Marvel chords: Difference between revisions

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'''Marvel chords''' are [[essentially tempered dyadic chord]]s tempered by the marvel comma, [[225/224]]. The '''marvel triad''', aka '''marvel augmented triad''', or '''septimal augmented triad''', is a marvel chord which in close position consists of two major thirds of approximately [[5/4]] and a supermajor third of approximately [[9/7]], or in other words a 5/4-5/4-9/7 chord, which closes at the octave since the [[marvel comma]], 225/224, is tempered out. In [[meantone]] this [[triad]] consists of two major thirds and a diminished fourth, the classic augmented triad of the meantone era. It can also be described as a marvel-tempered version of a 1-5/4-[[14/9]] chord.

'''Marvel chords''' are [[essentially tempered dyadic chord]]s tempered by the marvel comma, [[225/224]].

~~There are three~~ [[9-~~odd~~-~~limit~~]] marvel ~~triads:~~

The '''marvel triad''', aka '''marvel augmented triad''', or '''septimal augmented triad''', is a marvel chord which in close position consists of two major thirds of approximately [[5/4]] and a supermajor third of approximately [[9/7]], or in other words a 5/4-5/4-9/7 chord, which closes at the octave since the [[marvel comma]], 225/224, is tempered out. In [[meantone]] this [[triad]] consists of two major thirds and a diminished fourth, the classic augmented triad of the meantone era. It can also be described as a marvel-tempered version of a 1-5/4-[[14/9]] chord.

The [[9-odd-limit]] marvel chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1b]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures. In this article, voicing with the [[perfect fifth]] is prioritized.

The three 9-odd-limit marvel triads are

* The aforementioned marvel augmented triad;

* 5/4-[[9/8]]-[[10/7]] and its ~~inversion, temperings of~~ 1-5/4-7/5 ~~and 1~~-5/4-16/9.

* 1-5/4-7/5 with steps 5/4-[[9/8]]-[[10/7]], and its inverse

* 1-9/8-7/5 with steps 9/8-5/4-10/7.

[[File:marvel.jpg|alt=marvel.jpg|thumb|Marvel triad]]

~~There are~~ six 9-odd-limit marvel [[tetrad]]s:

The six 9-odd-limit marvel [[tetrad]]s are

* 1-5/4-7/5-7/4 with steps 5/4-9/8-5/4-8/7;

* 1-9/8-5/4-7/5 with steps 9/8-10/9-9/8-10/7;

* 1-5/4-7/5-14/9 with steps 5/4-9/8-10/9-9/7, and its inverse

* 1-9/8-7/5-9/5 with steps 9/8-5/4-9/7-10/9;

* 1-9/8-7/5-7/4 with steps 9/8-5/4-5/4-8/7, and its inverse

* 1-5/4-7/5-8/5 with steps 5/4-9/8-8/7-5/4.

* 5/4-9/8-10/9-9/7 and its inversion, temperings of 1-5/4-7/5-14/9 and 1-5/4-8/5-[[16/9]];

The last four tetrads contain the marvel augmented triad.

* 5/4-9/8-[[8/7]]-5/4 and its inversion, temperings of 1-9/8-7/5-7/4 and 1-5/4-7/5-8/5;

* 5/4-9/8-5/4-8/7, the tempering of 1-5/4-7/5-7/4;

* 9/8-10/9-9/8-10/7, the tempering of 1-9/8-5/4-7/5.

The ~~first~~ four tetrads contain the marvel augmented triad.

~~There are~~ two 9-odd-limit marvel [[pentad]]s:

The two 9-odd-limit marvel [[pentad]]s are:

* 9/8-10/9-9/8-5/4-8/7 and its inverse~~, which are the temperings of~~ 1-9/8-5/4-7/5-7/~~4 and 1-~~9/8-5/4-7/5-8/5.

* 1-9/8-5/4-7/5-7/4 with steps 9/8-10/9-9/8-5/4-8/7, and its inverse

One notable 15-odd-limit tetrad is 1-4/3-3/2-15/8 which has as its homonym 1-9/8-7/5-3/2.

* 1-9/8-5/4-7/5-8/5 with steps 9/8-10/9-9/8-8/7-5/4.

If we allow the [[15-odd-limit]], there are many more possibilities. One notable 15-odd-limit tetrad is 1-4/3-3/2-15/8 which has as its homonym 1-9/8-7/5-3/2.

Equal temperaments with marvel chords include {{EDOs| 19, 22, 31, 41, 43, 50, 53, 72, 84, 94, 103, 166 and 197 }}.

