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Extract from Robin Maconie: The Science of Music,
published by Oxford University Press (The Clarendon Press) 1997.

HARMONY is about multiplexing. Multiplexing is information management. For Edison, it was sending more than one telegraph message down a wire at the same time. In music, it is combining several lines of information in such a way that they can be followed independently. Music recognizes a variety of forms of multiplexing, the most basic being voices or instruments in unison, and extending via heterophony (playing the same tune but with individual decoration) through polyphony (playing the same music, but different parts) to counterpoint (multiple parts in call or answer mode based on a melodic model). For harmony to exist there has to be more than one message in transmission. The art of harmony lies in encoding multiple messages so that they do not interfere with one another in transmission and may successfully be decoded as separate strands by whoever is at the receiving end.

In conventional music theory, harmony is vertical thinking: the spacing and combination of notes in a multi-part composition at any given instant. The art of harmonization nevertheless implies a horizontal dimension, the management of multiple layers of information over an extended period, and the rules of harmony are designed to ensure that a balance is maintained between separation of individual lines and harmonic consistency within the group. Among the Greeks harmony in music was the term applied to the rules governing the mode or scale of pitches to which a musical instrument is tuned, rather than rules determining the choice of chord sequences in relation to a melody. By extension, the Greeks regarded harmony in other forms of collective behaviour as an imposed hierarchy within which freedom of action and expression could be sanctioned. Greek harmony thus signified a structure of standards of behaviour that determined individual scope for interaction rather than rules on how individuals should interact from moment to moment. Tonality, as the dominating system of early modern Western music, is our equivalent to harmony in the Greek sense; what students of music today learn as rules of harmony has much more to do with regulating a flow of information in multiple parts, and only residually with society or private morals (as in 'modern music is immoral').

Harmony in music is therefore a means of enquiry into the organization of complex natural phenomena. A sense of harmony can arise from what appears to be spontaneous obedience to natural impulse or law (for example, the behaviour of a flock of birds or shoal of fish moving as a group and avoiding collisions), or alternatively from collective uniformity to a signalling authority (soldiers marching in step, an orchestra under a conductor, etc.). Sheep or cattle respond collectively to human direction on the road (often with the aid of musical signals), and revert to individual behaviour once they are safely arrived in pasture. The purpose of shepherding a crowd on the road is to keep them moving at the same pace and toward the same goal. That is what classical harmony implies: continuity and coherence of collective movement toward a common goal. Having reached the safe haven, however, individual self-determination becomes the norm. When the limits to freedom are clearly defined, individuality can flourish. After the last emphatic chord, the players go home.

Like any other science, music is not just about making rules and restricting one's grasp of reality to those aspects that fit the rules. There is also an interest in contemplating natural disorderliness, which has its own consistencies and hidden regulations. A natural scientist takes account of the collective clamour of birds, bats, or chirping insects, and wonders how pairing connections are extablished in the general melee. Composers in the twentieth century have faced up to the challenge of creating alternative conditions for music-making in which individual freedom of action is possible within an overriding harmony. Schoenberg began by abandoning the classical hierarchy of tonality in favour of an intuitive, later more systematized, scheme of freely co ordinated parts. The problem he had to solve was inadvertent consonance, and banning octave relationships waas one way he hoped to avoid the distraction of unwanted harmonies. Messiaen took inspiration in the composition of complex effects modelled after birdsong. Cage devoted much of his life to compositional procedures designed to dissociate the composer's and performer's aesthetic and functional preconceptions from the musical end-product. He too faced enormous resistance from rank and file musicians all of whose training militated against independence of action and freedom of judgement. Boulez, Stockhausen, Berio, Lutolawski, late Stravinsky, and others devoted themselves to the development of serial and notational protocols designed to allow varying degrees of interpretative freedom to the conductor and individual musician.

In a paradoxical way, then, the science of harmony is interested just as much in the rules governing the isolation of individual lines of information from among a complex totality as it is concerned for the relationship of the parts to the whole. The Alpine herdsman who hangs a bell of different pitch round the neck of every cow has created a mechanism enabling him to track the movement of any chosen individual at will. It is exactly the same principle as implanting a radio transmitter on a wild animal, and just as it is vital to ensure that each transmitter sends out a clearly different signal, so the difference in pitch between one cowbell and another is also important: not only for the human observer, indeed, but for the cows themselves as badges of office (senior cows demanding the lower-pitched bells).

Copyright © Robin Maconie. maconie@earthlink.net

Robin Maconie is author of The Works of Karlheinz Stockhausen (Oxford University Press 1976, 2nd revised edition 1990, 3rd edition in preparation), editor and co-author of Stockhausen on Music (Marion Boyars 1989), and collaborator with Barrie Gavin in the production of the BBC 'Omnibus' 1981 Stockhausen film portrait Tuning in. He studied under Messiaen 1963-64, and with Stockhausen, Pousseur, Eimert, Aloys Kontarsky, Bernd-Alois Zimmermann and others 1964-65. His most recent publication is The Science of Music (Clarendon Press, 1997). He is currently Professor of Performing Arts at Savannah College of Art and Design, Savannah, Georgia.