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Home , Franchinus Gaffurius, Johannes de Muris, Music theory, Walter Odington

CHAPTER2

MUSIC IN CLIO'S MIRROR*

USIC THEORY, Carl Dahlhaus has warned us, is a subject that M notoriouslyresists its own history.How, he challenges us, is it possibleto write anymeaningful history of a disciplinewhose subject matter has shifted so dramaticallyover time?' Topics of musical pedagogythat we todaytake for granted as integral to theory were not alwaysso considered-rules for writing or realizinga fig• ured bass,for instance.Conversely, many of the traditionalcomponents that made up the quadrivial science of musica theorica are now considered peripheral subjects lyingprecariously close to occult and esoteric thought, or more benignly,perhaps, as part ofsome mathematical or acoustical sub• discipline.Nor are these contrasting allegiances mutually exclusive at any given historical period.Widely diverging conceptions of can often be found jostlingwith one another in the same historical culture, within the oeuvre of the same writer, and occasionallyeven in the same publication. As a pointedillustration of this diversity,we might consider three texts stemming from the same decade ofthe earlyseventeenth century:Thomas Campion's A New Way ofMaking Fowre Parts in Counter-point bya Most Familiar,and InfallibleRule (London:John Browne, ca. 1614),Rene Des• cartes's Mus icae compendium (ca.1618; printed Utrecht: Gisbertus a Zyll & Theodorus ab Ackersdyck, 1650),and Robert Fludd's Utriusque cosmi, maioris scilicet et minoris metaphysica,2 vols.(Oppenheim: Johann

*This article is an abbreviated and revised version ofthe author's Introduction to the Cambridge Historyof Western Music Theory (Cambridge:Cambridge UniversityPress) to appear in the Fall of2001. ICarl Dahlhaus, "Was heisst 'Geschichte der Musiktheorie?'" in ldeen zu einer Geschichte der Musiktheorie, Geschichte der Musiktheorie, ed.Frieder Zaminer, vol.I (Darmstadt:Wissenschaftliche Buchgesellschaft, 1985),8-39. 36 THE WORK OF MUSIC THEORY

2 THOMAS CHRISTENSEN

Theodor de Bry,1617-21 ). Each of these works has been classifiedas "music theoretical" (although, ironically,none ofthem actuallyemploys the title"music theory").2Yet it is certainlynot the case that all three works represent similar kinds oftheory. Campion's modest treatiseis an eminently practical guide for the novice looking for a quick and "easie" means ofharmonizing a given bass line using a number of simple rules of thumb. Descartes's treatise, evenshorter than Campion's,is on the contrary quite learned.The Compendium is a classic text ofmusical "canonics"-the science of plotting and measuring musical intervals on the monochord. Unlike Campion's text,it has no practical function except perhaps as a test case ofthe youngphilosopher's nascent deductivist method ofgeometrical reasoning.Finally, Fludd's mammoth treatiseof Rosicrucian lore and gnostic learning is an unapologetic paean to the harmonic cosmos of Plato's Timaeus.Given the profoundlydifferent contents and intendedreadership ofeach ofthese works, we may well ask ourselves how they could be uni• fiedwithin a singledisciplinary paradigm we call "music theory."What con• ceptual boundarycan we circumscribe that would help us defineand delimit the contents of historical music theory? Put baldly,is "music theory"ulti• matelyan intelligibleand meaningful historical subject,one that is both intel• lectuallycoherent and conceptually stable? To answer these questions,it might be helpful as a first step to begin with some Greek etymology.In pre-Socratic usage,theoria (8£ropia)is a visual term.It entails the action ofseeing or observing.A theoros (8£rop6c;) is a spectator at a theater or games.A theoros could also be a witness in a legal dispute or a delegate or ambassador conveyinginformation that he atteststo have witnessed)Although the two terms are etymologicallyunre• lated,a number of Greek writers also noted the striking similarityof the word to the6s (8£6c;)-agod and divineobserver, the seer who sees all. Itwas Plato who firstcalled the philosopher a special kind oftheoros. In the Republic, Glaucon points out to Socrates the parallels between the observer at a theater and the philosopher, whom Socrates had just definedas possessinga restlesscuriosity and "tastefor everysort ofknowledge." Like the theater audience,the philosopher too is an observer,curious about-but detached from-the events of which he is a spectator.Socrates agrees that

2As trivialevidence, we maynote that all three authors and these works are listedand discussed in the recent dictionaryof historical music theory:David Damschroder and David Russell Williams, Music Theory from Zarlino to Schenker: A Bibliographyand Guide, Harmonologia,no. 4 (Stuyvesant,NY: Pendragon Press,!990). 3Nicholas Lobkowicz, Theory and Practice: Historyof a Concept from Aristotle to Marx (South Bend,IN: ofNotre Dame Press,1967), 15. MUSIC THEORY IN CLIO'S MIRROR 37

MUSIC THEORY IN CLIO'S MIRROR 3

the parallel is certainlystriking, but he ultimatelyconsiders it deficient.For the real goal ofthe philosopher is differentfrom that ofthe theatergoer.His wish is not to be entertainedor to have his sensesravished; rather, it is to gainepisteme (btta"t~!lT])-the knowledge ofthe true and good."And this is the distinctionI draw between the sight-loving,-loving practical class and those of whom I am speaking,and who are alone worthy of the name of philosopher."4 In characteristic dialectical fashion,Aristotle contrasted the kind of episteme gained bytheoria with the practical knowledge (praktike [n:paKnK~]) gainedthrough action (ergon [£pyov]).This was to be a fateful pairing,for henceforth, theory and practice would be dialecticallyjuxtaposed as ifjoined at the hip.In Aristotle's conceptual schema, the end ofpraktike is change in some object,whereas the end oftheoria is knowledge of the object itself.5This is not to saythat it was impossibleto combine the two; on the contrary,Aristotle considered theoria not so much opposed to prak• tike as a higher form ofpraktike, while praktike was converselya kind of applied theory.6Still, there is a fundamental epistemological distinction drawn between the two as principles ofaction. To recast these categories in related Aristotelian terminology,we could saythat theoria is the discipline offinal causes (that why a thing is made) and praktike that offormal causes (that into which a thing is made).7 Itis helpful to understand these originalmeanings oftheoria. For in its most fundamental sense,music theory is a science offinal causes. Strictly speaking,music theory is not concerned with "formal"or "efficient"causes (how a piece ofmusic is composed or performed).Instead, theory is to con• cern itselfwith basic ontological questions:what is the essentialnature of music? What are the fundamental principles that govern its appearances? (Platowould have spoken ofmusic's "forms.")The great medieval transmit• ter ofancient Greek thought, Anicius Manlius Severin us (ca.480- 525/26)is famous for subdividingthis kind of music-ology(literally, the

4Plato Republic 5.18-20(473b-77b); trans. Benjamin Jowett, The Works ofPlato: Translated intoEnglish with Analysesand Introductions (New York: Tudor, n..),215. 5Aristotle Metaphysics 2.1.5-7. 6Terence Ball,"On the Unity and Autonomy of Theory and Practice,"in Political Theory and Praxis:New Perspectives(Minneapolis: University of Minnesota Press,1977), 65. 7 A form ofactivity discussed byAristotle that is also related to music was poie• sis(noincn<;), whose end is the object made and hence a disciplineof"efficient" causes• that bywhich a thing is made. But it would not be until the sixteenth century when musica poetica began to be taught as a distinct compositional disciplineon a par with musica practica and musica theorica. 38 THE WORK OF MUSIC THEORY

4 THOMAS CHRISTENSEN

"knowledge ofmusic") into three parts:musica mundana, musica humana, and musica instrumentalis.All these kinds of"music" were united by"har• monia,"the proper concordance ("symphoniae")ofmagnitudes and multi• tudes.Musica mundana concerned the macro-cosmic of the uni• verse-the motion of the planets and the of the four seasons; musica humana concerned the micro-cosmic harmony of the bodyand soul-the dispositionof the four humors and temperaments; and mus ica instrumentalisconcerned the sounding harmony of"" made bysingers and instrumentalists.For Boethius, a faithful student of Platonic thought, number and proportion was the "final"cause governing each ofthese three kinds ofharmony. The true philosopher ofmusic, the true musical theoros, was the one who understood this numerical basis ofharmony beyondthe shadows of its profane resonance in musica instrumentalis.And the disci• pline within which one studied the proportions underlyingmusic in all its macrocosmic and microcosmic manifestations-andhence music theory in its most fundamental and authentic sense-wastermed byancient writers as "harmonics." Itis worth notingthat no earlywriters actuallyused the double cognate "music theorist" to designatea student of harmonics. In a locution drawn from Plato but extended bygenerations of medieval exegetes,Boethius simplycalled one who aspired to the true knowledge ofmusic a "" (musicus,from the Greek mousikos [11ouou6~]). In one ofthe most widely repeated aphorisms from the , Guido ofArezzo could contrast a "musicus" who understood the philosophical nature ofmusic to the igno• rant singer ("cantor")who could onlysound the notes:"Musicorum et can• torum magna est distantia.Isti dicunt, illisciunt, quae componit musica."8 Of course we cannot forget that Guido was indeed concerned with real musica instrumentalis,unlike Boethius. We have unusuallyspecific evidence concerning Guido's activitiesat the Arezzocathedral during the early century as a director and teacher ofchoirboys. And he was widely credited with developing some of the most important and influentialpeda• gogical aids to help singers learn their craft: staffnotation for the accurate reading ofneumes, solfegesyllables to help learn and memorize , and

8Indeed,Guido at one point compared the singer who did not understand music to an animal ("bestia").For a masterlysurvey of the musicus/cantor dichotomy in medieval thought, see Erich Reimer, "Musicus-Cantor,"in Handworterbuch der musikalischen Ter• minologie,ed. H. H. Eggebrecht (Wiesbaden:Steiner, 1978). MUSIC THEORY IN CLIO'S MIRROR 39

MUSIC THEORY IN CLIO'S MIRROR 5

an elementarygrammatical taxonomyby which to compose and analyze these chants.9 Given the profound influence of Guido's "practical" writings-they were copied and distributedin the Middle Ages more widelythan anyother musical work save for Boethius's De institutionemusica10_we are clearly enteringa new period with new expectations for the mus icus.For all that of the earlyMiddle Ages may have revered the authority ofthe Greek and Hellenistic writers-or at least what they gleaned through Boethius and Martianus Capella-theywere also committed to another authority:that ofthe church and its sacred repertoire.Thus, as Joseph Smits van Waesberghe has pointed out, there was a pronounced tension between the auctoritas ecclesiastica and the auctoritas greca (although some theorists such as strove mightilyto reconcile the two ).11No longer could a true musician remain alooffrom musical practice and lead the con• templative lifeof the biostheoretikos (ifindeed that was ever possibleout• side of Boethius's lonelyprison cell, where he composed the Consolatio philosophiae shortly before his execution).Given that virtuallyall musical writers in the Middle Ages were associated in some way with the church, it would have been incredible for them not to have been concerned about the musica instrumentalisthey would have heard and chanted in their daily offices ofworship-the opus Dei.With the pressing need for Carolingian authorities to bring some kind of order to a burgeoning but chaotic chant practice, directors were pressed to think of means for classifying, notating,and teaching singersa stabilizedchant repertoire.Aurelian's mod• est tract, Musica disciplina,from the late century,was onlythe first such propaedeutic textbook ofmusica plana.And as more complex perfor• mance problems arose with the introduction ofimprovised and dis• cant ,new pedagogical demands faced the cantor, above all,that of mensuration.l2

9Joseph Smits van Waesberghe, Musikerziehung: Lehre und Theorie der Musik im Mittelalter,Musikgeschichte in Bildern,ed. Heinrich Besseler and Werner Bachmann, III/3 (Leipzig,VEB Deutscher Verlag fiirMusik, 1969),23. Ironically, the pedagogical aid with which his name is probablybest known-the Guidonian hand-was one for which he almost certainlyhad no responsibility. 10Michael Bernhard, "Das musikalische Fachschrifttum im Jateinischen Mittela1ter," in Rezeptiondes Antiken Fachs im Mittelalter, Geschichte der Musiktheorie, ed.Frieder Zaminer,vol. 3 (Darmstadt:Wissenschaftliche Buchgesellschaft, 1990),72. IISmits van Waesberghe, Musikerziehung, 19. 12rt was perhaps not so much issues ofmodal identityor dissonance regulation that offeredthe most intractable problem to medieval musicians with the rise of contrapuntal 40 THE WORK OF MUSIC THEORY

