Heinichen, Rameau, And the Italian Thoroughbass Tradition - Concepts of Tonality and Chord In

Duke University Press Yale University Department of Music Heinichen, Rameau, and the Italian Thoroughbass Tradition: Concepts of Tonality and Chord in the Rule of the Octave Author(s): Ludwig Holtmeier Source: Journal of Music Theory, Vol. 51, No. 1, Partimenti (Spring, 2007), pp. 5-49 Published by: Duke University Press on behalf of the Yale University Department of Music Stable URL: http://www.jstor.org/stable/40283107 Accessed: 21-10-2015 09:52 UTC

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Heinichen, Rameau, and the Italian ThoroughbassTradition Conceptsof Tonalityand Chord in the Rule of the Octave

Ludwig Holtmeier

This essay explores the understandingof tonality and in particularthe concept of chord, as demonstrated in the Italianthoroughbass tradition,especially in the didactic traditionof partimenti.Fora long time this traditionwas entirely overlooked because of the dominance of the neo-Ramellian Harmonielehretradition.The

Abstract

differences are exemplified by comparingRameau'sbasse fondamentalewWhHeinichen'sfluctuatingunderstanding of tonality.Itwas Heinichenwho, at the start of the eighteenth century,attempted most thoroughlyto conceptualize Italianmusic theory. LikeRameau, he, too, developed an overarchingexplanatorymodel of harmonythat involves coherent concepts of harmonicfunctionalityand chordmorphology.Heinichen'sand Rameau's"systems," however, rest on opposing assumptions. However many speculative aspects it may embrace, Heinichen'smusic theory nonetheless remains directly indebted to musical practice and consistently rejects that esprit du système that is so characteristic of Rameau'stheory. While Rameau, acting in the modern, scientific spirit of the early Enlightenment,attempts to derive all aspects of his theory from a few fundamental principles, Heinichenworks throughthe many tensions and contradictionsbetween the modern Klangprogression, as formalizedin the Rule of the Octave, and the old legacy of traditionalcounterpointinstruction.

A blind spot in the history of music theory in the last few years, with the strengthening of that movement within music or "historicallyinformed music Satzlehre theory commonly known as historische a of awareness if an as it seems forgotten "culture"of music theory has theory," tradition been given new life. The nineteenth-century German Harmonielehre occupied,1 well into the twenty-firstcentury, such an unquestioned, nearly

1 The bourgeois tradition of the Harmonielehre (meaning both "the theory of harmony" and "the harmony textbook") is "German" in view of the fact that those treatises that later served as models were nearly all published in Germany. During the course of the nineteenth century, these treatises were translated into several languages, and many

of the texts originating outside of Germany- particularly those in the English-speaking world- follow those models in their organization. It is not asserted, however, that the Harmonielehre tradition was the only one, or that there was a lack of relevant national differences.

Journal of Music Theory 51:1, Spring 2007

DOI 10.1215/00222909-2008-022 © 2009 byYale University


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monopolistic position that one must first come to terms with the notion that, existing alongside the theoretical lineage of Jean-Philippe Rameau, there was yet another music-theoretical culture no less significant in music history and the history of music theory. It is this forgotten culture and its renaissance that are the focus of this essay. The fixation of the Harmonielehre tradition on the late, "abstract"writings of Rameau2and his successors has led to one of the largest omissions of music-theoretical historiography:the nearly complete neglect of Italian music theory, its concept of tonality, and particularlythe so-called partimentotradition, which contributed so much to the true face of European composition teaching from the seventeenth to the early nineteenth century.3There can be little doubt, for instance, that the thoroughbass teachings of "Viennese classicism"were at their core a Ramellian reshaping of an Italian music theory,4just as the prevailing music theory at the ParisConservatorywas likewise minted in Italy.5In Europe, the Ramellian and neo-Ramellian tradition was an essential music-theoretical current, but until the mid-nineteenth century it was by no means the one with the greatest practical impact. In terms of reception history,there are many reasons why the partimento tradition could never step out from the shadow of Rameau's theory. Here it is sufficient to note only the most obvious: the textbooks of the partimento tradition usually consisted mainly of music notation. In these books, "theory" is not, in the common meaning of the word, presented and developed "scientifically."In general, nineteenth-century music theorists could no longer take this tradition to be, strictly speaking, "theory,"let alone take it seriously (Weber 1826). Viewed in retrospect, it decayed into Generalbasslehre (thoroughbass teaching), to "pure practice," and simply fell outside the concept of theory.6The sharp and often polemical delimitation of eighteenth-century thoroughbass teaching, which continues beyond Hugo Riemann up to Carl Dahlhaus, is a precondition for the rise of the nineteenth-century Harmonielehretradition.7 2 Meaning those writings produced after the Traité de l'Harmonie (1722). 3 Regarding the history of the Neapolitan conservatories, see Florimo 1882/83. In this connection, the works of Rosa Cafiero 1993, 1999, 2001, 2005 and Giorgio Sanguinetti 1999, 2005 merit special mention. After Carl Gustav Fellerer's early studies (1939), Florian Grampp gave a first larger overview of the topic (2004/2005). In 2007, Robert 0. Gjerdingen presented his comprehensive study (Gjerdingen 2007). Bruno Gingras 2008 followed with a study on the German partimento fugue. See also Aerts (2006). Holtmeier and Diergarten 2008 offers a general overview. 4 On this point, see especially Budday 2002, Holtmeier 2008, 2009, Grandjean 2006, Kaiser 2007a, and Diergarten 2008. The harmony and thoroughbass text of Bruckner's teacher Durrnberger (1841) is written in the spirit of

