source file: mills2.txt Date: Wed, 1 Nov 1995 10:05:06 -0800 From: "John H. Chalmers" From: mclaren Subject: Music & western science --- On encountering the interesting book "Measure for measure: a musical history of science," by Thomas Levenson, one passage in particular caught my eye: "Music and science have been intertwined in Western thinking from the moment of their shared origins, of course: the first even vaguely scientific theory of the universe was a musical one, Pythagoras' arrangement of the planets on the scaffolding of his musical intervals, with every heavenly body sounding out its note in what became known as the music of the spheres." [Levenson, T., 1994, pg. 13] Even though this is probably incorrect (the Bablyonians, Egyptians & Sumerians likely originated most of the musical and geometric discoveries attributed to Pythagoras), Levenson makes a cogent point. To a large extent the current schism in music can be described by the three stages of Western science: Newtonian science, quantum theory and nonlinear dynamics. The Newtonian model of the universe is a giant clockwork mechanism. Harmonic cycles naturally arise from such a scheme: the well-known example in elementary physics textbooks of planetary orbits as clocks naturally suggests the idea of ratios between oscillating cycles of both planetary and (inside the atom) electron- orbital motion. In the macroscopic everyday world, tides, rates of chemical reaction, the compounding increase in velocity produced by uniform Newtonian acceleration, as well as the densities of Maxwell's electric and magnetic fields as a function of distance from the charge center all produce sets of ratios. In a Newtonian universe, it's hard to escape from ratios--and many of them involve small integers. Such a worldview inevitably tilts toward just intonation. This bias is not necessarily conscious. It is so pervasive that it often shows up as an unconscious or even as a subsconscious assumption--a "well, of course...obviously" set of musical axioms from which all subsequent musical theorems derive. In the quantum universe, however, particles are replaced by probability waves--exotic critters often called "wavicles." The best way to deal with a quantum universe is a pragmatic approach: sum the probabilities, assume the most likely interaction, calculate the likely result. This sort of approach suggests equal temperament-- not a perfect intonation, but given the pragmatic realities (and the uncertainties in performed pitch and actual tuning) the best compromise. Chaos theory views the universe as a playground for nonlinear dynamics. Here, bifurcation and period-doubling render predictions useless even when made by the most powerful computers: an *infinite* number of digits is necessary to represent initial conditions accurately. In the real universe of nonlinear mechanics, planetary orbits grow chaotic and cannot be used as celestial clocks over more than a few hundred million years. (See "Newton's Clock," Ivars Peterson, 1994.) This view of the universe stresses the nonlinearity of real physical processes and naturally gives rise to non-just non-equal-tempered tunings (that is, tunings not generated either by Nth roots of K or by ratios of integers). These tunings are just as "natural" as the harmonic series...yet such tunings are profoundly alien to Western music. It occurs to me that a good deal of the friction on this tuning forum between advocates of this or that tuning system derives from a deeper cognitive dissonance twixt contrary worldviews. One of the implicit goals of the JI crowd seems to be a clear distinction between consonance and dissonance: this implies, presumably, that consonance can be unambiguously defined as *sensory* consonance, and that more complex notions like concordance and ambisonance can be derived directly therefrom. In a universe thus ordered, the JI view is that of a cosmos capable of balance, rationality, harmony and what the Hellenes called "taxis," along with the related concept of "logos" (which only very rarely means "word:" more often "logos" mean "underlying order behind," as in meteorology = "the underlying order behind the sky.") The main goal of the equal-tempered crowd, by contrast, seems to be "to get something that works with usable instruments." Equal temperament aficionados stress the ease of modulation, the ready-to-use simplicity of their tunings. No infinite sea of commas, no troubling hard-to-classify intervals like the 11/9 or the 9/7. This accords with a subconscious view of the universe as a place in which uncertainty and chance conspire to defeat efforts to attain harmony, balance, simplicity: instead, the best we can hope for (according to this view) is a workable compromise. The chaos-theory worldview is by far the most radical. It's one that's still working its way through our culture. While the Newtonian cosmos produced Baroque music and Christopher Wren's architecture, and the quantum worldview produced modernism and Bauhaus glass-cube monopitch-roof architecture, the chaos-theory universe hasn't yet made its full impact felt on art and music and literature. A few compositions like Bruno de Gazio's algorithmic works of the early 1990s and Mark Trayle's Mattel Power Glove compositions have filtered into our consciousness...but by and large the *weltbildung* suggested by chaos theory seems hallucinogenic to Western artists and composers and writers. The idea that the universe is a place shaped by violent, complex, unexpected events which grow out of microscopic chance events...well, it's not a comfortable one. The notion of huge effects blossoming from trivial causes is not something with which Aristotelian dramatic theory is well equipped to cope. It's as though Oedipus were and his entire family were to die horribly from infections caused by scratching mosquito bites(!) In music, however, the seeds of this kind of exponential and uncontrolled growth of emergent structure have always been nascent in Western tradition. Ever since composers began to generate huge compositions from small cellular motifs, the notion of order boiling out of chaos seems to have lurked just outside the peripheral vision of Western music theory. Of course, non-just non-equal-tempered tunings are particularly alien to our (read: white European) concept of music. And so it's fascinating to note the historical Western response to the Indonesian gamelan, which uses a classic n-j n-e-t tuning (in fact, each gamelan uses a different one). The first time a Western composer appears to have encountered the gamelan was when Debussy heard one at the Paris Exposition in 1895. He was struck most forcefully by the rhythms, which he ecstatically described as "complex enough to put the finest Western composers to shame" (or words to that effect; this is from memory). Mantle Hood's importation of a gamelan in 1956 appears to have sparked Lou Harrison's interest, and a general American gamelan movement--ironically founded on tunings using just intonation. As Marc Perlman has pointed out, this is a radical departure from actual Javanese/Balinese tuning practice... And it indicates just how completely *unable* Western composers are to assimilate the Javanese tuning in its *own terms.