6 THOMAS CHRISTENSEN

With the transmissionof many of Aristotle's most important writings into the West byArabic writers beginningin the twelfth century, musicians finallywere provided with an unimpeachable authority bywhich to legit• imizethe kinds of propaedeutic writings of Aurelian and Guido-or as musical praktike was rendered by the twelfth-century translators of al-FarabT,"musica activa."l3To be sure, as the venerable curriculum ofthe "studium generale"migrated from the Cathedral and monastic schools to the newlyformed universitiesof Bologna, Paris, and Oxford,scholars continued to studyand offertheir own glosses ofmusica speculativa in the Boethian paradigm.I4Much more vigorous, though, was the industryof music instructors (praeceptores)who attempted to offerregulation and codification for the various parameters ofrapidly changing musical practice through the textbook of the eisagoge.Is And even when speculative topics were taught, they were often done so within a treatisehaving largelypractical aims.I6Hundreds ofmusic treatiseswere penned and copied throughout the Middle Ages that offeredmore or less practical guidance on everypossible problem ofsinging and composition (the boundaries between the two hardly

singingas it was the conceptualizationand notationof a hierarchy ofrhythmic values by which to coordinate the voices ofmusica mensurabilis. 13HenryG. Farmer, ed.and trans.,Al-Farabf's Arabic-Latin Writings on Music (New York: Hinrichsen, 1965),22. 14Nan Cooke Carpenter, Music in the Medieval and Renaissance (Norman:University of Oklahoma Press,1958), 32ff. Properly speaking, we might note that the term "theoria"was never used in the Middle Ages to designatewritings on music, even for the most speculative genre ofharmonics. With the spread ofAristotelian thought in the century,however, a number of scholastically trained musical writers did start to employthe Latin cognates "theoria"and "practica"in their writings,including the likes ofFranco ofCologne, , ,and Johannes Grocheo. But as Jacobus ofLiege noted,there was alreadya perfectlygood Latin translationfor the Greek word thea ria: speculatio (Compendium de musica 1.1[Jacobi LeodiensisTractatus de consonantiismusicalibus, Tractatus de intonationetonorum, Compendium de musica, ed.Joseph Smits van Waesberghe, Eddie Vetter,and Erik Visser,Divitiae musicae artis, A/IXa (Buren:Knuf, 1988),89]; cf. Speculum musicae 5.13[Jacobi LeodiensisSpeculum musicae, ed.Roger Bragard, Corpus scriptorum de musica, vol.3/v ([Rome]: American Instituteof , 1968),39]). Hence, whereas earliermedieval writers would refer to the "scientia"of music in regard to its philosophical study,later medieval writers employedthe term "speculatio"(as in Jacobus's eponymous summa of musical knowl• edge).It was onlyin the later fifteenthcentury when some Italianhumanists (aboveall, ) explicitly entitledtheir musical writings "theoria." ISsmits van Waesberghe, Musikerziehung,24ff. 16soworks as earlyas the Musica enchiriadis and ,texts from the late ninth century,can be read as both theoretical and practical, each containingBoethian discussions ofmusical arithmetic in additionto practical guides for notating,classifying, and singing chant and organum. MUSIC THEORY IN CLIO'S MIRROR 41

MUSIC THEORY IN CLIO'S MIRROR 7 recognized).Even as scholastic rhetoric became increasinglyconspicuous during the thirteenth and fourteenth centuries, musicians trained in the newlyflourishing universitiesdevoted most of their energies to issues of musica activa.While it is perhaps an exaggerationfor Albrecht Riethmiiller to saythat music entered the Middle Ages as theory and leftit as practice, there is no question that the prestige of music theory was now declining precipitouslyas a philosophical and scientificdiscipline. 17 But it would be wrong to see this process simplyas one of an invigo• rated pedagogyof musica practica evermore encroaching upon the territory ofan enfeebledmusica speculativa,of usus triumphing over ars.Rather, it was more a case ofmusic theory being refocused,its principles reconfigured so as to accommodate better the domain ofmusica instrumentalis.Lawrence Gushee has remarked that theory and practice do not emerge in the Middle Ages as so much distinctepistemological as theydo a mix ofintellec• tual styles,social functions,and musical contexts-featuresthat maybe dif• ferentlycombined in anygiven treatise.18Most treatisesof "speculative" music theory in the late Middle Ages had dropped anyserious discussion of celestial harmony (or ifit was discussed,tempered bya healthy dose of Aristotelian skepticism ).19Instead, the authors of these treatises-mostly scholastic writers of encyclopedic Summae of comprehensive musical knowledge such as Johannes de Muris, Jacobus ofLiege, Walter Odington, Marchetta da Padua, or Hieronymus de Moravia-took many of the received quantitativetopics ofclassical harmonics-the , species,calculations ofinterval ,etc.-and adapted them with various degrees ofsuccess to issues ofcontemporary musical practice.Problems of pitch material (scales,intervals, mode, and solfege)were grouped under the rubric of"musica plana";that ofrhythm and mensural theory (reallya kind ofadvanced counterpoint)under the rubric of"musica mensurabilis."Even that venerated tool ofspeculative canonics-the monochord-was now used

17Albrecht Riethmtiller,"Probleme der spekulativen Musiktheorie im Mittelalter,"in Rezeptiondes Antiken Fachs im Mittelalter, 177. 18Lawrence Gushee, "Questionsof Genre in Medieval Treatises on Music," in Gat• tungen der Musik in Einzeldarstellungen,Gedenkschrift Leo Schrade, ed.Wulf Arlt et a!. (Bern:Francke, 1973),388. l9Again another terminological clarificationis in order.No late medieval writer would call such philosophical writings on music "speculativetheory" since it was understood that anyproperly "theoretical " discussion ofmusic was "speculative"in the original,Platonic sense ofthe word. Albrecht Riethmiiller has thus made the amusing pointthat the modern locution "speculative music theory"would have been triplyredundant for a medieval writer,since the originalconcept ofmusica as a quadrivial science alreadyentailed the con• cepts ofboth speculatio and theoria.Riethmiiller, "Probleme der spekulativen Musiktheo• rie im Mittelalter,"174. 42 THE WORK OF MUSIC THEORY

