Marveltwin chords: Difference between revisions

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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}}.

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

[[Category:13-limit]]

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,

* 1-6/5-13/9-[[26/15]] with steps 6/5-6/5-6/5-[[15/13]],

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]].

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

* 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,

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

[[Category:13-odd-limit]]

[[Category:Essentially tempered chords]]

[[Category:Triad]]

[[Category:Tetrad]]

[[Category:Hexad]]

[[Category:Marveltwin]]

~~[[Category:Triad]]~~

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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}}.
+A '''marveltwin chord''' is a [[13-odd-limit]] [[essentially tempered dyadic chord]] tempered by [[325/324]], the marveltwin comma.
-[[Category:13-limit]]
+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,
+* 1-6/5-13/9-[[26/15]] with steps 6/5-6/5-6/5-[[15/13]],
+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]].
+The marveltwin tonestack is a hexad where each interval belongs to the 13-odd-limit consonance set:
+* 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,
+Equal temperaments with marveltwin triads include {{EDOs| 19, 26, 34, 41, 46, 53, 72, 87, 121, 140, 159, 193, 212, 246, 299 and 333 }}.
+[[Category:13-odd-limit]]
+[[Category:Essentially tempered chords]]
+[[Category:Triad]]
+[[Category:Tetrad]]
+[[Category:Hexad]]
 [[Category:Marveltwin]]
-[[Category:Triad]]