the partimento tradition, and one can still clearly detect this provenance in Simon Sechter's already unequivocally Ramellian Practische Generalbass-Schule (1830). Only the neo-Ramellian turn taken in Sechter's Grundsâtze (1852/54) represents a real break. 5 On the reception of partimenti in France, see the article by Rosa Cafiero in this issue. 6 On this point, compare the disparaging remarks of Fétis quoted by Rosa Cafiero in her article in this issue (150). 7 Even a cursory glance at the leading music journals in the first half of the nineteenth century shows that "thoroughbass bashing" was pervasive. Gottfried Weber speaks of a "jumble of note numbers and other symbols that one calls thoroughbass" (1824, 55). In the context of his discussion of Johann Bernhard Logier's System der Musikwissen-


Ludwig Holtmeier ~ Heinichen, Rameau, and Italian Thoroughbass A digression on partimento reception desÉcolesd'Italie(1804) and his Alexandre-Etienne Choron 's Principesd'accompagnement desécolesd'Italie(1808) together represent what is monumental Principesde composition surely the most obvious source for the French reception of the partimento tradition, and the influence of Choron on François-JosephFétis is of central importance for French music theory (Simms 1975). But Choron 's direct influence on the teaching of remained limited. "Italian"influence, however, goes composition at the Conservatoire far beyond these explicit documents. The structure of Charles-Simon Catel's popular Traitéd'harmonie,for example, shows clear vestiges of "Italian"practice (1802). But it wasfirst and foremost Luigi Cherubini's teaching method (1847) that stood completely within this tradition. Even the bassesdonnéesand chantsdonnésexercises found in textbooks like Henri Reber's Traitéd'harmonie(1862) and François Bazin's Coursd'harmonie etpratique(1875) - both texts alreadyclearly marked as Ramellian- document théorique the continuing influence of the Italian partimento tradition. While for a long time partimento practice remained a living tradition in Parisian conservatories and in Italy (Vidal and Boulanger 2006), its decline in Germany was accelerated by the collapse of the old bourgeois and clerical institutions of music education. With the establishment of the Leipzig Conservatory (1843), the training of musicians in Germany was reprofessionalized. The Italian partimento tradition could find only sporadic admission into this new civil institution. Nevertheless, the traditionreshaped by other music-theoretical tendencies - did survive at other conservatories, especially in Munich. There Josef Gabriel Rheinberger taught "high-Romantic"partimen ti (both figured and unfigured; Rheinberger 2001; Irmen 1974), and the exercises (1907) of Rudolf Louis and Ludwig Thuille provided in the influential Harmonielehre also remain in this tradition. In Germany,however, the partimento tradition- and, in particular,the practice of the Rule of the Octave survived best in the "lower"music orientation a with seminars teacher of (Piel 1887). Their complete practical pedagogy abolition with the general program of the Kestenberg reforms in 1925 (Leo Kestenberg was an influential music educator in the Weimar Republic) sealed the fate of the partimento tradition in Germany.

From thoroughbass to Harmonielehre The purely performance-practice term thoroughbass(Gen: Generaibass,It.: bassocontinuo),which underlies the above-mentioned polemic, oversimplifies the facts. In 1873, the Beethoven researcher Gustav Nottebohm had already pointed out that in Beethoven's time one understood a "twofold"meaning by the term thoroughbass (Nottebohm 1873, 5): "(1) the embodiment of the rules for accompanying a figured bass, and (2) the science of the combination and connection of intervals and chords, with or without consideration of thoroughbass performance."Johann David Heinichen grounded his thoroughbass schaften (1827), Adolf Bemhard Marx speaks of the "antimusical sloppiness of thoroughbass" (1830, 414). As late as 1860, Heinrich Josef Vincent titled his text on the basics of music theory Kein Generalbass mehr (No More Thoroughbass; Vincent 1830).


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JOURNAL of MUSIC THEORY method on the categorical distinction between Accompagnistenand Componisten (Heinichen 1728, preface). In the eighteenth century, Heinichen's distinction became part of common sense and led to music theory differentiating between a "theory" and a "practice" of thoroughbass, as Johann Friedrich Daube described it (Daube 1756, vii). Johann Georg Sulzer even speaks of a "science of thoroughbass" (1771/74, 456). Although the borders between theory and practice were fluid, their relationship was nevertheless subject to a clear hierarchical order. As declared in Sulzer's Allgemeine Théorieder schônen Kunste (1771/74, 456), "Without a complete understanding of harmony it is impossible to play thoroughbass correctly." Daube defined the relationship between the theory and practice of thoroughbass as follows (1756, viii): To it [thoroughbass performance] belongs, besides a skill in the practical exercise, a theoretical cognisance so that one knows: (1) from whence most chords originate, (2) to where they may be connected, and (3) how, from the first chord, one can deduce the subsequent ones. ... In addition to the practice of thoroughbass, an accompanist should also understand the theory, so that he can know how the rules of composition derive from it. A well grounded composer could even dispense with the practice of thoroughbass if he only possessed a complete command of the theory. Nevertheless having both together is better still. A complete understanding of thoroughbass always remains the foundation for the melodic structures that can be built upon it.8 Thus, in the eighteenth century, the term thoroughbasscovered exactly the subject matter that, in the nineteenth century, would fall under the jurisdiction of a Harmonielehre.

