lattice applet/ finity

[Erlich:]
> but it seems you are using 'finity' in a sense quite
> inconsistent with your own definition of the term.
> At least I thought I had a grasp on your conception of
> finity when we were discussing the Fokker stuff.
> Since diamonds don't tesselate to fill ratio
> space, this use of the word seems quite incorrect.

What you say about Partch's diamonds is true.

But when we were talking about finity in connection
with Fokker it was in the specific sense of the
'periodicity blocks' he postulated. I was merely
drawing a parallel between my theories and Fokkers
in wanting to understand his, because up until February
I was largely ignorant of his work.

Daniel Wolf has suggested that my use of 'finity' is
redundant because we have Fokker's term. But I like
'finity' precisely because I think it can be used more
inclusively than just meaning the same thing as a
'periodicity block'. I feel that it can also be used
to describe the kind of arbitrary limitation on expansion
of musical resources that Partch 'invented', too.

I don't think I'm being inconsistent, I just think
'finity' can mean both types of reduction from infinity,
and probably others too.

Often, when Partch and other JI composers use
higher-identity triads in their compositions, the
triads function in ways analogous to the way
'major' and 'minor' triads function, a good example
being the 6:7:9. This is an implicit use of 'bridging',
even if the 'bridge' interval or 'unison vector' is
not as small as the ones I normally refer to in my
discussions.

I've also discussed Schoenberg in connection with
finity, in that he renounced microtonality and stuck
with 12-eq, even tho he wanted to be able to 'expand
tonality', because he also recognized 'bridges' (the
ones roundly criticized by Partch). They're *far*
larger than any intervals I would grace with the term,
but in his mind and his theories, that's how it worked.

I don't see any inconsistency in using 'finity' to
describe all three theories - Partch, Fokker, or
Schoenberg.

My conception of finity embraces the large idea that
there's an infinity of pitch-resources available to
musicians and no way that we can include infinity in
our actual working set, so we have to find ways to
make a finite set do the job.

And once you learn that there's more to music than
12-eq, you've got some work ahead of you to figure out
how you're going to impose finity, because the possiblities
are literally endless. Partch's method was just one good way.

-monzo

Joseph L. Monzo....................monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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