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'''Mynucumic chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the mynucuma, [[196/195]].
'''Mynucumic chords''' are [[dyadic chord|essentially tempered chords]] tempered by the mynucuma, [[196/195]].


There are 10 triads, 33 tetrads, 26 pentads and 6 hexads as 2.3.5.7.13 subgroup [[13-odd-limit]] essentially tempered chords.
There are 10 triads, 33 tetrads, 26 pentads and 6 hexads as 2.3.5.7.13 subgroup [[13-odd-limit]] essentially tempered chords.
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The ''mynucumic triads'' are temperings of  
The ''mynucumic triads'' are temperings of  
* 1-16/13-10/7 with steps of 16/13-7/6-7/5, and its inverse  
* 1–16/13–10/7 with steps of 16/13, 7/6, 7/5, and its inverse  
* 1-7/6-10/7 with steps of 7/6-16/13-7/5.
* 1–7/6–10/7 with steps of 7/6, 16/13, 7/5.


The rest four inversely related pairs of triads contain semitones, such as 13/12 or 14/13:  
The rest four inversely related pairs of triads contain semitones, such as 13/12 or 14/13:  
* 1-7/5-3/2 with steps of 7/5-14/13-4/3, and its inverse  
* 1–7/5–3/2 with steps of 7/5, 14/13, 4/3, and its inverse  
* 1-14/13-3/2 with steps of 14/13-7/5-4/3;
* 1–14/13–3/2 with steps of 14/13, 7/5, 4/3;
* 1-7/6-5/4 with steps of 7/6-14/13-8/5, and its inverse  
* 1–7/6–5/4 with steps of 7/6, 14/13, 8/5, and its inverse  
* 1-14/13-5/4 with steps of 14/13-7/6-8/5;
* 1–14/13–5/4 with steps of 14/13, 7/6, 8/5;
* 1-6/5-9/7 with steps of 6/5-14/13-14/9, and its inverse  
* 1–6/5–9/7 with steps of 6/5, 14/13, 14/9, and its inverse  
* 1-14/13-9/7 with steps of 14/13-6/5-14/9;
* 1–14/13–9/7 with steps of 14/13, 6/5, 14/9;
* 1-9/7-7/5 with steps of 9/7-13/12-10/7, and its inverse  
* 1–9/7–7/5 with steps of 9/7, 13/12, 10/7, and its inverse  
* 1-13/12-7/5 with steps of 13/12-9/7-10/7.
* 1–13/12–7/5 with steps of 13/12, 9/7, 10/7.


For tetrads, there are five palindromic chords and fourteen pairs of chords in inverse relationship.
For tetrads, there are five palindromic chords and fourteen pairs of chords in inverse relationship.


The ''mynucumic tetrad'' is palindromic, a tempering of  
The ''mynucumic tetrad'' is palindromic, a tempering of  
* 1-7/6-7/5-13/8 chord with steps of 7/6-6/5-7/6-16/13.
* 1–7/6–7/5–13/8 chord with steps of 7/6, 6/5, 7/6, 16/13.


The rest four palindromic tetrads contain semitones:  
The rest four palindromic tetrads contain semitones:  
* 1-14/13-7/5-3/2 chord with steps of 14/13-13/10-14/13-4/3;
* 1–14/13–7/5–3/2 chord with steps of 14/13, 13/10, 14/13, 4/3;
* 1-14/13-7/6-5/4 chord with steps of 14/13-13/12-14/13-8/5;
* 1–14/13–7/6–5/4 chord with steps of 14/13, 13/12, 14/13, 8/5;
* 1-6/5-9/7-13/7 chord with steps of 6/5-14/13-13/9-14/13;
* 1–6/5–9/7–13/7 chord with steps of 6/5, 14/13, 13/9, 14/13;
* 1-9/7-7/5-9/5 chord with steps of 9/7-13/12-9/7-10/9.
* 1–9/7–7/5–9/5 chord with steps of 9/7, 13/12, 9/7, 10/9.