Riemann spoke of thoroughbass as a "simple tool of performance practice." Equally problematical is the overgeneralizing discourse of "the" thoroughbass, which implicitly assumes a single two-hundred-yearperiod embracing a broadly static, self-contained historical and theoretical entity. But what one comprehends by thoroughbass around the year 1600 is entirely different from what the term implies around 1700 or even 1800. Notions of an "Ageof or of "Thoroughbass Harmony" (DahlThoroughbass" (Generalbasszeitalter) haus 1990, 125) provide little help. In particular,the typical German Harmonielehretradition, which attained international prevalence in the second half of the nineteenth century, had an undifferentiated and markedly one-sided theounderstanding of thoroughbass. In the process, nearly all Harmonielehre reticians developed an almost manic fixation on the numerical shorthand, on the "figures"of "figured bass."They read the figures as representatives of 8 Hierzu gehôrt, neben der der praktischen Ausubung auch eine theoretische Kenntnifc, dafc man wisse: (1) woher die meisten Accorde entspringen. (2) Wohin sie sich lenken lassen. (3) Und wie man aus dem ersten Accorde den darauffolgenden errathen solle. . . . Ein Accompagnist soil neben der Praxis auch die Théorie des General-Basses verstehen, damit er wisse: wie die Regeln der Composition daraus

entspringen. Ein grundlicher Componist kann noch eher die Praxis des General-Basses entbehren, wenn er nur die Théorie vollkommen besitzet. Doch ist beydes beisammen noch besser. Die vôllige Kenntniftdes General-Basses bleibt jederzeit der Grund des darauf zu bauenden melodischen Gebaudes.


Ludwig Holtmeier ~ Heinichen, Rameau, and Italian Thoroughbass

9

chords, understood them almost exclusively vertically,built "stacks"of thirds over the respective bass notes, and thus unconsciously transferred their own understanding of chord, harmonic progression, and, above all, harmonic analtradition, whether oriented ysis to the music of the past. For the Harmonielehre toward theories of scalar degrees (Roman numerals, Stufentheorie)or functional theory (Funktionstheorie) , harmonic progression meant the leap from chord to chord, and it was in this sense that even thoroughbass was understood and its figures read.9 In this purely vertical reading, the figures can be theorists were unable to engage with read off clearly.Hence, the Harmonielehre the and Konbecause separation of Harmonielehre thoroughbass appropriately trapunkthad already been completely internalized and transferred to the past as something self-evident. The opposition between "harmony"and "melody," and the resultant division between the teaching of harmony and counterpoint, The more is the starting point for the neo-Ramellian German Harmonielehre. theorists decried, wrote against, and tried to surmount this the Harmonielehre "artificial"separation, the more it became solidified and, as it were, a natural law.They attempted to resolve a self-inflicted problem. The reconciliation of harmony and melody, of line and Klang(i.e., a sonority perceived as a chord), tradition (Kuhn 1994). is ^central theme of the entire Harmonielehre In the seventeenth and eighteenth centuries, considering the typical case, thoroughbass figures had not only vertical but also linear significance. One is often unable to draw a line between the contrapuntal and harmonic sense of the figures.10The recurring formulation in Italian lesson books, where one learns counterpoint through thoroughbass or partimento, should be taken seriously and understood quite concretely- by contrapuntoone had in mind not just the "special disciplines" of counterpoint but above all the correct disposizione(Sanguinetti 2005, 496f.), that is, "diebesteLage" the correct voice leading above the thoroughbass (Fôrster 1818, 1; Holtmeier 2009). The trio sonatas of Arcangelo Corelli became the unquestioned pedagogical models for this ideal voice leading. They embodied a compositional ideal valid from the seventeenth century to the mid-eighteenth century. That is, a four-voice texture was considered a three-voice texture supplemented by the presence of an added voice (ad libitum), which could as easily be missing. For the Ramellian and neo-Ramellian Harmonielehre, however, a three-voice texture is an idealized four-voice texture missing one voice. I return later to the substantial difference between these concepts of chord.

9 Hugo Riemann also understood the figures as pure "instructions for hand positions" {Griffanweisung) to which no functional harmonic or contrapuntal significance is attached. Characteristically he put not only his notorious Klangschlùssel but also his symbols for harmonic function under all the exercises in his Anleitung zum Generalba&Spielen (Riemann 1889).

10 One is tempted to say - with all due caution - that at the beginning of the eighteenth century the linear significance still predominates, and that thoroughbass or the understanding of thoroughbass becomes increasingly "verticalized" during the course of the century under the influence of Ramellian thinking. The one-sided vertical reading of the German Harmonielehre is only a (radical) consequence of this development.