== See also ==

* [[Battaglia chord]]

* [[Undecimal marvel chords]]

[[Category:9-odd-limit]]

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-'''Marvel chords''' are [[essentially tempered dyadic chord]]s tempered by the marvel comma, [[225/224]]. The '''marvel triad''', aka '''marvel augmented triad''', or '''septimal augmented triad''', is a marvel chord which in close position consists of two major thirds of approximately [[5/4]] and a supermajor third of approximately [[9/7]], or in other words a 5/4-5/4-9/7 chord, which closes at the octave since the [[marvel comma]], 225/224, is tempered out. In [[meantone]] this [[triad]] consists of two major thirds and a diminished fourth, the classic augmented triad of the meantone era. It can also be described as a marvel-tempered version of a 1-5/4-[[14/9]] chord.
+'''Marvel chords''' are [[essentially tempered dyadic chord]]s tempered by the marvel comma, [[225/224]].
-There are three [[9-odd-limit]] marvel triads:
+The '''marvel triad''', aka '''marvel augmented triad''', or '''septimal augmented triad''', is a marvel chord which in close position consists of two major thirds of approximately [[5/4]] and a supermajor third of approximately [[9/7]], or in other words a 5/4-5/4-9/7 chord, which closes at the octave since the [[marvel comma]], 225/224, is tempered out. In [[meantone]] this [[triad]] consists of two major thirds and a diminished fourth, the classic augmented triad of the meantone era. It can also be described as a marvel-tempered version of a 1-5/4-[[14/9]] chord.
+The [[9-odd-limit]] marvel chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1b]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures. In this article, voicing with the [[perfect fifth]] is prioritized.
+The three 9-odd-limit marvel triads are
 * The aforementioned marvel augmented triad;
-* 5/4-[[9/8]]-[[10/7]] and its inversion, temperings of 1-5/4-7/5 and 1-5/4-16/9.
+* 1-5/4-7/5 with steps 5/4-[[9/8]]-[[10/7]], and its inverse
+* 1-9/8-7/5 with steps 9/8-5/4-10/7.
 [[File:marvel.jpg|alt=marvel.jpg|thumb|Marvel triad]]
-There are six 9-odd-limit marvel [[tetrad]]s:
+The six 9-odd-limit marvel [[tetrad]]s are
+* 1-5/4-7/5-7/4 with steps 5/4-9/8-5/4-8/7;
+* 1-9/8-5/4-7/5 with steps 9/8-10/9-9/8-10/7;
+* 1-5/4-7/5-14/9 with steps 5/4-9/8-10/9-9/7, and its inverse
+* 1-9/8-7/5-9/5 with steps 9/8-5/4-9/7-10/9;
+* 1-9/8-7/5-7/4 with steps 9/8-5/4-5/4-8/7, and its inverse
+* 1-5/4-7/5-8/5 with steps 5/4-9/8-8/7-5/4.
-* 5/4-9/8-10/9-9/7 and its inversion, temperings of 1-5/4-7/5-14/9 and 1-5/4-8/5-[[16/9]];
+The last four tetrads contain the marvel augmented triad.
-* 5/4-9/8-[[8/7]]-5/4 and its inversion, temperings of 1-9/8-7/5-7/4 and 1-5/4-7/5-8/5;
-* 5/4-9/8-5/4-8/7, the tempering of 1-5/4-7/5-7/4;
-* 9/8-10/9-9/8-10/7, the tempering of 1-9/8-5/4-7/5.
-The first four tetrads contain the marvel augmented triad.
-There are two 9-odd-limit marvel [[pentad]]s:
+The two 9-odd-limit marvel [[pentad]]s are:
-* 9/8-10/9-9/8-5/4-8/7 and its inverse, which are the temperings of 1-9/8-5/4-7/5-7/4 and 1-9/8-5/4-7/5-8/5.
+* 1-9/8-5/4-7/5-7/4 with steps 9/8-10/9-9/8-5/4-8/7, and its inverse
-One notable 15-odd-limit tetrad is 1-4/3-3/2-15/8 which has as its homonym 1-9/8-7/5-3/2.
+* 1-9/8-5/4-7/5-8/5 with steps 9/8-10/9-9/8-8/7-5/4.
+If we allow the [[15-odd-limit]], there are many more possibilities. One notable 15-odd-limit tetrad is 1-4/3-3/2-15/8 which has as its homonym 1-9/8-7/5-3/2.
 Equal temperaments with marvel chords include {{EDOs| 19, 22, 31, 41, 43, 50, 53, 72, 84, 94, 103, 166 and 197 }}.
+== See also ==
+* [[Battaglia chord]]
+* [[Undecimal marvel chords]]
 [[Category:9-odd-limit]]