The inversely related pairs of tetrads also contain semitones:  
The inversely related pairs of tetrads also contain semitones:  
* 1-9/7-7/5-3/2 with steps of 9/7-13/12-14/13-4/3, and its inverse  
* 1–9/7–7/5–3/2 with steps of 9/7, 13/12, 14/13, 4/3, and its inverse  
* 1-14/13-7/6-3/2 with steps of 14/13-13/12-9/7-4/3;
* 1–14/13–7/6–3/2 with steps of 14/13, 13/12, 9/7, 4/3;
* 1-6/5-9/7-3/2 with steps of 6/5-14/13-7/6-4/3, and its inverse  
* 1–6/5–9/7–3/2 with steps of 6/5, 14/13, 7/6, 4/3, and its inverse  
* 1-7/6-5/4-3/2 with steps of 7/6-14/13-6/5-4/3;
* 1–7/6–5/4–3/2 with steps of 7/6, 14/13, 6/5, 4/3;
* 1-6/5-7/5-3/2 with steps of 6/5-7/6-14/13-4/3, and its inverse  
* 1–6/5–7/5–3/2 with steps of 6/5, 7/6, 14/13, 4/3, and its inverse  
* 1-14/13-5/4-3/2 with steps of 14/13-7/6-6/5-4/3;
* 1–14/13–5/4–3/2 with steps of 14/13, 7/6, 6/5, 4/3;
* 1-7/6-7/5-3/2 with steps of 7/6-6/5-14/13-4/3, and its inverse  
* 1–7/6–7/5–3/2 with steps of 7/6, 6/5, 14/13, 4/3, and its inverse  
* 1-14/13-9/7-3/2 with steps of 14/13-6/5-7/6-4/3;
* 1–14/13–9/7–3/2 with steps of 14/13, 6/5, 7/6, 4/3;
* 1-13/12-7/5-3/2 with steps of 13/12-9/7-14/13-4/3, and its inverse  
* 1–13/12–7/5–3/2 with steps of 13/12, 9/7, 14/13, 4/3, and its inverse  
* 1-14/13-18/13-3/2 with steps of 14/13-9/7-13/12-4/3;
* 1–14/13–18/13–3/2 with steps of 14/13, 9/7, 13/12, 4/3;
* 1-7/5-3/2-9/5 with steps of 7/5-14/13-6/5-10/9, and its inverse  
* 1–7/5–3/2–9/5 with steps of 7/5, 14/13, 6/5, 10/9, and its inverse  
* 1-14/13-3/2-5/3 with steps of 14/13-7/5-10/9-6/5;
* 1–14/13–3/2–5/3 with steps of 14/13, 7/5, 10/9, 6/5;
* 1-7/5-3/2-7/4 with steps of 7/5-14/13-7/6-8/7, and its inverse  
* 1–7/5–3/2–7/4 with steps of 7/5, 14/13, 7/6, 8/7, and its inverse  
* 1-14/13-3/2-12/7 with steps of 14/13-7/5-8/7-7/6;
* 1–14/13–3/2–12/7 with steps of 14/13, 7/5, 8/7, 7/6;
* 1-7/5-3/2-12/7 with steps of 7/5-14/13-8/7-7/6, and its inverse  
* 1–7/5–3/2–12/7 with steps of 7/5, 14/13, 8/7, 7/6, and its inverse  
* 1-14/13-3/2-7/4 with steps of 14/13-7/5-7/6-8/7;
* 1–14/13–3/2–7/4 with steps of 14/13, 7/5, 7/6, 8/7;
* 1-9/7-3/2-24/13 with steps of 9/7-7/6-16/13-13/12, and its inverse  
* 1–9/7–3/2–24/13 with steps of 9/7, 7/6, 16/13, 13/12, and its inverse  
* 1-7/6-3/2-13/8 with steps of 7/6-9/7-13/12-16/13;
* 1–7/6–3/2–13/8 with steps of 7/6, 9/7, 13/12, 16/13;
* 1-7/5-3/2-13/8 with steps of 7/5-14/13-13/12-16/13, and its inverse  
* 1–7/5–3/2–13/8 with steps of 7/5, 14/13, 13/12, 16/13, and its inverse  
* 1-14/13-3/2-24/13 with steps of 14/13-7/5-16/13-13/12;
* 1–14/13–3/2–24/13 with steps of 14/13, 7/5, 16/13, 13/12;
* 1-7/6-5/4-13/8 with steps of 7/6-14/13-13/10-16/13, and its inverse  
* 1–7/6–5/4–13/8 with steps of 7/6, 14/13, 13/10, 16/13, and its inverse  
* 1-14/13-5/4-20/13 with steps of 14/13-7/6-16/13-13/10;
* 1–14/13–5/4–20/13 with steps of 14/13, 7/6, 16/13, 13/10;
* 1-7/6-5/4-10/7 with steps of 7/6-14/13-8/7-7/5, and its inverse  
* 1–7/6–5/4–10/7 with steps of 7/6, 14/13, 8/7, 7/5, and its inverse  
* 1-14/13-5/4-7/4 with steps of 14/13-7/6-7/5-8/7;
* 1–14/13–5/4–7/4 with steps of 14/13, 7/6, 7/5, 8/7;
* 1-6/5-13/10-13/7 with steps of 6/5-13/12-10/7-14/13, and its inverse  
* 1–6/5–13/10–13/7 with steps of 6/5, 13/12, 10/7, 14/13, and its inverse  
* 1-6/5-9/7-24/13 with steps of 6/5-14/13-10/7-13/12;
* 1–6/5–9/7–24/13 with steps of 6/5, 14/13, 10/7, 13/12;
* 1-6/5-12/7-13/7 with steps of 6/5-10/7-13/12-14/13, and its inverse  
* 1–6/5–12/7–13/7 with steps of 6/5, 10/7, 13/12, 14/13, and its inverse  
* 1-6/5-9/7-7/5 with steps of 6/5-14/13-13/12-10/7.
* 1–6/5–9/7–7/5 with steps of 6/5, 14/13, 13/12, 10/7.


