Let me begin with the oldest book represented in the Ritter collection, and certainly one of the key cornerstones of music-theoretical thought: Gioseffo Zarlino's of 1558. Now being the good Renaissance humanist that he was, Zarlino divided his famous summa of musical knowledge into a neat Aristotelean bifurcation between theory and practice. The first two books of the are "theoretical" in the authentic classical sense of the word. Each follows the ancient curriculum of : interval measurement, monochord divisions, discussion of the Greek systems, tonoi and genera, , and so forth.

There are no practical issues concerning how to compose or perform music. Rather, the questions raised and answered concern music's fundamental material and properties. Aristotle would have called this the study of material and final causes.

The second half of the treatise, however, is clearly practical in nature, and intended for the diligent composer and cantor. Specifically, we have one book on the rules of counterpoint-without question the most important codification of contrapuntal rules that would stand unrivaled in influence until the appearance of Fux's over 150 years later. This book on counterpoint is followed by a book on mode. There we may read Zarlino's polemics on behalf of

Now the categorization of Zarlino's books of counterpoint and mode as practical works seems evident enough-and they certainly were to Zarlino. Both offer essential knowledge that would be needed by a competent -the one concerning the proper disposition of consonance and dissonance, and the other for the character and use of the differing modes within which the contrapuntally-correct voices could now be set. Yet a critical reading of Zarlino's fourth book on mode shows in fact how precarious such practical knowledge may be. For unlike entities such as consonant or dissonant intervals, a mode was not something with an obvious empirical grounding. Rather, modes were tenuous-and highly contentious-constructs of theorists that were cobbled out of a rich mix of antiquarian lore, ecclesiastical tradition, and idealized categories. We gravely misunderstand the nature and use of mode in Renaissance music if we presume it represents some primitive analogue to the function of a key in tonal music. A mode is not a fixed background scale system entailing some normative compositional syntax. Rather, it is more an unstable composite of characteristic melodic procedures, species markers, and notational conventions. Put more bluntly: one does not compose "in a mode, rather one composes "out" a mode. It is not surprising then that every illustration of a mode in Zarlino's text was one that he himself composed precisely for that purpose. A mode, we might say, was a theoretical construct in search of empirical substantiation.

Now there is much more I could say about the precariousness of mode as a compositional/analytical construct in sixteenth-century music-a topic that has received quite thorough examination in recent decades by musicologists such as Carl Dahlhaus, Siegfried Hermelink, Cristal Collins Judd, and above all, Harry Powers. My point is simply to note that mode can by no means be presumed to be a self-evident category of practical music, and no matter how innocently or self-evidently Zarlino presents his arguments, his rhetoric masks a great deal of creative theorizing that went into his "practical" presentation of the modes.

It is telling that when Thomas Morley adapted Zarlino's rules of counterpoint for his own influential treatise of practical music in 1597-tellingly entitled "A Plaine and Easie Introduction to Practicall Musicke"-he dispensed completely with the book on mode. The "eight tunes" of the ancients, as he quaintly called them, were simply not necessary for a "descanter" to know about. (His remarks on mode come only 5 pages from the end of the treatise in a series of "annotations" [appendices], referring the interested reader to the writings of Glarean, Zacconi and Zarlino for further information.) His indifference to the modes was hardly because Morley's musical language had evolved so markedly beyond that of Zarlino's. It was rather that the humanistic impulse that undergrid Zarlino's system was one lacking in Morley's more insular, Elizabethean worldview. Strangely, the beautiful title page of the treatise engraved by John Bell is full of images related to antiquarian lore and allegories of musical cosmology that find no resonance at all in Morley's text. (Here is a case where you indeed cannot judge a book by its covers.)

