Re: [tuning] Digest Number 592

Shaun Van Ault wrote,
> (e.g. what all those nifty ascii pictures with all the dotted lines
mean).

Though I think Paul Erlich's lattice post should definitely cover what
it is that your looking for, I thought that I'd also add this excerpt
from an email I recently sent to someone else off-list, as it shows
some of the ways I've been recently experimenting here at the TD with
plotting higher primes in the two-dimensional ASCII format.

If you were to write the bimodal "triad" as C3-G3-E4-Eb6 and as a
series identity without octave reduction, you would have a 4:6:10:19,
i.e., a:

1/1 3/2 5/2 19/4

But the lattice assumes octave reduction, so the 16:19:20:24 harmonic
series identity that I had used was just culled from a:

16:17:(18):19:20:(21):22:23:24:(25):26:(27):28:29:(30):31:32

5/
/ \
19/ \
/ \
/ \11
/ 7, \
17/ 29, ` \23
/ , `13\
2/31, ` \3

prime template which attempts to collapse and plot higher primes (like
19) onto a two-dimensional, ASCII format.

So the whole 16 - 32 harmonic series segment from which I pulled the
16:19:20:24 interpretation of the bimodal "triad" would look something
like this:

25
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
5----------------15
/ \ / \
19 \ / \
/ \ / \
/ 11 / \
/ 7----\-------/----21 \
17 30' `. 23 / ,' `. \
/ ,' 13 \ / ,' `. \
/31' `. \ / ,' `.\
1-----------------3-----------------9---------------27

With inversional symmetry, this would mean that a series segment
reduced to primes would collapse into an overtonal identity as say
h...2h, and an undertonal identity as 2h...h (where h is a harmonic
series power of two). Or to put it another way, an 8 - 16 series would
map:

O = 8:(9):10:11:12:13:14:(15):16

and

U = 16:(15):14:13:12:11:10:(9):8

onto the collapsed O and U 4:5:6 "triangles" (assuming h is =/> 2^2)
as only the reducible primes of h...2h and 2h...h:

5/4
/ \
/ \
/ \
/ \
/ \
/ 11/8
/ \
/ , 7/4 . \
/ ,' `. \
/ ,' 13/8 \
/ ,' `. \
4/3---------------------1/1---------------------3/2
\ `. ,'/
\ 16/13 ,' /
\ `. ,' /
\ ` 8/7 ' /
\ /
16/11 /
\ /
\ /
\ /
\ /
\ /
8/5

Dan Stearns