8 THOMAS CHRISTENSEN

in a highly practical way byteachers: as a to establish pitches and scales for singers.The task ofthe music theorist was now that ofthe practical pedagogue:to teach the elements ofmusic to be appliedby the would-be performer or composer, while converselyhelping to discipline that practice through the establishment of regulative rules.This is byno means to saythat "speculative"knowledge ofmusic was in complete disre• pute; such knowledge was valued, but mainlyto the extent it could be of value to musica practica. The true "musicus" ofthe later Middle Ages was now the "cantor peritus et perfectus"-onewho not onlyknew, but could do,to tum Guido's aphorism on its head.20 With the humanistic revival ofancient Greek thought in the later half of the fifteenth century,we find some renewed interest in the Boethian paradigm ofcosmic harmonics. Indeed,among manyItalian humanists, we witness a veritable"mania for music theory"as Knud Jeppesen has so aptly put it.2IQuestions of interval calculation and tuning were attacked with a vigor not seen since the mysteriousgroup of "harmonicists"reported by almost two thousand yearsearlier. Franchinus Gaffurius (1451- 1522)was one such individual.It is not without significancethat his major incunabulum of 1492,the Theorica musice, explicitlyresurrected the Greek appellation"the6ria."22 In the scramble to findand translateany ancient text concerning musical topics,scholars ofthe late quattrocento made the first real inroads in understanding Greek music theory.23The resulting publica• tions of music theory-such as Gaffurius's-constituteda heady mix of antiquariantopics: the ancient Greek tonoiand genres,monochord calcula• tions based on and ,and reflections upon the cathartic and magical powers of music. Yet it is noteworthy that Gaffurius did not see himself restricted as a writer to the ancient parameters ofmusica theorica, for in his next major treatise,he dealt head on with practical issues ofcoun• terpoint, mode,and mensuration.His Practica musice of 1496was con• ceived not so much in oppositionto the text thatpreceded it,but rather, as a logical and necessarycomplement to it,and upon the foundationof which it

20Gushee, "Questionsof Genre," 408. 21Quoted in Claude Palisca,Humanism in ItalianRenaissance Musical Thought (New Haven,CT: Yale UniversityPress, 1985), 8. 22Theorica musice (:Iohannes Petrus de Lomatio, 1492;reprint in Bibliotheca musica bononiensis,11/5, Bologna: Forni, 1969);The Theory ofMusic, trans.Walter K. Kreyszig,ed. Claude V. Palisca,Music Theory Translation Series (New Haven,CT: Yale UniversityPress, 1993). Gaffurius had actuallypublished a shorter version ofthis treatise in 1480entitled: Theoricum opus musicae disciplinae. 23A storybrilliantly told in Palisca's Humanism in ItalianRenaissance Musical Thought. MUSIC THEORY IN CLIO'S MIRROR 43

MUSIC THEORY IN CLIO'S MIRROR 9

builds.It is worth notingthat ofthe most important treatisesof speculative music theory that would be penned over the following centuries byGioseffo Zarlino,Francisco Salinas,Pietro Cerone, , and Jean• Philippe Rameau, all were paired with complementing treatisesof musica practica-all indeedbound within the covers ofthe same volume. As Barto• lomeus Ramis de Pareia (ca.1440-91) put it poetically, thenew integration of theory and practice was as if"mouse and elephant can swim together; Daedalus and Icarus can flytogether."24 The increasinglyclose dialectic that constituted Renaissance theoria and practica is paradigmaticallyevident in the area oftuning. As were increasinglyemploying sonorities in their compositions bythe fifteenthcentury, the received Pythagoreantuning ofthe ditone(81 :64) was proving unsustainable.But the theoretical argument for tuning the major third to a just superparticular (5:4)required considerable effortin the face oftenacious canonist traditions.The extendedand passionatearguments waged on behalf ofthe justlytuned major third byRamis and his alliesshow vividlyhow traditionalmusica theorica was being bent in the service of practice.25Indeed, tuning became an area of speculative thought in the Renaissance that was in manyways far ahead ofpractice, contrary to the widespread notion that theory must necessarilylag behind practice. The various proposals for or quasi-equaltemperaments bythe likes ofVincenzo Galilei, Nicola Vicentino,and Simon Stevin far outpaced the practice oftheir contemporaries and would have to wait at leastanother one hundred years before enjoyingwider acceptance and application by mustctans. An even more striking change in the fortunes ofmusic theory,however, occurred in the late sixteenth and earlyseventeenth centuries at the advent of the so-called"scientific revolution." Many ofthe hitherto classical problems ofmusical harmonics-in particular the generationand ranking of conso• nances-were newlytreated byscientists as problems ofacoustical mechan• ics.This shift towards mechanics did not in fact dislodgemusic theory as a quantitativescience. One merely substituted proportions measured by vibrationalfrequency for those plotted out on a monochord. But the shift did change much ofthe metaphysical grounding bywhich consonance was

24Musica practica Bartolomei Rami de Pareja Bononiae,ed. Johannes Wolf, Publika• tionen der IntemationalenMusikgesellschaft, Beihefte,vol. 2 (Leipzig:Breitkopf und Hartel, 1901);Bartolomeo Ramis de Pareia,Musica Practica, trans.Clement A. Miller, Musicological Studies and Documents, no.44 (Stuttgart:Hanssler; American Instituteof Musicology, 1993),42. 25Palisca,Humanism in ItalianRenaissance Musical Thought, 235-44. 44 THE WORK OF MUSIC THEORY

10 THOMAS CHRISTENSEN

understood.No longer evaluated bynumerological constructs (such as Zarlino'ssenario), consonance could be seen as a purelyphysiological con• sequence of coincidental vibrational frequencies; hence the boundary between consonance and dissonance could now be a continuum that shifted based upon context and .26 Music theory thus seemed to have suffered a double loss bythe end of the seventeenth century.On the one hand, it graduallyreceded from its Boethian heights in prominence and prestigethrough the robust growth of musica practica as a discipline.More and more energyseemed to be devoted to systematizingand regulating the parameters ofa rapidlychanging musical practice and poetics.On the other hand, manyof the most time-honored problems with which music theory was historicallyidentified, such as the measurement and evaluation ofconsonance, were now being appropriated bydisciplines of natural science.27 "Music theory"continued to be cultivated bya few scholars throughout the Enlightenment in the model oftraditional classical canonics.But for the most part,any treatise employing "music theory"in its titlepresented a limited and bynow rather impoverished picture ofthe venerable discipline, one usually limited to rather pedantic calculations of intervals and tuning systems.28To be sure, new mathematical techniques such as were applied in order to quantifywith meticulous precision the various kinds ofmean-tone and quasi-equaltemperaments thought up byscientists and musicians.But many of these tunings,it should be stressed,were "paper"temperaments with littlerelevance to the ad hoc practice ofmost keyboardists.

