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A '''marveltwin chord''' is a [[13-odd-limit]] [[essentially tempered dyadic chord]] tempered by [[325/324]], the marveltwin comma.
'''Marveltwin chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the marveltwin comma, [[325/324]].


One marveltwin triad consists of a stack of two [[6/5]] minor thirds followed by an [[18/13]], that is,
There are 6 triads, 18 tetrads, 14 pentads and 3 hexads as 2.3.5.13 subgroup [[13-odd-limit]] essentially tempered chords.
* 1-6/5-[[13/9]], with steps 6/5-6/5-18/13,


in a temperament tempering out the marveltwin comma.  
One marveltwin triad is a palindrome since it identifies [[13/9]] by a stack of two [[6/5]] minor thirds, that is,
* 1–6/5–13/9 with steps of 6/5, 6/5, [[18/13]].


It makes for an instructive comparison with the septimal diminished triad, 1-6/5-[[10/7]] in [[starling]], and might also be called a tridecimal diminished triad. It can be extended to the marveltwin tetrad,
It makes for an instructive comparison with the septimal diminished triad, 1–6/5–[[10/7]] in [[starling]], and might also be called a tridecimal diminished triad.


* 1-6/5-13/9-[[26/15]] with steps 6/5-6/5-6/5-[[15/13]],
Another palindromic triad consists of [[16/13]] found as a stack of two [[10/9]] whole tones, that is,
* 1–10/9–16/13 with steps of 10/9, 10/9, [[13/8]].


which is a [[15-odd-limit]] essentially tempered dyadic chord.  
We also have those built by
* 1–[[5/4]]–18/13 with steps of 5/4, 10/9, 13/9, and its inverse
* 1–10/9–18/13 with steps of 10/9, 5/4, 13/9;
* 1–[[5/3]]–[[24/13]] with steps of 5/3, 10/9, [[13/12]], and its inverse
* 1–10/9–24/13 with steps of 10/9, 5/3, 13/12.  


Another triad consists of a stack of two [[10/9]] whole tones followed by a [[16/13]], that is,  
For tetrads, there are four palindromic chords and seven pairs of chords in inverse relationship. The palindromic chords are
* 1-10/9-16/13, with steps 10/9-10/9-[[13/8]],  
* 1–10/9–18/13–20/13 with steps of 10/9, 5/4, 10/9, 13/10;
* 1–10/9–5/4–18/13 with steps of 10/9, 9/8, 10/9, 13/9;
* 1–10/9–6/5–4/3 with steps of 10/9, 13/12, 10/9, 3/2;
* 1–13/12–6/5–13/10 with steps of 13/12, 10/9, 13/12, 20/13.


as well as one built by
The inversely related pairs of chords are
* 1-10/9-18/13, with steps 10/9-5/4-13/9
* 1–18/13–3/2–5/3 with steps of 18/13, 13/12, 10/9, 6/5, and its inverse
* 1–13/12–3/2–9/5 with steps of 13/12, 18/13, 6/5, 10/9;
* 1–5/4–3/2–9/5 with steps of 5/4, 6/5, 6/5, 10/9, and its inverse
* 1–6/5–3/2–5/3 with steps of 6/5, 5/4, 10/9, 6/5;
* 1–5/4–18/13–3/2 with steps of 5/4, 10/9, 13/12, 4/3, and its inverse
* 1–13/12–6/5–3/2 with steps of 13/12, 10/9, 5/4, 4/3;
* 1–10/9–16/13–4/3 with steps of 10/9, 10/9, 13/12, 3/2, and its inverse
* 1–13/12–6/5–4/3 with steps of 13/12, 10/9, 10/9, 3/2;
* 1–5/4–18/13–20/13 with steps of 5/4, 10/9, 10/9, 13/10, and its inverse
* 1–10/9–16/13–20/13 with steps of 10/9, 10/9, 5/4, 13/10;
* 1–6/5–13/10–13/9 with steps of 6/5, 13/12, 10/9, 18/13, and its inverse
* 1–10/9–6/5–13/9 with steps of 10/9, 13/12, 6/5, 18/13;
* 1–9/8–5/4–18/13 with steps of 9/8, 10/9, 10/9, 13/9, and its inverse
* 1–10/9–16/13–18/13 with steps of 10/9, 10/9, 9/8, 13/9.


