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Molecules and Music

ISSUE:  Summer 1981

Puzzling over the continued reluctance of music lovers to accept new music, I have turned to reading what critics had to say about earlier music when it, too, was new. It is difficult to remember today that even Beethoven did not meet with immediate comprehension. A modern reader may well be shocked by this review of Beethoven’s Fidelio from a Vienna paper of 1806. “All impartial observers were in agreement that never was anything as incoherent, shrill, chaotic, and ear-splitting produced in music. The most piercing dissonances clash in a really atrocious harmony, and a few puny ideas only increase the disagreeable and deafening effect.” Wagner fared no better with a critic of 1873 who found his music a wild chaos of tones. “It was as if a bomb had fallen into a large music factory and had thrown all the notes into confusion.” In Boston the Evening Transcript of November, 1885, reporting that large numbers of people left the concert hall between movements of the Brahms C minor Symphony, adds regretfully that “to the larger part of our public Brahms is still an incomprehensible terror.” Even Debussy’s La Mer was, to a New York Post critic of 1907, “the dreariest kind of rubbish. Does anyone for a moment doubt that Debussy would not write such chaotic, meaningless, ungrammatical stuff if he could invent a melody?”

Composers today may find consolation in such fragments of history. Clearly, a time lag in acceptance of new sounds is not unusual. The problem, however, is more acute today for composers, critics, and audiences alike. We are living through the transition not just from one generation to another, or even one century to another, but from one era to another. In this first century of a new era many still ask that music remain what it was for the preceding three centuries, the voice of a small, man-centered world. The world, however, has grown so vast that the space our human senses command is no more than a narrow interface between the unimaginable reaches of an expanding universe and the invisible inner mysteries of atomic particles. Must music then remain in the small orbit of its past?

Change is accepted more readily in arts other than music. Sculptors of this century have tended to ignore the human body in order to capture, in the tensions and balances of metal, wire or plastic, the laws of nature. Where the biological form remains, it is fragmented into planes by Picasso, perforated by Henry Moore or attenuated almost out of existence by Giacometti. Painters create abstractions of color, line, and mass, poets speak more through the sound than the syntax of words. But when composers fragment a line of tones into single resonances, thin out harmonic masses into open webs of sound, ignore the regular meters of march or dance, this, to most audiences, is not music.

For these listeners, the term “music” apparently belongs only to the three-century-old art of tonal harmony and tonal melody, a music that grew out of the era of rationalism, of scientific materialism, of belief in man’s ability to understand and master nature. The music of that age was a great and abiding achievement, a monument to mankind. Now, however, we recognize our species as only a fraction of an indivisible whole, a part of, not apart from, nature. We may function, Lewis Thomas suggests, as “handyman for the earth,” fetching and carrying information, seeds and energy, or even as the nervous system of the planet but not as its owner or operator. This planet, to the astronauts who have viewed it from space, looks like “a small blue-green sphere about the size of a Christmas-tree ornament,” and just as fragile. Ours is a universe more mysterious than any dreamt by man’s religions of the past. In it we are no longer observers sure of ultimate understanding but participants forced to realize that there are ineluctable limits to our knowledge. Are we, then, to paint the same landscapes, carve the same statues, write only the melodies that can be sung in the cadences of our speech over the time-directed harmonies of a simpler, smaller world? Composers, like all creative artists, all creative minds, are responding to new relationships between man and world. As sculptors have abandoned what Herbert Ferber calls “the biological envelope” and painters the outward appearance of nature and man, so composers have sought release from the phrases of speech and the meters of human motion.

Music in all ancient cultures grew as companion to worship and ceremonial dance, shaped by words or by physical movement. When in 17th-century Europe music for instruments evolved into a style of its own, it still retained the linguistic outlines and the physical pulse of its origins. In the dramatic atmosphere of that baroque period, composers sought an equivalent for the rhetoric of the orator. Eloquence was necessary “to move the spirit, in particular to rouse the passions,” as a contemporary writer put it. States of emotion, Descartes’ “passions of the soul,” were characterized in musical figures of a few notes: for anger, wide leaps of melody and a rapid rhythmic motion, or for sadness, small intervals, chromatic harmony, and a quiet tempo. The musical figures were ambiguous, of course, since definite meaning could be established only where there was some prior association with words. A figure was intended to signify an emotion rather than to express or develop it, for the emotion was static, a condition, and presumed to last until displaced by another. Therefore a whole movement could be based on one figure spun out through many keys, gathering musical richness as it moved irresistibly toward its close. With these baroque figures, instrumental music could stand alone, free from the words and the limited range of human voices.

