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1993-11-18
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The Well Tempered Fractal
v. 2.0
Copyright 1993 By
Robert Greenhouse
The Well Tempered Fractal is a program for the creation of fractal based
musical melodies. The roots of this program lay in the series of
experimental programs, Music From the Fringe, which I started three years
ago as a means of exploring the possibilities of using fractals to produce
music. For the most part Music from the Fringe produced outrageous sounds
which polarized listeners into those who hated the noise and those who were
fascinated by the music.
With The Well Tempered Fractal, Music A Bit In From The Fringe begins to
emerge. Now the music is less outrageous and more melodic. At the risk of
losing the interest of those who have been fascinated by the screams and
squawks of Music from the Fringe, in this program I have begun to make
music which sounds more like traditional music and less like swarms of
locust and howling banshees. I use the sometimes chaotic, sometimes
self-similar properties of several fractal types in an attempt to imitate
the human creative process in composing musical melodies. The application
of symmetry operators to the fractal design adds a measure of self-
similarity which often makes the melodies more interesting.
The program is simple to use. Upon startup, the default Mira type fractal
begins plotting with the parameters chosen at random. The function keys F1
- F4 control the fractal type. The music is toggled on and off by hitting
<M>usic. The style of music can be varied among <S>taccato, <N>ormal, and
<L>egato. The staccato mode sounds curiously like a kind of bizarre disco
music while the legato mode produces synchopated melodies by joining
together adjacent notes of similar pitch. <Q>uit or <ESC> will exit the
program at any time. <I>mprovise adds the interesting effect of random
embellishments to the melody.
The <Up> and <Down> arrows retune the music by half steps while the <PgUp>
and <PgDn> keys shift the pitch by an octave at a time. The <Left> and
<Right> arrows change the scale upon which the melody is created. The
<Home> and <End> keys control the tempo from 40 - 250 beats per minute.
Currently there are twenty-one choices of scale. The number keys 1 - 0
control the symmetry of the fractal (C1 to C10 symmetry). The shifted
number keys produce other symmetry effects which are best explored by
trying them and observing.
The <Space> bar starts a new fractal of the same type while the <Enter> key
begins the current one from the start. The parameters for each new fractal
are determined at random. The fractal automatically advances to the next
one if it exceeds the boundaries set for the particular type or if the
randomly selected parameters send it off to infinity. The <M>usic toggle is
convenient as a fast forward button if the music becomes tedious or seems
stuck on an endless cycle.
I encourage users to find a pleasing fractal and then concentrate on the
changes produced by varying the scales (e.g. major vs. mid-eastern vs.
Japanese vs. Chinese vs. whole-tone, etc.) as well as symmetry types.
Experiment with the <Shift> number symmetry transformations. One of my
favorite settings is the KAM Torus fractal <F2> with the Japanese scale in
the <L>egato <I>mprovise mode at about 120 - 150 beats per minute using
symmetry transformation "%" (<Shift> 5).
---------------------------------------------------------
Key Summary:
F1: Mira Fractal
F2: KAM Torus
F3: Martin Fractal
F4: Seahorse Fractal
Enter: Begin current fractal again
Space: Begin a new fractal
M: Music toggle
L: Music Legato (Full nominal note value)
N: Music Normal (7/8 nominal note value)
S: Music Staccato (3/4 nominal note value)
I: Toggle Improvise Mode (Try it)
Up/Down: Retune music by half steps
PgU/PgD: Retune music by octaves
Home/End: Tempo (40 - 250)
Rt/Lft: Change scale (21 possibilities)
1-0: Change symmetry of fractal C1 to C10.
<SH>1-0: Other symmetry and similarity transformations.
--------------------------------------------------------
The program is by no means finished developing. Many more features will be
added including more fractal types, saving to file, other scales, MIDI
output, and perhaps a more friendly interface and just maybe, better
documentation.
I welcome suggestions and/or comments.
Robert Greenhouse
3401 Hillview Ave
Palo Alto, CA
94304
<robert.greenhouse@spacebbs.com>
==========================================================================
Release History:
10/93
v 1.0 - 1.99: Not publically released. No title. Just testing the concept.
Twenty-one scale types. Improvise mode, legato, normal, staccato music;
offset by half-tone as well as by octave. Four fractal types. Music toggle.
Restart and Next functions.
11/14/93
v 2.0 - Title was given; corrected logic error in the musical algorithm
(oops!); 20 symmetry functions were added; code was tightened up and made
modular for later expansion; tempo control was added. First public release.
===========================================================================