TD 1000

I think that for the 1000 fisrt TD's, the best poster has been Brian
McLaren. For the amount of text he has written and for the discussions he
made possible.

And the winner for best article is....

Gary Morrison !!! for his serie of post about the 9/7 interval.


-Kami

** I am a peach tree,
** Blossoming in a deep pit.

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Personally, I disagree with Danielou that music is a hard science. I
don't think of it as a science really, much less a hard science with
universally invariable laws. Certainly some basic premises of Music Theory
are more universally observable and agreed-upon than others. It's
difficult, although not impossible, to prevent an authentic cadence from
producing a sense of finality. But the effects of various variants on
sonata form are a bit more difficult characterize in a manner that
everybody of every culture would agree with. Many people won't even notice
the variants at all, consciously at least.

Invariable musical laws a lot closer to realistic when it comes to
psychoacoustics though, and perhaps that's more specifically what Danielou
was commenting on. They can be statistically quantified with much more
universal applicability. But even in psychoacoustics, it's easy to show,
as Bill Sethares has investigated, that how we perceive harmony is heavily
dependent upon the timbres of the tones involved.

I believe that when you really get down to it, the various theories
regarding cent-level tuning are best viewed as models. That in the sense
that they are based upon at least reasonably solid evidence, and allow us
to use mathematics to draw conclusions that would not otherwise be
apparent. But also, and I think that this is very critical, in the sense
that those conclusions must be experimentally verified. Does a tuning that
has lots of nontraditional thirds present an eerie sound? Try it; that's
the only way to know.

But unlike psychoacoustic aspects, there are some structural aspects of
the theory of tuning and scales that are pretty much impossible to deny.
For example, it's easy to show that it's next to impossible to build a
scale of two identical tetrachords in most scales of less than 12
steps/octave. That has important effects upon the sorts of melodies you
can realize in that tuning.

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Gary Morrison wrote (a couple of weeks ago):

> But unlike psychoacoustic aspects, there are some structural aspects of
>the theory of tuning and scales that are pretty much impossible to deny.
>For example, it's easy to show that it's next to impossible to build a
>scale of two identical tetrachords in most scales of less than 12
>steps/octave. That has important effects upon the sorts of melodies you
>can realize in that tuning.

Gary,

Could you please explain why it requires a scale of 12 steps/octave to
built an 8-tone scale? (i.e., if there are 4 steps in each tetrachord,
there are 8 steps if both tetrachords are identical, although one
of the steps is usually the octave of the first step).

Lydia Ayers


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