Re: so thats what I'm doing...

Thanks for the answers Paul.

>
> Anyway, my decatonic system has a form of transposability, only slightly
> more complex than "transpoability" as you've defined it. This is evident
> from a table of decatonic key signatures. To see a correct version of that,
> you may order my paper _The Forms of Tonality_ from Bill Alves.

I want it, shouldn't this and other papers from the Microfest go online
somewhere?

>
> >2) Is this orderring, "maximally even"?
>
> baa baa baaa
>
> might be maximally even depending on what b and a are. If b and a are 1 and
> 2 or 2 and 1, yes. If b and a are 1 and 3 or 3 and 1, no. Maximal evenness
> is only defined with respect to the cardinality of the "chromatic set".
> Another reason I don't like maximal evenness -- why should you have to
> postulate a chromatic set in a musical style which doesn't make use of one?

Okay, I was thinking of it in terms of the set of "3 b's and 7 a's" rather
than the numeric values.

>
> >Is this tuning "proper"? I would say no becuase the
> >largest third (333) is larger than the smallest
> >fourth (1331). Is there a special word fo improper
> >but unique?
>
> You mean there's only one impropriety? Like the Pythagorean diatonic?
>

Here's what I was asking, demonstrated with three pentatonics.

chroma seconds thirds fourths
43343 4,3 7,6 10,11 14,13
42242 4,2 6,4 8,10 12,10
41141 4,1 5,2 6,9 10,7

As I understand propriety, tuning one has it by having all
"all thirds bigger than all seconds" etc.

Tuning three certainly doesn't have this property, BUT, all
intervals are unique. So "7", despite being a "fourth" between
the two flavors of "third" is still uniquely a fourth. (This
is the special word I was looking for).

Tuning two is ordered but non-unique, "all thirds are greater
than or equal to all seconds". If this is not proper then the
12tet diatonic is improper...

Thanks for the post regarding ways to think of transposability
with decatonics. I like the 'disjoint MOS' interpretation the
best.I had considered 'multi-step' and 'vectors of
accidentals' approaches but couldn't make them come out 'neat'.
In some cases, it looks like this approach may do it, as well
as providing an interesting approach wo working with tunings
which have disjoint sets.

Bob Valentine

Robert Valentine wrote,

>> To see a correct version of that,
>> you may order my paper _The Forms of Tonality_ from Bill Alves.

>I want it, shouldn't this and other papers from the Microfest go online
>somewhere?

This paper didn't actually make it to the MicroFest. I put a good month of
work into it, so I'm hoping to make a couple of dollars from each copy sold.

>Okay, I was thinking of it in terms of the set of "3 b's and 7 a's" rather
>than the numeric values.

Then the term you're looking for is "distributionally even" rather than
"maximally even".

>Tuning three certainly doesn't have this property, BUT, all
>intervals are unique. So "7", despite being a "fourth" between
>the two flavors of "third" is still uniquely a fourth. (This
>is the special word I was looking for).

Oh, that would be the case for any non-ET tuning of the scale, right?

>Tuning two is ordered but non-unique, "all thirds are greater
>than or equal to all seconds". If this is not proper then the
>12tet diatonic is improper...

It's proper, but not strictly proper.

>Thanks for the post regarding ways to think of transposability
>with decatonics. I like the 'disjoint MOS' interpretation the
>best.

You mean MOS within a half-octave periodicity, or two interlaced MOSs?

Anyway, I find all five types of modulations musically useful.