Undecimal marvel chords

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An //undecimal marvel chord// is an [[Dyadic chord#Essentially tempered dyadic chord|essentially tempered chord]] of undecimal (11-limit) marvel, with intervals in the tonality diamond of the 11 odd limit. Since 225/224 is tempered out in undecimal marvel, 9-limit [[marvel chords]] are undecimal marvel chords. Since 385/384 is tempered out, [[keenanismic chords]] are also undecimal marvel chords. Finally, since 540/539 is tempered out, [[swetismic chords]] are undecimal marvel chords. There are also undecimal marvel chords which are none of these, the essentially undecimal marvel chords. These are four pairs of inversely related tetrads, 1-5/4-11/8-8/5 with steps 5/4-11/10-7/6-5/4 and 1-5/4-16/11-8/5 with steps 5/4-7/6-11/10-5/4; 1-9/8-8/5-7/4 with steps 9/8-10/7-12/11-8/7 and 1-9/8-9/7-7/5 with steps 9/8-8/7-12/11-10/7; 1-9/8-11/8-8/5 with steps 9/8-11/9-7/6-5/4 and 1-5/4-16/11-16/9 with steps 5/4-7/6-11/9-9/8; and 1-5/4-8/5-7/4 with steps 5/4-9/7-12/11-8/7 and 1-5/4-10/7-14/9 with steps 5/4-8/7-12/11-9/7. There are six pairs of inversely related essentially undecimal marvel pentads: 1-9/8-5/4-11/8-8/5 with steps 9/8-10/9-11/10-7/6-5/4 and 1-5/4-16/11-8/5-16/9 with steps 5/4-7/6-11/10-10/9-9/8; 1-5/4-7/5-8/5-7/4 with steps 5/4-9/8-8/7-12/11-8/7 and 1-9/8-7/5-8/5-7/4 with steps 9/8-5/4-8/7-12/11-8/7; 1-5/4-16/11-8/5-7/4 with steps 5/4-7/6-11/10-12/11-8/7 and 1-8/7-5/4-11/8-8/5 with steps 8/7-12/11-11/10-7/6-5/4; 1-5/4-11/8-8/5-7/4 with steps 5/4-11/10-7/6-12/11-8/7 and 1-8/7-5/4-16/11-8/5 with steps 8/7-12/11-7/6-11/10-5/4; 1-9/8-11/8-8/5-7/4 with steps 9/8-11/9-7/6-12/11-8/7 and 1-11/9-11/8-11/7-12/7 with steps 11/9-9/8-8/7-12/11-7/6; and 1-9/8-5/4-8/5-7/4 with steps 9/8-10/9-9/7-12/11-8/7 and 1-9/7-10/7-8/5-11/6 with steps 9/7-10/9-9/8-8/7-12/11.

The three essentially undecimal marvel hexads are particularly interesting. One is palindromic: 1-9/8-5/4-7/5-8/5-7/4 with steps 9/8-10/9-9/8-8/7-12/11-8/7. The two others are an inversive pair: 1-9/8-5/4-11/8-8/5-7/4 with steps 9/8-10/9-11/10-7/6-12/11-8/7 and 1-8/7-5/4-16/11-8/5-16/9 with steps 8/7-12/11-7/6-11/10-10/9-9/8. The latter two have steps which are permutations of the steps of the 11-limit JI hexads.

Equal divisions with undecimal marvel chords include 19, 22, 31, 41, 50, 53, 72, 81, 94, 103, 166, 175, 197e, 269ce and 341ce.

Original HTML content:

<html><head><title>undecimal marvel chords</title></head><body>An <em>undecimal marvel chord</em> is an <a class="wiki_link" href="/Dyadic%20chord#Essentially tempered dyadic chord">essentially tempered chord</a> of undecimal (11-limit) marvel, with intervals in the tonality diamond of the 11 odd limit. Since 225/224 is tempered out in undecimal marvel, 9-limit <a class="wiki_link" href="/marvel%20chords">marvel chords</a> are undecimal marvel chords. Since 385/384 is tempered out, <a class="wiki_link" href="/keenanismic%20chords">keenanismic chords</a> are also undecimal marvel chords. Finally, since 540/539 is tempered out, <a class="wiki_link" href="/swetismic%20chords">swetismic chords</a> are undecimal marvel chords. There are also undecimal marvel chords which are none of these, the essentially undecimal marvel chords. These are four pairs of inversely related tetrads, 1-5/4-11/8-8/5 with steps 5/4-11/10-7/6-5/4 and 1-5/4-16/11-8/5 with steps 5/4-7/6-11/10-5/4; 1-9/8-8/5-7/4 with steps 9/8-10/7-12/11-8/7 and 1-9/8-9/7-7/5 with steps 9/8-8/7-12/11-10/7; 1-9/8-11/8-8/5 with steps 9/8-11/9-7/6-5/4 and 1-5/4-16/11-16/9 with steps 5/4-7/6-11/9-9/8; and 1-5/4-8/5-7/4 with steps 5/4-9/7-12/11-8/7 and 1-5/4-10/7-14/9 with steps 5/4-8/7-12/11-9/7. There are six pairs of inversely related essentially undecimal marvel pentads: 1-9/8-5/4-11/8-8/5 with steps 9/8-10/9-11/10-7/6-5/4 and 1-5/4-16/11-8/5-16/9 with steps 5/4-7/6-11/10-10/9-9/8; 1-5/4-7/5-8/5-7/4 with steps 5/4-9/8-8/7-12/11-8/7 and 1-9/8-7/5-8/5-7/4 with steps 9/8-5/4-8/7-12/11-8/7; 1-5/4-16/11-8/5-7/4 with steps 5/4-7/6-11/10-12/11-8/7 and 1-8/7-5/4-11/8-8/5 with steps 8/7-12/11-11/10-7/6-5/4; 1-5/4-11/8-8/5-7/4 with steps 5/4-11/10-7/6-12/11-8/7 and 1-8/7-5/4-16/11-8/5 with steps 8/7-12/11-7/6-11/10-5/4; 1-9/8-11/8-8/5-7/4 with steps 9/8-11/9-7/6-12/11-8/7 and 1-11/9-11/8-11/7-12/7 with steps 11/9-9/8-8/7-12/11-7/6; and 1-9/8-5/4-8/5-7/4 with steps 9/8-10/9-9/7-12/11-8/7 and 1-9/7-10/7-8/5-11/6 with steps 9/7-10/9-9/8-8/7-12/11.<br />
<br />
The three essentially undecimal marvel hexads are particularly interesting. One is palindromic: 1-9/8-5/4-7/5-8/5-7/4 with steps 9/8-10/9-9/8-8/7-12/11-8/7. The two others are an inversive pair: 1-9/8-5/4-11/8-8/5-7/4 with steps 9/8-10/9-11/10-7/6-12/11-8/7 and 1-8/7-5/4-16/11-8/5-16/9 with steps 8/7-12/11-7/6-11/10-10/9-9/8. The latter two have steps which are permutations of the steps of the 11-limit JI hexads.<br />
<br />
Equal divisions with undecimal marvel chords include 19, 22, 31, 41, 50, 53, 72, 81, 94, 103, 166, 175, 197e, 269ce and 341ce.</body></html>
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