For pentads, there are thirteen pairs of chords in inverse relationship, all of them involve semitones and the perfect fifth:  
For pentads, there are thirteen pairs of chords in inverse relationship, all of them involve semitones and the perfect fifth:  
* 1-6/5-9/7-7/5-3/2 with steps of 6/5-14/13-13/12-14/13-4/3, and its inverse  
* 1–6/5–9/7–7/5–3/2 with steps of 6/5, 14/13, 13/12, 14/13, 4/3, and its inverse  
* 1-14/13-7/6-5/4-3/2 with steps of 14/13-13/12-14/13-6/5-4/3;
* 1–14/13–7/6–5/4–3/2 with steps of 14/13, 13/12, 14/13, 6/5, 4/3;
* 1-13/12-7/6-7/5-3/2 with steps of 13/12-14/13-6/5-14/13-4/3, and its inverse  
* 1–13/12–7/6–7/5–3/2 with steps of 13/12, 14/13, 6/5, 14/13, 4/3, and its inverse  
* 1-14/13-9/7-18/13-3/2 with steps of 14/13-6/5-14/13-13/12-4/3;
* 1–14/13–9/7–18/13–3/2 with steps of 14/13, 6/5, 14/13, 13/12, 4/3;
* 1-14/13-9/7-7/5-3/2 with steps of 14/13-6/5-13/12-14/13-4/3, and its inverse  
* 1–14/13–9/7–7/5–3/2 with steps of 14/13, 6/5, 13/12, 14/13, 4/3, and its inverse  
* 1-14/13-7/6-7/5-3/2 with steps of 14/13-13/12-6/5-14/13-4/3;
* 1–14/13–7/6–7/5–3/2 with steps of 14/13, 13/12, 6/5, 14/13, 4/3;
* 1-9/7-7/5-3/2-9/5 with steps of 9/7-13/12-14/13-6/5-10/9, and its inverse  
* 1–9/7–7/5–3/2–9/5 with steps of 9/7, 13/12, 14/13, 6/5, 10/9, and its inverse  
* 1-14/13-7/6-3/2-5/3 with steps of 14/13-13/12-9/7-10/9-6/5;
* 1–14/13–7/6–3/2–5/3 with steps of 14/13, 13/12, 9/7, 10/9, 6/5;
* 1-6/5-9/7-3/2-9/5 with steps of 6/5-14/13-7/6-6/5-10/9, and its inverse  
* 1–6/5–9/7–3/2–9/5 with steps of 6/5, 14/13, 7/6, 6/5, 10/9, and its inverse  
* 1-7/6-5/4-3/2-5/3 with steps of 7/6-14/13-6/5-10/9-6/5;
* 1–7/6–5/4–3/2–5/3 with steps of 7/6, 14/13, 6/5, 10/9, 6/5;
* 1-6/5-9/7-3/2-12/7 with steps of 6/5-14/13-7/6-8/7-7/6, and its inverse  
* 1–6/5–9/7–3/2–12/7 with steps of 6/5, 14/13, 7/6, 8/7, 7/6, and its inverse  
* 1-7/6-5/4-3/2-7/4 with steps of 7/6-14/13-6/5-7/6-8/7;
* 1–7/6–5/4–3/2–7/4 with steps of 7/6, 14/13, 6/5, 7/6, 8/7;
* 1-6/5-7/5-3/2-12/7 with steps of 6/5-7/6-14/13-8/7-7/6, and its inverse  
* 1–6/5–7/5–3/2–12/7 with steps of 6/5, 7/6, 14/13, 8/7, 7/6, and its inverse  
* 1-14/13-5/4-3/2-7/4 with steps of 14/13-7/6-6/5-7/6-8/7;
* 1–14/13–5/4–3/2–7/4 with steps of 14/13, 7/6, 6/5, 7/6, 8/7;
* 1-14/13-7/5-3/2-7/4 with steps of 14/13-13/10-14/13-7/6-8/7, and its inverse  
* 1–14/13–7/5–3/2–7/4 with steps of 14/13, 13/10, 14/13, 7/6, 8/7, and its inverse  
* 1-14/13-7/5-3/2-12/7 with steps of 14/13-13/10-14/13-8/7-7/6;
* 1–14/13–7/5–3/2–12/7 with steps of 14/13, 13/10, 14/13, 8/7, 7/6;
* 1-9/7-18/13-3/2-24/13 with steps of 9/7-14/13-13/12-16/13-13/12, and its inverse  
* 1–9/7–18/13–3/2–24/13 with steps of 9/7, 14/13, 13/12, 16/13, 13/12, and its inverse  
* 1-13/12-7/6-3/2-13/12 with steps of 13/12-14/13-9/7-13/12-16/13;
* 1–13/12–7/6–3/2–13/12 with steps of 13/12, 14/13, 9/7, 13/12, 16/13;
* 1-6/5-9/7-3/2-24/13 with steps of 6/5-14/13-7/6-16/13-13/12, and its inverse  
* 1–6/5–9/7–3/2–24/13 with steps of 6/5, 14/13, 7/6, 16/13, 13/12, and its inverse  
* 1-7/6-5/4-3/2-13/8 with steps of 7/6-14/13-6/5-13/12-16/13;
* 1–7/6–5/4–3/2–13/8 with steps of 7/6, 14/13, 6/5, 13/12, 16/13;
* 1-7/6-7/5-3/2-13/8 with steps of 7/6-6/5-14/13-13/12-16/13, and its inverse  
* 1–7/6–7/5–3/2–13/8 with steps of 7/6, 6/5, 14/13, 13/12, 16/13, and its inverse  
* 1-14/13-9/7-3/2-24/13 with steps of 14/13-6/5-7/6-16/13-13/12;
* 1–14/13–9/7–3/2–24/13 with steps of 14/13, 6/5, 7/6, 16/13, 13/12;
* 1-9/7-3/2-12/7-24/13 with steps of 9/7-7/6-8/7-14/13-13/12, and its inverse  
* 1–9/7–3/2–12/7–24/13 with steps of 9/7, 7/6, 8/7, 14/13, 13/12, and its inverse  
* 1-7/6-3/2-13/8-7/4 with steps of 7/6-9/7-13/12-14/13-8/7;
* 1–7/6–3/2–13/8–7/4 with steps of 7/6, 9/7, 13/12, 14/13, 8/7;
* 1-7/5-3/2-13/8-7/4 with steps of 7/5-14/13-13/12-14/13-8/7, and its inverse  
* 1–7/5–3/2–13/8–7/4 with steps of 7/5, 14/13, 13/12, 14/13, 8/7, and its inverse  
* 1-14/13-3/2-12/7-24/13 with steps of 14/13-7/5-8/7-14/13-13/12.
* 1–14/13–3/2–12/7–24/13 with steps of 14/13, 7/5, 8/7, 14/13, 13/12.