During the 18th century the short baroque figure gave way to the longer musical phrase and sentence, question and answer, thesis and antithesis. The punctuation of speech remained; the rhythms of speech overlaid the regular metric pulse of march or dance. The music had the quality of discourse, of a conversation without words, a quality that reached its climax in the music of Beethoven. Linguistic influences, although surviving into this century, lessened after Beethoven’s death.

Tonal harmony, based on the gravitational attraction of a central key and a central chord in that key, was the underlying premise of those same three centuries. Indeed, it cannot be separated from linguistic characteristics, for it reinforced the phrases, periods, and paragraphs of musical discourse. It was as one-directional as language and more forceful than rhythm in pursuing that single direction. It was at once a syntax and a propulsive force. Bach and Handel relied on it for dynamic power, Mozart and Haydn for clarity of design, Schumann and Chopin for color and suspense, Wagner for the dramatic intensity of delayed expectation.

But new theories of reality, new interpretations of nature, whether based on science or religion, affect the very foundations of the arts. Tonality had taken shape in the century of the first Scientific Revolution; it ceased to be a valid premise just as the Newtonian world was giving way to the Einsteinian world. Newton had postulated a coherent closed system that seemed to be a final description of the natural world. Tonality for equally long was considered to be the “natural” basis for music. But as the word “nature” took on new meaning, the tonal system and the linguistic forms that had helped to shape it lost their long-sustained hold over music.

They had been, in their way, as anthropocentric as the sculptor’s statue and the painter’s portrait. Now fragmented sound supersedes sentence, rhythmic organization no longer depends on the gestures of speech and the meter of human step or pulse. If words are used, they may be pulverized into their constituent particles or filtered electronically into new sounds, for words are to the composer like natural objects to the painter. They may sound through or they may be blotted out as sound develops independently from them. Voices and words, vowels and consonants, are simply sources of sound.

“The world of words has shrunk,” George Steiner points out in Language and Silence. There are ever-larger areas of experience that are not accessible through words. There is, as he says, a retreat from the word in all the arts, a turning toward the abstraction of mathematics on the one hand and on the other toward silence as a realm of understanding beyond verbal forms of thought. Music, which had had a syntax parallel to language, now takes another step beyond the range of words. Composers turn to mathematics for new methods of organization and to silence as an active force surrounding, intensifying sound.


There is nothing new, of course, in an association of music with mathematics. It is not necessary to cite Pythagoras as a reminder that the acoustical material of music is inseparable from number. The contrapuntal music of the late medieval period relied on numbers to align its separately conceived voices. Composers of the 14th century played mathematical games in sound. Meters in the music of the West have long depended on the multiplication or division of standard units of time. In the East, and now increasingly in the West, additions of or to such units are common practice. It is not the use of mathematics that is significant today but its predominance over the linguistic influences of the past.

An old mathematical resource put to new uses is the Fibonacci series, where each number is the sum of the preceding two. This sequence of 1,1,2,3,5,8,13,21,34, etc. can be used in pitch determination, in note durations, or, perhaps most effectively, in sectional proportions. Avoiding the regularity of an arithmetical or geometric progression, it still offers order and proportion. Because it approximates a series of golden sections, it satisfies the need for a quality of authority that transcends a composer’s private organizing method.

Probability theory, information theory, the serial ordering of one or all dimensions of sound, set theory—all these have been used by one or many composers. Perhaps it is enough to mention that the excellent Dictionary of Contemporary Music, edited by John Vinton (1971), has five columns under “Mathematics,” whereas the respected Harvard Dictionary of Music (1944) had no entry for that subject. But what must be emphasized is that these theories or methods are pre-compositional processes. They are sources of inaudible order, replacements for the long-accepted limitations of harmonic and linguistic syntax.

Some limitations a composer must have, resistant material, difficulties to overcome, restrictions to circumvent, The choice of sounds, thanks to electronic synthesizers, is no longer limited to the ranges and timbres of instruments, of human voices, or even to the traditional Western division of the octave into twelve equidistant tones. If a composer is not to drown in a new chaos of sound, he must pre-select his material and define his boundaries. “If nothing offers me any resistance,” Stravinsky said, “then any effort is inconceivable. . . . In art as in everything else, one can build only on a resisting foundation.” There are a stubborn few, to be sure, who try to build happenings on sand, but there are many more who find that mathematical logic can provide the necessary limitations within which their imaginations are free to roam.

Mathematical devices obviously increase the tendency to abstraction, to the absorption in pure structure that is apparent in the other arts and sciences of this century. Science has passed through stages of increasing abstraction in its search for the unitary laws that bind all nature together, and mathematics has become the language in which the scientist’s understanding of nature is expressed. The arts follow a different road to the same end, uncoupling (Suzanne Langer’s word) a work from actual objects, scenes, or verbal language. Thus the basic realities behind the facade of nature can be more clearly reflected. Structure becomes the key word of both disciplines, for structure, not matter, is the key to our universe.

