Eight tones was your last message? So the =x is the number of connected permutations for each set of superparticulars? More with eight tones than with 1-7 or 9, 10, 12, 15!?

--- In tuning-math@y..., "clumma" <carl@l...> wrote:

> > (25/24)^2(16/15)(6/5)^3 = 2 > > (81/80)(10/9)^3(6/5)^2 = 2 > > Not quite following this post, Gene...

The only 5-limit superparticulars are 2/1,3/2,4/3,5/4,6/5,9/8,10/9, 16/15,25/24 and 81/80. I took these three at a time, and calculated whether or not they lead to a partition of the octave, and if so, how many of each tone were required. So, for intance, 2 25/24's one 16/15 and three 6/5 make up an octave, and by arraging them in various ways give us six-tone scales.

> > Seven tones: > > > > (16/15)^2(10/9)^2(9/8)^3

> Eight tones was your last message?

Seven tones--the same steps as above, which it seems is the only seven-tone possibility.

>>> Seven tones: >>> >>> (16/15)^2(10/9)^2(9/8)^3 >> >> Eight tones was your last message? > > Seven tones--the same steps as above, which it seems is the only > seven-tone possibility.

Right, they all =2, means they sum to an octave, duh. So you only checked for connectednes in the 7-tone case. Got it, thanks.