[comp.sources.wanted] Fractal Music Generation

alex@bilver.UUCP (Alex Matulich) (03/11/90)

I need some kind souls to send me some algorithms to generate music based
on fractals.

I don't know much about this subject, but it occurred to me that a fractal
music algorithm might be used as an aid in writing fugues.  I have tried
one experiment already, based on the geometrical shape known as a "Koch
curve", where a pitch and duration corresponds to segment angle and length,
respectively.

My suspicion is that I'm going about it all wrong.  My experimented generated
a sequence of notes that sounded interesting.  The problem is that it was
a single sequence and the notes were all the same length.  How can a fractal
generator be made to create overlapping sequences of notes which have
harmonically correct relations to each other?

Music is a serial event that unfolds as time passes.  I am only able to
visualize fractals as geometric entities which where all parts exist at once.

Please e-mail me suggestions, no matter how simple or bizarre.  They will
be appreciated.  Thanks.

-- 
     ///  Alex Matulich
    ///  Unicorn Research Corp, 4621 N Landmark Dr, Orlando, FL 32817
\\\///  alex@bilver.UUCP    ...uunet!tarpit!bilver!alex
 \XX/  From BitNet use: bilver!alex@uunet.uu.net

alex@bilver.UUCP (Alex Matulich) (04/09/90)

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
 \XX/  From BitNet try: IN%"bilver!alex@uunet.uu.net"

mvolo@uncecs.edu (Michael R. Volow) (04/09/90)

I apologize for the inappropriate followup posting, but this is the
only music news group we receive; moreover I'm not allowed to post
new articles, only followups. Here goes anyway:

Does anyone know which Gilbert and Sullivan operetta the following
song comes from?
  "I am the very model of a modern major general"

Flame away for the inappropriate posting if you wish, but please
*post* the answer if you know. Thanks.

M Volow, VA Medical Center, Durham, NC 27705
mvolo@uncecs.edu           919 286 0411

george@shumv1.ncsu.edu (George Browning) (04/09/90)

In article <562@bilver.UUCP> alex@bilver.UUCP (Alex Matulich) writes:
>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:
>

	I have an article from the book Fundamental Algorithms for
Computer Graphics written by Richard F. Voss that talks about fractal
music.  Voss says "One of my exciting discoveries was that almost all
musical melodies also mimic 1/f noise."  He gives some pictures and
examples, including a couple of "spectral density measurements of the
pitch variations in various types of music showing their common
correlations as 1/f noise"  These graphs show such things as Medieval
music up to 1300, Beethoven's 3rd Symphony and the Beatles Sgt. Pepper.
I am not sure exactly how to generate 1/f noise (it doesn't look too
easy) but I will know how to by the end of the semester, as my graphics
project depends on it.  I am going to use it to make both terrain maps
and texture maps for water.


You may also want to look at:

Voss, R. F. and Clarke, J. "1/f Noise in Music: Music from 1/f Noise",
J. Accous.  Soc. Am. 63, (1978), 258-263.

Voss, R. F. and Clarke, J. "'1/f noise' in music and speech", Nature
258, 317-8 (1975).



				- Jeff
--
_____________________________________________________________________
| George Browning                  North Carolina State University  |
| george@shumv1.ncsu.edu                               Raleigh, NC  |
|___________________________________________________________________|

terry@pride386.UUCP (Terry Lyons) (04/10/90)

In article <562@bilver.UUCP>, alex@bilver.UUCP (Alex Matulich) writes:
> 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:

[rest deleted]

I used to do this sort of thing ... sounded like what you want to hear
eqip: 3 arp 2600's
a vic 20 commodore
3 homemade sequencers

the sequencers could supply the note OR and the note
the program on the vic 20 picked a seq. of 30 notes (what do you want it was
1974 or 75) using a random program  (selected from 0 to 9 I think) this was
divided up like so     0 = down a 7th ,1 = down a 5th, 3 = down a 3rd ,4 =No
Change, 5 up a 3rd etc.
the program would load a seq. into # 1 then load a seq. into 2 then 3
a switch on the sequencer would tell you how many times the seq would repeat
I would set 1 on 2 ,3 7 or whatever turned me on at the time
then I would play the melody. every thing was triggered off the main kbd.

this should be easier to do this now  but I don't think anyone left the ability
to and different kbd triggers & notes.
but then we could only play 1 or 2 notes per synth.   and had to PROGRAM the
next "sound.
terry

billd@fps.com (Bill Davidson) (04/11/90)

In article <562@bilver.UUCP> alex@bilver.UUCP (Alex Matulich) writes:
[asks for info on fractal music]

I have two references:

Dietrick E. Thomsen, "Making Music Fractally", Science News, Mar 22, 1980

Richard F. Voss, "Random Fractal Forgeries", SIGGRAPH '85 Course Notes
	for Fractals: Basic Concepts, Computation and Rendering.

