Marveltwin chords: Difference between revisions

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

A '''marveltwin chord''' is a [[13-odd-limit]] [[essentially tempered dyadic chord]] 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,

* 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 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,

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as well as one built by

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

* 1-[[5/4]]-18/13, with steps 5/4-10/9-13/9, and its inverse

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

Each of these has multiple ways to extend to tetrads. For example,

* 1-[[3/2]]-[[5/3]]-[[24/13]] with steps 3/2-10/9-10/9-[[13/12]], and its inverse

* 1-3/2-13/8-9/5 with steps 3/2-13/12-10/9-10/9.

A palindrome exists as

* 1-3/2-5/3-9/5 with steps 3/2-10/9-13/12-10/9.

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

In the 15-odd-limit we may have

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

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,

* 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, its inverse being

* 1-6/5-4/3-3/2-8/5-24/13, with steps 6/5-10/9-9/8-10/9-10/9-13/12.

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

Equal temperaments with marveltwin triads include {{EDOs| 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]]

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-A '''marveltwin chord''' is a [[13-odd-limit]] [[essentially tempered dyadic chord]] tempered by [[325/324]], the marveltwin comma.
+A '''marveltwin chord''' is a [[13-odd-limit]] [[essentially tempered dyadic chord]] 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,
 * 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 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,
@@ Line 16: / Line 10: @@
 as well as one built by
-* 1-10/9-18/13, with steps 10/9-5/4-13/9
+* 1-[[5/4]]-18/13, with steps 5/4-10/9-13/9, and its inverse
+* 1-10/9-18/13, with steps 10/9-5/4-13/9.
+Each of these has multiple ways to extend to tetrads. For example,
+* 1-[[3/2]]-[[5/3]]-[[24/13]] with steps 3/2-10/9-10/9-[[13/12]], and its inverse
+* 1-3/2-13/8-9/5 with steps 3/2-13/12-10/9-10/9.
+A palindrome exists as
+* 1-3/2-5/3-9/5 with steps 3/2-10/9-13/12-10/9.
-and its inversion. Each of these has multiple ways to extend to tetrads.
+In the 15-odd-limit we may have
+* 1-6/5-13/9-[[26/15]] with steps 6/5-6/5-6/5-[[15/13]].
 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,
+* 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, its inverse being
+* 1-6/5-4/3-3/2-8/5-24/13, with steps 6/5-10/9-9/8-10/9-10/9-13/12.
-Equal temperaments with marveltwin triads include {{EDOs| 19, 26, 34, 41, 46, 53, 72, 87, 121, 140, 159, 193, 212, 246, 299 and 333 }}.
+Equal temperaments with marveltwin triads include {{EDOs| 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]]