One can certainly find stated in music textbooks that polyphony — and harmony — are Western inventions, and one can observe this notion as well in the behavior of ordinary musicians. Perhaps they do not say so explicitly, but many adopt a Western harmonic stance in their interaction with world music. However, literal definitions are becoming more popular in today's world, and literally speaking, most of the world's musical traditions involve more than one simultaneous sound. In statements such as "polyphony is a Western invention," something rather more specific is intended, but it is an intention which does not necessarily stand to scrutiny.
Perhaps the most widely known non-Western "polyphonic" tradition is the gamelan music of Indonesia. There, many instruments work together to articulate a large-scale piece of music, often performing only the tiniest of individual parts. In the typical gamelan, different types of parts are very distinct, such that they move at completely different speeds, with a faster part fitting into the framework established by a slower part, etc. Such a description fits some important historical styles of Western polyphony too, especially that of the Notre Dame school. Besides Perotin et al., the later cantus firmus mass also adopts "framing" parts in different tempi. One facet which differentiates gamelan music from these examples, though, is its imprecise sense of tuning. The tuning of individual ensembles is internally consistent & distinctive, however, even if it is the completion of differently-timed cycles which dictates musical form. It is nearly impossible not to consider the gamelan to be "polyphonic" in all important senses, negating the idea that polyphony is a Western invention. Moreover, various Southeast Asian styles exhibit similar traits, although often labeled "heterophony." A melody or melodies is passed back and forth between various performers, each elaborating it in their own way, simultaneous with, but largely indifferent to, what the other performers are doing. The process is not unlike jazz improvisation, and again it is timing which lets each performer know when to stop. In these styles, each instrument can be equal, yielding what is essentially an imitative texture. Without differentiated functions, though, there is little or no planned simultaneity in vertical intervals.
The rhythmic basis for combination is at its most starkly clear in traditional African drumming, where rhythms move around a loosely coordinated ensemble. The sense of simultaneity can be very high here — especially moving into and out of phase — but there are no chords. The importance of timing as a basis for combining parts is also evident in Western music, as it was the desire to commit polyphony to writing which spurred the development of mensural notation, and with it the ability to coordinate differentiated parts over larger spans. While it is difficult to identify a single factor which identifies "Western polyphony" as a distinct technical undertaking, this act of balancing horizontal & vertical concerns over a span of time is certainly one characteristic. It, of course, also gave rise to the more specific idea of composer per se, someone who had orchestrated beforehand how the various individual parts would interact, instead of letting them unfold on their own. A planned sequence of cadences, based on a vertical theory, has long been a part of the most advanced Western composition, and this adjunct to the use of rhythmic cycles and overlapping parts might be the most distinctively Western aspect of polyphony.
Moreover, the earliest Western polyphony can be traced not to works with clearly distinguished and segmented parts as in Perotin or Dufay, but to note-against-note writing. It is difficult to find any analog elsewhere to the early conductus in this style, and indeed the evident origin of polyphony in improvisation makes the early emphasis on simultaneous motion of individual lines even more difficult to explain on the world stage. Indian music has a very strong sense of vertical interval, of course, and is not content with the rather indistinct tuning associated with gamelan or Arabic classical music. However, there is no sense in which the individual lines are equal in Indian classical music, as the vertical space is largely defined by drones. More generally, accompanied song is ubiquitous, whatever the derivation of the accompaniment, and so one can perceive Monteverdi's innovations as making Western music more like other traditions, even if the harmonic underpinning based on earlier polyphony became that much more specific. The realm of continuo is distinguished from heterophonic accompaniment primarily by the enforced relationship between the secondary parts, although a relationship of a different sort is just as mandatory in the notes of an Indian tanpura.
Even the notion that the West uniquely chose to balance linear independence against vertical planning is not necessarily true. While early Chinese ceremonial music bears a general resemblance to gamelan, there was more attention to chords and tuning. Classical Chinese texts already define a Pythagorean style of tuning, based on both ascending and descending fifths, and the relatively deprecated scholarly music still shows a keen & subtle attention to verticality. More recently, Near Eastern music has devoted increasing attention to vertical & orchestral combinations reminiscent of Western counterpoint. While classical texts do not discuss this style, suggesting that it is indeed inspired by more recent interaction with the West, the vertical styles themselves are not merely derivative. Composed orchestral compositions go back at least to the Ottoman court in the era of Mozart, and so have their own history rivaling that of the Western classical style. The Central Asian empires between China & the Near East might provide a different source of historical continuity. In terms of possible influence on the West, Eastern styles of group chanting suggest a long-established form of polyphony, even if vertical rules were not written. This is true not only of more noticeably Westernized styles such as Eastern Orthodox or Bulgarian choral singing, but of e.g. the Syrian chant arguably traceable to the early Christian era. While our own scholars' historical bewilderment at (e.g. Welsh) polyphonic folk singing in the West can be taken as direct evidence that any transmission of plainchant from the East was not accompanied by a polyphonic style, the sheer murkiness of that origin precludes definitive statements. There is no question but that the Eastern Mediterranean played a critical role in early Western culture, as eventually crystallized by the medieval era.
What people end up meaning, of course, is that polyphony & harmony in other cultures do not sound to us much like our own. While one or two technical definitions might not distinguish them, more restrictions can be added. The West's specific adoption of tonality is its own, almost by definition. The way any particular combination of sounds is perceived by musicians is also tradition-specific, based as it is on centuries of development for both notation and historical context. It is then a more general sense of contrapuntal style which is unique, rather than a succinct technical definition. What the West eventually defined as its own crystallized after contact was renewed with the rest of the world. This is true of the basic locus I have termed melody determining form, as well as vertical structure per se. The nature of sonata form, its basis in argument, is also an expression of aggression & power, one not found in the refined classical traditions of many cultures. In that sense, and in many others, the West's sudden self-consciousness acted to shift its own style, making the self-consciousness itself — the tantrums of Beethoven — the aspect which defines Western music for many other cultures. The poised equality of line which seems so uniquely Western was swept aside, a transfiguration brought on by dominance itself.
Administrivia: Next column in three weeks.