For hexads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are  
For hexads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are  
* 1-14/13-7/6-5/4-3/2-5/3 chord with steps of 14/13-13/12-14/13-6/5-10/9-6/5;
* 1–14/13–7/6–5/4–3/2–5/3 chord with steps of 14/13, 13/12, 14/13, 6/5, 10/9, 6/5;
* 1-13/12-7/6-7/5-3/2-13/8 chord with steps of 13/12-14/13-6/5-14/13-13/12-16/13.
* 1–13/12–7/6–7/5–3/2–13/8 chord with steps of 13/12, 14/13, 6/5, 14/13, 13/12, 16/13.


The inversely related pairs of chords are  
The inversely related pairs of chords are  
* 1-6/5-9/7-7/5-3/2-12/7 with steps of 6/5-14/13-13/12-14/13-8/7-7/6, and its inverse  
* 1–6/5–9/7–7/5–3/2–12/7 with steps of 6/5, 14/13, 13/12, 14/13, 8/7, 7/6, and its inverse  
* 1-14/13-7/6-5/4-3/2-7/4 with steps of 14/13-13/12-14/13-6/5-7/6-8/7;
* 1–14/13–7/6–5/4–3/2–7/4 with steps of 14/13, 13/12, 14/13, 6/5, 7/6, 8/7;
* 1-14/13-9/7-7/5-3/2-12/7 with steps of 14/13-6/5-13/12-14/13-8/7-7/6, and its inverse  
* 1–14/13–9/7–7/5–3/2–12/7 with steps of 14/13, 6/5, 13/12, 14/13, 8/7, 7/6, and its inverse  
* 1-14/13-7/6-7/5-3/2-7/4 with steps of 14/13-13/12-6/5-14/13-7/6-8/7.
* 1–14/13–7/6–7/5–3/2–7/4 with steps of 14/13, 13/12, 6/5, 14/13, 7/6, 8/7.


Equal temperaments with mynucumic chords include {{Optimal ET sequence|19, 27, 31, 41, 46, 58, 68, 77, 87, 118, 145 and 232}}.
[[Equal temperament]]s with mynucumic chords include {{Optimal ET sequence| 19, 27, 31, 41, 46, 58, 68, 77, 87, 118, 145 and 232 }}.


[[Category:13-odd-limit]]
[[Category:13-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Triads]]
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