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.netalex@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 | |___________________________________________________________________|
kassover@jupiter.crd.ge.com (David Kassover) (04/10/90)
In article <1990Apr9.135036.2476@uncecs.edu> mvolo@uncecs.edu (Michael R. Volow) writes: > >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. Lehrer, "Elements" Oops, sorry, it's Pirates of Penzance Flame me for answering, if you will. This gave me the chance to use my Asimov's Guide to Gilbert and Sullivan for the first time. >M Volow, VA Medical Center, Durham, NC 27705 >mvolo@uncecs.edu 919 286 0411
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
mvolo@uncecs.edu (Michael R. Volow) (04/11/90)
Thanks for the very generous replies (15 including from Australia!). Most opinions were that "I am the very model of a modern major general" was from Pirates of Penzance. Now I'll go out and buy a copy. Thanks again. M Volow, VA Medical Center, Durham, NC 27705 mvolo@uncecs.edu 919 286 0411
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.
smoliar@vaxa.isi.edu (Stephen Smoliar) (04/11/90)
In article <9613@sdcc6.ucsd.edu> mu298ac@sdcc6.ucsd.edu (Philip Marlowe) writes: >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." > > 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.) > There have been no end of attempts in this direction, and none have been particularly successful. The problem is that random procedures are being applied at the wrong level of granularity. To try to draw an appropriate analogy, it is sort of like assuming that you could construct sentences through random selection of syllables. Lejaren Hiller actually tried to do something like this in his "Computer Cantata," experimenting with Markov processes with different "prior memory capacity;" and the best he could do was come up with the occasional coherent word or two. People who have been interested in random sentence generation know that you get a lot more mileage out of defining your world in terms of a context-free grammar and then using random procedures to determine which productions you invoke. There are a few analogies to this practice in music. If we consider the model era, which preceded tonality, we can find an example of such a context-free grammar in Dom Paolo Ferretti's ESTHETIQUE GREGORIENNE. (The French translation of this book appeared in 1938, so don't expect to find any of Chomsky's terminology in it.) Ferretti devotes considerable text to the analysis of CENTONIZATION, a process by which new plainchants were made up by piecing together fragments (CENTONS, from the French for a patch in a patchwork quilt) of old ones. Ferretti was astute enough to realize that one could not put the patches together any old way; and he offers up a table which, for all intents and purposes, is a set of productions for centonizing chants in the Dorian mode. It works rather well; and I implemented a "random sentence generator" based on this table as part of my doctoral thesis. There are any number of "dice composers" which apply a similar principle to tonal music, the most famous being by Mozart. Here, a random procedure is invoked only for the selection of the terminals. The nonterminal nodes of the parse tree have been fixed by the "composer." The bulk of his work has gone into making sure that the choices of terminals for any given node are interchangeable. I find it slightly disheartening that people continue to disregard what appears to be an important lesson from these experiments, which is that composers tend to work at a higher level of granularity than individual notes. This is not to say that there are not situations in which choosing a specific note is not important. Certainly, every writer has situations in which it is critically important to choose just the right word; but if every writer applied that attention to EVERY word, very little would get written. Composition is a matter of working which "musical ideas." None of us may be able to pin down just what that phrase denotes, but my own intuition tells me that it has a lot to do with memories of past listening experiences. To some extent, all composers centonize--picking up materials from past experiences and finding new ways in which to assemble them. If we are determined to seek out algorithmic rules, then it would seem that these rules should be directed at two key questions: 1. How do we identify such units of material? 