In any case, Morley's text was not the decisive epistemological wedge that would henceforth

If musical modes show an example of practice being guided by theory, we can easily turn the relationship around. Consider what is arguably the most famous theoretical construct Zarlino offers in the first book of his treatise: the . Now most of you probably know that the senario is simply the collection of the first six whole integers continaing the ratios of consonant intervals. In other words, within the confines of the numbers one through six, we can model the just ratios of all perfect consonances-fifths and fourths-as well as all imperfect consonances-thirds and sixths. (Actually, the minor sixth, whose ratio is 8:5, falls outside the . But that is a problem I won't get into here.) In any case, Zarlino expends extraordinary effort justifying the using arguments and analogies drawn from numerology, astronomy, geometry, and even theology. His arguments at times seem as abstract and speculative as one could imagine. Why does Zarlino find it necessary to expend such energy in expanding the hallowed Greek -which stopped at the number four-to the number six? The answer is that Zarlino was trying to justify and sanction the justly-tuned major and minor thirds that composers were increasingly using, but were hitherto unavailable in received Pythagorean tunings. In other words, changes in the practice of singers and composers necessitated a change in the theory.

Printz is a fascinating musical figure who deserves to be far better known than he is. While active through his life as a composer and Kantor at a number of petty-German courts, he wrote extensively on a dizzying array of musical topics, betraying an extraordinarily broad knowledge of music and literature. Incidentally, he also was a writer of some skill, and penned a number of morality stories and satirical novels. Certainly there is no music text from the seventeenth century that displays as much literary sophistication as does the .

Still, the genre of the work is curiously ambiguous. It is at once a down-to-earth textbook of musical fundamentals for a budding musician, as well as a learned discourse of musical philosophy and antiquarian esoterica, all dished out with a mixture of wit, hubris, and Baroque bombast. Here, if anyone cares to look, is the source of these self-same qualities found in the writings of Johann Mattheson in the following generation.

The prolix title of the book illustrates Printz's didactic pretenses perfectly: This is my

And indeed, Printz's treatise is full of irreverent lasiciviousness, wit and iconoclasm. He heaps scorn upon received traditions of , finding their pomposity and pretense insufferable, their parading of scientific learning of no worth to a real musician. Invoking Occam's razor, he admonished the student "All that is unnecessary [in learning music] is to be dismissed;" and later on, "all that is easy should be preferred to that which is more difficult." Elsewhere he writes that the essential skills needed are those of ""-which he subdivides into two parts: 1) that of , or how to write a good melody and accompaniment; and 2) -how to sing and play music. . And true to his word, the subsequent chapters in his treatise offer practical guides to counterpoint, triads and their placement, musical figures, figured bass, and a fascinating and important chapter on musical meter. (Printz was one of the first theorists to offer a full accounting and description of meter that dispensed with the lingering conceptual baggage of the mensural system; Part 3, pp. 96-101.) Printz was well aware that musical styles in his own day had changed rapidly. (It is not surprising, incidentally, that he also wrote one of the very first histories of music in the German language in 1690-the "Historische Beschreibung der edelen Sing- und Klingkunst."). Through and through, Printz's texts reveal his pragmatic, pedagogical orientation and modern outlook

Yet it would be wrong to call Printz a writer of "practical" music treatises and leave it at that. For much in Printz's writings is in fact built upon a rather sophisticated-if not always explicitly articulated-foundation of sophisticated musical theorizing. His important discussion of the nature of the harmonic triad and its invertibility is drawn from a distinguished lineage of musical speculation that may be traced back to Zarlino via a number of early seventeenth-century German exegetes (Part 1, pp. 52-53). Printz's discussion concerning the reason for the prohibition of parallel fifths in voice leading is also surprisingly philosophical, drawing upon contemporaneous discussions of sufficient reason (Part 1, pp. 69-76). Even aspects of musical harmonics-the classical theoretical discipline of numerical interval calculations drawn from monochord divisions-makes appearances in Printz's text, although updated with new mathematical tools and acoustical research (Part 3, pp. 40-41). If Printz was a staunch advocate of Occam's razor, it seems that the shortest and simplest avenues of his explanation nonetheless ran through terrain bristling with theoretical and philosophical underbrush. In this light, we might better understand the intriguing fronticepiece of his book, in which the dual characters of Phrynis and Euclid hold up the banner inscribed with the book's title. Phrynis was one of the great Attic tragic poets, and Euclid, of course, the famous geometrician and purported author of the musical Canonics. For Printz, both the Dionysian passion of the poet and the Apollinian rationality of the mathematician seemed essential qualities for a musician.

