By a "multiple view" is implied that each of the styles of music requires a theoretical explanation all its own, or, expressed differently, that a theory that is illuminative of one style may actually be inappropriate for another. Such a view has not been generally held by music theorists, however; instead they have been inclined to look upon all (or some) of music from a single vantage point, attempting to explain the various styles using a single theoretical system as a basis.
Among the problems engendered by the "single view" of theory is the imposing of criteria appropriate to one musical style onto another. This is evident, for example, in a number of recent theory texts that have tried to be more far-reaching in their musical coverage, although at the same time (perhaps unwittingly) they have retained a point of view typical of 18th-century harmonic theory. One example from among many that could be chosen is Elie Siegmeister's treatment of "Twentieth-century Harmony" as "new ways of using traditional chords," or as "expanded tonality."1 On a rather more sophisticated level is Paul Hindemith's attempt to apply (his own) harmonic logic to the tone rows of Schoenberg's Klavierstück, Op. 33a: "I have analyzed the piece only from the harmonic point of view because the melodic element seems to me to have receded far into the background."2 Or to take an example of a vastly different kind, Felix Salzer, in describing a passage by Perotin in which the Cantus firmus revolves around the note A in long-held tones, emphasizes the need to grasp "the main prolongation" of the A-chord lest one "merely acknowledge a flow of lines and a succession of intervals."3
I would suggest further that the statistical approach to theory that has been gaining in favor recently, as is evidenced, for example, in frequency-distribution curves of chords, intervals, or even single tones, actually reflects a point of view corresponding with that of recent avant-garde composition (e.g. Xenakis), and therefore represents an imposing of a kind of standard upon past styles that has nothing to do with their original conception.
By and large, however, the predominant trend reflected in recent theoretical studies is that tonality has been the real generating force behind the historical styles—a point of view that could be a result of the prevailing harmonic orientation in our classroom theory. In these many attempts to reveal the presence of tonality in Medieval, Renaissance, and even in contemporary music we have a particularly vivid illustration of how our perception of the music of these periods can become directed away from those very qualities that are most essential to the style in question.
How, then, are such qualities to be perceived? The solution I am setting forth in the present essay is that of a "multiple theory," which implies that it is essential to approach each of the styles on its own terms. Only then do we become aware that a coherent simplicity runs through each of the styles, extending to all its aspects large and small, shaping and investing these with expressivity and meaning. Such a simplicity is most apparent, I suppose, in the harmonic structure of the Classic period, which reaches out to control all the various attributes of the style (the themes, the rhythms, the formal continuity). That a similarly coherent quality is present in other musical styles as well, however, has generally not been acknowledged. Perhaps the most persuasive argument for its presence is an inner morphology within each of the styles, that is, that they each proceed gradually from a state of stylistic simplicity towards one of formal complexity. Initially the coherent principle of a style tends to be conspicuous in the music (the preponderance of style over forms), but little by little, as the principle comes to be absorbed into the creative mentality of a period, musical forms are conceived that give it a greater fullness of expression, until in the late stages these forms in themselves come to outweigh in importance the underlying principle. It is at this very juncture that the most imaginative and innovative creative geniuses make a leap into the unknown, and in so doing discover a new means of achieving musical simplicity (usually through some element that had been a mere detail in the style just preceding), and thus a new style is brought into being alongside the old.
In the brief summary that follows I will indicate only the main outlines of such a morphological development, and at the same time suggest in words what I feel constitutes the essential simplicity within each of the various musical styles:
1. Melody (ethnic, Oriental, Medieval): an early phase, in which melodic lines are shaped by central tones (initially one, and subsequently two or more) around which the other tones revolve; and a later phase, in which melodic segments are repeated exactly (centonization), culminating eventually in the repetition of entire phrases or refrains. (Recent folk melodies, which are for the most part derived from key-center tonality, are not to be considered here.)
2. Organum and heterophony—the enhancement of a known melody by the adding of other sounds or pitches (ethnic, Oriental, Medieval): an early phase marked by the use of parallel intervals; a later phase, in which the added tones are of varying intervallic sizes (e.g. 11th c. Medieval organum) or are introduced only occasionally (e.g. African pygmy music); and a highly complex phase, in which accompaniments are based on elaborate rhythms (e.g. Indian talas), or on slightly displaced melodic segments (e.g. Japanese heterophony), or on several decorative versions of the main melody presented simultaneously (e.g. Indonesian heterophony).
3. Superimposed rhythmic patterns (the later Middle Ages): an early phase, in which the voice parts above a Cantus firmus are organized according to metric patterns (the rhythmic modes); a middle phase, in which the repeated rhythmic patterns of the tenor, contrasting with those of the upper voices, are gradually lengthened, culminating in the isorhythmic motet; and a late phase, in which syncopations both within and between measures reach an unparalleled degree of complexity, culminating in the chansons of the late 14th century. (This style should be distinguished from heterophony, in that the added parts do not simply enhance a main melody, but assume genuine independence in themselves.)
