the cart and the horse

Paul Erlich wrote,

<<One can simply write beautiful non-functional progressions, riding
along the tetrads and hexanies, or harmonizing the various scalar
subsets, without any particular goal. Think of the state of 5-limit
music in the pre-tonal era. As time goes on, composers may find
functionality and tonality emerging, whether it be in ways anticipated
by theorists or not.>>

I agree with most of what you say, but I think your analogy about the
state of 5-limit music in the pre-tonal era only holds water for a
strict JI type interpretation and not for the types of theoretical
optimizations that these scales are designed to achieve.

My point was more of a cart in front of the horse sort of thing... and
I guess I also think that these scales are benefiting from a bit of
nepotism as well, as they're largely the theoretical what-ifs of
diatonicisim, tempering and tonality. Not that there's anything wrong
with that of course and I applaud the efforts, but I think
optimizations of this specific sort assume a lot -- especially at the
eleven limit.

Anyway, it was all just a desire on my part to see a bit more
interrelated music theory to go along with all the scale theory.
Because in this case I do think there's a big gap there.

--Dan Stearns

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> Paul Erlich wrote,
>
> <<One can simply write beautiful non-functional progressions, riding
> along the tetrads and hexanies, or harmonizing the various scalar
> subsets, without any particular goal. Think of the state of 5-limit
> music in the pre-tonal era. As time goes on, composers may find
> functionality and tonality emerging, whether it be in ways
anticipated
> by theorists or not.>>
>
> I agree with most of what you say, but I think your analogy about
the
> state of 5-limit music in the pre-tonal era only holds water for a
> strict JI type interpretation and not for the types of theoretical
> optimizations that these scales are designed to achieve.

Can you elaborate on why you feel this way?
>
> My point was more of a cart in front of the horse sort of thing...
and
> I guess I also think that these scales are benefiting from a bit of
> nepotism as well, as they're largely the theoretical what-ifs of
> diatonicisim,

Don't see it.

>tempering

Are you opposed to that?

>and tonality.

Again, I see it as completely pre-tonal . . . not understanding your
arguments to the contrary (above).

> Not that there's anything wrong
> with that of course and I applaud the efforts, but I think
> optimizations of this specific sort assume a lot -- especially at
the
> eleven limit.

All that's assumed, mathematically, is that there's a single
generator . . . and even that won't be assumed when (if) Dave Keenan
runs the multi-generator optimizations . . . we're not expecting any
further surprises, but you never know . . .
>
> Anyway, it was all just a desire on my part to see a bit more
> interrelated music theory to go along with all the scale theory.
> Because in this case I do think there's a big gap there.
>
The field is wide open! Let it flow, like a river! Five thousand
music theories for this one scale! (we already have at least that
many for 12-tET)

Paul,

The way I see it the this scale, as well as your decatonic, proceed
from the assumption that the tempered diatonic's optimization of
consonant identities is the way to go.

Might be, might not too though... but I think it's fair to say that
it's pretty difficult to say either way when these things are so ahead
(or separate) from any musical practice to support or underscore the
ideas.

Again, I think you and Dave K's "generalized diatonic" modus operandi
benefits from more than a bit of nepotism. Nothing wrong with that,
but where is the musical evidence that these types of generalizations
and optimizations are really the best way to go about things at the
seven and eleven limits?

Might be. Might not too.

There's been quite a bit of 72 music now. Is there any evidence that
musicians or composers have been nosing up to these ideas with it? Not
that I'm aware of.

The idea of a thoroughgoing tonal music at the eleven limit excites
me. Maybe this scale would help. It would be nice if there were some
corresponding indication of this musically.

--Dan Stearns

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:

> The idea of a thoroughgoing tonal music at the eleven limit excites
> me. Maybe this scale would help. It would be nice if there were some
> corresponding indication of this musically.

Maybe there will be eventually. Maybe there won't. I certainly _don't_ see the MIRACLE scale
as having the potential to support this by design, which is what you seem to be implying. On
the contrary, it's just a way to get a remarkable amount of quasi-JI sonorities with a reasonable
number of notes. That's all!