26claude V. Palisca,"Scientific Empiricism in Musical Thought," in Seventeenth Century Science and the , ed.H. H. Rhys (Princeton,NJ: Princeton UniversityPress, 1961),109. 27rtwas in 170I that the French scientistJoseph Sauveur christened one area ofthis studyas "acoustique." 28A representativesampling ofsuch theory titlesis suggestive:Otto Gibe!,Introduc• tio musicae theoreticae didacticae ...cum primis vera mathematica (Bremen:Jacob Koh• ler,1660); Thomas Salmon, "The Theory ofMusick Reduced to Arithmetical and Geomet• ric Proportions,"Philosophical Transactions ofthe RoyalSociety, London, 241302(1705): 2072-77;, Tentamen novae theoriae musicae (St.Petersburg: Academia scientiarum, 1739); Friederich Wilhelm Marpurg, Anfangsgriindeder theoretischen Musik (Leipzig:Breitkopf, 17 57); Giovanni BattistaMartini, Compendia della teoria de' numeri per uso del musico (Bologna:Lelio dalla Volpe, 1769).Jean- Philippe Rameau's Nouveau systemede musique theorique (Paris:Jean-Baptiste-Christophe Ballard, 1726)is also in the tradition,it being "new"only in the sense that it substituted an acoustical principal-the corps sonore-asthe origin of musical proportions rather than the traditionalcanonist originin string divisions(as was proposed in his Traite de l'harmonie four yearsearlier). MUSIC THEORY IN CLIO'S MIRROR 45

MUSIC THEORY IN CLIO'S MIRROR 11

Thus, bythe eighteenth century,music theory had become onlya shell ofits former glory.Rameau feltobliged on numerous occasions to defendthe honor and dignityof music theory,while at the same time conceding such knowledge maybe oflittlepractical use to musicians.Yet for everydefender ofmusic theory-such as Rameau or LorenzMizler (1711-78), the founder ofthe "CorrespondingSociety ofMusical Science"-there were critics like Johann Mattheson (1681-1764),who would lambaste music theoria (or as he preferred to call it,"musical ") as a discredited remnant of unenlightened prejudice, its advocates as "systembuilders" blindly-or deafly-constructingtheir elaborate numerical edifices with no regard to musical reality.With the weapons of empirical bequeathed by Locke, writers such as Mattheson could militantlyhoist the Aristoxenian flag of"sensus"over that of"ratio."Indeed, for most progressive thinkers of the Enlightenment,theory of most anysort was viewed suspiciouslyin comparison to the measured empiricism ofinductive reasoningdrawn from practice. The French philosophes would contrast this as the espritde sys• teme versus the espritsystematique. Perhaps because music theory had been so emptied of its traditional prestigeand content,then, it was ripe to be rehabilitatedwith new empirical sobriety.By reconceiving theory as a systematicprogram ofreasoning and pedagogy,Johann Georg Sulzer (1720-79)could appropriate the term in his ambitious encyclopediaof , the Allgemeine Theorie der schonen Kiinste(1771-74). For Sulzer, theory was not so much an abstracted foun• dation ofa given science from which are deduced empirical in geo• metric fashion as it was a general process ofreasoning by which the empiri• cal and metaphysical components ofa science were systematicallyitemized and coordinated.29Thus, in Sulzer'sprogram, "theory"would necessarily encompass those "practical"elements oftaxonomy and regulation necessary to the instruction of anyart in additionto its more abstracted,normative principles.But while Sulzer's encyclopediamay have sketched out what such a program of music might entail(in the various articles written by Johann Kimberger and his student J.A. P.Schulz), it was Johann Forkel (17 49-1818), the famed music lexicographer, historian,and educator who firstproposed a systematicprogram ofstudy he called "Theorie der Musik" in 1777that seemed to fulfillSulzer's plan.30

29Although it would not be until the end ofthe century when Kant completed Sulzer's great rescue project byrigorously working out the epistemological basisupon which valid theoretical reasoningmay be conducted. 30Johann Forkel, "Uber die Theorie der Musik" (1777);reprinted in Carl Friedrich Cramer, Magazinder Musik I (1783):855-912. 46 THE WORK OF MUSIC THEORY

12 THOMAS CHRISTENSEN

Far from restricting music theory to a rarifiedscience ofinterval calcula• tions and tuning,Forkel redefinesit as a broad pedagogical disciplineof musical study"insofar as it is necessaryand useful to amateurs and con• noisseurs."Specifically, Forkel includes five parts within his program of music theory:(1) Physics, (2) Mathematics, (3)Grammar, (4)Rhetoric, and (5)Criticism. Parts 1 and 2,roughly speaking,cover the traditionalspecula• tive domain ofmusica thea ria,albeit updated with new scientificknowledge and languages.Parts 3 and 4 cover the traditionalregulative functions of musica practica and poetics:systems of scales, keys, harmony, and meter, as well as their application bycomposers in terms ofphrasing, genre, and rhetoric. Finally,part 5 foretokens a new concern that will playan increas• inglyimportant role in music-theoretical discussions:critical analysis.Here the theorist is concerned with such elusive qualitiesas the "innercharacter" ofa musical work. Forkel's program constitutes an extraordinarychange in the meaning ofmusic theory byradically expanding its domain in relation to practical pedagogyand criticism.No longer was music theory a preliminary or metaphysical foundation to practice. On the contrary,it was practical pedagogythat was now a subset oftheory. With the advent ofthe nineteenth century and the founding ofthe many music conservatories and schools throughout Europe that would institu• tionalizethe trainingof the next generationsof performers, composers, and conductors, music theory fractured into a number ofcompeting disciplinary paradigms that elude easysynthesis. On the one hand, the utilitariantum of music theory evidenced in Forkel's program was taken up by a few nineteenth-centurytheorists where theory was colloquiallyunderstood as a general program of music pedagogy.Characteristic is Gottfried Weber's comprehensive Kompositionslehre,the Versuch einer geordneten Theorie der Tonsetzkunst(Mainz: Schott, 1817-21).Yet in its tendentiousempiri• cism, Weber's "SystematicallyArranged Theory of Composition"hardly would be recognizedas a theory of music in anysense bya writer such as Gaffurius-or even Mattheson for that matter.31On the other hand, some authors continued to use the term in the area ofmusic in its more traditional sense of speculative foundations(.., in Moritz Hauptmann's treatiseof pseudo-Hegelianmusical dialectics,Die Natur der Harmonik und Metrik: Zur Theorie der Musik [Leipzig:Breitkopf und Hartel, 1853]).Still other