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JOURNAL of MUSIC THEORY A digression on Corelli reception

Corelli had as authoritaWithout exaggeration, can one assert that for the stilontoderno, tive a stature as that of Palestrina for stilo antico.He was, in terms of the reception of his style and the diffusion of his works, a composer of European importance. Angelo Berardi had already called him the "new Orfeo of our time" ("nuovo Orfeo nostri giorni";Berardi 1689, 45). ForJohann Mattheson he was "the prince of all composers" (Mattheson 1739, 326). And Michel de Saint Lambert referred to him as the "famous Corelli, so celebrated now in all Europe, and for several years so fashionable among us" ("fameux Corelli, si célèbre maintenant dans l'Europe, & si à la mode parmi nous depuis quelques années"; Saint Lambert 1707, 41). Corelli's music was so popular that Denis Arnold spoke of a "Corelliancult" (Arnold 1978). In 1681, the Pasquini pupil George Muffat became personally acquainted with Corelli in Rome. One could point to Muffat's RegulaeconcentuumPartiturae(1699) as f/œtheoretical document for the modern (Corellian) trio-sonatastyle of composition. Here composition in four or more voices is consistently presented as an extension of three-voice composition. Mattheson stressed, "If one can deal with three voices properly, singably,and with full sonority, then all will go happily even with twenty-four voices" (1739, 344). Even in Joseph Riepel's dialogues, the Teacher explains to his Student that one must "patchin" the fourth voice (Riepel 1996, 571). This procedure can still be seen clearly in Stanislao Mattei'sfour-voicesettings of bassinumerati(1850) - the viola part is an optional filler voice. The single voice of the thoroughbass stood as representative of an essentially three-voice, contrapuntal constellation of voices, whose contrapuntal topoi had already been practiced during instruction in composition.11 Given a schematic excerpt of the bass and/or the figures, one assigned it a two-voice accompaniment. By no means could the harmonic "content" of a bass be logically derived, as it were, in the abstract from the figures themselves. Thus one knew that the two-voice 2-6-7-3 model for the upper voices (bracket "a" in Example lb) was assigned to a rising fifth with the figures 4-3 (Example 1, Ledbetter 1990, 12; Fenaroli 1978, bk. 3, 9). Likewise, one knew which upper voices corresponded to the clausula of the cadenza composta (slur "b" in Example lb). One recognized larger contexts and allocated the missing voices, but on no account was the point to be "counting outMchord tones from the bass.

11 Particularlyin recent German music theory, the discussion of compositional models represents its own strong tradition. In this regard, Ernst Seidel's article on the "devil's mill" {Teufelsmûhle; 1969) is of special significance (see also Holtmeier 2008, s.v. "Teufelsmûhle"; Dietrich 2007; Yellin 1998). Furthermore, one should mention, on the one hand, the teaching methods and the less historically than systematically oriented works of the "Berlin school" centered around Hartmut Fladt (2005, 2007), which found its most powerful expression in Ulrich Kaiser's influential

two-volume Gehôrbildung {Ear Training-,2000) and, on the other hand, the works developed in the environment of the so-called "historical composition training" {historische Satzlehre). Here the teaching methods and the writings of Markus Jans have been exemplary (Jans 1987, 1993; see also Holtmeier 2002, 2008, s.v. "Satzmodelle"; Dodds 2006; Froebe 2007; Menke 2008; Schwenkreis 2008). See also the current discussions around these models: Aerts 2007, Kaiser 2007b, and Schwab-Felisch 2007.


Ludwig Holtmeier ~ Heinichen, Rameau, and Italian Thoroughbass 43

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Toward a history and theory of the Rule of the Octave At the beginning of the eighteenth century, the splitting of thoroughbass into "science"and "practice,"along with the "invention"of the Rule of the Octave around 1700, was a pivotal turning point in the history of both thoroughbass and harmonic tonality. It is a still widespread misunderstanding that the Rule of the Octave is only a "model harmonization,"one among several possibilities for furnishing major and minor scales with chords. But that view recognizes only the most extrinsic aspect of the Rule of the Octave and overlooks its intrin-, sic significance for music history and the history of music theory. At heart the Rule of the Octave is not merely "pragmatic"legerdemain (Christensen 1993, 170) , but the crucial step towarda theorlzation of thoroughbass. It is not solely a concrete statement of compositional norms but aboye all an instrument of harmonicanalysis.12The Rule of the Octave codifies what is generally understood by the terms "major-minortonality,""cadential harmony,"or "modern tonality."With the Rule of the Octave thoroughbass becomes a Harmonielehre in the modern sense. The Rule of the Octave frees thoroughbass from traditional thinking in terms of model-bound (contrapuntal) contexts, isolates the individual Klang,and leads to a hitherto unknown verticalization of harmonic discourse- the Rule of the Octave is a theory of harmonic functionality.

12 Scholars did not follow up on Walter Heimann's remarks on "Rule-of-the-Octave texture" (Oktavregelsati) in his splendid study of Bach's chorale style (Heimann 1973, 62f.). Only with Wolfgang Budday's Harmomelehre Wiener Klassik. Théorie- Satztechnik-Werkanalyse (Harmony in Viennese Classicism; 2002) was the Rule of the Octave brought back into the discourse of practical music theory. FranckThomas

Arnold's monumental study on thoroughbass from 1931 must also be mentioned in this context. Arnold comes close to many of the insights that were presented in the works of Heimann and Budday. But his general historical approach is underpinned by that tenacious neo-Ramellianism that was so typical for his time.


