lattices vs./pro st ;) :) <:) :(

me:
> > I guess this is obvious.
> >
> > Question: What about latticing non-triads in JI?
> > 1) is there a point? (i.e. the whole point of JI seems
> > to be to be able to have vertical sonorities that are
> > otonal/utonal, preferably lower on the series).
>

Joe Pehrson:
>
>Hasn't a lot of the latticing been TETRADIC in nature, using the 7th
>partial as the THIRD dimension, going off the page??
>
>Or, am I misunderstanding something....
>

Actually, I should have said, instead of triads, any sonorities using
immediate combinations of the lower overtonal collections. I.e. derived
out of 1 3 5 7 9 or combinations of these.

It seems that initially, the point of JI is to get perfectly in tune
triads (or 1 3 5 7 tetrads, or 1 3 5 7 9 pentads, or 1 3 5 7 9 11 hexads).
Overtone segments.

With set theory, the idea is you could make a piece out of any collection,
using is as an Ur-scale, or chord or sonority. So I Was wondering about
the same thing in JI.

I did think of one example: A year ago or so, Dan Stearns posted about
doing a 1-b3-#3-5 (that's in diatonic scale degree notation) tetrads,
getting it to happen with JI lattices.

i.e.
15/8
/ \
7/4 / \
| / \
`3/2-----9/8

( eg G-A#-B-D )

or something.

Another idea might be basing a piece on

7/4
/
/
7/5
5/4_-
/
/
1/1

(C-E-F#-A#)

(Did I "lattice" that correctly? That would ROCK MY WORLD!!) :)

Neither are immediately derivable directly from the overtone series.
(i.e. some of the fractions aren't divisible by 2). (well, the first is,
but you have to go higher than 13 . .)

This is the kind of thing I'm talking about.

But I guess CPS's do get at this sort of thing.

***From: Christopher Bailey******************

http://music.columbia.edu/~chris

**********************************************

--- In tuning@y..., Christopher
Bailey <cb202@c...> wrote:

> This is the kind of thing I'm talking about.

It's very similar to what I'm
getting at with Joseph Pehrson.
I've shown him two things in
Blackjack so far: how to find the
7-limit tetrads in the lattice, and
how to find many more different
kinds of chords on the keyboard. I
was planning to proceed by
showing Joseph what shapes a
lot of the other chords make on
the lattice, introducing Graham
Breed's lattice (perhaps) when
dealing with 11-limit sonorities.

>
> But I guess CPS's do get at this sort of thing.

Or just about any other sizable
chunk of the lattice, whether
finite as in JI, or infinite as in a
temperament.