Marvel chords
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.
The 9-odd-limit marvel chords are of 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;
- 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.
The six 9-odd-limit marvel tetrads 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.
The last four tetrads contain the marvel augmented triad.
The two 9-odd-limit marvel pentads are:
- 1-9/8-5/4-7/5-7/4 with steps 9/8-10/9-9/8-5/4-8/7, and its inverse
- 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 19, 22, 31, 41, 43, 50, 53, 72, 84, 94, 103, 166 and 197.