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JOURNAL of MUSK. THEORY

No one more clearly recognized the verticalization of harmonic discourse and more radically formulated it than Rameau. If one does a close reading of his Traitéde l'Harmonie(1722), then there can be no doubt that Rameau's theory of the bassefondamentalearose from the attempt to theoretically pinpoint the Rule of the Octave (see Heinichen 1728, 764). In the first two books of the Traité,he develops theoretically what in the central, third book he achieves by practical application in the example of the Rule of the Octave. That is, the bassefondamentaleexplains the modus vivendi of the Rule of the Octave, its ruling principe.The bassefondamentaleconstitutes the inner "essence"of harmony, the Rule of the Octave its outward appearance.13It is no doubt correct that, after the Traité,Rameau's music theory distanced itself ever further from its origins in the Rule of the Octave. From the publication of the Nouveausystème(1726) onward, Rameau's theory becomes noticeably more abstract and formalistic. The internal aspects of the theory turn ever more clearly toward the external. The bassefondamentalebecomes the paramount principle which usurps even musical practice. Paradoxically,the Rule of the Octave itself becomes, at least dating from the public argument between Rameau and Michel-Pignolet Montéclair in the MercuredeFrance(Rameau and Montéclair 1729/30; Christensen 1993, 56) , first a counterproposal to the basse fondamentale,and finally the epitome of a spiritless,atheoretical practice pitted against the lone scientific theory in the form of the bassefondamentale.™ One must alwaysbear in mind the Janus-faced character of Ramellian theory in order to understand its complex reception history.This divides along two main paths, which one could reify and characterize as the "practical"and the "speculative."The practical takes its point of departure from the third and fourth books of the Traité,in which the Rule of the Octave plays a central role. The speculative derives from the first two books, which deal exclusively with the bassefondamentale.The German, and above all the north German, reception of Rameau can be predominantly assigned to the speculative path, the French and Italian reception, save for isolated exceptions, to the practical. The Viennese tradition of thoroughbass teaching is, as already mentioned, in the broadest sense associated with the Italian tradition. In the French and Italian school of teaching composition (and the Viennese school can be regarded as belonging to it), the bassefondamentalefirmly integrated itself into the deepseated educational tradition of the Rule of the Octave. There the Rule could hold its central position across the whole of the eighteenth century without 13 The Rule of the Octave occupied Rameau's attention his whole life. He was always finding new interpretations of it (Christensen 1993). 14 This becomes clear, for instance, in the statement by FriedrichWilhelm Marpurg that "since the time of his [Rameau] Traitéde l'Harmonie, the Testore musico of someone likeTevo cuts as poor a figure as, for example, the logic of Christian Weisen since the advent of [Christian)Wolff's

philosophy of reason" ("seit der zeit seines [Rameausl Traité de l'Harmonie macht der Testore musico einesTevo und andrer eine so schlechte Figur, als etwa eine Logik von ChristianWeisen, seit die WolfscheVernunftlehre existiert"; Marpurg 1760, 57). That the basse fondamentale succeeded to become the epitome of "modern" scientific method may have been the essential reason behind the extraordinary success story of Ramellian theory.


LudwigHoltmeier~ Heinichen, Rameau,and Italian Thoroughbass any real dispute. On the other hand, alreadyin the worksof FriedrichWilhelm Marpurg and Johann Philipp Kirnberger,who more than any others spread Ramellian theory into German-speaking lands, the Rule of the Octave plays only a marginal role. And from the early writings of the German Harmonielehretradition (Gottfried Weber,Adolf Bernhard Marx) it finally disappeared almost completely. In the first half of the nineteenth century the Rule of the Octave also begins to lose its significance in France and Italy.Toward the end of the century it was displaced across nearly all of Europe by the modern scaletraditiondegree (i.e., Roman numeral) theory of the German Harmonielehre a global export success. It was completely forgotten that the Rule of the Octave had once actually founded the "modern"conception of tonality. A digression on Rameau reception

The receptionof Rameau'steachingswasalsohamperedby the factthat,apartfroma relativelyearlytranslationof the thirdand fourthbooksinto English(Rameau1737), no furthertranslationswerepublishedduringthe eighteenthand nineteenthcenturies. Rameau'stheorycame to GermanyprincipallythroughFriedrichWilhelmMarsummaryofJean Le RondD'Alembert(1757). purg'stranslationof the "theory-laden" Yetthere were tracesof Italianmusictheoryeven in the Prussiannorth. Maximilian a friendof Haydn,broughtthe Italiantraditionto the districtof von Droste-Hûlshoff, Munster(Droste-Hûlshoff 1821;Fellerer1939;Kantsteiner1974/75); BernhardKlein in to the Sing-Akademie tradition of the ParisConservatory the brought partimento RamellianBerlin(Eitner1882).Klein'spupil,the archivistandmusictheoristSiegfried Dehn, was a great connoisseurof Italianmusic theory.Towardthe mid-nineteenth century,Dehnpublishedtwonotabletextbooksin the Italianspirit(Dehn 1840,1859). Kleinbroughtdownon himselfthe oppositionof the all-powerful Characteristically, CarlFriedrichZelter(Eitner1882),and Dehn'sharmonybookbecamethe targetof a famouspolemicalattackfromAdolfBernhardMarx(1841). The fact that the Rule of the Octave was consistently understood as "practice"and not as "theory"is based on the nature of the Rule of the Octave itself. In contrast to the closed system of Ramellian theory, the Rule of the Octave developed through a long history and melded together different, occasionally divergent music-theoretical contents and traditions. The Rule of the Octave has neither a sole "inventor"nor an unambiguously defined form. But one can come up with three factors that define the nature of the Rule of the Octave, and which I would like to describe schematically as the sequential, the cadential, and the systematic.The intrinsic multiplicity of the Rule of the Octave even explains its diverse manifestations- some emphasize the sequential factor, others the cadential or the systematic. The Rule of the Octave is usuallydescribed as standing in the tradition of models used in improvised contrapuntoalla mente- from Guilielmus Monachus (1965) to Fray Tomâs de Sancta Maria (1565) to Spiridionis (1670/71/75; Lamott 1980; Christensen 1992; Jans 2007; Gjerdingen 2007, 467f.). Thus,