--Bill Davidson

mu298ac@sdcc6.ucsd.edu (Philip Marlowe) (04/11/90)

In article <1990Apr9.151958.26859@ncsuvx.ncsu.edu> george@shumv1.ncsu.edu (George Browning) writes:
>In article <562@bilver.UUCP> alex@bilver.UUCP (Alex Matulich) writes:
>
>	I have an article from the book Fundamental Algorithms for
>Computer Graphics written by Richard F. Voss that talks about fractal
>music.  Voss says "One of my exciting discoveries was that almost all
>musical melodies also mimic 1/f noise."  He gives some pictures and

	This is an incredibly obvious statement to make.  Stepwise
motion is an important attribute of many tonal melodies,and 1/f
noise
generates stepwise motion.  So why can't you program 1/f noise to
produce good tonal melodies?  Because tonal melody is not random; it
has very strong directionality, and any programmer who wants to
have an algorithm that would produce good tonal melodies has to take
goal-oriented motion into account, which I don't believe is possible
with fractals.  Traditional tonal melody is incredibly causal.  It
can not be modeled on random procedures.  If there is any way for
computers to write good, catchy, tonal melodies, I suspect it must
be through an alogrithm which is contructed on the rules that most
musicians learn in theory class for writing melodies (too much
stepwise motion in the same directionis boring; an upward leap is
usually followed by a downward resolution by step, unless it's
outlining a triad; etc.)  

	If you really want some insight into how tonal melody works,
and why good melodies *sound* good, try reading Leonard Meyer's
_Emotion_and_Meaning_in_Music_ and _Explaining_Music_.

	Previous discussions in this group about fugues being
"self-similar" shows a lack of understanding about just what a fugue
is.  Just because something is repeated at the same level, it doesn't
imply self-similarity (or does it?)  If you examine a Bach fugue at
the middleground or background level, you will see absolutely no
replication of the subject or countersubject, say.  What is
self-similar, perhaps, on these levels will be the movement from
tonic to dominant to tonic, but even this isn't guaranteed, and
besides, it's a self-similarity shared by just about every other
piece of baroque and classical music, as Schenker would have us
believe.  I really don't think you can call thematic unity
self-similarity.

andyn@stpstn.UUCP (Andy Novobilski) (06/03/90)

Somewhere in the 1984-87 time frame, there was an article published
in the proceedings of USENIX (or some UNIX conference) by a research 
team at AT&T on the topic of Binary Stocastic Subdivision as an algorithm 
for generating music.  Included in the article was a number that you 
could call to hear a demonstration of the algorithm played on a set of 
MIDI controlled instruments.  

I know the information is sketchy, but a little time at a technical
library should yield the reference.  If anyone is interested and can't 
locate the paper in a local library, I'd be happy to try and find it
at home.

Best of luck,
Andy

-- 
Andy Novobilski     | The Stepstone Corp.  | The expressed views have been
andyn@stepstone.com | 75 Glen Rd.          | approved by a committee of three:
(203)426-1875       | Sandy Hook, CT 06482 | the goldfish, blackfish, and me.

mo@flash.bellcore.com (Michael O'Dell) (06/03/90)

Sorry, folks, it tweren't AT&T, but Bellcore's own Peter Langston
	-Mike O'Dell
	-Mike O'Dell

"I can barely speak for myself, much less anyone else!"
----------------------------------------
The Center for Virtual Reality --
"Solving yesterday's problems tomorrow!"

smasters@gmuvax2.gmu.edu (Shawn Masters) (06/03/90)

I saw an article a number of years back about something like that.  It
was in Science News, and was talking about AI algorithm design this one
team of researchers was doing.  Not only did calling this  number just
play music, I seem to remeber that it was semi-interactive, and they
wanted the general public to test it.  In the end the reponse was to
great, so they shut down the line.

smasters@gmuvax2
smasters@gmuvax