* Indeed, Lou Harrison himself admitted to being terrified of the non-just non-equal-tempered intervals of "slippery slendro;" without the Western rationalistic landmark of small integers, he found himself at sea. And finally during the 80s and early 90s digital signal processing compositions produced with the spectra and tones of gamelans (for example, Robert Valin's "Tat tvam asi," 1990, UMUS CD "Bali In Montreal," UMM CD 104) again emphasize Fourier manipulations and transformations. *Again* the Western composer is reduced to grasping at harmonics and integer-ratio frequencies *even* when manipulating the raw non-integer, inharmonic, non-just non-equal-tempered partials and spectra of Javanese/Balinese gamelan: *again,* there is a complete inability to incorporate the gamelan worldview into the composer's milieu and assimilate it as part of Western compositional process. Instead, the Javanese n-j n-e-t tuning and chaos-theory worldview of clashing rhythms producing a mysteriously regular emergent order can *only* be assimilated by the Western composer/theorist if *first* coated with the antibodies of Fourier theory and harmonic overtones. Thus it's fascinating to observe the clashes between these three factions on this tuning forum. My observations concerning non-just non-equal-tempered tunings matched to n-j n-e-t additive-synthesis timbres have provoked incomprehension, with some outright hostility and no little puzzlement thrown in; meanwhile, the main hot spot seems to be the flash point between equal temperament advocates and JI enthusiasts. This is particularly revealing because it shows not only the tremendously long lead time for new ideas to percolate from the sciences into the arts, but it also clearly demonstrates the enormous staying power of classic worldviews. Many writers on just intonation evoke a view of Apollonian poise and balance, and a yearning for perfect order. Indeed, the title of one of the best current compilation series of JI music is in itself revealing: "Rational Music For An Irrational World." A vision of literally classical order in a disarrayed universe. And (also revealingly) JI composers see  have a fondness for classical Hellenic subject matter: from Partch's exceptional series of settings of Greek drama to Fonville's setting of poems by Sappho, the nostalgic quest for order and balance harks back to the Italian Renaissance, the early part of the 19th century in England, and the early 20s of this century in England and America. In such a worldview, Keats' Greek vase is the ideal: "Heard melodies are sweet, but those unheard/are sweeter; therefore, ye soft pipes, play on;/ not to the sensual ear, but, more endeared,/Pipe to the spirit ditties of no tone..." [Keats, John, "Ode On A Grecian Urn," lines 11-14] (Sounds almost as though Keats yearned for a yet- unheard xenharmonic music far outside the 19th century 12-tone equal tempered scheme of things...) Modernism rarely evokes such longings. Instead, the emphasis in modernist music is often on statistical and probabilistic effects. From the regular distribution of pitch classes in the 2nd School of Vienna to the thermodynamically- and quantum-theory inspired stochastic sound-clouds of Xenakis, much modernist music might almost be called "quantum probability- clouds made audible." Subsequent refinement of these procedures in algorithmic compositions programs changed the emphasis, but not the essential inspiration-- nor the worldview implied. And thus the best of modernist compositions conjure up for me a statistically determined universe of strange and terrifying beauty...and notably one in which tuning is a secondary consideration. Modernist music appears to have emphasized the processes by which pitches were *ordered,* rather than by which they were *derived.* Perhaps the existence of this forum signals a shift toward the third or nonlinear worldview. As the ideas of chaos theory and complexity theory seep into our culture, the notion of emergent order generated at the edge of nonlinear musical processes becomes more "natural" (the single word most fiercely argued over on this forum, and perhaps the one word used by the largest number of subscribers with the largest numbers of different meanings) and more acceptable. Pushing forward, it's hard to see where this worldview might take music... The terrain ahead is indeed alien. One imagines algorithmic compositions generated by nonlinear processes in which even the tuning is produced at run-time, and is a different non-just non- equal-tempered set of pitches in each performance. On the level of the microstructure of musical tones, Sethares', Pierce's, Carlos', Dashow's and (yes) my notion of matching partials to tuning raises many possibilities from hierarchical order in n-j n-e-t compositions: notes whose overtone structure changes kaleidoscopically as the pitches run through various timbral strange attractors. Jean-Claude Risset, Paul Lansky, John Chowning, James Dashow, William Schottstaedt, Richard Karpen, Mark Trayle, Cindy McTee, Richard Boulanger, Hugh Davies, Jonathan Harvey, Warren Burt, William Sethares and others have already produced compositions which give a glimpse of this brave new musical world: and they are indeed breathtakingly beautiful. Still, very little work has been done in this area. To quote Ivor Darreg, "It will require the work of many composers for many years to map out the vastness of xenharmonic territory." --mclaren Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Wed, 1 Nov 1995 20:55 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id KAA19194; Wed, 1 Nov 1995 10:55:39 -0800 Date: Wed, 1 Nov 1995 10:55:39 -0800 Message-Id: <199511011848.AA22720@net4you.co.at> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu