Microtonal barbershop

Given that the "barbershop chord", as in "Play That Barbershop Chord",
is an otonal tetrad, and given that commatic adjustments are a part of
the style, it would seem barbershop is already microtonal. However,
the chord relations are based on the chain of fifths, whereas the
native chord relations of 7-limit music involves the whole 7-limit
diamond. (I also wonder incidentally if 6:7:9:10 gets much play in
barbershop.)

If take an otonal tetrad, and look at all the otonal tetrads which, up
to octave equivalence, share a note with it, we get twelve chords.
These define twenty-eight notes, with thirteen otonal tetrads and ten
utonal tetrads, which I think would be a nice addition to the Scala
directory. It would be very interesting to see if a barbershop quartet
could be induced to sing music in a scale such as this, and it would
also be interesting to know how easily they could learn some such
notation as Sagittal for that purpose. I could certainly write such
music, if someone wanted to try singing it.

! notchedcube.scl
Otonal tetrads sharing a note with the root tetrad, a notched chord cube
28
!
49/48
25/24
21/20
15/14
35/32
9/8
8/7
7/6
6/5
49/40
5/4
9/7
21/16
4/3
7/5
10/7
35/24
3/2
49/32
25/16
8/5
5/3
12/7
7/4
25/14
9/5
15/8
2