RE: RE: JI pentatonic, "diatonic", and decatonic scales as periodicity blocks

>You bet! Of course any chain-of-fifths tuning can be viewed as a
>periodicity block whose unison vector is the chromatic interval, not just
>the pentatonic scale, and not just the MOS's.

Hmm . . . a 6-note chain of fifths has the tritone as unison vector, and I
would hardly call a tritone a single chromatic step . . .

>>In the 5-limit diatonic case, 81:80 is already assumed as a unison vector,
>>and the chromatic interval by which one note moves when modulating by a
>>ratio of 3 is 25:24.

>Hmmm. What are you transposing by 3:2 to get one 25:24 move? When I
>traspose the first major lattice you give up a 3:2, I get...

>27/16 - 5/3 = 81/80
>45/32 - 4/3 = 135/128

I already said 81:80 is assumed as a unison vector. So 27/16 "=" 5/3, and
135:128 "=" 25:24. I use 25:24 instead of 135:128 to construct the
periodicity block since one of Kees' special blocks (the first one with 7
notes, in fact) has UVs 81:80 and 25:24. Curiously, if we did construct it
using 81:80 and 135:128, we would get a Pythagorean diatonic scale! (This is
easy to see -- the diagonals of the periodicity block are the sum and
difference of the unison vectors -- in this case (7 0) and (1 2).)

Oops -- that's (7 0) and (1 -2).

Which means that the following can also come out as periodicity blocks with
UVs 81:80 and 135:128:

B
/ \
/ \
/ \
F-------C-------G-------D-------A-------E

and

C-------G-------D-------A-------E-------B
\ /
\ /
\ /
F