stuff (Kris Peck)

>Yes. The 5ths and 4ths are off just enough that it's not safe to tune by
>them.

Do you have a 22ET guitar? I was only aware of your 20-tone just axe...

>Many MOS scales are "improper". What are some people's thoughts on MOS vs
>propriety for melodic viability? The few improper MOS's I've played with
>do seem to have a feeling of unevenness and big skips -- but that also
>contributes to their "exotic" sound.

You'll find the "worst" scales sometimes have an exotic sound, and in any
case may be useful.

Propriety is the basic measurement of a melodic scale. Rothenberg assures
us that all scales are proper one way or the other. The other is usually
pretty tricky, since there may be hundreds or thousands of ways to cover an
improper scale with its proper subsets. Even proper scales are probably
broken down this way as music unfolds over time... One also has to be
careful, because small (in terms of the rest of the scale?) overlaps may
simply not be noticed.

The harmonic component of Erlich's generalized diatonicity is concerned
with covering the scale with consonances. Propriety may be strongly
influenced or even overpowered by the strong organizing force of harmony,
which is seldom absent in music.

The real gem of Rothenberg's theory is the notion of equivalence classes,
which says that the number of distinct melodic scales may be finite. This
is the part of his theory that had me so excited a few months back.

For the record, I'll say that I place little or no stock in maximal
evenness, distributional evenness, Myhill's property, or any of that.

>Also, is there any explanation of why melodic symmetry should be important?

I don't know of a magic formula that shows why MOS's work so well, and it's
probably because they do a number of important things...

1. If the generator is a strong melodic interval, you'll have lots of them.
2. Every acoustic interval is always subtends the same number of scale steps.
3. You get symmetry about interval of equivalence (IE) and the generator.

Notes...

#1 In fact, you'll have as many of them as possible. This satisfies the
demands of an "extended reference" tuning (ref. Boomsliter and Creel) as
well as any fixed scale can.

#2 This is the killer, and I believe it (and not #3) is the origin of the
"S" in MOS. Note that the reverse is not true -- every scalar interval is
not the same acoustic size (this would seem true only for ET's...)! This
is very important.

#3 I don't put much stock in this one. I put a little stock in symmetry
about the 3/2 (which happens to be the generator in the vast majority of
historical scales), but less than Chalmers or Erlich seem to.

Keep up the good work! I love Endangered Species, as do the several people
I've played it for.

C.