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"edgar@shape.mps.ohio-state.edu (Gerald Edgar) (04/09/90)
In article <562@bilver.UUCP> alex@bilver.UUCP (Alex Matulich) writes: > >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 This sounds like something I have done. I used about 10 of the common "dragon curves" (including Koch). The change in pitch was related to the angle (360 degrees corresponds to an octave), and duration was related to line segment length. Of course, the duration should be a POWER of the line length (the exponent is the reciprocal of the fractal dimension) in order to achieve true self-similarity. The curve known as "McWorter's pentigree" uses angles of 72 and 144 degrees, which correspond to intervals not used in Western music. Peculiar. If there is some interest I can post the programs. (Logo source code, or Macintosh executable.) (By the way, there is some literature on "fractal music", and it is NOT this!!!) -- Gerald A. Edgar Department of Mathematics Bitnet: EDGAR@OHSTPY The Ohio State University Internet: edgar@mps.ohio-state.edu Columbus, OH 43210 ...!{att,pyramid}!osu-cis!shape.mps.ohio-state.edu!edgar
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 | |___________________________________________________________________|
err@fibercom.COM (Eric Rubin) (04/10/90)
In article <1990Apr9.123724.4027@zaphod.mps.ohio-state.edu> edgar@shape.mps.ohio-state.edu (Gerald Edgar) writes: >If there is some interest I can post the programs. (Logo source code, >or Macintosh executable.) I'd like to see the Logo source code. -- Eric Rubin INTERNET: err@fibercom.com FiberCom, Inc. UUCP: ...!uunet!fibercom!err P.O. Box 11966 PHONE: 703-342-6700, 800-423-1183 x348 Roanoke, VA 24022-1966 FAX: 703-342-5961
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 Davidsonmu298ac@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!"
mcnamara@vixvax.mgi.com (06/03/90)
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: > > 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? > In 1988 or thereabouts Charles Dodge (_Earths' Magnetic Field_) came to Mpls. to lecture about computer music. He brought with him a tape of several pieces of music, one generated using fractal relationships between the parts of the composition. As I recall, he generated an initial fractal sequence, and then used fractal relations to generate the other parts from the original one. The music was interesting. Sort of like 101 Strings does Phillip Glass. As he put it: "This is the first computer music I've heard which sounds like bad music(previous attempts didn't sound like music at all)." There were several other interesting pieces on the tape. The best one was by Curtis Braun, titled _Brontosaurus_. It was a child's poem, read by a computer voice synthesis program, and then modified by the composer into a sort of self-similar composition. I think he would send you the tape, and/or provide details of his algorithms. He is at the Brooklyn College Center for Computer Music. Phone (718) 780-5582. Curt McNamara mcnamara@mgi.com
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