Fokker chord: Difference between revisions

Revision as of 14:30, 2 April 2014

IMPORTED REVISION FROM WIKISPACES

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

This revision was by author genewardsmith and made on 2014-04-02 14:30:43 UTC.

The original revision id was 500130866.

The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

[[toc|flat]]

By a //Fokker chord// is meant a chord which is also a strongly epimorphic Fokker block. Such chords belong to an [[Fokker blocks#First definition of a Fokker block|arena]] of related chords, which includes its various inversions, but other chords besides. Often a Fokker chord is a wakalix, so that it belongs to more than one arena.

=5-limit triads=
The major and minor 5-limit triads are wakalixes; in terms of the [[Fokker blocks#The Fokblock function and modal UDP notation|Fokblock function]] the major triad in root position can be denoted by Fokblock([16/15, 10/9], [0, 1]), Fokblock([[25/24, 10/9], [2, 0]) or Fokblock([25/24, 16/15], [1, 0]) and the minor triad Fokblock([16/15, 10/9], [1, 0]), Fokblock([25/24, 10/9], [1, 0]), or Fokblock([25/24, 16/15], [0, 0]). Each of these arenas contain the three inversions of both the major and minor triads, plus the inversions of another triad. In the case of the [16/15, 10/9] arena, that's the qunital triad, in its quintal (1-9/8-3/2) and quartal (1-4/3-16/9) forms. [25/24, 10/9] adds the three inversions of the diminished triad, 1-6/5-5/3, and [25/24, 16/15] adds the three inversions of the augmented triad, 1-5/4-8/5.

=7-limit tetrads=

|| Arena || Major tetrad offsets || Minor tetrad offsets || Paired vals ||
|| [21/20, 15/14, 35/32] || [2, 2, 2] || [3, 3, 0] || 1, 3, 2 ||
|| [25/24, 15/14, 35/32] || [1, 2, 3] || [0, 3, 2] || 1, 3, 7 ||
|| [25/24, 21/20, 15/14] || [2, 3, 2] || [0, 2, 3] || 2, 7, 3 ||
|| [36/35, 21/20, 15/14] || [0, 3, 3] || [2, 2, 2] || 2, 7, 5 ||
|| [36/35, 25/24, 21/20] || [2, 3, 3] || [3, 2, 2] || 3, 5, 7 ||
|| [49/48, 21/20, 15/14] || [2, 2, 3] || [0, 3, 2] || 2, 1, 5 ||
|| [49/48, 21/20, 35/32] || [1, 2, 3] || [0, 3, 2] || 3, 1, 5 ||
|| [49/48, 36/35, 15/14] || [3, 2, 3] || [2, 3, 2] || 7, 1, 5 ||

Original HTML content:

<html><head><title>Fokker chord</title></head><body><!-- ws:start:WikiTextTocRule:4:&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:4 --><!-- ws:start:WikiTextTocRule:5: --><a href="#x5-limit triads">5-limit triads</a><!-- ws:end:WikiTextTocRule:5 --><!-- ws:start:WikiTextTocRule:6: --> | <a href="#x7-limit tetrads">7-limit tetrads</a><!-- ws:end:WikiTextTocRule:6 --><!-- ws:start:WikiTextTocRule:7: -->
<!-- ws:end:WikiTextTocRule:7 --><br />
By a <em>Fokker chord</em> is meant a chord which is also a strongly epimorphic Fokker block. Such chords belong to an <a class="wiki_link" href="/Fokker%20blocks#First definition of a Fokker block">arena</a> of related chords, which includes its various inversions, but other chords besides. Often a Fokker chord is a wakalix, so that it belongs to more than one arena.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x5-limit triads"></a><!-- ws:end:WikiTextHeadingRule:0 -->5-limit triads</h1>
The major and minor 5-limit triads are wakalixes; in terms of the <a class="wiki_link" href="/Fokker%20blocks#The Fokblock function and modal UDP notation">Fokblock function</a> the major triad in root position can be denoted by Fokblock([16/15, 10/9], [0, 1]), Fokblock([[25/24, 10/9], [2, 0]) or Fokblock([25/24, 16/15], [1, 0]) and the minor triad Fokblock([16/15, 10/9], [1, 0]), Fokblock([25/24, 10/9], [1, 0]), or Fokblock([25/24, 16/15], [0, 0]). Each of these arenas contain the three inversions of both the major and minor triads, plus the inversions of another triad. In the case of the [16/15, 10/9] arena, that's the qunital triad, in its quintal (1-9/8-3/2) and quartal (1-4/3-16/9) forms. [25/24, 10/9] adds the three inversions of the diminished triad, 1-6/5-5/3, and [25/24, 16/15] adds the three inversions of the augmented triad, 1-5/4-8/5.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="x7-limit tetrads"></a><!-- ws:end:WikiTextHeadingRule:2 -->7-limit tetrads</h1>
<br />


