On Thu, Nov 17, 2011 at 8:18 PM, genewardsmith
> --- In firstname.lastname@example.org, Mike Battaglia <battaglia01@...> wrote:
> > How can I talk about one dimensional lattices and convex sets without using
> > the language of one dimensional lattices and convex sets?
> You are just talking about a generator chain, so why not call it that?
How do I define a generator "up" vs "down" then? Do I just say in the
positive direction on the chain? What's "positive?"
How about this:
1) Let M be an MOS.
2) Let g be the generator for that MOS which, when iterated in the
positive direction, eventually passes through the chroma L-s, which
means it also eventually passes through L.
3) Pick a point along the chain, one which doesn't necessarily have to
be in the scale, and call it the "root" or "tonic."
4) Let n be the number of generators required to go down from the
tonic to get to the negative-most point in the block,
and let p be the number of generators required to go up from the tonic
to get to the positive-most point in the block.
5) Let P be the number of periods per equivalence interval.
6) Let U = p*P, D = -n*P.
7) The UDP notation for the mode is U|D(P).
So here we get
Root C, C lydian 6|0
Root C, C dorian 3|3
Root C, C locrian 0|6
Root C, C# locrian 7|-1
Root C, B lydian -1|7
Myna with the root picked to be a "4" for one of the 5:6:7's in the
scale - 10|-4
> > Can you be as precise in your criticisms of my definition as you'd like me
> > to be in the actual definition?
> I could write a revised version, and then restore your version and you could have a look at it if you like.