Fokker chord
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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:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- 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: -->
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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:<h1> --><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:<h1> --><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>
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