Marvel chords

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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.
Marvel triad

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 19, 22, 31, 41, 43, 50, 53, 72, 84, 94, 103, 166 and 197.