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.
See also
- Battaglia chord – a 15-odd-limit hexad
- Undecimal marvel chords