2. How do we determine how, given a collection of those units, they may be properly assembled? > 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_. > Meyer probably deserves due credit for being one of the first to recognize that a question like "how tonal melody works" is probably as much a matter of psychology as it is of music theory (if not more so). However, Meyer's understanding of psychology is rather naive. He seems more interested in exhibiting the BREADTH of his reading in non-musical subjects than in trying to apply any of those areas in DEPTH. Anyone interested in a more serious exposition of how cognitive psychology may provide the sorts of insights Philip has in mind would do better to turn to a book like John Sloboda's THE MUSICAL MIND. (I disagree with a good deal of what Sloboda says in this book, but he DOES know how to lay out the relevant issues.) > 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. Again, the issue seems to be one of granularity. What is REALLY important about Schenker is that he tried to make us acknowledge that analysis must proceed at many different levels of granularity. Unfortunately, his (German?) sense of order led him to assume that these granules could be neatly embedded in a hierarchy; and this assumption has been carried on by both Meyer and Narmour, on one hand, Lerdahl and Jackendoff, on another, and Yeston, on a third. (There are probably several more hands lurking out there, but I am not particularly inclined to catalog them.) Fortunately, Lewin seems to have broken out of this "dictatorship of the hierarchy" in his recent "Music Theory, Phenomenology, and Modes of Perception" paper; and my own guess is that he will benefit from this liberation. Another question is why we wish to place so much emphasis on "self-similarity." Do we, as listeners, devote so much of our cognitive attention so simply being able to recognize that we have heard something before? Let me try sticking my neck out on a hypothesis here which has been inspired by the work of Marvin Minsky (who has written about music, as well as artificial intelligence). Minsky believe that much of understanding is a matter of being able to recognize, and account for, DIFFERENCES. This is a bit like saying that much of music is concerned with what we loosely call "variation" and the fact that, as music history has progressed, we have become more and more liberal about what constitutes a variation. What makes the game interesting, however, is that we cannot perceive differences unless we gauge them against some standard of SAMENESS. For example, in BOLERO, we quickly recognize that variation is almost entirely a matter of orchestral color (all that parallel motion is almost like trying to build up new sound spectra) while everything else stays the same. Thus, we seek out self-similarity not for its own sake but for the ability to detect differences. Fugues are exercises in how a melodic motif may be engaged in many different contexts, so that it is CONTEXT which becomes the basis for variation. In all fairness, I should point out that Meyer has tried to pursue a similar line of thought. Much of his writing in music theory is concerned with EXPECTATIONS. However, he seems to believe that expectations may be grounds on universal principles, such as those of gestalt psychology. I, on the other hand, think they are grounded on our ability to perceive self-similarity, either within the context of a single composition or with respect to our past listening experiences. In other words, we seek out trying to identify what we are hearing as being like something we have heard before, because then we will assume that it will "go the same way." This becomes a basis for our expectations, and we listen to hear if those expectations are satisfied or if something different occurs. Thus, the mind is engaged; and we are now exhibiting the behavior of listening to music. (One final point: I am cross-posting this to rec.music.classical, since that bulletin board provides a home for many opinions about both composition and music theory.) ========================================================================= USPS: Stephen Smoliar USC Information Sciences Institute 4676 Admiralty Way Suite 1001 Marina del Rey, California 90292-6695 Internet: smoliar@vaxa.isi.edu "Only a schoolteacher innocent of how literature is made could have written such a line."--Gore Vidal
kassover@jupiter.crd.ge.com (David Kassover) (04/11/90)
In article <9613@sdcc6.ucsd.edu> mu298ac@sdcc6.ucsd.edu (Philip Marlowe) writes: | 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. ... About a year and a half ago, I was at a lecture given by Mandelbrot. Someone asked him about fractal music. He replied to the effect that he had heard the output of some experiments in that area, and that they didn't "sound good". (Whatever that means) We in the audience were not given references, nor the opportunity to hear similar musical pieces and thus form our own opinions. De gustibus non est disputandum. Or as my father would say, "Sahzeechizone" -- =================================================== David Kassover kassover@ra.crd.ge.com kassover@crd.ge.com
wmg@cbnewsk.ATT.COM (william.m.gilroy) (04/11/90)
In article <1990Apr9.135036.2476@uncecs.edu> mvolo@uncecs.edu (Michael R. Volow) writes: >Does anyone know which Gilbert and Sullivan operetta the following >song comes from? > "I am the very model of a modern major general" That line is from the "The Pirates of Penzence" (sp?).
