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The marveltwin triad is a 13-limit [[Dyadic_chord|essentially tempered dyadic chord]] which consists of two stacked minor thirds followed by an [[18/13]], that is, a [[6/5]]-[[6/5]]-18/13 chord, tempered in [[marveltwin]]. In other words, an 1-6/5-[[13/9]] chord tempered in a temperament tempering out [[325/324]], the marveltwin comma. 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, 1-6/5-13/9-[[26/15]] in marveltwin, which is a 15-limit essentially tempered dyadic chord with steps 6/5-6/5-6/5-[[15/13]]. Another marveltwin chord of interest is the marveltwin tonestack: 1-[[9/8]]-[[5/4]]-[[3/2]]-[[13/8]]-[[9/5]] tempered in marveltwin. Equal temperaments with marveltwin triads include {{EDOs|19, 26, 34, 41, 46, 53, 72, 87, 121, 140, 159, 193, 212, 246, 299 and 333}}.
'''Marveltwin chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the marveltwin comma, [[325/324]].


[[Category:13-limit]]
There are 6 triads, 18 tetrads, 14 pentads and 3 hexads as 2.3.5.13 subgroup [[13-odd-limit]] essentially tempered chords.
 
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.
 
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]].
 
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.
 
For tetrads, there are four palindromic chords and seven pairs of chords in inverse relationship. The palindromic chords are
* 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.
 
The inversely related pairs of chords are
* 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.
 
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 inversely related pairs of chords are
* 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.
 
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.
 
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:Triads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Hexads]]
[[Category:Marveltwin]]
[[Category:Marveltwin]]
[[Category:Triad]]
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