my JI/ET lattices

Kami Rousseau asked me a question privately
about my ideas on combining ET and JI on the
same lattice, and I wrote him an explanation
that I thought worth sending here:

-------------------------

[I wrote:]
>> amalgamating ET with JI.

[Kami Rousseau wrote:]
> Do you mean like (-1,1) - (7/12) = 7/12(-12,19),
> a just fifth minus a tempered fifth = a fraction of
> a pythagorean comma?

What I'm really saying is something like this:

My lattices are not 'octave'-reduced, so that
3^1 is not 3/2, but rather 3/1.

But generally, for theoretical purposes *and*
for composing music, I think of it as 'octave'-reduced,
so that 3^1 *does* represent 3/2 in a generic sense,
as a pitch-class.

If this is how the lattice model is working, then
I thought it would be easy to incorporate a sense
of ET structure, because all the ratios *and* all
the ET degrees can be represented as fractional
exponents along any prime axis. So actually:

3/2 = 3^~.3690703

2^(7/12) = 3^~.3680424

and so forth for all the other prime vectors.

- monzo

|\=/|.-"""-. Joseph L. Monzo....................monz@juno.com
/6 6\ \ http://www.ixpres.com/interval/monzo/homepage.html
=\_Y_/= (_ ;\
_U//_/-/__/// |"...I had broken thru the lattice barrier..."|
/monz\ ((jgs; | - Erv Wilson |

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