quiniou@calculo.irisa.fr (Rene Quiniou) (04/12/90)
Could you post the exact references of the sources cited in your article as well as your thesis, please? In article <12859@venera.isi.edu>, smoliar@vaxa.isi.edu (Stephen Smoliar) writes: |> In article <9613@sdcc6.ucsd.edu> mu298ac@sdcc6.ucsd.edu (Philip Marlowe) |> writes: |> >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 |> grammar in Dom Paolo Ferretti's ESTHETIQUE GREGORIENNE. (The French |> translation of this book appeared in 1938, so don't expect to find any |> There are any number of "dice composers" which apply a similar principle to |> tonal music, the most famous being by Mozart. Here, a random procedure is |> >and why good melodies *sound* good, try reading Leonard Meyer's |> >_Emotion_and_Meaning_in_Music_ and _Explaining_Music_. |> > |> sorts of insights Philip has in mind would do better to turn to a book |> like John Sloboda's THE MUSICAL MIND. (I disagree with a good deal of |> in a hierarchy; and this assumption has been carried on by both Meyer and |> Narmour, on one hand, Lerdahl and Jackendoff, on another, and Yeston, on a |> third. (There are probably several more hands lurking out there, but I am |> not particularly inclined to catalog them.) Fortunately, Lewin seems to have |> broken out of this "dictatorship of the hierarchy" in his recent "Music Theory, |> Phenomenology, and Modes of Perception" paper; and my own guess is that he =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= QUINIOU Rene quiniou@irisa.fr INRIA / IRISA Phone : +33 99 36 20 00 Campus Universitaire de Beaulieu Fax : 99 38 38 32 35042 RENNES CEDEX - FRANCE Telex : UNIRISA 950 473F =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
d88-jwa@nada.kth.se (Jon W{tte) (04/12/90)
In article <9613@sdcc6.ucsd.edu>, mu298ac@sdcc6.ucsd.edu (Philip Marlowe) writes: > In article <1990Apr9.151958.26859@ncsuvx.ncsu.edu> george@shumv1.ncsu.edu (George Browning) writes: > 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 Actually, try making a plot of baroque music, and compare that to 1/f-squared noise. You'll find some interesting similarities ! (Yes, it's 1/f-squared and not 1/f as the original poster said) Gregorian music is closer to 1/f-cubed or even to the fourth... Now, where does that leave acid house ? (oh, sorry...) > 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 Look at the mandelbrot set. It is self-similar, but skewed, rotated, mirrored and transformed in various ways. Actually, I think you could create reasonable fuge-LIKE music (actually, a whole new type) that was enjoyable using fractals. --- Stay alert ! - Trust no one ! - Keep your laser handy ! --- h+@nada.kth.se == h+@proxxi.se == Jon Watte longer .sig available on request
music@batman.moravian.EDU (music) (04/13/90)
But is it MUSIC? ;-) I personally believe that all you've discussed regarding the algorithmic process of producing (or attempting to produce) "good tonal music" is rather more of a verbose punishment to the reader than the gleaning of any insight to the process being attempted (no offense intended!). I have worked around with algorithmic composition off and on for many years, but "gave up" on attempting to create an artificial musical learning base from which an algorithm could draw upon to produce anything more interesting than (and this is a bad example) the Mozart "Dice Minuet". So I personally decided that the goal of creating "good tonal music" through "pure math" was a non sequitur to the nature of the beast known as "tonal music". I therefore treaded into the teritory of composers such as Xenakis (and Cage from a philosophical, more than "technical" sense). In certain works of Xenakis, Herma (piano) for example, the music is about as far from "tonal" as it is from "12-tone serial" (we limit ourselves here to a system of 12 notes; if we were to explore beyond to the reaches of quarter-tones, arbitrary systems (i.e. Partch) we would be streaching the mind beyond most peoples comprehenshion, something I REALLY WANT TO DO (but that's another story!)). Xenakis uses algorithms to plot his pitch classes, tempi, dynamics, etc. in a way that is more or less "highly organized randomness". Personally, I think his advanced math has little to do with the ultimate outcome of the music, but I like what he does regardless. The music produces more of a gestalt experience than a profoundly complex serial work (like Boulez' Structures and any number of other works by strict 12-tone serialists). The music comes from that great unknown: CHANCE. By carefully controlling the elements of CHANCE on many levels (a grain of sand to an astroid) we can then begin to produce CHANCE-based organization, letting "nature control the music" (think of all the combined chaos and symetry in the universe) and the "composer" guide nature either via algorithms (serialization of chance structures) or by subjective reasoning (nurturing nature). Regardless of the outcome, "tonality" will be replaced by something of a higher