13

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Example 2. An improvised

scale harmonization

6

66

as precursor to the Rule of the Octave

the Rule of the Octavecarriesforwardthe traditionalcategoriesof intervals and their "dynamic" qualities.The triadrepresentsperfect consonance,the "cadential" sonorityof repose, the initialand goal chord of a harpersistent monic progression.By contrast,the chord of the sixth representsimperfect consonance,the sonorityof motion,whichdemandsa stepwisecontinuation. Therefore,the primitivemodel of the Rule of the Octavewould involvea stepwisesuccessionof chords of the sixth, linkinga perfect consonanceon the firstdegree to a perfectconsonanceon the fifthdegree,and ultimatelyto a perfectconsonanceon the eighth degree (see Example2). But the specificGestaltof the Rule of the Octavecannot be attributed solely to the traditionof improvisedscale harmonizations.On the contrary, there is an auraof mysticalrevelationthat surroundsthe descriptionof the sources.15 One can Ruleof the Octavein quitea fewearlyseventeenth-century music-theoretical still sense it in that intrinsicallyGerman-language, concept of the "naturalscale"(naturlicher ambitus)or "naturalharmony"(naturliche s.v."Ambitus") ("Itseems to me Harmonie)(Heinichen 1728,750 and register as if thisharmonicscalehasbeen implantedinto our earsfromthe beginning of the world"["Mirdeucht,es seydièseharmonischeLeiterunsermGehôrvon Anbeginnder Welteingepflanzt"];Riepel1996,580), and the manyclaimsof prioritymakeclearthat the Rule'sappearancewasfelt as a remarkableevent andan importantdemarcationwithinthe historiesof compositionand theory. Thatwouldhardlyrequireexplanationwereit nothingmorethana pureconmodels.The forerunnersof tinuationof the traditionalinterval-progression the Ruleof the Octavepresupposeda separationbetweena logic of progression tied to a model- in the sense of improvisedGymel(Jans 1987)- and of a cadential,punctuatingsegment.Modeland cadenceare the centralcategoriesof compositionalinstructionin the seventeenthcentury.To compose,one might say somewhatsimplistically,meant an alternatingexchange between cadentialand sequentialmodels.The second half of the seventeenthcentury can be describedas a processduring which these sequentialand cadential modelscome ever closer to each other.The Ruleof the Octavefinallymelds both factorstogether. 15 Here one must mention François Campion (1716, 1730), who claimed for himself the authorship of the Rule of the Octave - an old musician bequeathed it to him, as it were, on his deathbed (Mason 1981). This story spread quickly and remained in circulation for a long time in northern Europe, particularlythrough David Kellner's frequently reprinted Treulicher Unterricht im General-Bass (Kellner 1732).



15

In the early eighteenth century, contemporary writersclearly recognized that the changed role of the "false"(diminished) fifth and the "major"(augmented) fourth was the central sign of the new harmonic language. It is also one of the central theorems of Italian music theory and of Ramellian teaching that the relationship between the "leading tones" 7 and 4 forms the core of a theory of harmony. As a matter of fact, the feature that most clearly differentiates the Rule-of-the-Octaveharmony in the eighteenth and nineteenth centuries from the harmony of the seventeenth century is the compelling assignment of the (dominant-function) six-four-twochord to the descending fourth degree.16It is precisely that new role for the "false"fifth and "major" fourth that differentiates the Rule of the Octave, in qualitative respects, from all the older harmonization models of the scale.17 A digression on the "false" fifth

A remark made by Angelo Berardi in the context of discussing a resolution of the dissonant second into a "false"fifth supports the thesis that the "consonant"and free use of the diminished fifth in the modern harmony at the close of the seventeenth century was borrowed from popular music: "Some moderns have resolved the suspended second to the false fifth; one allows this method of resolution, it being hard and harsh, only in popular song for the expression of certain words. Thus, one should use it with caution" ("Alcunimoderni hanno legato la seconda con la quinta falsa: questo modo di legare, per essere duro e aspro, si concede solamente nelle cantilene volgari per esprimere qualche parola. Si deve perciô usare con prudenza"; Berardi 1687, 137). Mattheson grasped the changed role of the diminished fifth precisely when, in Der he maintained one would have "good reasons" (billigeUrsache) volikommene Kapellmeister, the it to for "appending consonances," since "itdoes far more harmonious service than fifth" the perfect (Mattheson 1739, 235). At the beginning of the nineteenth century, de Momigny still maintained that one had to treat the tritone and the Jerome Joseph if false fifth "as they were consonant, ... for thirds, sixths, false fifths, and tritones are the true harmonic intervals that can be used in two-partcomposition" ("comme s'ils étaient des consonnans, ... les tierces, les sixtes et les fausses quintes ou tritons sont les vrais intervalles harmoniques, employable dans la composition à deux partie"; Momigny 1803/1806, 1:284). Similarly,Fétis regarded both the diminished fifth and the augmented fourth as consonant intervals (Simms 1975, 122). Nicolô Zingarelli 16 And likewise, the (dominant) six-five chord on the ascending seventh degree. In terms of historical development, the fact that (along with the four-two chord on the descending fourth degree) it concerns a harmonic passing-chord phenomenon remains evident for a long time in the Italian partimento tradition. According to Giovanni Paisiello (Dellaborra 2007), the dominant four-two chord occurs "when one descends from the fifth of the key to the third of the key" ("quando discende dalla Quinta delTono allaTerza delTono"; Paisiello 1782, 5; Holtmeier, Menke, and Diergarten 2008). In the course of this development, however, this passingchord phenomenon becomes emancipated from its origin,

