Marveltwin chords

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A marveltwin chord is a 13-odd-limit essentially tempered dyadic chord tempered by 325/324, the marveltwin comma.

One marveltwin triad consists of a stack of two 6/5 minor thirds followed by an 18/13, that is,

  • 1-6/5-13/9, with steps 6/5-6/5-18/13,

in a temperament tempering out 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,

which is a 15-odd-limit essentially tempered dyadic chord.

Another triad consists of a stack of two 10/9 whole tones followed by a 16/13, that is,

  • 1-10/9-16/13, with steps 10/9-10/9-13/8,

as well as one built by

  • 1-10/9-18/13, with steps 10/9-5/4-13/9

and its inversion. Each of these has multiple ways to extend to tetrads.

The marveltwin tonestack is a hexad where each interval belongs to the 13-odd-limit consonance set:

Equal temperaments with marveltwin triads include 19, 26, 34, 41, 46, 53, 72, 87, 121, 140, 159, 193, 212, 246, 299 and 333.