RE: constant structure

>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".

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.

As Paul stated earlier, all strictly proper scales are CS, since they, by definition, have no ambiguous intervals.

-Carl

>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

> 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.

No, a simple counterexample is 1 1 1 3.

Manuel Op de Coul coul@ezh.nl

>>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 . . .

That one is by Chalmers.

-C.

>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 :)

You may be confusing "ambiguous" intervals with "contradictory" ones. A contradictory interval is when one degree is larger than the next higher degree, as you say. An ambiguous interval is _the same_ size as another degree. CS rules out ambiguous intervals by definition.

Your point, that CS does not rule out contradictory intervals, was quite surprising to me when Paul Erlich pointed it out on this list last summer.

-Carl