source file: mills2.txt Date: Fri, 9 Aug 1996 10:33:20 -0700 Subject: Post from Mclaren From: John Chalmers From: mclaren Subject: algorithmic composition in non-12 -- Paul Turner asked about Markov processes applied to computer-controlled composition some while back. This is an interesting subject & it relates to microtonality with especial cogency because as the number of pitches in a just or equal-tempered scale grows large, it's attractive (at least in theory) for a computer to handle at least some of them automatically. To date, the definitive article on the history of algorithmic composition is "Composing With Computers: A Survey," by Gareth Loy, pp. 291-396 in the anthology "Current Directions In Computer Music Research," MIT Press, 1991, edied by Max V. Mathews & John R. Pierce. Lejaren Hiller was the first to apply Markov methods to composition. Hiller was a chemist by trade: apparently Markov analysis is sometimes applied to the study of chemical reactions. It is essentially a rule-based random number sieve. Markov analysis can be applied to note-groups of zero length (zeoth-order analysis), length 1 (first-order analysis), length 2 (second-order analysis), etc. Statistical analysis of a composition as a first-order Markov process establishes the probability of a given note following another note-- for instance the probability that C will follow D. A first-order analysis can be run for each of the 12 pitch-classes of 12-TET music, giving a list of probabilities derived from an input composition (or group of compositions). However, such analyses could just as easily be run for a non-12 set of notes--31-TET, 15-TET, Partch 43-note JI, and so on. Analyzing the composition as a second- order Markov process establishes the probability of a given note following two given previous notes; a third-order Markov analysis yields the probability of a given note following three previous notes-- and so on. Thus "the process of composition consisted in sequentially applying each random number generated to the appropriate sets of rules. If the number chosen violated a rule, another number was selected from the random series until all rules were satisfied, and the successful number was appended to the end of the sample being generated." [Loy, G, "Composing With Computers: A Survey," pg. 310, in Current Directions Of Computer Music Research, 1991, ed. Max V. Mathews & John R. Pierce] Markov methods appear most useful at the level of the phrase. At shorter time-scales the music sounds like sample-and-hold white noise, while at longer time-scales it sounds like a random bricolage of precomposed sections. Essentially the Markov analysis reduces the generation of musical notes & phrases to a single probability 0< x<1 plus a rule-set. Thus, Markov composition represents yet another example of the 20th century's love of extreme reductionism. In this case, the conceit is that a musical composition can be reduced to a set of unsigned probabilities between 0 and 1 mated with some modus ponens logic tree. If this sounds ridiculous...well, so do many of the ideas that have proven popular in the 20th century. If someone told you that the world's 2 great superpowers would go hog-wild for a nutty theory known as "mutual assured destruction," damn near bankrupt themselves building enough nuclear weapons to vaporize the biophere and then tear all those bombs apart and throw 'em out because they they finally realized it was a terminally stupid idea to begin with...well, hey-- Welcome to the 20th century, folks! Markov analysis basically establishes the size of the sieve through which random numbers will pass, given some rule-set (i.e., the rule that if notes X, Y, Z...U, V have already occurred, there is a probability Q that note W will occur subsequently.) The advantage of Markov compositional processes is that [A] they can be scaled up to the size of the entire composition (in which case there's a finite probability that the entire piece of music will occur) or down to the level of the individual note. Thus, unlike many other compositional algorithms, Markov analysis gives the composer some control over the specific time-scale at which s/he works; [B] Markov analyses of two radically different musical styles of composition can be used to "morph" from one compositional style to the next, producing striking effects; abnd [C] Markov analyses can prove useful in dating and authenticating compositions by generating a set of note and phrase probabilities unique to each composer. The disadvantages of Markov compositional algorithms are [A] the process does not even remotely model a composer's cognitive functions; I know of no composer who sets up a bunch of predetermined rules and then flips coins to see whether a note is generated. (Well--no worthwhile composer. There's always Cage, of course.) This is so alien to the way humans compose that it's bound to produce musically unsatisfactory results; [B] The Markov algorithms remove control of all but continuous "chunks" from the composer. To use an inapprropriate term, Markov composition isn't random access-- its strictly sequential. The Markov composer never knows what's in measure 12 if it's on measure 2. In the real world, a composer will typically start by deciding what form s/he will use--rondo, variations, canon, etc. Markov methods make it impossible for the composer to control this highest level of compositional order. At the other extreme, human composers will typically jump back and forth in time, composing the end of piece before the middle, making sketches, inserting "extraneous" notes in themes or passages or chord progressions--yet the theme or passage or chord progression remains to listeners recog- nizably thematic. Markov processes are very brittle in this regard. Toss in one extraneous note, require the analysis to jump discontinuously in time from begining to end or vice versa and the rule-set breaks and the Markov analysis apart. In particular, Markov processes cannot handle or model a method of composition in which the composer jumps discontinuosuly between various points in time, forward then back, &c. This is violently contradictory to both human perception of music (we instantly jump back in time via memory to the first appearance of a theme the second time we hear it), and to the way human composers handle themes and chord progressions. The final problem is that [D] because Markov analysis operates only with pitch classes, Markov analysis is completely blind to the contour of a melody--yet this is clearly the most important characteristic of any melody. Markov analysis is also utter blind to the "orchestration" of a chord and to the "contour" of the bass progression of the set of chords used--thus Markov analysis destroys the information of where the chord's component notes are distributed in the frequency spectrum, and the specific melodic contour of the bass note in those chords. Now, Stravinsky clearly thought of one orchestration of a chord as actually a different chord than another orchestration-- thus he typically said "I was glad to discover that chord" when speaking of the Firebird. Many composers think this way. But Markov analysis destroys this information. This is another way in which Markov procedures are violently antithetical