"&gt;Applications&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt; | &lt;a href="#x^/P4"&gt; ^/P4 &lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt; | &lt;a href="#v/A2"&gt; v/A2 &lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt; | &lt;a href="#x^\A2"&gt; ^\A2 &lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;pergen names&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:8:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:8 --&gt;&lt;!-- ws:start:WikiTextTocRule:9: --&gt;&lt;a href="#Definition"&gt;Definition&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:9 --&gt;&lt;!-- ws:start:WikiTextTocRule:10: --&gt; | &lt;a href="#Derivation"&gt;Derivation&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:10 --&gt;&lt;!-- ws:start:WikiTextTocRule:11: --&gt; | &lt;a href="#Applications"&gt;Applications&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:11 --&gt;&lt;!-- ws:start:WikiTextTocRule:12: --&gt; | &lt;a href="#x^/P4"&gt; ^/P4 &lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;
&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Definition"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;u&gt;&lt;strong&gt;Definition&lt;/strong&gt;&lt;/u&gt;&lt;/h1&gt;
&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Definition"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;u&gt;&lt;strong&gt;Definition&lt;/strong&gt;&lt;/u&gt;&lt;/h1&gt;
  &lt;br /&gt;
  &lt;br /&gt;
A &lt;strong&gt;pergen&lt;/strong&gt; set (pronounced &amp;quot;peer-gen&amp;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. The pergen set is chosen to use the fewest, and smallest, prime factors possible. Fractions are allowed, e.g. half-octave, but avoided if possible.&lt;br /&gt;
A &lt;strong&gt;pergen&lt;/strong&gt; set (pronounced &amp;quot;peer-gen&amp;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. The pergen set is chosen to use the fewest, and smallest, prime factors possible. Fractions are allowed, e.g. half-octave, but avoided if possible.&lt;br /&gt;
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of the 5th&lt;br /&gt;
of the 5th&lt;br /&gt;
&lt;/th&gt;
&lt;/th&gt;
         &lt;th&gt;split intervals&lt;br /&gt;
         &lt;th&gt;split interval(s)&lt;br /&gt;
&lt;/th&gt;
&lt;/th&gt;
         &lt;th&gt;enharmonic&lt;br /&gt;
         &lt;th&gt;enharmonic&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;mohajira,&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;mohajira,&lt;br /&gt;
^1 = 33/32&lt;br /&gt;
^1 = j1 = 33/32&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;14*, 17, 20*, 21*, 24 &lt;br /&gt;
         &lt;td style="text-align: center;"&gt;14*, 17, 20*, 21*, 24 &lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;bb&amp;amp;aaT,&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;bb&amp;amp;aaT,&lt;br /&gt;
^1 = 33/32,&lt;br /&gt;
^1 = j1 = 33/32,&lt;br /&gt;
/1 = 64/63&lt;br /&gt;
/1 = r1 = 64/63&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;14, 18b, 20*,&lt;br /&gt;
24, 28*, 30*&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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P4/2 = /M2 = \m3,&lt;br /&gt;
P4/2 = /M2 = \m3,&lt;br /&gt;
P5/2 = ^/m3 = v\M3&lt;br /&gt;
P5/2 = ^/m3 = v\M3&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="v/A2"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt; v/A2 &lt;/h1&gt;
&lt;/td&gt;
^\d4&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;^^d2,&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;^^d2,&lt;br /&gt;
\\m2,&lt;br /&gt;
\\m2,&lt;br /&gt;
vv\\A1,&lt;br /&gt;
vv\\A1&lt;br /&gt;
^^\\dd3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;C - F#v=Gb^ - C,&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;C - F#v=Gb^ - C,&lt;br /&gt;
C - D/=Eb\ - F,&lt;br /&gt;
C - D/=Eb\ - F,&lt;br /&gt;
C - Eb^/=Ev\ - G,&lt;br /&gt;
C - Eb^/=Ev\ - G&lt;br /&gt;
C - D#v/=Fb^\ - G&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;sgg&amp;amp;bbT,&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;sgg&amp;amp;bbT,&lt;br /&gt;
^1 = 81/80,&lt;br /&gt;
^1 = g1 = 81/80,&lt;br /&gt;
/1 = 64/63&lt;br /&gt;
/1 = r1 = 64/63&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;&amp;quot;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;P8/2 = ^A4 = vd5,&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;P8/2 = vA4 = ^d5,&lt;br /&gt;
P5/2 = /m3 = \M3,&lt;br /&gt;
P5/2 = /m3 = \M3,&lt;br /&gt;
P4/2 =^/M2 = v\m3&lt;br /&gt;
P4/2 =v/M2 = ^\m3&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="x^\A2"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt; ^\A2 &lt;/h1&gt;
&lt;/td&gt;
v/d3&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;^^d2,&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;vvd2,&lt;br /&gt;
\\A1,&lt;br /&gt;
\\A1,&lt;br /&gt;
vv\\m2,&lt;br /&gt;
^^\\m2&lt;br /&gt;
vv//dd2&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;C - F#^=Gbv - C,&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;C - F#v=Gb^ - C,&lt;br /&gt;
C - Eb/=E\ - G,&lt;br /&gt;
C - Eb/=E\ - G,&lt;br /&gt;
C - D^/=Ebv\ - F,&lt;br /&gt;
C - Dv/=Eb^\ - F&lt;br /&gt;
C - D#^\=Ebbv/ - F&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;sgg&amp;amp;aaT,&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;sgg&amp;amp;aaT,&lt;br /&gt;
^1 = jr1&lt;br /&gt;
^1 = g1 = 81/80,&lt;br /&gt;
^/1 = 64/63&lt;br /&gt;
/1 = j1 = 33/32&lt;br /&gt;
/1 = 33/32&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;&amp;quot;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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