The basic consonant meantone tetrads

There are 120 basic tetrads; below I give the consonant ones. The
initial numbers gives the order in base two ordering.

7-limit tetrads

69: [0, 3, 6, 9] diminished seventh
88: [0, 1, 4, 10] otonal tetrad = German sixth
118: [0, 6, 9, 10] utonal tetrad = Tristan chord

9-limit tetrads

1: [0, 1, 2, 3]
2: [0, 1, 2, 4]
3: [0, 1, 3, 4]
4: [0, 2, 3, 4]
13: [0, 2, 3, 6]
15: [0, 2, 4, 6]
16: [0, 3, 4, 6]
40: [0, 2, 4, 8]
47: [0, 2, 6, 8]
49: [0, 4, 6, 8]
58: [0, 1, 3, 9]
83: [0, 6, 8, 9]
85: [0, 1, 2, 10]
89: [0, 2, 4, 10]
96: [0, 2, 6, 10]
98: [0, 4, 6, 10]
107: [0, 2, 8, 10]
109: [0, 4, 8, 10]
111: [0, 6, 8, 10]
113: [0, 1, 9, 10]
120: [0, 8, 9, 10]

--- In tuning-math@yahoogroups.com, "Gene Ward Smith"
<genewardsmith@...> wrote:

Here are the strictly proper (considered as scales) chords in 31-et
tuning out of these.

> 7-limit tetrads
>
> 69: [0, 3, 6, 9] diminished seventh
> 88: [0, 1, 4, 10] otonal tetrad = German sixth
> 118: [0, 6, 9, 10] utonal tetrad = Tristan chord

All strictly proper.

> 9-limit tetrads

> 3: [0, 1, 3, 4] added sixth
> 13: [0, 2, 3, 6] dominant seventh
> 16: [0, 3, 4, 6]
> 47: [0, 2, 6, 8]
> 58: [0, 1, 3, 9]
> 83: [0, 6, 8, 9]
> 96: [0, 2, 6, 10]
> 98: [0, 4, 6, 10]
> 109: [0, 4, 8, 10]
> 113: [0, 1, 9, 10]