<table class="wiki_table">
    <tr>
        <td>Arena<br />
</td>
        <td>Major tetrad offsets<br />
</td>
        <td>Minor tetrad offsets<br />
</td>
        <td>Paired vals<br />
</td>
    </tr>
    <tr>
        <td>[21/20, 15/14, 35/32]<br />
</td>
        <td>[2, 2, 2]<br />
</td>
        <td>[3, 3, 0]<br />
</td>
        <td>1, 3, 2<br />
</td>
    </tr>
    <tr>
        <td>[25/24, 15/14, 35/32]<br />
</td>
        <td>[1, 2, 3]<br />
</td>
        <td>[0, 3, 2]<br />
</td>
        <td>1, 3, 7<br />
</td>
    </tr>
    <tr>
        <td>[25/24, 21/20, 15/14]<br />
</td>
        <td>[2, 3, 2]<br />
</td>
        <td>[0, 2, 3]<br />
</td>
        <td>2, 7, 3<br />
</td>
    </tr>
    <tr>
        <td>[36/35, 21/20, 15/14]<br />
</td>
        <td>[0, 3, 3]<br />
</td>
        <td>[2, 2, 2]<br />
</td>
        <td>2, 7, 5<br />
</td>
    </tr>
    <tr>
        <td>[36/35, 25/24, 21/20]<br />
</td>
        <td>[2, 3, 3]<br />
</td>
        <td>[3, 2, 2]<br />
</td>
        <td>3, 5, 7<br />
</td>
    </tr>
    <tr>
        <td>[49/48, 21/20, 15/14]<br />
</td>
        <td>[2, 2, 3]<br />
</td>
        <td>[0, 3, 2]<br />
</td>
        <td>2, 1, 5<br />
</td>
    </tr>
    <tr>
        <td>[49/48, 21/20, 35/32]<br />
</td>
        <td>[1, 2, 3]<br />
</td>
        <td>[0, 3, 2]<br />
</td>
        <td>3, 1, 5<br />
</td>
    </tr>
    <tr>
        <td>[49/48, 36/35, 15/14]<br />
</td>
        <td>[3, 2, 3]<br />
</td>
        <td>[2, 3, 2]<br />
</td>
        <td>7, 1, 5<br />
</td>
    </tr>
</table>

