RE: [tuning] RE: constant structure

I wrote,

>>It would appear that all MOSs are indeed CS but calling an MOS a CS would
be
>>like calling a diamond bracelet a "carbon bracelet".

Carl Lumma wrote,

>Whoa- that's not right. The diatonic scale in 12-tet is MOS but not
>CS. CS means there are no ambiguous intervals (to use Rothenberg's
>term). Which means, Dan, that when you construct a scale's interval
>matrix, that no number appears in more than one column (scale degree). The

>infamous tritone is the ambiguous interval in the 12-tet diatonic.

Right. Thanks for catching the error, Carl.

[Carl Lumma:] > Whoa- that's not right. The diatonic scale in 12-tet
is MOS but not CS. CS means there are no ambiguous intervals (to use
Rothenberg's term). Which means, Dan, that when you construct a
scale's interval matrix, that no number appears in more than one
column (scale degree). The infamous tritone is the ambiguous interval
in the 12-tet diatonic.

OK, this makes sense to me as well (and I was indeed thinking along
these lines in the three 3L & 4s examples I gave as well), but what if
the intervals in question are something like a 17/12 and a 24/17
though? Strictly proper but oh so close to not being so... is their
some agreed upon practical range to draw the line with scales that
might recognize these tiny commatic differences that would perhaps
only trivially distinguish them from being strictly proper or just
proper?

Dan

Carl!
It is possible in a CS to have intervals in one step size larger than
those found in the next largest step size. That the aug 4 =dim. 4 is not a
problem for a Constant structure. But we are really picking this bone dry :)

Carl Lumma wrote:

> From: Carl Lumma <CLUMMA@NNI.COM>
>
> >Whoa- that's not right. The diatonic scale in 12-tet is MOS but not
> CS. CS >means there are no ambiguous intervals (to use Rothenberg's term).
>
> I think that only MOS's with A/B = 1/2 (or 2/1) are non-CS (where A and B
> are the two types of 2nds). Like the 12-tet diatonic or my decatonic chain
> of 5/4's in 13-tet.
>
> -Carl
>
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Carl Lumma wrote,
>I think that only MOS's with A/B = 1/2 (or 2/1) are non-CS (where A and B

>are the two types of 2nds). Like the 12-tet diatonic or my decatonic chain

>of 5/4's in 13-tet.

Fascinating if true . . .

Kraig Grady wrote,

>Carl!
>It is possible in a CS to have intervals in one step size larger than those
found in the next largest step >size.

That doesn't contradict anything Carl or I have said. We said propriety
implies CS, not CS implies propriety.

Dan, much as with consistency, propriety does involve a very sharp boundary,
and crossing that boundary by a very small amount, while possibly having no
audible effect, can amount to a change from a strictly proper scale to a
proper one to an improper one. I was once bothered by the fact that the
Pythagorean diatonic scale was improper, but it turns out that Rothenberg
believed that as long as the worst impropriety (in this case, a Pythagorean
comma) was to small to be perceived (since you're comparing B-f with f-b in
this case, it would be hard to perceive the difference), the scale is
essentially perceived as proper. Carl, am I representing Rothenberg
correctly here?