Re: Rothenberg's Efficiency and 22tET

Carl, I think I need to read Rothenberg's papers. Where did you find
them?

>P.S. I just noticed, both the pentachoral and symmetrical decatonic
scales
>are strictly proper in 22tET :~)

So they are! For those playing along at home, these are the
diatonic-like scales I propose in my paper (modes of 0 2 4 6 9 11 13 15
17 19 and 0 2 4 6 8 11 13 15 17 19, respectively). Also, the symmetrical
dodecatonic scale (0 2 4 6 8 10 11 13 15 17 19 21) is strictly proper,
but the hexachordal dodecatonic scale (0 2 4 6 8 9 11 13 15 17 19 21) is
not (it's just proper). These scales are the richest 12-tone sources of
7-limit harmony if you allow a maximum error of 17 cents. (Increasing
the maximum error won't help until you allow 27-cent errors, with which
15tET presents some candidates, but then you almost may as well allow
33-cent errors, with which 12tET allows all chords in 12
transpositions.)