[eu-gene] the general

[Michael Gogins]

I am referring to work by David Lewin and others, based on the work of
the Hugo Riemann the musicologist. The Riemannian group (in 12 tone
equal temperament) is the 12 major and 12 minor triads, generated by
the parallel, leading-tone exchange, and relative neo-Riemannian
transformations, which are the closest voice-leadings from one triad
to another. This group is intimately related to the Tonnetz of triads.

If you want a quick education in this stuff, go to the same place I
hit paydirt: mathematician John Baez' blog entry:

http://math.ucr.edu/home/baez/week234.html

Then you can google around on titles and names to find more. I find
Google Scholar to be the most useful tool for this. It is surprising
how few of the references require an actual visit to a research
library.

Regards,
Mike

On Thu, Jan 8, 2009 at 3:06 PM, Philip Galanter <list at philipgalanter.com> wrote:
>
> Without arguing specific details I'll just note that mathematical
> technical aspects and rule following in *some* of the arts implies
> they are not essential to art.  My point was that objective external
> verification is essential to mathematics as a discipline, but not
> essential to art.  So like I said, art and mathematics are different
> disciplines.  They are games with different rules.
>
> On Jan 8, 2009, at 10:43 AM, Michael Gogins wrote:
>
>> Insofar as mathematics is essential to the practice of an art, as it
>> is in musical counterpoint or visual perspective, objective external
>> verification is equally crucial (though, usually, taken by granted by
>> practitioners who need to get things right, but are not usually
>> involved in advancing the state of that mathematical aspect of their
>> art).
>>
>> In other words, notions of proof and verification, although less
>> formal than in academic mathematics, certainly do exist in the
>> technical aspect of some of the arts. In Western harmony, e.g., a
>> composer will instantly hear whether a progression follows "the rules"
>> and will applaud a novel means of following those rules that leads in
>> an expected but satisfying direction. "Cool changes, man." This is
>> entirely analogous to proving a new theorem in mathematics. And a
>> musicologist will be able to demonstrate how and why "the rules" are
>> followed - or not.
>>
>> Regards,
>> Mike
>>
>> On Thu, Jan 8, 2009 at 11:12 AM, Philip Galanter
>> <list at philipgalanter.com> wrote:
>>>
>>> I was mostly just looking for an excuse to say "math math" and "art
>>> art."  ;)
>>>
>>> But the more serious point I would make is that while mathematical
>>> structures appear in art, and while there can even be a meaningful
>>> discussion of the "aesthetics" of mathematical proofs and the like,
>>> as
>>> *disciplines* math and art are quite different.  Each is a different
>>> game with different rules.  In mathematics objective external
>>> verification is absolutely crucial.  Conjectures are all well and
>>> good, but real mathematical progress is made when a mathematician
>>> constructs proofs and other mathematicians can verify them.  In art
>>> notions of proof and objective external verification don't really
>>> apply.
>>>
>>> --
>>> '"generative" is where you lose control of a machine which does
>>> exactly
>>> what you tell it.'
>>> To unsubscribe from eu-gene visit
>>> http://www.generative.net/mailman/listinfo/eu-gene
>>>
>>
>>
>>
>> --
>> Michael Gogins
>> Irreducible Productions
>> Michael dot Gogins at gmail dot com
>> --
>> '"generative" is where you lose control of a machine which does
>> exactly
>> what you tell it.'
>> To unsubscribe from eu-gene visit
>> http://www.generative.net/mailman/listinfo/eu-gene
>
> --
> '"generative" is where you lose control of a machine which does exactly
> what you tell it.'
> To unsubscribe from eu-gene visit
> http://www.generative.net/mailman/listinfo/eu-gene
>



-- 
Michael Gogins
Irreducible Productions
Michael dot Gogins at gmail dot com