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An '''undecimal marvel chord''' is an [[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-odd-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.  
An '''undecimal marvel chord''' is an [[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-odd-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:  
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;  
* 1–5/4–11/8–8/5 with steps 5/4, 11/10, 7/6, 5/4, and its inverse
* 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;  
* 1–5/4–16/11–8/5 with steps 5/4, 7/6, 11/10, 5/4;  
* 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;
* 1–9/8–8/5–7/4 with steps 9/8, 10/7, 12/11, 8/7, and its inverse
* 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.  
* 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 its inverse
* 1–5/4–16/11–16/9 with steps 5/4, 7/6, 11/9, 9/8;
* 1–5/4–8/5–7/4 with steps 5/4, 9/7, 12/11, 8/7, and its inverse
* 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:  
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;  
* 1–9/8–5/4–11/8–8/5 with steps 9/8, 10/9, 11/10, 7/6, 5/4, and its inverse
* 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;  
* 1–5/4–16/11–8/5–16/9 with steps 5/4, 7/6, 11/10, 10/9, 9/8;  
* 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;  
* 1–5/4–7/5–8/5–7/4 with steps 5/4, 9/8, 8/7, 12/11, 8/7, and its inverse
* 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;  
* 1–9/8–7/5–8/5–7/4 with steps 9/8, 5/4, 8/7, 12/11, 8/7;  
* 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;  
* 1–5/4–16/11–8/5–7/4 with steps 5/4, 7/6, 11/10, 12/11, 8/7, and its inverse
* 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.
* 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 its inverse
* 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 its inverse
* 1–11/9–11/8–11/7–12/7 with steps 11/9, 9/8, 8/7, 12/11, 7/6;  
* 1–9/8–5/4–8/5–7/4 with steps 9/8, 10/9, 9/7, 12/11, 8/7, and its inverse
* 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:  
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.  
* 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:  
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.  
* 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 its inverse
* 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.
The latter two have steps which are permutations of the steps of the 11-limit JI hexads.
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The essentially undecimal marvel chords number tetrads: 8, pentads: 12, hexads: 3, for a total of 23.
The essentially undecimal marvel chords number tetrads: 8, pentads: 12, hexads: 3, for a total of 23.


Equal divisions with undecimal marvel chords include {{EDOs| 19, 22, 31, 41, 50, 53, 72, 81, 94, 103, 166, 175, 197e, 269ce and 341ce }}.
[[Equal temperament]]s with undecimal marvel chords include {{EDOs| 19, 22, 31, 41, 50, 53, 72, 81, 94, 103, 166, 175, 197e, 269ce and 341ce }}.


[[Category:11-odd-limit]]
[[Category:11-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Essentially tempered chords]]
[[Category:Tetrads]]
[[Category:Tetrads]]
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