Jacob Bronowski said that modern art and modern physics began at the same time because they began in the same ideas.

Both work from the smallest element, building from inside out, from the particle within the atom, from the painter’s dot of color, the sculptor’s module, the musician’s single sound. The composer does not begin with a theme; he places sounds in a frame-work of space and time. His tones are no longer members of an established family of seven tones with a center to which the other tones gravitate. They are separate entities, building stones available for use in any order or combination. All twelve tones of the octave were declared equal by Arnold Schoenberg early in this century, and so they have remained for the most part, though not always used in Schoenberg’s method.

William Barrett, in Time of Need, sees in this equality the premise of Nihilism, “that all the elements in its world are indifferently equal.” It is an arresting view, one of the multiple perspectives from which this age must be seen. But from another angle I see, in this equality, the atoms and molecules of nature, the atoms of carbon, for example, that join in varying number and pattern to form molcules as different as those of graphite and diamond. When Anton Webern combined three tones at certain fixed distances from one another, he created not a theme but a molecule or a cell, three points of sound in a triangle that retained its identity whether heard as clockwise, counterclockwise or upside down. From that molecule grew a piece of music, a delicate open structure of sound and silence, the Concerto for Nine Instruments, op. 24.

Such structures of musical molecules may take many outward forms as do structures in nature. It is a new way of building, a new kind of order based on discrete clusters in ever-changing relationships. The unity of a composition lies at the molecular level, not in an outward form of balanced sections and repetitions nor in the dramatic discourse, the conflict and resolution of the sonata form.

Webern’s sounds are clearly articulated, precisely placed in space and time. Other composers weave thin strands of sound so closely that no one strand is heard but only a cloud of sound, scarcely moving. Bruno Maderna spoke of the sounds in his Aura as radiating from a central musical object. Gyorgi Ligeti’s shimmering atmospheres of sound hover in space, seeming to suggest the absence of all solid forms, the dissolution of line and mass.

It might be wiser for a musician to avoid trespassing in the domain of science with such suggested parallels. I am well aware that scientists scorn a layman’s arguments built upon what they feel to be mere accidental likenesses of language. But the major conclusions of 20th-century science are now in the public domain, very much a part of our current thinking. One need not be a scientist to have absorbed an awareness of the permeability of matter, the dual identity of matter and energy, the motionlessness of time, the chemical elements common to both organic and inorganic structures. “The human brain,” Lewis Thomas declares, “is the most public organ on the face of the earth, open to everything, sending out messages to everything. . . . We pass thoughts around, from mind to mind, so compulsively and with such speed that the brains of mankind often appear, functionally, to be undergoing fusion. . . . Already, by luck, we have seen the assembly of particles of exchanged thought into today’s structures of art and science.” Artists have sensitive antennae; it would be strange indeed if they did not register what Thomas calls “the bits of human thought that are constantly adrift, like plankton, all around us.” Each art, to be sure, has its own internal history, the record of its gradual solution of a set of technical problems (the syntax of tonality in music, of perspective in painting), but it exists in the presence of public ideas. Our curiosities, the questions we ask, the explorations we undertake are shaped by those bits of shared human thought.

Bronowski, in the Identity of Man, maintains that science and art, though different, “are vastly more alike than they are different. For what makes them different is their expression in action, but what makes them alike is their origin in imagination.” The physicist David Bohm speaks of science and art as “complementary ways of coming in contact with the world,” and Werner Heisenberg recognized that science and the arts are moving separately but simultaneously toward ever higher stages of abstraction. Modern art, Heisenberg said, “seeks to present a sense of life which perceives man in relation to the whole earth, and sees earth in the cosmos as if from other stars.” The biologist C.W. Waddington, in Behind Appearances, considers the effect of our knowledge that in the physical world “everything is really everywhere, though in some places more than in others.” He was thinking particularly of painters, but his sentence calls vividly to mind the sonic atmospheres of Ligeti, Xenakis and Stockhausen, as well as paintings of all-over interest like Monet’s Waterlilies, Mark Tobey’s Messengers or many of Jackson Pollock’s cavanses.


In this universe to which our minds are now adjusting, music is more like a tapestry of interwoven events than a scroll unrolling in time. It is seldom a smooth flow of sound, more often stressing discontinuity with its frequent silences and its juxtapositions of self-contained “moments.” By showing little motion in time it calls attention to space, to where the next sound will come from, not when. It is a sounding structure that reaches a level of abstraction beyond not only the words but the shapes of speech.

Some music lovers, nostalgically comparing this music to that of the 19th century, complain that in its abstraction the new music is dehumanized. But to remove the thematic sentence from music, the human face from painting, the “I” from poetry is not necessarily to dehumanize an art. It may be a way to extend its reach into the world. “If abstraction were really unnatural,” Suzanne Langer said, “no one could have invented it.”