All this suggests again that the dividing line between theory and practice-between knowing something and doing something-is not one easily drawn. Even the most abstracted and learned disquisitions of music theory at some point must bow to the empirical verification of practice, just as the most innocent pedagogical prescriptions can be seen to be premised upon theoretical presumptions, however disguised.

Perhaps the clearest indication of this intimacy of theory and pedagogy can be seen in the practice of the thorough bass. On the surface, thorough bass seems like a skill that is innocently practical and devoid of speculative theorizing. It is the most empirical of musical skills: one learns to encode vertical harmonies in a shorthand numerical notation that is placed above a basso continuo line, and conversely, a keyboardist learns to play (or "realize") these figures in real time. Figured bass, one might crassly say, is simply about playing the right harmony at the right time. It tells us nothing about what key we may be in, what relationship harmonies may have to one another, why certain dissonances resolve as they do. It is a numerical tablature that can be mechanically realized by anyone. Or so it might seem.

For if we look at any of the many thorough-bass treatises contained in the Ritter collection, we find that even the most overtly didactic of them must at some point turn to theory. Consider the case of Johann Mattheson. I have already alluded to Mattheson when speaking of Printz, noting how both shared common characteristics of scholarly erudition, Baroque pomposity, literary wit, and a streak of pragmatic iconoclasm. Just as was Printz, Mattheson was a vigorous champion of new musical styles-in his case that of the Italian opera he knew from his native Hamburg-and an equally sharp critic of conservative traditions of scholastic and ecclesiastical music theory. Mattheson was one of the first music theorists to follow the lead of English empirical philosophy and advocate a sensory basis for any musical argument.

As he forcefully announced in his first major musical treatise, of 1713, no genres of were of any value unless they were first based on the validation of the ear. But just as Printz's own writings betrayed significant epistemological tensions, so too do Mattheson's.

For even the empirical Mattheson finds that it is necessary to bring in some amount of theorizing through the back door. Whether it is in calculating the minute ratios of intervals in his various keyboard temperaments or offering the occasional historical digression on Greek genera or the latest acoustical research of French scientists, Mattheson finds that he must invoke his otherwise disparaged language of "musical mathematics." What I am suggesting, then, is that the polarization of theory and pedagogy is fallacious. Far from the teaching of eschewing theory, it often turns out that the best pedagogies of music are those based on principles derived from theory. Conversely, the most naively empirical of musical methods are ones that are often the poorest pedagogical models.

The irony in all this, of course, is that it is the fundamental bass of Mattheson's arch rival-Jean Philippe Rameau which actually offers beginning students just such an efficient and practical heuristic by which to learn to realize the figured bass by employing such theoretical notions as chordal inversion and octave identity. This is why someone like Johann Friedrich

We arrive, then, finally to Rameau, the classic figure of music theory in the eighteenth century. And certainly, those elements of learned speculation and analysis with which we characterize music theory today-or at least its "second" branch--may be found in Rameau's many writings. No one seemed to epitomize more the caracature of a music theorist is than Rameau, with his tortured explanations of the minor triad or the dissonant seventh using poorly- understood mathematical and acoustical arguments, with his frustrated attempts to model fundamental bass motion using a restricted syntax of consonant root motion, with his Sisyphisian attempts to define tonal keys within the confines of his three primary harmonic functions. Yet for all the scientific pretense and theoretical cul-de-sacs of Rameau, we must not over look that at heart he was a practicing musician: a keyboardist and composer. Again and again he would return to the practice he knew so well to test his explanations, never satisfied with his theory unless it correlated accurately with the empirical evidence of the musical score and the

Emblematic of this dialectic of theory and practice is his third major treatise, the of 1737. Notably, this work is subtitled "." For the first 17 chapters of the work-which takes us about three-quarters of the way through the book, we have a learned summary of Rameau's speculative theory, explaining his views on the acoustical generation of harmony, the nature of mode, the rules of the fundamental

In short, the fundamental bass as presented in the as a product of both theory and practice. It is at once a formal explanation of the origin and behavior of musical material, while at the same time being an ideal analytic tool for students to learn to write and control the harmonic succession of music. I have often wondered if the engraving of two musical putti adorning Rameau's title page under the words "harmonia et concordia" might not be an allegory for this idealized union of .