31 It is not surprising that at leastin German-speaking countries,"Musiktheorie" never caught on as a broad disciplinaryappellation, superseded at the end ofthe nineteenthcen• tury bythe program of "SystematischeMusikwissenschaft" articulated byGuido Adler. And to this day,"Musiktheorie" is equated in German-speaking countries with practical skills ofmusicianship, found primarilyin the music conservatories (orHochschulen) rather than the universities. MUSIC THEORY IN CLIO'S MIRROR 47

MUSIC THEORY IN CLIO'S MIRROR 13

writers conflated "theory"with the most rudimentary program of music pedagogy,as in the following pocket catechism published in America in 1876:Palmer's Theory ofMusic: Being a Practical Guide to the Study of Thorough-Bass, Harmony, and Form (Cincinnati: Church, 1876). If there is one element that might tie many of these various configurations of nineteenth-century"music theory"together, it is that authors increasinglyrelied upon the studyof musical works from which they deduced-and illustrated-theirteachings. While selected examples of music analysiscan be cited as far back as the Middle Ages, it was onlyin the nineteenth century that theorists would regularlycite musical examples in their texts,more oftenthan not drawn from a rapidlycoalescing canon of "classical"masterworks. The aim in most cases was not-aswith earlier -tolook at individualworks in order to derive normative patterns ofcompositional practice; rather, analysiswas employedto gaininsight and understanding of the individuatingparticulars of the artwork, the analysis oftencouched in the rhetoric ofbiological organicism.For the most ardent Romanticists,in fact,masterworks were definedprecisely by their unique• ness,their status as creations ofgenius that we mayonly beginto comprehend-though never replicate-through profound and prolonged contemplation.32Such then does the activityof music analysiscurl back and connect with the originalPlatonic occupation ofthe theoros. By the beginningof the twentieth century,a sharp reaction to music theory as a pedagogical discipline hadset in.Partly in response to the grand theoretical projects of scholars such as (who, ironically, never actually entitledany of his works as theoretical),33writers such as would castigate the pretensionsand conservatism ofaca• demic music theorists; indeed,the whole preface to the third editionof Schoenberg's own Harmonielehre (Leipzig:Universal, 1911;3d ed.,1921) opens with a blistering assaulton the hidebound discipline of "Musik• theorie" and its stultifiedpedantry.34 's own betes noires

32IanBent's Musical Analysisin the Nineteenth Century,2 vols.(Cambridge: Cam• bridge UniversityPress, 1994) offers a valuable survey of some of this literature,with insightful commentary and lucid translations. 33His veryfirst publication,a series ofarticles that appeared in 1872under the title "Musikalische Logik: Ein Beitrag zur Theorie der Musik" (NeueZeitschrift for Musik 68 [1872]:279-82, 287-88,353-55, 363-64,and 373-74), is the exception that proves the point. 34Yet it is as ironic as it is indicativethat the English translationof Schoenberg's Harmonielehre published sixtyyears later would bear a titlethat would surelyhave its 48 THE WORK OF MUSIC THEORY

14 THOMAS CHRISTENSEN

were the " guides"of musical hermeneutics penned bythe likes of Hermann Kretzschmar. Pointedly,Schenker entitledhis own rehabilitation project "New Musical Theories and Fantasies"in clear contradistinctionto the impressionisticpoetical readingsof Kretzschmar and his company. Polemics aside,the twentieth century witnessed an unprecedented explosionof music theory.Not since the late fifteenthcentury was there such a fermentationof theoretical thought in all its various guises:specula• tive,practical, and analytical.Certainly one explanationcan be posited:the loss ofa common language ofharmonic .In the case ofSchoenberg, of course, this entailedthe formulation of an entirelynew compositional systemof "usingtwelve tones related to one another" that he believedwas the natural and inevitablesuccessor ofharmonic tonality.For Heinrich Schenker, on the other hand, this entaileda defensive,almost reac• tionarymusic theory that sought to rescue and validatea waning tonal tradi• tion of which he believedhimself to be a guardian and expositor.The two theoretical paradigms Schoenberg and Schenker bequeathed-that ofcom• positional(prescriptive) serial theory and of analytic(descriptive) tonal theory,respectively-proved to be two ofthe most resilientand resonant in the twentieth century. Another remarkable development of twentieth-century music theory was its broad professionalizationas it became increasinglyinstitutionalized within universityprograms. As with its medieval precursor, the modern university,particularly in North America, has offereda congenial home to the dedicated music theorist.This professionalizationofmusic theory may be credited to a number offactors. There was ofcourse the growth ofmusi• cologyitself as an academic discipline,in which the scholarly studyof music and musical documents (includingthose ofhistorical music theory)was cul• tivated.There was also a favorable intellectual climate,particularly at mid• century,in which "positivistic"sciences were widelycultivated, and music analysiswas a beneficiary-orat least certain stylesof more "formalistic" analysis(of which Schenker's, ironically,became a prime example).35 Finally,there was a growing sense that the practical subject matter ofmusic theory pedagogy(historically considered the domain of"musica practica," as we have seen)demanded specialistsfor its teaching.

author turning in his grave:Theory ofHarmony, trans.Roy E. Carter (Berkeley:University ofCalifornia Press, 1978). 35for an insightful narrative of the intellectual origins of contemporary American music theory,see Patrick McCreless, "Rethinking Contemporary Music Theory,"in State ofthe Art: RefiguringMusic Studies in the 1990s,ed. A. Kassabian and D. Schwarz (Charlottesville:University of Virginia Press, 1996). MUSIC THEORY IN CLIO'S MIRROR 49

