Re: periodicity blocks algorithm (was: KvP please!)

It is intuitively obvious that:

----- Original Message -----
From: Paul H. Erlich <PErlich@Acadian-Asset.com>
Subject: RE: [tuning] Kees van Prooijen please!

> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
>
> Of course, but a mathematical procedure doesn't justify a musical result;
it
> has to be the other way around.
>

Actually, the two are 100% equivalent to me.

> Anyway, let me ask you this: Considering the 5-limit case for now, how do
> you know that there won't be an interval in the scale that is smaller than
a
> unison vector? Even if the unison vectors both are the smallest within the
> half-hexagonal "boundary", the parallogram defined by those vectors may
> extend beyond the boundary, and may happen to include one or more smaller
> unison vectors. (Flipping the sign of one of the unison vectors will lead
to
> a parallelogram that extends over a different part of the boundary, and
> again one or more unison vectors may lie in that region.) Isn't that so?

The unison vectors determine an equivalence relation over the lattice space.
Flipping the sign of a unison vector doesn't change the relative properties.
That's why I only searched half the hexagon. Half of the parallelogram lies
inside this hexagon. The 'faraway' triangle is equivalent with the mirror of
the 'inside' triangle in the mirror of the traversed half hexagon. So any
smaller intervals therein should have been found within the current level of
complexity (I think)

Kees