and one could thus with equal justification designate the fifth degree as a "preparation" for the descending fourth degree. 17 Johann Georg Albrechtsberger stresses that there is a "bass scale of the old composers" and a "bass scale of the newer composers" (Albrechtsberger 1790, 12/13). For the chord on the descending fourth degree, the four-two chord suits the "newer" scale - the modern Rule of the Octave, while the simple six-three chord, which only serves the distinction between perfect and imperfect triads, suits the older scale.


16

JOURNAL of MUSIC THEORY opened up his lessons in composition with what he considered to be the core relation of harmony. He wrote the tritone and the diminished fifth and their resolutions on a piece of paper with the words: 'You shall begin from the scale in two voices; and remember, in harmony the fourth descends, and the seventh ascends" (Sanguinetti 2005, 451f.).

It is not difficult to discern the derivation of the harmonic formula for the descending 4-3-2-1 scale-degree progression in the Rule of the Octave: its source is the cadenzadoppia(see Example 3) , which playssuch a prominent role in the music of the seventeenth and eighteenth centuries (Gjerdingen 2007, 169). Early-eighteenth-centuryItalian thoroughbass manuals recognized three types of cadences, which were designated in the eighteenth-century partimento tradition by the terms semplice(simple), composta(compound) , and doppia (double).18Thus, semplicegenerally signifies a simple dominant-tonic relationship, compostathe classical4-3 suspension cadence, and doppiathe "grand" cadence with the consonant fourth. These cadences have not merely an articulating, punctuating function, but in the seventeenth century they become comprehensive compositional models that pervade entire compositions. It is crucial to note that these cadences are contrapuntalmodels. At its core, each cadence consists of three voices, which relate to each other in triple counterpoint: although the unfigured bass clausula of the cadenzadoppia(Example 3a) can only be set over a soprano clausula, not over the tenor clausula, some other standardized figurations (c-f ) even permit the later arrangement.19 Underlying the Rule of the Octave is less a collection of interval-progression models and more a Durchkadenzierung (thorough cadentializing) of the scale by means of these contrapuntal cadence models- above all the cadenza doppia.Starting points for the emergence of the Rule of the Octave might be phrases "in the style of Corelli,"as in Example 4. In Example 4a, the slurs mark the doppiaversions of tenor clausulae, the brackets mark the doppiaversions of soprano clausulae (see also Example 4b), and the wavyline designates the figuration of a doppiabass clausula. One can easily clarifythe derivation of the Rule of the Octave from the modern Italian 18 See Gjerdingen 2007, 141 f. A historical investigation of this concept is a topic of current scholarship and would exceed the limits of this essay. The term doppia and the quasi-standardized use of the conceptual triad of semplice, composta, and doppia is a relatively late feature of Italian music theory. Also, the terms are hardly used in a consistent way. Even in the late eighteenth century, depending on the author, the terms may overlap in content, especially with semplice and composta. In earlier sources the doppia cadence is designated by a multiplicity of terms like cadenza major, gro&e Cadenz, grande cadence, great cadence (Godfrey Keller), gantze Cadenz or cadentia maior perfectis (Muffat), and so forth. Even later- despite a clearly

perceptible process of standardization- the terminology is by no means consistent. Similarlyambiguous are the derivation and meaning of the term doppia (double). On the one hand, it can refer to the (metrical) breadth of the cadence, and on the other hand, to the combination of semplice and composta into one "doubled" cadence. 19 The fifth scale degree thereby becomes a superjectio of the fourth degree. The bass clausula thus actually becomes a variant in double counterpoint of the alto clausula. This quasi identity between figurations of bass and alto clausulae is an essential element of innumerable contrapuntal designs in the music of the seventeenth and eighteenth centuries.


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of of the Corelli-styletrio-sonataformatif one makesa "reduction" "tonality" To That 4a.20 that one first removes all the end, Example suspensionfigures,. includesthe 7-6 suspensionsin mm. 4 and 5, the 4-3 suspensionin the third measure,and even the 7-5 progressionin thatsamebar,whichis actuallyonly an "elision"of a 7-6-5-4-3 progression.In this form the progressionalso appearsin the then-currentmodel-basedphrasesshownin Example5. If one 20 In the early eighteenth century, this kind of dissonance reduction is a common procedure in thoroughbass pedagogy. In particular, see Michel de Saint Lambert 1707 and Godfrey Keller 1707.


