Truth and Beauty

I hear that millenia ago folks could reason from one mathematical proposition
to another, but they didn't have the idea that there was some nice neat
foundation from which all other true propositions could be derived. Euclid's
name is often associated with that technique. & of course Goedel's.

So with music. Certainly there are lots of musical systems, including
alternative tuning systems. We can compare these, discover relationships of
mutual support or conflict, etc. And we can also try to dig or distill to
find some foundation or essence, some secure truth from which we can infer
the truth value of the many musical propositions we entertain.

Somehow it seems that when folks go foundation hunting, they often bag quite
a variety of game. Variety is not altogether bad in fruit, but it's death to
roots. The effort to resolve conflicts instead intensifies the conflicts.

If science cannot resolve a conflict, is the matter worth pursuing? If we say
"no", then don't we discard the most important treasures of humanity? If we
say "yes", do we thereby enlist in new rounds of religious warfare?

Stephen Toulmin's COSMOPOLIS: THE HIDDEN AGENDA OF MODERNITY nicely argues
that science grew out of the bitter religious conflicts that arose during the
16th & 17th Centuries. Toulmin describes some of the devastation of the 30
years war, 1618-1648. I was eating lunch with a Polish friend the other day,
who recalled that the Polish population declined from 10 million to 6 million
during just a few years of that conflict. I've heard that some regions of
Central Europe suffered 70% mortality during that war.

So science was more or less an agreement to focus on issues that could be
resolved by recourse to objective observation, logic, etc. To remove other
issues from the political sphere. To decriminalize (religious) heresy.

I've just started looking at ECOLOGIES OF KNOWLEDGE: WORK AND POLITICS IN
SCIENCE AND TECHNOLOGY, ed. by Susan L. Star. A sentence:

The sociology of art has been concerned with the question of whether some
things aren't *really* just beautiful (in a timeless or transcendental
fashion).

There's a note on this sentence to Howard Becker, no specific work. But in
the bibliography his ART WORLDS is listed, so that might have some relevance
to the matter.

This issue is perhaps the fundamental problem of our time, so its scope is
far vaster than music and tuning. But music and tuning might actually capture
the issue in a nutshell. Mathematics meets aesthetics, face to face.

Out of the muck grows and blossoms the most beautiful flower!

Jim

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Replying to Charles Lucy:

> It seems that by taking steps of fourths and fifths, from a given pitch,
> all "harmonics" (ghosttones?) can be mapped in a continuous series.
> The interval between the fourth and the fifth is exactly [1200/(2*pi)> 190.9858 cents] . This interval Harrison called the "larger" interval.
> I have used the term "Large"(L).

Can you show us any specific evidence that this maps to partials of any
pitch from any instrument instrument more accurately than integer
multiples? Or is the closeness of the mapping not your main point?



> It seems that notes, which are closer on the spiral of fifths and
> fourths are more consonant than those which are a greater number of
> steps apart..

Are you sure that "consonant" is the best choice of words here? Would
you for example view a major second (two fifths apart) as more consonant
than a major sixth (three fifths apart)?

"Consonant" is probably a good term in one sense but not another: Since
consonance REALLY means closeness to resolution to the tonic in a tonal
system (despite its common but technically incorrect usage as more or less
the opposite of "discordant"), closeness on the circle of fifths (spiral or
whatever) is a pretty good measure of closeness to the tonic in a tonal
system. But it's probably not a very good measure of consonance in thee
sense of discord (for the reason I suggested above). Discord is another
way in which a harmony can sound farther from resolution.

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