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]]. 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. | ||
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]] | [[File:marvel.jpg|alt=marvel.jpg|thumb|Marvel triad]] | ||
There are | 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]]; | * 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; | * 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. | * 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 | 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. | * 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. | |||
Equal temperaments with marvel chords include [[19edo]], [[22edo]], [[31edo]], [[41edo]], [[43edo]], [[50edo]], [[53edo]], [[72edo]], [[84edo]], [[94edo]], [[103edo]], [[166edo]] and [[197edo]]. | Equal temperaments with marvel chords include [[19edo]], [[22edo]], [[31edo]], [[41edo]], [[43edo]], [[50edo]], [[53edo]], [[72edo]], [[84edo]], [[94edo]], [[103edo]], [[166edo]] and [[197edo]]. | ||
Revision as of 08:40, 21 September 2021
Marvel chords are essentially tempered dyadic chords 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.
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.
There are six 9-odd-limit marvel tetrads:
- 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;
- 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 pentads:
- 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.
Equal temperaments with marvel chords include 19edo, 22edo, 31edo, 41edo, 43edo, 50edo, 53edo, 72edo, 84edo, 94edo, 103edo, 166edo and 197edo.