4. Counterpoint—melodic lines and their combination (the Renaissance): an early phase that sees the melodic smoothing out and decorating of the borrowed Cantus firmus and a more linear or melodic conception of the dissonance (both the Cantus firmus and the dissonance had primarily a rhythmical interpretation in the Middle Ages): a middle phase, in which melodic lines are ingeniously combined in canons or points of imitation; and a late phase, in which the melodic lines are broken up into distinct motivic patterns (e.g. instrumental music) or are combined in a rich variety of textures (e.g. the late madrigal).
5. The concertato principle—contrasts of vocal and instrumental tone color (the Baroque era): an early phase, in which the motives and textures of the late Renaissance are newly invested with tone colors, these being often of a strikingly contrasting nature, and in which soloistic voices and instruments (made highly distinctive with ornaments) are set apart from the heavy chordal background provided by the continuo (the idea of line as contrasted with mass); a middle phase that sees the application of these new coloristic possibilities to lengthier formal designs, as in the aria or the trio sonata; and a late phase, in which the concerto idea, with its broad alternation of soloistic and tutti elements, is transferred to a variety of vocal and instrumental forms (aside from the concerto itself).
6. Key-center contrasts (the Classic and earlier Romantic periods): an early phase, which sees the emergence of the "sonata" principle, characterized especially by elongated dominant harmonies that emphatically point up the arrival of new keys, and the "song" principle, characterized by surprising turns to different, and sometimes remote (e.g. third-related), keys; a middle phase, in which these principles are applied to more expansive forms, especially as evidenced by the sonatas, symphonies, or concertos of Mozart and Beethoven; and a late phase in which frequent modulations, chromatically altered chords, and the increased emphasis on III, VI, and 
(modal harmony) tend to obscure or weaken the feeling of broad key centers.
7. Motivic transformations (generally from Liszt to Schoenberg): an early phase, in which highly distinctive melodic ideas (often endowed with programmatic connotations) are spun out in a sequential continuity, and assume a variety of different rhythmic shapes as the form moves from one musical section to another (e.g. the tone poem); a middle phase marked by the use of "complexes of motives," that is, of submotives being continually rearranged to form larger motives (the concept of a "motive" now extending to harmonic progressions, to individual chords, and even to particular instrumental tone colors), these complexes of motives forming the main substance of extended works, such as the music dramas of Wagner or the symphonies of Mahler; and a late phase, represented by the highly intricate motivic techniques of serial and 12-note music, in which a fixed intervallic background tends to be set off against a fleeting succession of surface motives.
8. Static entities of sound—groups of unordered pitches or tone colors that create a composite (or essentially static) impression (the 20th century, from Stravinsky to the present); an early phase, in which polytonal formations or clusters of pitches are set apart as opposing spheres of sound (Stravinsky and Bartok); and a later phase, in which such contrasting spheres are realized purely in terms of instrumental or vocal tone colors (e.g. Varèse and Xenakis), or in terms of concrete or electronic sounds. (The idea of even trivial or ugly sounds now being treated as static entities clearly suggests a parallel with the collage or the mobile in the visual arts.)
How might theory in the school attend to such a diversity of styles yet at the same time maintain its integrity as a discipline? Certainly the severe limitations of time in the classroom might lead many to conclude that theory should remain as it is now, restricted to the traditional disciplines of harmony or counterpoint, while the acknowledged riches of ethnic, Medieval, or contemporary music are dealt with in the study of music history. But why not a coordination of theory and history? The past division between these areas now seems entirely anachronistic, reflecting a time when theory was concerned primarily with the producing of better practicing musicians, instead of with its true aim, which is the producing of musicians with increased musical understanding. And surely many of the activities now commonly a part of music theory—listening, analyzing, performing, composing—could be dedicated not only to the bettering of musicianship but to the developing of historical and musical knowledge as well.
A final question: Does not such diversification encourage mere dillettantism, a smattering of ignorance in many areas? I would counter that such need not be the case if the students' attention remains focused upon the essential principals of a style, and that they not become distracted with its details. This requires a new and imaginative kind of theory teacher, one whose knowledge and insight has been developed to a point where he can recognize and properly interpret these details, making clear their relationship with the larger principles. This could apply to each of the "activities" normally associated with theory. Student performances should begin by emphasizing the essential quality (in Medieval pieces, for example, by simply clapping the rhythms). Analysis and listening should likewise begin with the recognition of this quality, and then gradually proceed downwards to its manifestation in the details—and herein, too, lies a meaningful basis for aesthetic comparison (an activity to be encouraged even in beginning students), that is, the success with which one composer or another (but always within a single style) is able to relate the details of a piece to its essential principle. And, finally, the composition of short passages by the student requires a teacher who is able to point out clearly the differences between the student's handling of details and the model composer's handling of these same details (an activity that should foster an ever increasing admiration for the works of the masters). These various activities now need to be meaningfully brought together, and this can be accomplished only when teachers and students alike become aware of the uniqueness of styles, of their essential simplicity, and of their imaginative realization in the hands of a master composer.
1Harmony and Melody (Belmont, Calif., 1965), II, xii.
2The Craft of Musical Composition, tr. Arthur Mendel, 4th ed. (New York, 1945), I, 219.
3Structural Hearing (New York, 1952), I, 271.