Schismatic family: Difference between revisions

Line 1:

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-~~26 21~~:25:16 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-11 22:09:30 UTC</tt>.<br>

: The original revision id was <tt>~~205322542~~</tt>.<br>

: The original revision id was <tt>209781362</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>

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The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. Adding |25 -14 0 -1> gives garibaldi, |-44 26 0 1> grackle, |6 -2 0 -1> schism and |-59 39 0 -1> pontiac; these all have a fifth as generator. Bischismic adds |-69 40 0 2> and has a fifth generator with a half-octave period. Guiron adds 1029/1024 = |-10 1 0 3>, with an 8/7 generator, three of which give the fifth, and term adds |-94 54 0 3> with a 1/3 octave period. Sesquiquartififths adds |-35 15 0 4> and slices the fifth in four.

==Garibaldi==

=Garibaldi=

Commas: 225/224, 3125/3087

Line 37:

Badness: 0.0216

===11-limit===

==11-limit==

Commas: 225/224, 385/384, 2200/2187

Line 51:

Badness: 0.0274

====13-limit====

===13-limit===

Commas: 225/224, 275/273, 325/325, 385/384

Line 60:

Badness: 0.0207

===Cassandra===

==Cassandra==

Commas: 100/99, 225/224, 245/242

Line 69:

Badness: 0.0236

====13-limit Cassandra====

===13-limit Cassandra===

Commas: 100/99, 105/104, 196/195, 245/242

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Badness: 0.0207

==Guiron==

=Guiron=

[[Comma|Commas]]: 1029/1024, 10976/10935

Line 93:

Badness: 0.0475

===11-limit===

==11-limit==

[[Comma|Commas]]: 385/384, 441/440, 10976/10935

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Badness: 0.0266

==Pontiac==

=Pontiac=

Commas: 32805/32768, 4375/4374

Line 128:

Badness: 0.0141

==Grackle==

=Grackle=

Commas: 126/125, 32805/32768

Line 144:

Badness: 0.070

==Bischismic==

=Bischismic=

Commas: 3136/3125, 32805/32768

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Badness: 0.0547

==Term==

=Term=

Commas: 32805/32768, 250047/250000

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Badness: 0.0200

==Sesquiquartififths==

=Sesquiquartififths=

Commas: 2401/2400, 32805/32768

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The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which 7-limit family member we are looking at. Adding |25 -14 0 -1&gt; gives garibaldi, |-44 26 0 1&gt; grackle, |6 -2 0 -1&gt; schism and |-59 39 0 -1&gt; pontiac; these all have a fifth as generator. Bischismic adds |-69 40 0 2&gt; and has a fifth generator with a half-octave period. Guiron adds 1029/1024 = |-10 1 0 3&gt;, with an 8/7 generator, three of which give the fifth, and term adds |-94 54 0 3&gt; with a 1/3 octave period. Sesquiquartififths adds |-35 15 0 4&gt; and slices the fifth in four.<br />

<br />

<h2 id="toc1"><a name="x-Garibaldi"></a>Garibaldi</h2>

<h1 id="toc1"><a name="Garibaldi"></a>Garibaldi</h1>

Commas: 225/224, 3125/3087<br />

<br />

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Badness: 0.0216<br />

<br />

<h3 id="toc2"><a name="x-Garibaldi-11-limit"></a>11-limit</h3>

<h2 id="toc2"><a name="Garibaldi-11-limit"></a>11-limit</h2>

Commas: 225/224, 385/384, 2200/2187<br />

<br />

Line 237:

Badness: 0.0274<br />

<br />

<h4 id="toc3"><a name="x-Garibaldi-11-limit-13-limit"></a>13-limit</h4>

<h3 id="toc3"><a name="Garibaldi-11-limit-13-limit"></a>13-limit</h3>

Commas: 225/224, 275/273, 325/325, 385/384<br />

<br />

Line 246:

Badness: 0.0207<br />

<br />

<h3 id="toc4"><a name="x-Garibaldi-Cassandra"></a>Cassandra</h3>

<h2 id="toc4"><a name="Garibaldi-Cassandra"></a>Cassandra</h2>

Commas: 100/99, 225/224, 245/242<br />

<br />

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Badness: 0.0236<br />

<br />

<h4 id="toc5"><a name="x-Garibaldi-Cassandra-13-limit Cassandra"></a>13-limit Cassandra</h4>

<h3 id="toc5"><a name="Garibaldi-Cassandra-13-limit Cassandra"></a>13-limit Cassandra</h3>

