shortest path

[Erlich:]
> Well, if you are allowed to declare an odd limit
> for consonance, it _can_ measure intervals that
> are composites of consonant intervals (using the
> lattice), it just can't measure intervals using
> higher prime numbers. But since those prime
> numbers aren't used in any consonances, then
> they're completely analogous to irrationals in
> the prime-based measures we've discussed --
> irrevocably outside the system.

Unless you mathematically include the probability
distribution range that covers the bridges.

[Erlich, another post:]
> another reason I assumed you meant primes is
> that if you meant odds, you would need an
> additional step in the algorithm where the user
> specifies the odd limit (dimensionality) of the
> lattice. That step is clearly needed to apply the
> algorithm unambiguously. As the prime-based
> complexity measures do not require this step,
> I proposed an interpretation where the dimensionality
> was infinite, and the complexity of the interval
> turns out to be just the (log of the) odd limit
> of the interval. But that makes the whole lattice
> kind of superfluous and I would definitely prefer
> a means of limiting the dimensionality . . .

Again, the bridges.

- Monzo
http://www.ixpres.com/interval/monzo/homepage.html

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