MUSIC THEORY IN CLIO'S MIRROR 15

Thus, bythe 1950s,we find the first academic appointments of music theory in several American music departments and the foundation of advanced degree programs in music theory.(The Yale UniversityDepart• ment ofMusic, under the leadership ofPaul Hindemith, seems to have been the firstacademic institutionto establish a music theory degree in the mod• em era.36)Significant, too, was the founding of several scholarly journals devoted to music theory,including the Journal ofMusic Theory (1957)and Perspectives ofNew Music (1962).The former journal was associated appropriatelyenough with the Yale program, the latter journal with the music department at Princeton University,where a combined program of composition and theory was developed under the leadership of .Noteworthy, too, was the founding of the Society for Music The• oryin 1977,the first scholarly societydevoted to the disciplineof music theory since Mizler's organizationsome two hundred yearsearlier. And while this professionalizationofmusic theory was initiallylimited to North American universities,in more recent years,it has become broadlyinterna• tional in scope, with new courses of study,degree programs, conferences, and publications devoted to music theory springingup around the world each year. At the openingof the twenty-firstcentury, then, there seems littledoubt that music theory has once again firmlyfound its place in the scholarly studyof music. To be sure,there remain manyof the same disciplinaryten• sionswe have witnessed in previous centuries between practical and specu• lative strainsof musical study,between descriptive and prescriptive meth• ods of inquiry.And music theory has continued to suffer its share ofcriti• cisms in the wake ofthe general rise ofpostmodem malaise at the close of the twentieth century.In particular, a number ofmusicologists have faulted theorists for cleaving to a perceived modernist mentalityinnocent ofques• tionsconcerning cultural or social context.Certainly among music theorists themselves, there have been spiriteddebates and some anxious hand-wring• ing concerning the identityand methods ofmusic theory.But as we enter a new millennium in the now two-and-one-halfmillennia old disciplineof music theory,a new sense ofconfidence and energyseems to be animating the work of theorists.One ofthe most remarkable signs of this new vital• izationis seen in the recent resurgence ofunabashed speculative theorizing

36Ironically,Yale had established an endowed chair in the Theory ofMusic as earlyas 1890(the firstappointment was ofJakob Stoeckel, bythen a senior music instructor at the Yale School of Music), but the real florescence of scholarly music theory came to Yale onlywith Hindemith's arrival in 1940in the newly constituted Department of Music (, "Paul Hindemith's Contribution to Music Theory in the United States," Journal ofMusic Theory 42 [1998]:6). 50 THE WORK OF MUSIC THEORY

16 THOMAS CHRISTENSEN

among a number ofscholars. For example,under the general rubric of"neo• Riemannian"theory, some music theorists have sought to extend imagina• tivelyideas drawn from Hugo Riemann's theory ofharmonic functions using advanced tools ofalgebraic .37The aim oftheir theoretical work is not so much to deduce insight analyticallyfrom musical practice nor to regulate music pedagogically.Rather, theyaim for a most traditionalgoal: to explore the universe of tonal materia in order to understand its boundless properties and potential.This resuscitation ofthe seeminglydormant tradi• tion of speculative harmonics constitutes a remarkable chapter in the long theory and suggests that the venerable studyof musica scientiaas envisionedalmost 1500years ago byBoethius mayyet have the capacityto animate the imaginationof musicians.

I have offeredthis abbreviated-andobviously highly selective-survey ofthe disciplinaryperegrinations of music theory as it vividlyopens up the manyhistoriographical challenges facing anyhistorian ofmusic theory.The problem is not simplyone ofvicissitudes oflabels and lexical taxonomies; rather, it goes to the fundamental ontological changes ofmeaning concerning musica theorica. To return to Dahlhaus's challenge raised at the beginningof this introduction,we can see how the writing ofa "historyof music theory" poses anynumber offormidable paradoxes.To be at all meaningful,such a historywould have to be both prospective and retrospective; it would need to look forward to the changes and ruptures ofmeaning that theoria under• went from its earliestconceptions-its migration intothe emerging fieldsof acoustics and analysis,for example-aswell as look backwards and recon• struct an idealizeddiscipline of music theory containingtopics that were not originallyconsidered to be part of its program of study,such as the propaedeutic writings ofthe Middle Ages or manyof the treatisesof musi• cal poetics and performance from the Baroque and Classical eras.Put simply,a comprehensive historyof "music theory"must include a prodi• gious quantityof topics and problems that were at differingtimes not prop• erlyconsidered to be part ofit. Such a historyof music theory is onlyconceivable, then, ifwe abandon anyfixed definitionof theory and allow insteadfor a flexiblenetwork of meanings.Dahlhaus has proposed one way to do this bydistinguishing

37Iam thinking here ofthe work ofDavid Lewin, Richard Cohn, and John Clough. A useful introduction to the work of these theorists is provided in Richard Cone's essay, "Introductionto Neo-RiemannianTheory: A Survey and a Historical Perspective,"Journal ofMusic Theory 42 (1999):167-80. MUSIC THEORY IN CLIO'S MIRROR 51

MUSIC THEORY IN CLIO'S MIRROR 17

various "traditions"of music theory.38For Dahlhaus, the "speculative"and "practical"tensions we have just analyzedconstitute two discrete traditions of"theorizing" that need be kept conceptually separate,however entangled theymay appear within anygiven text.The "speculative"tradition he char• acterizesas the "ontologicalcontemplation of tone systems."This would encompass, then, not onlythe traditionalprograms of classical harmonics and canonics but much research in the areas ofacoustics and tuning theory during the seventeenth and eighteenth centuries and tone inthe nineteenthand twentieth centuries.The second "practical"tradition is char• acterizedby Dahlhaus as the "regulation"and "coordination"of these tone systemsapplied to compositional practice. As a regulatorydiscipline, such music "theory"seeks to draw from practice normative rules of syntaxand models ofstructure, while at the same time discipliningthat practice through pedagogical strictures.Here we would have an even more expansivecategory of pedagogical writings crossing the centuries and touching on just about everyparameter of music: counterpoint,harmony, , meter, , form, genre,and .Dahlhaus adds a third theoretical traditionto his out• line,one that reallyonly rose to prominence in the nineteenth century, although it was foretokened,as we have seen,by Forkel: music analysis. Here, the music analyststudies individualmusical works not so much to derive normative patterns of compositional practice as to gain insight and understandingof the individuatingparticulars ofthe artwork. Dahlhaus calls each ofthese theoretical traditions"paradigms" (borrow• ing from the historian of science, Thomas Kuhn).39It should be obvious from our briefhistorical overview that the boundaries among these three traditionsare porous.Many theories and theorists mix them dialecticallyin oftenquite intricateways. For example,it would hardly be an effortlesstask to disentanglethose elements ofSchenker's theory that are regulative from those that are analytic-letalone even speculative.Still, these three tradi• tions can be useful heuristics in sorting out the diversityof theoretical "styles"we find throughout history.By thinking of music theory not so much as epistemologythan as a conceptual attitude,perhaps it is possible to map out a kind of historical evolution of musical thought while at the same time accounting for divergences and diversitywithin this thought. The resulting picture is one that seeks not to flattenhistorical theories into a seamless narrative but rather to reveal-indeedeven highlight-the