Commas: 100/99, 105/104, 196/195, 245/242<br />

<br />

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Badness: 0.0207<br />

<br />

<h2 id="toc6"><a name="x-Guiron"></a>Guiron</h2>

<h1 id="toc6"><a name="Guiron"></a>Guiron</h1>

<a class="wiki_link" href="/Comma">Commas</a>: 1029/1024, 10976/10935<br />

<br />

Line 279:

Badness: 0.0475<br />

<br />

<h3 id="toc7"><a name="x-Guiron-11-limit"></a>11-limit</h3>

<h2 id="toc7"><a name="Guiron-11-limit"></a>11-limit</h2>

<a class="wiki_link" href="/Comma">Commas</a>: 385/384, 441/440, 10976/10935<br />

<br />

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Badness: 0.0266<br />

<br />

<h2 id="toc8"><a name="x-Pontiac"></a>Pontiac</h2>

<h1 id="toc8"><a name="Pontiac"></a>Pontiac</h1>

Commas: 32805/32768, 4375/4374<br />

<br />

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Badness: 0.0141<br />

<br />

<h2 id="toc9"><a name="x-Grackle"></a>Grackle</h2>

<h1 id="toc9"><a name="Grackle"></a>Grackle</h1>

Commas: 126/125, 32805/32768<br />

<br />

Line 330:

Badness: 0.070<br />

<br />

<h2 id="toc10"><a name="x-Bischismic"></a>Bischismic</h2>

<h1 id="toc10"><a name="Bischismic"></a>Bischismic</h1>

Commas: 3136/3125, 32805/32768<br />

<br />

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Badness: 0.0547<br />

<br />

<h2 id="toc11"><a name="x-Term"></a>Term</h2>

<h1 id="toc11"><a name="Term"></a>Term</h1>

Commas: 32805/32768, 250047/250000<br />

<br />

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Badness: 0.0200<br />

<br />

<h2 id="toc12"><a name="x-Sesquiquartififths"></a>Sesquiquartififths</h2>

<h1 id="toc12"><a name="Sesquiquartififths"></a>Sesquiquartififths</h1>

Commas: 2401/2400, 32805/32768<br />

<br />

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-26 21:25:16 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-11 22:09:30 UTC</tt>.<br>
-: The original revision id was <tt>205322542</tt>.<br>
+: The original revision id was <tt>209781362</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>
@@ Line 18: / Line 18: @@
 The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. Adding |25 -14 0 -1&gt; gives garibaldi, |-44 26 0 1&gt; grackle, |6 -2 0 -1&gt; schism and |-59 39 0 -1&gt; pontiac; these all have a fifth as generator. Bischismic adds |-69 40 0 2&gt; and has a fifth generator with a half-octave period. Guiron adds 1029/1024 = |-10 1 0 3&gt;, with an 8/7 generator, three of which give the fifth, and term adds |-94 54 0 3&gt; with a 1/3 octave period. Sesquiquartififths adds |-35 15 0 4&gt; and slices the fifth in four.
-==Garibaldi==
+=Garibaldi=
 Commas: 225/224, 3125/3087
@@ Line 37: / Line 37: @@
 Badness: 0.0216
-===11-limit===
+==11-limit==
 Commas: 225/224, 385/384, 2200/2187
@@ Line 51: / Line 51: @@
 Badness: 0.0274
-====13-limit====
+===13-limit===
 Commas: 225/224, 275/273, 325/325, 385/384
@@ Line 60: / Line 60: @@
 Badness: 0.0207
-===Cassandra===
+==Cassandra==
 Commas: 100/99, 225/224, 245/242
@@ Line 69: / Line 69: @@
 Badness: 0.0236
-====13-limit Cassandra====
+===13-limit Cassandra===
 Commas: 100/99, 105/104, 196/195, 245/242
@@ Line 78: / Line 78: @@
 Badness: 0.0207
-==Guiron==
+=Guiron=
 [[Comma|Commas]]: 1029/1024, 10976/10935
@@ Line 93: / Line 93: @@
 Badness: 0.0475
-===11-limit===
+==11-limit==
 [[Comma|Commas]]: 385/384, 441/440, 10976/10935
@@ Line 108: / Line 108: @@
 Badness: 0.0266
-==Pontiac==
+=Pontiac=
 Commas: 32805/32768, 4375/4374
@@ Line 128: / Line 128: @@
 Badness: 0.0141
-==Grackle==
+=Grackle=
 Commas: 126/125, 32805/32768
@@ Line 144: / Line 144: @@
 Badness: 0.070
-==Bischismic==
+=Bischismic=
 Commas: 3136/3125, 32805/32768
@@ Line 160: / Line 160: @@
 Badness: 0.0547
-==Term==
+=Term=
 Commas: 32805/32768, 250047/250000
@@ Line 176: / Line 176: @@
 Badness: 0.0200
-==Sesquiquartififths==
+=Sesquiquartififths=
 Commas: 2401/2400, 32805/32768
@@ Line 204: / Line 204: @@
 The second comma of the &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt; defines which 7-limit family member we are looking at. Adding |25 -14 0 -1&amp;gt; gives garibaldi, |-44 26 0 1&amp;gt; grackle, |6 -2 0 -1&amp;gt; schism and |-59 39 0 -1&amp;gt; pontiac; these all have a fifth as generator. Bischismic adds |-69 40 0 2&amp;gt; and has a fifth generator with a half-octave period. Guiron adds 1029/1024 = |-10 1 0 3&amp;gt;, with an 8/7 generator, three of which give the fifth, and term adds |-94 54 0 3&amp;gt; with a 1/3 octave period. Sesquiquartififths adds |-35 15 0 4&amp;gt; and slices the fifth in four.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Garibaldi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Garibaldi&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Garibaldi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Garibaldi&lt;/h1&gt;
 Commas: 225/224, 3125/3087&lt;br /&gt;
 &lt;br /&gt;
@@ Line 223: / Line 223: @@
 Badness: 0.0216&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-Garibaldi-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Garibaldi-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h2&gt;
 Commas: 225/224, 385/384, 2200/2187&lt;br /&gt;
 &lt;br /&gt;
@@ Line 237: / Line 237: @@
 Badness: 0.0274&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc3"&gt;&lt;a name="x-Garibaldi-11-limit-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h4&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="Garibaldi-11-limit-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h3&gt;
 Commas: 225/224, 275/273, 325/325, 385/384&lt;br /&gt;
 &lt;br /&gt;
@@ Line 246: / Line 246: @@
 Badness: 0.0207&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="x-Garibaldi-Cassandra"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Cassandra&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Garibaldi-Cassandra"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Cassandra&lt;/h2&gt;
 Commas: 100/99, 225/224, 245/242&lt;br /&gt;
 &lt;br /&gt;
@@ Line 255: / Line 255: @@
 Badness: 0.0236&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc5"&gt;&lt;a name="x-Garibaldi-Cassandra-13-limit Cassandra"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;13-limit Cassandra&lt;/h4&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="Garibaldi-Cassandra-13-limit Cassandra"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;13-limit Cassandra&lt;/h3&gt;
 Commas: 100/99, 105/104, 196/195, 245/242&lt;br /&gt;
 &lt;br /&gt;
@@ Line 264: / Line 264: @@
 Badness: 0.0207&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="x-Guiron"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Guiron&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Guiron"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Guiron&lt;/h1&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 1029/1024, 10976/10935&lt;br /&gt;
 &lt;br /&gt;
@@ Line 279: / Line 279: @@
 Badness: 0.0475&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="x-Guiron-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;11-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Guiron-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;11-limit&lt;/h2&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 385/384, 441/440, 10976/10935&lt;br /&gt;
 &lt;br /&gt;
@@ Line 294: / Line 294: @@
 Badness: 0.0266&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="x-Pontiac"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Pontiac&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Pontiac"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Pontiac&lt;/h1&gt;
 Commas: 32805/32768, 4375/4374&lt;br /&gt;
 &lt;br /&gt;
@@ Line 314: / Line 314: @@
 Badness: 0.0141&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="x-Grackle"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Grackle&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Grackle"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Grackle&lt;/h1&gt;
 Commas: 126/125, 32805/32768&lt;br /&gt;
 &lt;br /&gt;
@@ Line 330: / Line 330: @@
 Badness: 0.070&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="x-Bischismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Bischismic&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Bischismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Bischismic&lt;/h1&gt;
 Commas: 3136/3125, 32805/32768&lt;br /&gt;
 &lt;br /&gt;
@@ Line 346: / Line 346: @@
 Badness: 0.0547&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="x-Term"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Term&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Term"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Term&lt;/h1&gt;
 Commas: 32805/32768, 250047/250000&lt;br /&gt;
 &lt;br /&gt;
@@ Line 362: / Line 362: @@
 Badness: 0.0200&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="x-Sesquiquartififths"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Sesquiquartififths&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="Sesquiquartififths"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Sesquiquartififths&lt;/h1&gt;
 Commas: 2401/2400, 32805/32768&lt;br /&gt;
 &lt;br /&gt;