order: music that exists etearnally just waiting to be "guided into place". This may smack of musical anarchy, but is the UNIVERSE anarchic? It may seem so on certain levels but ultimately "GOD" controls the "laws of nature" the way I like to control the "laws of the music of nature". Strict tonality/serialism is UN-natural. Only out of cultivating chaos can we deliver the truth of music. Humans have too long restrained themselves into believing that man-made rules about tonality (in the Western world at least) they have unwhittingly enslaved themselves into a very narrow "band" of the musical spectrum (as visible light is to the entire electromagnetic spectrum). We must explore the outer limits of sound and learn to appreciate them as we now appreciate "tonal" music. (Think (philosophically) of the music of the Krell in the film "Forbidden Planet" from the '50's. Think of 4'33". Think of the cosmic background radiation. Think of the Universe as "music in the making". And, finally, you'll probably think of ME as a raving lunatic...) --------------------------------------------------- | Stephen Heller - Music Technician | In transit from | CSNET -> music@batman.moravian.edu | the center of | UUCP -> ...!rutgers!liberty!batman!music | Time & Space... | INET -> music%batman.moravian.edu@relay.cs.net | ---------------------------------------------------
mcdonald@aries.scs.uiuc.edu (Doug McDonald) (04/13/90)
On a slightly different subject, but related - I have tried to write computer programs that imitate the paintings of Jackson Pollock - and it is very difficult. It is probably not impossible, but it would require essentially coding in the exact style of any painting. I did produce programs that make nice screen images, quite arty, but I never got close to the real thing. Doug McDonald
bdb@becker.UUCP (Bruce Becker) (04/13/90)
In article <1990Apr12.150201.12739@kth.se> d88-jwa@nada.kth.se (Jon W{tte) writes: |In article <9613@sdcc6.ucsd.edu>, mu298ac@sdcc6.ucsd.edu (Philip |Marlowe) writes: |> In article <1990Apr9.151958.26859@ncsuvx.ncsu.edu> |george@shumv1.ncsu.edu (George Browning) writes: |[...] |> 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 | |Look at the mandelbrot set. It is self-similar, but skewed, |rotated, mirrored and transformed in various ways. Actually, I |think you could create reasonable fuge-LIKE music (actually, a whole |new type) that was enjoyable using fractals. I know some folks who actually did this. They seem to have used Scho:nberg's "Principles of Harmony" (I might have the name wrong) to translate fractal states into MIDI outputs. I don't know how they interpreted the text to produce the results, but it was reasonably musical, but not particularly melodic. As the fractal was being generated on an Amiga, the music would change according to the part of the M set and depth of recursion... -- ,u, Bruce Becker Toronto, Ontario a /i/ Internet: bdb@becker.UUCP, bruce@gpu.utcs.toronto.edu `\o\-e UUCP: ...!uunet!mnetor!becker!bdb _< /_ "Free your ass and your mind will follow" - Punkadelic
smoliar@vaxa.isi.edu (Stephen Smoliar) (04/13/90)
The French edition of Paolo Ferretti's ESTHETIQUE GREGORIENNE was published by Desclee & Co. (Tournai, Belgium) in 1938. The "context-free grammar" for Dorian antiphons may be found in Volume I of this treatise. I cannot give you page references, since I no longer have a Music Library readily available. However, I found it by trying to track down what he had to say about centonization. Mozart's "Dice Composer" was packaged (complete with dice) by Guild Publications of Art and Music in 1941. I'm pretty sure it's still available under that name. I assume that Leonard Meyer's EMOTION AND MEANING IN MUSIC is still in print by The University of Chicago Press. The same should be true for his EXPLAINING MUSIC, which is published by the University of California Press. I recently purchased John Sloboda's THE MUSICAL MIND: THE COGNITIVE PSYCHOLOGY OF MUSIC from Clarendon Press. It is Number 5 in their Oxford Psychology Series. My uncited reference to Eugene Narmour was to his book BEYOND SCHENKERISM, published by The University of Chicago Press in 1977. The Lerdahl-Jackendoff reference is A GENERATIVE THEORY OF TONAL MUSIC, by Fred Lerdahl and Ray Jackendoff, published by The MIT Press. The Maury Yeston reference was to his doctoral dissertation, published as the book THE STRATIFICATION OF MUSICAL RHYTHM, by Yale University Press. Finally, David Lewin's "Music Theory, Phenomenology, and Modes of Perception" was published in the journal MUSIC PERCEPTION, Volume 3, Number 4 (Summer 1986), on pages 327-392. ========================================================================= USPS: Stephen Smoliar USC Information Sciences Institute 4676 Admiralty Way Suite 1001 Marina del Rey, California 90292-6695 Internet: smoliar@vaxa.isi.edu "Only a schoolteacher innocent of how literature is made could have written such a line."--Gore Vidal
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