to the way humans think about composition. It's worth noting that the Markov algorithm is the earliest compositional method used on an actual computer. Lejaren Hiller employed it in back in 1957 to produce the first computer- composed piece of music, The Illiac Quartet. Thus Markov processes represent an extremely early stab at computer composition. It's also worth noting that Hiller, in his book "Experimental Music," was careful never to make the claim that his computer programs composed actual music. Instead, Hiller described his efforts as attempts to probe the cognitive processes of the human mind. The idea (a typcally grandiose early computer dream) was that by modelling human music composition, a series of computer programs would gradually illuminate the process of human musical thought to a greater and greater degree, until finally the process of composition as a mental activity was fully understood. At that point (it was fondly imagined back in 1956) computer programs could take over and produce music even more interesting, even more inspiring, and even more exotic and beautiful than any human. Typically, just the opposite has actually happened. Instead of illuminating the operation of the human mind, computer composition has pointed up how complex and imponderable human compositional thought actually is. Thus, what has actually happened with computer composition is that a series of musically godawful results inspired researchers to grab a ragbag of mathematical procedures willy- willy from other disciplines and press 'em into service as compositional algorithms. All of these algorithms have so far *reduced* the composer's control over one or another vital aspect of the musical composition, rather than enhancing it. The net result has typically been a series of computer compositions about which as Max Mathews remarked "the music tends to wander, and with it the listener's attention." -- What does all this have to do with non-12 tunings? Because Max Mathews' Music V acoustic compiler and its descendents allow total freedom to choose pitches, xenharmonic composers face what Wendy Carlos calls "option paralysis." You've got so many options you spend all your time trying to decide what to do, until you've no time left to actually worry about composing. Computer-controlled composition offers a way out of "option paralysis." It's inherently attractive to let a computer handle all the Dedalaean complexities proferred by all those notes--thus one might well understand why a composer would prefer to have a computer handle composition (or some aspect of composition, such as, say, chordal accompaniment, or melodic episodes) in 53 tones or 171 tones per octave. -- Future generations will look back with wonder and astonishment at the peculiarly 20th-century conceit that computers could generate music even remotely as interesting as a composition written by a human. People used to drink coal tar in the 1870s as a cancer cure because there was a lot of coal tar around, the oil business was glamorous, and nobody could think of much else to do with coal tar. A lot of composers probably use computers to make music nowadays for the same reason-- there are a lot of computers around, anything connected with computers is automatically glamorous and hi-tech, and the composers likely can't think of anything better to do with their PCs. Thus algorithmic composition is fashionably trendy nowadays, very chic, and highly "in," and it's yet another example of the kind of musical tulipomania that has periodically deluded groups of otherwise sane composers since 1948: row-based serialism, pitch-class matrix methods, aleatoric composition, neo-dadaism, and so on. Algorithmic composition may well be another fad, like the miniskirts of the 60s and the men's platform shoes of the 70s. Time will tell. Because computer algorithms never permit the composer to simultaneously control large and small time-scales of the composition, and systematically prevent composers from assigning emotional values to sets of chords or notes, algorithmic computer composition has never produced much music worth listening to. Typical computer compositions fade in from nowhere and fade out after some indetermine length of time, giving the impression of sonic wallpaper. Algorithmic compositions can work very effectively as background music, however. The net musical result is generally a very low-quality Muzak, or a particularly dull & repetitive kind of fusion jazz. This applies with especial force to Tod Machover's computer-generated hyperinstrument noodlingsm, although the problem is endemic through the computer composition field. Why spend so many millions of man-hours and so many trillions of CPU cycles to generate sub-par Muzak and boring fusion jazz? Well...why did so many composers spend so many millions of man-hours composing row-based serial music in the 1940s and 1950s? As Charles Mackay pointed out in his classic book "Extraordinary Popular Delusions and the Madness of Crowds" (1843): "Men, it has been said, think in herds, and they go mad in herds, while they only recover their senses slowly, and one by one." The essential problem is one of mapping. All computer composition programs either sieve (from the top down) or generate (from the bottom up) random noise, then assign values to that subset of random noise. In the case of Markov-type and other top-down noise-sieve algorithms, the mapping is determined by the rule-set pre-entered by the composer. In the case of cellular automata and MAX-type recursive shift-register algorithms, the mapping is out of the composer's control and is determined by the emergent order of the cellular automaton or that paritcular topology of feedback shift register. In both cases, the essential problem (other than the fact that composer loses control over either the very large or the very small time-scale in a piece of music) is that no one has yet determined how to meaningfully map a chord or note to an emotional affect. Thus the mappings have to date been extra-musical and the results thus trivial. There is no sign that the mapping problem will be solved any time soon, since the same chord or note can have *many* different emotional affects depending on its context. To determine what emotional impact a chord or note will have, you have to *listen.* And this, computers can't do. Lejaren Hiller addressed this concern in his 1957 book "Experimental Music:" "The composer is traditionally thought of as guided in his choices not only by certain technical rules but also by his `aural sensibility,' while the computer would be dependent entirely upon a rationalization and codification of the `aural sensibility.'" [Hiller, L., Experimental Music," 1957] To date, no such rationalization and codification has proven musically successful. --mclaren Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 9 Aug 1996 21:06 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA05065; Fri, 9 Aug 1996 21:06:38 +0200 Received: from eartha.mills.edu by ns (smtpxd); id XA05062 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id MAA12890; Fri, 9 Aug 1996 12:06:36 -0700 Date: Fri, 9 Aug 1996 12:06:36 -0700 Message-Id: <009A69BF00630380.055B@vbv40.ezh.nl> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu