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From: alex@bilver.UUCP (Alex Matulich)
Newsgroups: comp.music,alt.fractals,comp.sources.wanted
Subject: Fractal Music Generation (summary)
Keywords: I need help
Message-ID: <562@bilver.UUCP>
Date: 9 Apr 90 01:19:56 GMT
Organization: William J. Vermillion, Winter Park, FL
Lines: 73

Several weeks ago I posted an a plea for help in comp.music and
comp.sources.wanted for an algorithm to generate fractal music.  I lost the
original text of my posting, but the gist of it was this:

A fugue is a piece of music rich in self-similar structure.  J. S. Bach, a
master at writing fugues, was able to maintain up to six instrumental parts
playing a short theme in different ways -- at different pitches, different
speeds, inverted, upside-down, backwards, and so on -- and it all fit
together too!

Fractals also are rich in self-similar structure.  By definition, after all,
a fractal IS a self-similar object.  The parallels between fractals and
fugues seem so close, I thought, that maybe a MUSICAL fractal generator
could be developed as an aid in writing fugues.

I tried an experiment based on the generation of a Koch curve, assigning
a relationship between note pitch and line angle, and another relationship
between note duration and line length.  My experimented generated a
sequence of notes that sounded interesting.  The problem is that it was
a single monotonic sequence.  How can a fractal music generator be made
to create overlapping sequences of notes which have harmonically correct
relations to each other?

I got 10 replies.  Three offered algorithmic advice, and everyone else
wanted the same information I was asking.  Apparently there is a fair
amount of interest out there, but little knowlege.

You there, reading this:  If you know anything about generating fractal
music, send e-mail or post an article, and quit lurking in the shadows!

Now for the summary [My comments are in brackets]:

(From Kevin Quitt  uunet!demott!kdq)
Use 6 dice for the note to be selected and another six for the length.
Roll die 0 for every note, die 1 half as often, die 2 half as often as
die 1, etc., and add then numbers to determine a number for selecting a
note within a predetermined key.  Accidentals are also randomly played.
More dice tends to smooth out the music, larger values gives more variation.

[Very interesting, but I was looking for something more deterministic.]

(From Doug Bischoff  uunet!psumv.psu.edu!deb110)
A 3-D fractal may be used to control 3 different musical event attributes
plus a fourth if the points are colored.  Use the X axis as a time scale.
For each X-axis time point, perform additive synthesis using the Y axis
for harmonics or frequencies and the Z axis for volume, and use the color
of the point on the X axis to determine a fundamental frequency from which
each harmonic is calculated.

[Yes, a more deterministic algorithm, but it seems to me that such an
 algorithm would create music having little natural unity and flow since
 (depending on the initial 3-D object) unfolding musical events might not
 have any real dependence on previous events.  I'd like to be able to
 give the fractal music generator an initial theme and see where it goes.]

(From Fred Sena  uunet!samsung.com!infinet!sena)
Map the numerical values from an iterative fractal generator onto some
harmonic rules.  For example, choose notes that have some harmonic relation
to each other (like a blues scale) and let the generator choose the
sequence.  Other levels of structure could be added to fractally change
fundamental keys, note lengths, and so on.

[This is very similar to what I was trying to do with the Koch curve
 generator.]

Since I posted my original question, the alt.fractals newsgroup has been
created, so I'm also posting this summary there.

-- 
     ///  Alex Matulich
    ///  Unicorn Research Corp, 4621 N Landmark Dr, Orlando, FL 32817
\\\///  alex@bilver.UUCP    ...uunet!tarpit!bilver!alex
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