Fokker chord: Difference between revisions
Wikispaces>genewardsmith **Imported revision 500101846 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 500130866 - 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:genewardsmith|genewardsmith]] and made on <tt>2014-04-02 | : 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> | : The original revision id was <tt>500130866</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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=5-limit triads= | =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> | <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>Fokker chord</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>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: | <!-- 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 /> | 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 /> | <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> | <!-- 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.</body></html></pre></div> | 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></pre></div> | |||