</body></html>

@@ 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>2014-04-02 12:41:05 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-04-02 14:30:43 UTC</tt>.<br>
-: The original revision id was <tt>500101846</tt>.<br>
+: The original revision id was <tt>500130866</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 11: / Line 11: @@
 =5-limit triads=
-The major and minor 5-limit triads are wakalixes; in terms of the [[Fokker blocks#The Fokblock function and modal UDP notation|Fokblock function]] the major triad in root position can be denoted by Fokblock([16/15, 10/9], [0, 1]), Fokblock([[25/24, 10/9], [2, 0]) or Fokblock([25/24, 16/15], [1, 0]) and the minor triad Fokblock([16/15, 10/9], [1, 0]), Fokblock([25/24, 10/9], [1, 0]), or Fokblock([25/24, 16/15], [0, 0]). Each of these arenas contain the three inversions of both the major and minor triads, plus the inversions of another triad. In the case of the [16/15, 10/9] arena, that's the qunital triad, in its quintal (1-9/8-3/2) and quartal (1-4/3-16/9) forms. [25/24, 10/9] adds the three inversions of the diminished triad, 1-6/5-5/3, and [25/24, 16/15] adds the three inversions of the augmented triad, 1-5/4-8/5.</pre></div>
+The major and minor 5-limit triads are wakalixes; in terms of the [[Fokker blocks#The Fokblock function and modal UDP notation|Fokblock function]] the major triad in root position can be denoted by Fokblock([16/15, 10/9], [0, 1]), Fokblock([[25/24, 10/9], [2, 0]) or Fokblock([25/24, 16/15], [1, 0]) and the minor triad Fokblock([16/15, 10/9], [1, 0]), Fokblock([25/24, 10/9], [1, 0]), or Fokblock([25/24, 16/15], [0, 0]). Each of these arenas contain the three inversions of both the major and minor triads, plus the inversions of another triad. In the case of the [16/15, 10/9] arena, that's the qunital triad, in its quintal (1-9/8-3/2) and quartal (1-4/3-16/9) forms. [25/24, 10/9] adds the three inversions of the diminished triad, 1-6/5-5/3, and [25/24, 16/15] adds the three inversions of the augmented triad, 1-5/4-8/5.
+=7-limit tetrads=
+|| Arena || Major tetrad offsets || Minor tetrad offsets || Paired vals ||
+|| [21/20, 15/14, 35/32] || [2, 2, 2] || [3, 3, 0] || 1, 3, 2 ||
+|| [25/24, 15/14, 35/32] || [1, 2, 3] || [0, 3, 2] || 1, 3, 7 ||
+|| [25/24, 21/20, 15/14] || [2, 3, 2] || [0, 2, 3] || 2, 7, 3 ||
+|| [36/35, 21/20, 15/14] || [0, 3, 3] || [2, 2, 2] || 2, 7, 5 ||
+|| [36/35, 25/24, 21/20] || [2, 3, 3] || [3, 2, 2] || 3, 5, 7 ||
+|| [49/48, 21/20, 15/14] || [2, 2, 3] || [0, 3, 2] || 2, 1, 5 ||
+|| [49/48, 21/20, 35/32] || [1, 2, 3] || [0, 3, 2] || 3, 1, 5 ||
+|| [49/48, 36/35, 15/14] || [3, 2, 3] || [2, 3, 2] || 7, 1, 5 ||</pre></div>
 <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;Fokker chord&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:2:&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:2 --&gt;&lt;!-- ws:start:WikiTextTocRule:3: --&gt;&lt;a href="#x5-limit triads"&gt;5-limit triads&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:3 --&gt;&lt;!-- ws:start:WikiTextTocRule:4: --&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;Fokker chord&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:4:&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:4 --&gt;&lt;!-- ws:start:WikiTextTocRule:5: --&gt;&lt;a href="#x5-limit triads"&gt;5-limit triads&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:5 --&gt;&lt;!-- ws:start:WikiTextTocRule:6: --&gt; | &lt;a href="#x7-limit tetrads"&gt;7-limit tetrads&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:6 --&gt;&lt;!-- ws:start:WikiTextTocRule:7: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:4 --&gt;&lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:7 --&gt;&lt;br /&gt;
 By a &lt;em&gt;Fokker chord&lt;/em&gt; is meant a chord which is also a strongly epimorphic Fokker block. Such chords belong to an &lt;a class="wiki_link" href="/Fokker%20blocks#First definition of a Fokker block"&gt;arena&lt;/a&gt; of related chords, which includes its various inversions, but other chords besides. Often a Fokker chord is a wakalix, so that it belongs to more than one arena.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x5-limit triads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;5-limit triads&lt;/h1&gt;
-The major and minor 5-limit triads are wakalixes; in terms of the &lt;a class="wiki_link" href="/Fokker%20blocks#The Fokblock function and modal UDP notation"&gt;Fokblock function&lt;/a&gt; the major triad in root position can be denoted by Fokblock([16/15, 10/9], [0, 1]), Fokblock([[25/24, 10/9], [2, 0]) or Fokblock([25/24, 16/15], [1, 0]) and the minor triad Fokblock([16/15, 10/9], [1, 0]), Fokblock([25/24, 10/9], [1, 0]), or Fokblock([25/24, 16/15], [0, 0]). Each of these arenas contain the three inversions of both the major and minor triads, plus the inversions of another triad. In the case of the [16/15, 10/9] arena, that's the qunital triad, in its quintal (1-9/8-3/2) and quartal (1-4/3-16/9) forms. [25/24, 10/9] adds the three inversions of the diminished triad, 1-6/5-5/3, and [25/24, 16/15] adds the three inversions of the augmented triad, 1-5/4-8/5.&lt;/body&gt;&lt;/html&gt;</pre></div>
+The major and minor 5-limit triads are wakalixes; in terms of the &lt;a class="wiki_link" href="/Fokker%20blocks#The Fokblock function and modal UDP notation"&gt;Fokblock function&lt;/a&gt; the major triad in root position can be denoted by Fokblock([16/15, 10/9], [0, 1]), Fokblock([[25/24, 10/9], [2, 0]) or Fokblock([25/24, 16/15], [1, 0]) and the minor triad Fokblock([16/15, 10/9], [1, 0]), Fokblock([25/24, 10/9], [1, 0]), or Fokblock([25/24, 16/15], [0, 0]). Each of these arenas contain the three inversions of both the major and minor triads, plus the inversions of another triad. In the case of the [16/15, 10/9] arena, that's the qunital triad, in its quintal (1-9/8-3/2) and quartal (1-4/3-16/9) forms. [25/24, 10/9] adds the three inversions of the diminished triad, 1-6/5-5/3, and [25/24, 16/15] adds the three inversions of the augmented triad, 1-5/4-8/5.&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="x7-limit tetrads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;7-limit tetrads&lt;/h1&gt;
+&lt;br /&gt;
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;td&gt;Arena&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Major tetrad offsets&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Minor tetrad offsets&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Paired vals&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;[21/20, 15/14, 35/32]&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;[2, 2, 2]&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;[3, 3, 0]&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1, 3, 2&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;[25/24, 15/14, 35/32]&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;[1, 2, 3]&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;[0, 3, 2]&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1, 3, 7&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;[25/24, 21/20, 15/14]&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;[2, 3, 2]&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;[0, 2, 3]&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2, 7, 3&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;[36/35, 21/20, 15/14]&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;[0, 3, 3]&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;[2, 2, 2]&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2, 7, 5&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;[36/35, 25/24, 21/20]&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;[2, 3, 3]&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;[3, 2, 2]&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3, 5, 7&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;[49/48, 21/20, 15/14]&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;[2, 2, 3]&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;[0, 3, 2]&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2, 1, 5&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;[49/48, 21/20, 35/32]&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;[1, 2, 3]&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;[0, 3, 2]&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3, 1, 5&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;[49/48, 36/35, 15/14]&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;[3, 2, 3]&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;[2, 3, 2]&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7, 1, 5&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
+&lt;/body&gt;&lt;/html&gt;</pre></div>

Fokker chord: Difference between revisions

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IMPORTED REVISION FROM WIKISPACES

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