Re: Lattice Wrap Up (Joe Monzo)

>> 49/32 isn't more complex than 25/16 because it
>> took two 7-limit rungs and 25/16 took two 5-limit ones.
>
>You really think not? 49 isn't more complex than 25?
>It isn't because 7 is more complex than 5?

49 may be more complex than 25, but I don't see what the shortest route
concept adds here. If we want to measure this type of complexity, let's
just use a limit concept, or the (arithmatic or geometric) mean of n and d.

My problem with weighted lattice metrics is that the weighting destroys the
information which I feel is most useful. If such and such interval is
binary at the 7-limit but trinary at the 5-limit in 34tET, that tells me
something. But adding some value for each rung, you don't know what's
going on.

>Inasmuch as all the different lattices and tonal systems
>we have been considering with this topic are based on
>an implicit assumption of a 1/1, they are all Monophonic
>(in the Partchian sense), and therefore *ALL* ratios
>are in one sense theoretically one rung away from 1/1.

Has Paul Erlich got a lattice metric for you!