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.

~~Another~~ marvel ~~essentially tempered~~ triad ~~is the~~ 5/4-[[9/8]]-[[10/7]] ~~chord~~ and its inversion, ~~which means the marvel tempering~~ of 1-5/4-7/5 and 1-10/7-~~[[8~~/~~5]]~~.

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

* 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.

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

There are ~~also~~ marvel [[tetrad]]s:

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

* 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]];

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* 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 ~~also~~ two marvel [[pentad]]s:

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

* 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.

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.

~~The [[9~~-odd-limit~~]] marvel chords number triads:~~ 3~~, tetrads: 6, pentads:~~ 2~~, for a total of 11~~.

Equal temperaments with marvel chords include [[19edo]], [[22edo]], [[31edo]], [[41edo]], [[43edo]], [[50edo]], [[53edo]], [[72edo]], [[84edo]], [[94edo]], [[103edo]], [[166edo]] and [[197edo]].

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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.
-Another marvel essentially tempered triad is the 5/4-[[9/8]]-[[10/7]] chord and its inversion, which means the marvel tempering of 1-5/4-7/5 and 1-10/7-[[8/5]].
+There are three [[9-odd-limit]] marvel triads:
+* 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.
 [[File:marvel.jpg|alt=marvel.jpg|thumb|Marvel triad]]
-There are also marvel [[tetrad]]s:
+There are six 9-odd-limit marvel [[tetrad]]s:
 * 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]];
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 * 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 also two marvel [[pentad]]s:
+There are two 9-odd-limit marvel [[pentad]]s:
 * 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.
+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.
-The [[9-odd-limit]] marvel chords number triads: 3, tetrads: 6, pentads: 2, for a total of 11.
 Equal temperaments with marvel chords include [[19edo]], [[22edo]], [[31edo]], [[41edo]], [[43edo]], [[50edo]], [[53edo]], [[72edo]], [[84edo]], [[94edo]], [[103edo]], [[166edo]] and [[197edo]].