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Re: [tuning] Re: monzo as vector?

🔗Carl Lumma <ekin@lumma.org>

8/15/2004 10:18:18 PM

>> The o-limit Hahn-style n-tuples have a 1:1 mapping with all
>> pairs of points in the o-limit lattice.
>
>Not hardly. What are these pairs of points?

Whoops, I went back to lattice there. For this purpose, all
I need is a graph. But I don't know a notation for graphs.

Perhaps you're worried that the odd-limit isn't a group.
I know I am. Let's see:

>1. Closure: If A and B are two elements in G, then the product
>AB is also in G.

Note that "product" is being used in the abstract here -- it isn't
necessarily multiplication as we know it.

It is multiplication in this case, though. And sadly, unlike
prime limit, multiplying two elements of an odd-limit can quickly
get you outside of the set. For example 3 * 5 = 15, which is
outside the 5-odd-limit. Therefore, it doesn't look like the
odd-limit is a group.

However, if we could somehow include log weighting in our
operator, then we might regain closure...

-Carl