and its inversion. Each of these has multiple ways to extend to tetrads.  
For pentads, there are two palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are
* 1–9/8–5/4–3/2–9/5 with steps of 9/8, 10/9, 6/5, 6/5, 10/9;
* 1–13/12–3/2–13/8–9/5 with steps of 13/12, 18/13, 13/12, 10/9, 10/9.


The marveltwin tonestack is a hexad where each interval belongs to the 13-odd-limit consonance set:
The inversely related pairs of chords are
* 1-[[9/8]]-[[5/4]]-[[3/2]]-[[13/8]]-[[9/5]], with steps 9/8-10/9-6/5-13/12-10/9-10/9,  
* 1–18/13–3/2–5/3–9/5 with steps of 18/13, 13/12, 10/9, 13/12, 10/9, and its inverse
* 1–13/12–3/2–5/3–9/5 with steps of 13/12, 18/13, 10/9, 13/12, 10/9;
* 1–5/4–3/2–5/3–9/5 with steps of 5/4, 6/5, 10/9, 13/12, 10/9, and its inverse
* 1–6/5–3/2–5/3–9/5 with steps of 6/5, 5/4, 10/9, 13/12, 10/9;
* 1–5/4–3/2–13/8–9/5 with steps of 5/4, 6/5, 13/12, 10/9, 10/9, and its inverse
* 1–6/5–3/2–5/3–24/13 with steps of 6/5, 5/4, 10/9, 10/9, 13/12;
* 1–5/4–18/13–3/2–9/5 with steps of 5/4, 10/9, 13/12, 6/5, 10/9, and its inverse
* 1–13/12–6/5–3/2–5/3 with steps of 13/12, 10/9, 5/4, 10/9, 6/5;
* 1–9/8–5/4–18/13–3/2 with steps of 9/8, 10/9, 10/9, 13/12, 4/3, and its inverse
* 1–13/12–6/5–4/3–3/2 with steps of 13/12, 10/9, 10/9, 9/8, 4/3;
* 1–9/8–5/4–13/8–9/5 with steps of 9/8, 10/9, 13/10, 10/9, 10/9, and its inverse
* 1–9/8–5/4–18/13–9/5 with steps of 9/8, 10/9, 10/9, 13/10, 10/9.


Equal temperaments with marveltwin triads include {{EDOs| 19, 26, 34, 41, 46, 53, 72, 87, 121, 140, 159, 193, 212, 246, 299 and 333 }}.
For hexads, there are one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is
* 1–5/4–18/13–3/2–5/3–9/5 with steps of 5/4, 10/9, 13/12, 10/9, 13/12, 10/9.


[[Category:13-odd-limit]]
The inversely related pair of chords is
* 1–6/5–4/3–3/2–5/3–24/13 with steps of 6/5, 10/9, 9/8, 10/9, 10/9, 13/12, and its inverse
* 1–9/8–5/4–3/2–13/8–9/5 with steps of 9/8, 10/9, 6/5, 13/12, 10/9, 10/9.
 
Equal temperaments with marveltwin chords include {{Optimal ET sequence| 19, 26, 34, 41, 46, 53, 72, 87, 121, 140, 159, 193, 212, 246, 299 and 333 }}, with 333edo giving the [[optimal patent val]].
 
[[Category:13-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Essentially tempered chords]]
[[Category:Triad]]
[[Category:Triads]]
[[Category:Tetrad]]
[[Category:Tetrads]]
[[Category:Hexad]]
[[Category:Pentads]]
[[Category:Hexads]]
[[Category:Marveltwin]]
[[Category:Marveltwin]]
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