> Thanks Carl. But the above definition means that I can make an
> infinitesimal change to the generator (in either direction) and the
> scale suddenly becomes CS. Not a very useful scale property. Or not
> a very useful definition of it.

Hate to say it Dave, but I don't think CS is that useful a property
anyway. Or, maybe I should say, I can almost hear Wilson crying
out, 'Of course! It's only a guide, an idea. Why would you expect
it to be so precise?'.

> Anyone want to propose a better definition? One that doesn't have
> this defect.

A treatment along the lines of what I did for propriety and
stability would be one approach. But by that time, I'd just be
using those measures anyway.

Now, Erlich's consonant constant structures I can live with.
One could imagine...

1. Listing the target consonances. Say, for easy of what follows,
there is only one target consonance.

2. In h.e. fashion, find for each interval in the scale the
probability it will be heard as the target interval.

3. Sum these probabilities for each scale degree.

4. Subtract from the largest sum all the other sums. Or maybe
take the difference between the two largest sums. Or maybe the
difference between the largest sum and the mean sum. Or something
like that.

...hmmm... if one insisted on normal CS and not consonant CS (CCS?),
he might use the statistical approach above, but include all the
intervals in the scale in #1, and use all the intervals instead
of a farey series in #2 (and midpoints between these instead of
mediants).

-Carl