In any even, this is a lesson that Mattheson never seemed to comprehend, as he continued over the remaining four decades of his life to heap sarcastic scorn upon the Frenchman's writings. Nor did any of Rameau's German exegetes help much. Friedrich Wilhelm Marpurg in Berlin--the self-appointed "music critic on the Spree" and Director of the Prussian lottery-claimed to be the champion of Rameau's theories in Germany. Yet one would get a very distorted impression indeed of Rameau's thought by wading through the pedantic explanations and stilted musical examples of chordal generation and dissonance resolution contained in a work such as Marpurg's from 1756.

(Incidentally, the title of Marpurg's book indicates how closely identified the skills of composition and the playing of thorough bass had become in the eighteenth century.) The abstraction of Marpurg's book is clear to see in his examples chords containing 6 to 9 (!) voices or his exhaustive list of doublings and dissonance resolutions using a short-hand tablature.

Given the ironic situation of one of Rameau's self-professed followers writing a treatise in which the Frenchman's thought is woefully misrepresented, you will surely not be surprised to hear that it was actually one of the most vocal opponents of Marpurg and Rameau in Germany who ended up writing what was to be arguably the most clear-headed presentations of Rameau's fundamental bass in German during the eighteenth century. This was Johann Philipp Kirnberger

This is not to say that there were no examples in Kirnberger's day of a more resolute kind of speculative theorizing-the "dry mathematical stuff" scorned by Bach. For we can find an instance of a treatise whose credentials as a pure theory treatise seem impeccable precisely by

Yet to say that this book has nothing whatsoever to do with musical practice would again be gravely mistaken. In fact, the whole impetus of the book, Marpurg tells us in the preface, was to bring the esoteric subject of musical harmonics to the grasp of practical musicians. The very subject which culminates the book-that of musical temperament-is in one sense, the most practical subject of all. Every self-respecting keyboardist in Marpurg's day needed to know something about tuning and temperament; and the revolutionary changes of musical style in the eighteenth century that brought to common practice the application of musical temperaments (of which equal temperament we must recall was only one species-and hardly the most common, either), made it imperative that keyboardists know how to temper their instrument accurately. Still, we must not forget that it was practice that helped to drive the theory-by exploring ever more remote key areas, composers prodded, as it were, performers and theorists to come up with ever more creative temperaments so to accommodate what would otherwise be horribly out of tune sonorities. The dynamic was exactly what we saw in the case of Zarlino seeking to justify his beloved .

Marpurg himself was quite explicit about this mutual dependence of theory and practice. In his preface, he writes:

Times have truly changed. Today, practicioners are beginning to sense the value of music theory, and theorists are striving to obtain real practical insight. Each supports the other in their endeavors, and no one believes himself to be alone the sole master of musical composition at the exclusion of the other. . . Today, music theorists and practicioners often gather together in order to discuss all sorts of musical verities. One offers the other his insights, and the favor is then returned. It would not occur to the philosopher to judge some practical thing that must only be drawn from practice. The practicing musician would correct him. On the other hand, the musician might try to verify various theoretical hypotheses. Each helps the other, and together they seek to make progress through rational inquiry. (Pp. 1-2)

If Marpurg's description seems just a tad naive in its idealistic commerce of theoretical and practical concerns-the lamb and lion of musical academia breaking bread in a pacific musical arcadia--I think he is nonetheless on the mark in pointing out a mutual dependence. Practice and speculation seem to drive one another, if at times who is leading and who is following may change. Nonetheless, they seem the dual motors of the discipline of music theory. It is precisely in the tension between theory and practice, in the friction generated by their discrepant aims, that the very energy and impetus of modern music theory may be found.