38carJ Dahlhaus, Die Musiktheorie im 18.und 19.Jahrhundert: Grundziigeeiner Sys• tematik,Geschichte der Musiktheorie, ed.Frieder Zaminer, vol.10 (Darmstadt:Wissen• schaftliche Buchgesellschaft, 1984),6-9. 39Dahlhaus, "Was heisst?"29. 52 THE WORK OF MUSIC THEORY

18 THOMAS CHRISTENSEN

pointsof disjunction, rupture, and tension.For inherent in the music-theo• retical enterpriseis a series ofontological paradoxes: musictheory is a dis• cipline that seems to stand apart from practice yetis inextricablytied to that practice; a disciplinethat claims to transcend history yetis through and through historical.Ultimately, I believe,none ofthese tensionscan be-or should be-resolved.Rather, each can be seen as helping to provide the energyand impetus ofthe discipline.For theory is not just a set ofobserva• tionaltools: these tools also tell us something about those who use them. If we recall that the traditionalLatin translationof"theory"- speculum-also means "mirror,"we can begin to understand how historical music theories act as a mirror ofpast musical intellectual cultures, ones in which the theo• rist too is reflected as an observer.For the veryact ofreflection must neces• sarilyput the interlocutor in a recursive relation with the object under scrutiny.There is ultimatelyno transcendental point of observation,given that such reflection must alwaystake place at a given positionin culture and in time.A true theory ofmusic, then,reflects in both directions,telling us as much about the individualtheorist as it does about the musical problem under consideration.At the same time,we as historians enter into this opti• cal nexus,with our own reflections upon the past shining back in our own faces, revealing something about our own position in this geometric labyrinthof historical hermeneutics. This reflexivityof music theory was alreadyunderstood in the eigh• teenth century byan insightful,though todaylittle-known music pedagogue named Johann Kessel (ca.1766-1823). Inspired by the historicist theories of his contemporary,Johann Gottfried Herder, Kessel recognizedthat the evolution ofmusic theory-likemusical art itself-couldoffer a revealing window to our understandingof past musical cultures: Since music itselfis alwayschanging and will continue to change, so must from time to time new theories of composition be developed that can explain and justifythese new changes . .Whoever . . wishes to penetrate the spirit of an entire nation and an age or the history of mankind should perhaps give attentionto musical artworks and their theories in order to gain deeper understanding ....40

40"Dasich also die Musik selbst immer verandert und verandern muss, so mi.issen auch von Zeit zu Zeit neue Theorieen der Tonkunst ans Licht treten,welche die neuen Wendungen derselben erklaren und begri.inden.... Auch dem Weisen,der in den Geist einer ganzenNation und einesZeitalters oder in die Geschichte der Menschheit tiefeinschauen will,konnten vielleicht musikalische Kunstwerke und Theorieen Winke geben zur tiefern Untersuchung und Entrathselung mancher psychologischen Erscheinung, wei!sie uns den Gang der menschlichen Empfindungen darstellen."Johann Christian Kessel, Unterricht im Generalbasse zum Gebrauche for Lehrer und Lernende (Leipzig:Hertel, 1790), preface. MUSIC THEORY IN CLIO'S MIRROR 53

MUSIC THEORY IN CLIO'S MIRROR 19

The shiftingconfigurations ofmusic theory over the centuries,then, far from undermining anyepistemic claims to transcendence or logical coherence, in fact endow the disciplinewith cultural vitalityand relevance.The differing questions posed as well as the differingtools and languages used bywhich to answer these questions constitute windows through which the historian may look and glimpse a view of past musical cultures, allowing us to see what problems of music theory were considered pressing to solve,what topics ofpedagogy critical to teach. In short, a theory text maybe itselfa speculum of intellectual and spiritual valuesas we observe the struggle of theorists to answer anew the age-oldquestion ofthe scholastics: "Quid sit musica?"41

"Grau, teurer Freund, ist aile Theorie"-Grey,dear friend,is all theory-Goethe's Mephisto warns Faust in a famous passage.And from the perspective ofthe author ofthe Farbenlehre, the systematictheorizing ofNewton'smechanical universe might have indeedseemed dishearteningly monochromatic in comparison to the livingcolors ofthe "goldentree oflife." Yet theories ofmusic, whether lyinglow to the empirical ground or soaring high into the rarifiedair of speculation and abstraction,have nonetheless alwayspossessed the capacityto instruct and inspire.Far from findingthe• oryonly an etiolatingagent of impoverishment, countless generationsof musicians have on the contrary found the intellectual contemplation of music to be enriching and ennobling,one that endows the musical with increased pleasure and profounder meaning. Ithas been a crooked journeysince first stumbled into the blacksmith's forge and contemplated the numerical ratios that underlaythe harmonious sounds he had heard. But as long as we continue to contemplate that delightful phenomenon which so enchants our ears,engages our minds, agitatesour ,and liftsour souls,there will alwaysbe those who will pursue the intellectual quest.They will wish to engage in that ethical contemplation ofmusic, to assume the venerable and honorable occupation that is the true theoros ofmusic.

41 I have elaborated this hermeneutic thesis further in my essay"Music Theory and Its Histories,"in Music Theory and the Exploration ofthe Past,ed. Christopher Hatch and David W. Bernstein (Chicago: Universityof Chicago Press,1993), 9-39.