Semisixths

As a 5-limit temperament, semisixths is defined by the semisixths
comma, or medium semicomma, of 78732/78125. This gives a decent
5-limit temperament, but the generator makes a sharp 9/7 and so we are
immediately led onwards to the 7-limit. Here we have two commas,
126/125 and 245/243. Two generators now get us to a 5/3, and so we
have a 9/7-9/7-6/5 magic triad as a ubiquituous semisixths chord,
based on (5/3)/(9/7)^2 = 245/243. Of course as usual 126/125 gives us
6/5-6/5-6/5-7/6 diminished seventh chords as a natural part of the system.

We get a decent 11-limit system by adding 176/175 as a comma, but this
gets us up to a Graham complexity of 31; in the 7-limit the Graham
complexity is 13, and in the 9-limit 14, so Semisixths[19] is
plentifully supplied with tetrads.

The 7-limit tetrads, of course, project down to a one-dimensional
system; in the case of semisixths the generator is [1, -1, -1]; this
corresponds to the 7/6-35/24-5/3-35/18 chord. Organzing the tetrads by
the generator is a useful start towards organizing your understanding
of the harmony of a 7-limit linear temperaments in my experience.