From: Marc Geddes (marc_geddes@yahoo.co.nz)
Date: Sun Feb 06 2005 - 21:02:09 MST
--- Thomas Buckner <tcbevolver@yahoo.com> wrote:
> >
> This is a subject I have thought on for years,
> and there are some answers already available.
> Music has a Kolmogorov complexity like most
> everything else; there is finite number of sounds
> you could put into three minutes, as there is a
> finite number of possible novels (we are assuming
> that nobody but transhumans and SAI's want to
> hear million-minute symphonies or read
> billion-page epics, and that's still finite). The
> arrangements you would find pleasing to hear are
> a small subset, and they have mathematically
> interesting properties. It follows that there are
> finite types/ways of enhancement, some of which I
> will describe.
> The music we usually listen to is based on a
> twelve-tone scale (even if there are odd noises
> and samples thrown in). To go up an octave, you
> double the frequency, and this is divided into
> twelve equal steps. Twelve is a groovy number
> which divides evenly in a lot of ways for such a
> small number, and musical theory has been digging
> around its divisors and their incestuous
> relationships for centuries.
>
> One can imagine getting tired of twelve-tone
> music. I once read that its possibilities had
> been fully explored by jazz musicians early in
> the last century and that more recent popular
> music was simply regurgitating what they had
> discovered; I was scandalized, but this view is
> not necessarily wrong, and Brian Eno says that
> newer music innovates in other areas while using
> older forms (i.e. sonic textures and samples,
> laid over the same twelve tone scales). Other
> microtonal scales exist which divide the octave
> in many different ways (quarter tones, 43-note
> scales, 31 notes, and so on). Google 'microtonal
> music' for more. This sort of music has been
> around for quite a while too, but it's an
> acquired taste limited to ethnic minorities and
> scholars, and perhaps needs its own Mozart or
> Beatles to reach the masses. Microtonal scales,
> however, theoretically offer many forms of beauty
> which have never been heard by the human ear.
>
> It is worth noting that what humans find pleasing
> has mathematical interest as well, and
> corollaries exist in other arts; a Discover
> Magazine article shows how Jackson Pollock
> masterpieces have fractal dimension, while fakes
> do not. The best music contains interesting
> melodic/harmonic patterns, interesting rhythmic
> patterns (time broken up in mathematically
> interesting ways), and, if there are lyrics,
> interesting word structures and emotive
> components.
> For example, one book recommends that songwriters
> sit down with their lyrics and lots of colored
> markers. Rhymes should be marked with one color,
> internal rhymes another. Metaphors, similes,
> onomatopoeia, visual words, words which evoke
> touch, smell, etc., all get different colors.
> Ideally, the lyric sheet will be a riot of color
> when you are done, giving a visual key to the
> complexity of the lyric. I recently read a poet
> who explained that a poem was like a machine
> where every single word should be necessary, like
> a screw or a cam.
> In addition, the melody should reflect the lyric,
> and vice versa, as for example in "Animals" when
> David Byrne sings "down, down, down, down" in
> descending, gruff notes suggesting a command
> given to an unruly dog.
>
> If you have followed me this far, you can see
> that there are layers of psychoacoustic
> complexity underlying the best music. In this
> case, a 'degradation algorithm' is easy to make,
> because almost any random change you can make is
> likely to degrade a well-made piece of music,
> which can in reality be a fiendishly subtle and
> balanced creation. An 'enhancement algorithm', as
> you can see, is likely to be limited in its
> reach. It may be effective on a very simple or
> flawed piece of music, but music of high quality
> is already the product of a number of enhancement
> algorithms which the artist has consciously or
> subconsciously applied (the latter case will be
> described as 'having a good ear' just as Jackson
> Pollock's ability to create fractal dimension
> with drips and splatters might be termed 'a good
> eye').
>
> Tom Buckner
>
>
>
>
Cool. Interesting. Just one point - I'm a little
puzzled why you say there is only a finite number of
sounds or a finite number of novels. *In principle*
at least, that's not the case. And a proper
mathematical/logical/philosophical approach has to to
look at things 'in principle'.
Logician John Myhill talked about
'prospective'/'productive' attributes such as beauty
which are in principle of infinite complexity.
('Productive' atrribute- no finite algorithm can list
or recognize 100% of things possessing the attribute).
=====
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