Werckismic chords

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Original Wikitext content:

A //werckismic chord// is an [[dyadic chord|essentially tempered dyadic chord]] in werckismic (441/440) tempering in the 2.9.5.7.11 subgroup in the 11-odd-limit.

The werckismic triads consist of three pairs of inversely related chords: 1-11/9-7/5 with steps 11/9-8/7-10/7 and 1-11/9-7/4 with steps 11/9-10/7-8/7; 1-11/7-7/4 with steps 11/7-10/9-8/7 and 1-11/7-9/5 with steps 11/7-8/7-10/9; and 1-7/5-11/7 with steps 7/5-9/8-14/11 and 1-14/11-10/7 with steps 14/11-9/8-7/5.

The werckismic tetrads consist of three palindromic (self-inversive) chords and five pairs of chords in an inverse relationship. The palindromic chords are 1-5/4-10/7-7/4 with steps 5/4-8/7-11/9-8/7; 1-9/8-10/7-11/7 with steps 9/8-14/11-11/10-14/11; and 1-14/11-7/5-16/9 with steps 14/11-11/10-14/11-9/8. The pairs of chords are 1-11/9-11/7-7/4 with steps 11/9-9/7-10/9-8/7 and 1-9/7-11/7-9/5 with steps 9/7-11/9-8/7-10/9; 1-10/7-11/7-7/4 with steps 10/7-11/10-10/9-8/7 and 1-8/7-14/11-7/5 with steps 8/7-10/9-11/10-10/7; 1-9/8-10/7-7/4 with steps 9/8-14/11-11/9-8/7 and 1-11/9-14/9-7/4 with steps 11/9-14/11-9/8-8/7; 1-11/9-11/8-7/4 with steps 11/9-9/8-14/11-8/7 and 1-14/11-10/7-7/4 with steps 14/11-9/8-11/9-8/7; 1-9/8-5/4-10/7 with steps 9/8-10/9-8/7-7/5 and 1-10/9-5/4-7/4 with steps 10/9-9/8-7/5-8/7; and 1-9/8-9/7-10/7 with steps 9/8-8/7-10/9-7/5 and 1-9/8-11/7-7/4 with steps 9/8-7/5-10/9-8/7.

The werckismic pentads consist of three pairs of chords in an inverse relationship: 1-9/8-5/4-10/7-7/4 with steps 9/8-10/9-8/7-11/9-8/7 and 1-11/9-7/5-14/9-7/4 with steps 11/9-8/7-10/9-9/8-8/7; 1-11/9-11/8-11/7-7/4 with steps 11/9-9/8-8/7-10/9-8/7 and 1-9/8-11/8-11/7-7/4 with steps 9/8-11/9-8/7-10/9-8/7; 1-9/8-9/7-10/7-11/7 with steps 9/8-8/7-10/9-11/10-14/11 and 1-9/8-10/7-11/7-7/4 with steps 9/8-14/11-11/10-10/9-8/7.

The count of chords is therefore triads: 3, tetrads: 13, pentads: 6, for a total of 22.

Equal temperaments with werckismic chords include 31, 41, 43, 46, 58, 72, 77, 84, 103, 118, 130, 159, 171, 190, 248, 289, 320, 727d, 929d and 1249d.

Original HTML content:

<html><head><title>werckismic chords</title></head><body>A <em>werckismic chord</em> is an <a class="wiki_link" href="/dyadic%20chord">essentially tempered dyadic chord</a> in werckismic (441/440) tempering in the 2.9.5.7.11 subgroup in the 11-odd-limit.<br />
<br />
The werckismic triads consist of three pairs of inversely related chords: 1-11/9-7/5 with steps 11/9-8/7-10/7 and 1-11/9-7/4 with steps 11/9-10/7-8/7; 1-11/7-7/4 with steps 11/7-10/9-8/7 and 1-11/7-9/5 with steps 11/7-8/7-10/9; and 1-7/5-11/7 with steps 7/5-9/8-14/11 and 1-14/11-10/7 with steps 14/11-9/8-7/5.<br />
<br />
The werckismic tetrads consist of three palindromic (self-inversive) chords and five pairs of chords in an inverse relationship. The palindromic chords are 1-5/4-10/7-7/4 with steps 5/4-8/7-11/9-8/7; 1-9/8-10/7-11/7 with steps 9/8-14/11-11/10-14/11; and 1-14/11-7/5-16/9 with steps 14/11-11/10-14/11-9/8. The pairs of chords are 1-11/9-11/7-7/4 with steps 11/9-9/7-10/9-8/7 and 1-9/7-11/7-9/5 with steps 9/7-11/9-8/7-10/9; 1-10/7-11/7-7/4 with steps 10/7-11/10-10/9-8/7 and 1-8/7-14/11-7/5 with steps 8/7-10/9-11/10-10/7; 1-9/8-10/7-7/4 with steps 9/8-14/11-11/9-8/7 and 1-11/9-14/9-7/4 with steps 11/9-14/11-9/8-8/7; 1-11/9-11/8-7/4 with steps 11/9-9/8-14/11-8/7 and 1-14/11-10/7-7/4 with steps 14/11-9/8-11/9-8/7; 1-9/8-5/4-10/7 with steps 9/8-10/9-8/7-7/5 and 1-10/9-5/4-7/4 with steps 10/9-9/8-7/5-8/7; and 1-9/8-9/7-10/7 with steps 9/8-8/7-10/9-7/5 and 1-9/8-11/7-7/4 with steps 9/8-7/5-10/9-8/7.<br />
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The werckismic pentads consist of three pairs of chords in an inverse relationship: 1-9/8-5/4-10/7-7/4 with steps 9/8-10/9-8/7-11/9-8/7 and 1-11/9-7/5-14/9-7/4 with steps 11/9-8/7-10/9-9/8-8/7; 1-11/9-11/8-11/7-7/4 with steps 11/9-9/8-8/7-10/9-8/7 and 1-9/8-11/8-11/7-7/4 with steps 9/8-11/9-8/7-10/9-8/7; 1-9/8-9/7-10/7-11/7 with steps 9/8-8/7-10/9-11/10-14/11 and 1-9/8-10/7-11/7-7/4 with steps 9/8-14/11-11/10-10/9-8/7.<br />
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The count of chords is therefore triads: 3, tetrads: 13, pentads: 6, for a total of 22.<br />
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Equal temperaments with werckismic chords include 31, 41, 43, 46, 58, 72, 77, 84, 103, 118, 130, 159, 171, 190, 248, 289, 320, 727d, 929d and 1249d.</body></html>
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