Ortega y Gasset, the title of whose essay, “The Dehumanization of Art,” seems to be much better known than its substance, used “dehumanization” as a term of praise. He was commending artists such as Debussy and Mallarme for disencumbering the arts of their emotional overload and their excess of realistic detail. Artistic creation requires stylization, he said, and to stylize means to de-realize, de-form, de-humanize in order to extract the intrinsic meaning from a confusion of fact and a miasma of sentiment. The 19th-century preoccupation with personal emotional states was to him an aberration, a deviation from the norm of cultural development. Primitive man, he said, lives with his attention “nailed to the cosmic scene, leaving his own self at his back.” In Oriental cultures man was always seen as a part of nature. Even in ancient Greece man was only a detail of the cosmos. A slow turn inward came to the West with Christianity, but it was not until the 17th century that the separation of self from nature was sharply drawn by Descartes. Thereafter the self grew out of proportion to its world, its disproportion culminating in the 19th-century. “The self has enjoyed a brilliant career,” Ortega said, “It cannot complain.” But, he added, it now needs to find the world around it, to co-exist with that world.

Perhaps we are in some ways primitives again today, a very young species in a very old universe. We are looking out, listening out, to a new cosmic scene, relocating ourselves in it. And, correcting the 19th-century tendency to let the self obscure the view, we try to push ourselves behind our backs. The change is well indicated in what Pierre Boulez calls “The search for anonymity.” Asked to explain the phrase, Boulez replied to his questioner with the story of an ancient Chinese painter “who drew a landscape so beautifully that he entered the picture and disappeared.” Disappearance may be impossible; an artist’s thumbprints are all over his work and artists can scarcely be said to lack strong egos. But although not always approximated, the ideal remains of disappearance into the picture or into the music. Sounds, colors, stone, metal— these have their own natures and are not to be subverted for the expression of an ingrown self.

All great works of art inevitably reveal in some degree both the artist’s self and his world. “World” may mean religion, as it did to medieval musicians; humanity, as it did to Beethoven; visible nature, as to Debussy; or it might mean the invisible cosmos of macro and micro dimensions, as we comprehend it today. The proportions of world and self vary from age to age, culture to culture, style to style; and when world overshadows self, abstraction is likely to predominate over naturalistic elements in artistic style as it did in primitive cultures and as it has in this century.

This is not an easy time to make music. Elliott Carter calls the situation “fascinating but infuriating—as though you had to write every letter in a different language—well, not a language, exactly, more like a dialect.” No one today can compose with the ease and prodigality of Haydn. No one can absorb, as the child Mozart did, a musical language widely known but still fresh, flexible, adaptable to his maturing purpose. Each serious composer born in this century has to establish a method and write his own laws of procedure before he can begin to compose music. From Debussy and Webern he can learn the values of silence, from Webern and Schoenberg the uses of number, from Varêse the delight in sounds free from the traditional tempered scale, from Stravinsky and Messaien fresh uses of rhythm. But a commonly accepted syntax does not yet exist. The lack of it demands more of listeners as well as composers. The latter can ask only for imaginatively open minds and critical but receptive ears.

No doubt audiences will continue for some time to find an easier enjoyment in music of the past, although, from too much repetition, it loses its essential quality of surprise, its ability to command our taut attention. Popular music, rock and folk and Western, will doubtless continue to celebrate everyday existence, everyday moods and problems, in a style conservative enough to appeal to a wide audience. But there are other things to sing about. If we want music that pushes back the horizons of the everyday world, music that calls us out of the nostalgic past and helps us to assimilate the beauties and excitements of our present expanded world, we will find it in such compositions as Bartok’s Music for Strings, Percussion and Celeste, Varêse’s lonization, Boulez’s Le Marteau sans Maitre, Maderna’s Aura, Takemitsu’s Quatrain, or perhaps in the cosmic echoes of the best of George Crumb’s music.

Music such as this charts new realms for the imagination, invites us as listeners to a new wakefulness, a new awareness of our world. We will be the poorer if we ignore the invitation. In any case we can no more turn music back to the age of linguistic forms and time-directed harmonies than astronomy can be returned to the limits of one galaxy or particle physics to the certainties of the Newtonian world. The multiple perspectives of relativity have destroyed our provincialism, and the principle of indeterminacy has reduced our old role of spectator, hyphenating it to participant-observer. While space has expanded in all directions, time has stretched backward to a duration of billions of years. This is not an age in which music can progress steadily through time toward a foreseen end. Nor can it be shaped to the clarities of speech or weighted with the richness of massed harmonies. It can, and at its best does, bring us intimations of the mystery, the vastness, the timelessness, and the strange beauty of our newly discovered cosmos.


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