Preliminary Studies in the Virtual Pitch Continuum

[Paul Erlich:]
>Hence 72-tET-based notation is an excellent notation for Partch's
music. 144-tET, by contrast, is not consistent at all in the 11-limit

[Joe Monzo:]
>Well, we've been thru *that* before... I'm not going to go
there, except to say that in some circumstances the greater
pitch discrimination provided by 144-tET, with only one
extra symbol as Dan Stearns and I use it, [see TD 144.16]
http://www.onelist.com/messages/tuning?archive=144
is useful, even if it's not consistent.

Though I think Paul is just referencing the Partch lattice Joe made in
144-tET (in which case I can't exactly disagree), I will say that I
came up with the 144e symbols as a *notational* aid only -- with the
hope that the performer who could tame the 72 notation, as I had
learned it from Joe Maneri's book (Maneri, Joseph Gabriel Esther and
Scott Van Duyne, _Preliminary Studies in the Virtual Pitch Continuum_,
Accentuate Music, Plainview NY, 1986) could at least approximate *and
readily understand* what the crosshatch modifiers were indicating --
and as such I don't think it's quite fair to rigidly hold it up to the
measure of it's consistency. And as I've tried to point out before, in
at least some cases, consistency seems a much better theoretical
measure than it does an actual musical one (where naturally
occurring -- and often times substantial -- errors are the norm):

"...if the slight altering of ETs with low consistency levels (the 14
to 13.95-tET example for instance, which for all intents and purposes
14-tET) result in a very different consistency measure, shouldn't that
taken into account? An even better example than 14-tET - though
working in the opposite direction (i.e., from a higher consistency to
lower consistency), would be something like ~26.03-tET... where the
largest cents deviation from 26-tET is a practically nonexistent ~1�,
and yet the consistency falls from an integer limit of 14 down to one
of 8..."

[Joe:]
> I really don't want to argue this point, but there are cases (my _A
Noiseless Patient Spider_ was one of them)where 72-tET just doesn't
provide enough accuracy to portray what's happening, and 144-tET does.
Once you get used to working with it, you learn how to accomodate the
inconsistencies.

Or as 72 is obviously a subset of 144, I don't see why you couldn't
use the consistent mappings of 72 theoretically (for lattice
representations, note naming and the like) and the crosshatch much
like a quarter or eighth tone symbol in standard notation: as an
indicator to get between one place and another...

[Joe:]
>But as a *general* rule, I'll agree that 72-tET works much better.

I think one of the best things that it has going for it is that there
seems to be a pretty sizeable 'school of 72e' up and running
already... though this view/opinion may be distorted by my location,
i.e., the fact that both Simms and Maneri are in the Boston area.

Dan