re: The CPS Blues [combination product sets]

>Carl, look at (and feel free to criticize) the definitions in the
>Tuning Dictionary. So the difference is that chords like 10:12:15:18
>are saturated at the 9-limit but not a complete 9-limit otonality or
>utonality.

The definitions are good. Yes, I understand the difference between
complete and saturated in general, and I conclude that the meaning of
the two terms is essentially the same within the context of my post.

In CPS land, the initial factor set can be anything -- consecutive odd
numbers are only one option. Whatever it is, the "complete" chords of
a CPS will be saturated, the "basic" un-saturated, with respect to it,
by definition.

-Carl

--- In tuning@egroups.com, Carl Lumma <CLUMMA@N...> wrote:
> >Carl, look at (and feel free to criticize) the definitions in the
> >Tuning Dictionary. So the difference is that chords like
10:12:15:18
> >are saturated at the 9-limit but not a complete 9-limit otonality
or
> >utonality.
>
> The definitions are good. Yes, I understand the difference between
> complete and saturated in general, and I conclude that the meaning
of
> the two terms is essentially the same within the context of my post.
>
> In CPS land, the initial factor set can be anything -- consecutive
odd
> numbers are only one option. Whatever it is, the "complete" chords
of
> a CPS will be saturated, the "basic" un-saturated, with respect to
it,
> by definition.

Well I was thinking of the case where the factors are consecutive odd
numbers beginning with 1, in which case "completing all the
incomplete chords" is a less ambiguous description of stellation
than "saturating all the unsaturated chords". But if the factors are
not consecutive odds beginning with 1, then you're not really doing
either according to the definitions in the Tuning Dictionary. But by
analogy, I'd still rather say you're completing the chords with
respect to the initial factor set, rather than saturating the chords
with respect to the initial factor set.