Xref: utzoo comp.music:1054 rec.music.classical:13000 Path: utzoo!attcan!uunet!samsung!usc!venera.isi.edu!smoliar From: smoliar@vaxa.isi.edu (Stephen Smoliar) Newsgroups: comp.music,rec.music.classical Subject: Re: Fractal Music Generation (summary) Summary: tonal music and random procedures Keywords: music theory, composition, Meyer Message-ID: <12859@venera.isi.edu> Date: 11 Apr 90 14:34:03 GMT References: <562@bilver.UUCP> <1990Apr9.151958.26859@ncsuvx.ncsu.edu> <9613@sdcc6.ucsd.edu> Sender: news@venera.isi.edu Reply-To: smoliar@vaxa.isi.edu (Stephen Smoliar) Organization: USC-Information Sciences Institute Lines: 170 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