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now- retainingthis organizingprinciple- also begins the descendingscale witha perfectconsonance,thereemergesthe classicalformof the Ruleof the Octave(Example6). It becomesclearduringthis processof derivationwhatis reallyrevolutionaryabout the Rule of the Octave:the derhythmizationof the cadence, the decoupling of dissonancefrom ligatura,from syncopatio. In short, the of the traditional cadential the dissolution breakup interrelationships.Only of the "bonds"(ties) in the clausulaefrees the Klang.21 This emancipationof individualsonoritiesinevitablyaccompaniesa far-ranginglooseningof superordinaterhythmicand linear relationships.Thus, in the context of the doppia tenor clausula,the thirdscale degree in the bassactuallybecomesonly a "passingchord"on a weakbeat, carrierof a consonantpreparationfor the followingdissonanttenor clausula(Example7a). The principleof the stepwiseprogressionisolatesthe sonoritiesand permitsa largelyderhythmicized "binaryrelationship"of chords to replacethe three-and four-notecontexts 21 Nowhere can one more clearly discern the factor of abstraction, the "material character" of the Rule of the Octave, than in this process. Here too lies the crucial difference between the sequential and cadential models, which

as concrete compositional building blocks can be, as it were, directly adopted and employed in compositional practice. The Rule of the Octave, by contrast, always requires positioning within the rhythmic design.


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of the clausulae(Example7b). Thus, the thirddegree takeson a sonorityin its own right. It is particularly here in the Ruleof the Octavethatone finds"old"interval progressionsand the "new"Corelli-stylecadentialharmonyin a relationship of dialecticaltension.As a chord of motion, the imperfectconsonance on the thirdscaledegree leadsacrossthe imperfectsecond degree to resting point on the perfectfirstdegree (Example7a). Yetas a more "emancipated" componentof the cadenzadoppia,the chordof the sixthis a goal and point of resolutionfor the dissonantsix-four-two chord on the fourth degree, which precedesit (Example7b). It is thusjust asmucha chordof repose.The cadenza doppiacarriesthe factorof harmonictensionand relaxationinto the old progressionmodel. This is exactlywhereRameau's theorybegins- the model of tension and relaxationbecomes the centralfeatureof his bassefondamentale. Consonanceand dissonanceassumethe place held by perfectand imperfect consonancein the musictheoryof the seventeenthcentury.Dissonancetakes overthe functionof imperfectconsonance.Harmonicmovementis no longer the progression,by means of a multiplicityof imperfectconsonances,from an opening perfect consonance through a series of intermediatecaesuralike perfect consonancesto a closing perfectconsonance (the so-calledpipprinciple;Jans 1987). Now harmonicmovementis a routineconsequenceof dissonanceand consonance, of tension and relaxation(Christensen1993, 120f.).22ForRameau,thejuxtapositionof doppiaclausulaein the Ruleof the Octavebecomes a routine consequence of two-stagecadences parfaites.The close dependencedevelopedby Rameau's bassefondamentale on the cadential harmonyof the Ruleof the Octavebecomesclearif one sets belowthe doppia cadencesof Example4a a bassvoicewithoutfiguration(Example8a givestwo alternativeversions)and then comparesthissupporting"fundamental voice" 22 Or the connection of two consonances by a chain of dissonances. Thomas Christensen points out that for Rameau "every non-tonic scale degree carries a seventh chord" (1993, 129).


19

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ascending

with the bassefondamentale(Example 8b) that Rameau provided for the Rule of the Octave (Rameau 1722, 382). Even Rameau's bassefondamentaleuses only the tones of the doppiabass clausulae: C, G, and D.23One clearly recognizes, however, the differences. Rameau applies, as it were, the same model to the succession of the descending scale as to the ascending scale. Thus, in the descending scale, the fifth degree is treated like a first degree (as a nottetonique), and the leading tone ( nottesensible)is treated like a third degree ( mediante). These degrees are thus interpreted as if ascending: for Rameau, the schematic progression in Example 9 implicitly underlies the ascending scale (Rameau 1722, 208). The diatonic arrangement of the mode prohibits the leading tone to the fifth degree from actuallysounding (Rameau conceives the fifth degree comme une nottetonique)(Rameau 1722, 213). Yet regarded functionally, the progression of the leading tone to the tonic {nottesensibleto nottetonique)is identical to that of the fourth degree to the dominant (quatrièmeto dominante)(Rameau 1722, 208). At the end of Rameau's ascending scale (Example 8b) a scarcely motivated, apparent leap from the leading tone to the fifth degree owes its existence to Rameau's logic of progressions. It clarifies the dual function of the seventh scale degree, which must at the same time support an inversion of a perfect triad (parfait)and a seventh chord (Vaccordde la septième).On the one hand, it is a medianteof a "tonicized"dominant accordingly ushered in by its own dominant (D3 in the bassefondamentaleof Example 8b) (Rameau 1722, 211). On the other hand, it really is the nottesensible,obliged to lead into the tonic and to support a (dominant) six-five chord (l'accordde la fausse quinte). One can clearly detect these changes of function from the bassefondamentale. The bassefondamentaleunder the leading tone (G3) does not bear the signature of a seventh chord, because the sounding dissonance of the six-fivechord on this seventh scale degree is just an apparent one. In its true essence this dissonance is a parfaitin first-inversionform. Only with the next chord does the fundamental seventh chord become "material"and resolve itself properly. 23 The much discussed problem area of the double emploi (see Example 8b, m. 3) lies outside the scope of this essay.


21

22


That the seventh of the bassefondamentaleunder the sixth scale degree (C above D), which performs the function of a dominant to the medianteoî the tonicized dominant, is not resolving correctly but ascends to the D, justifies Rameau in the prohibition of doubling the leading tone (B), which a proper resolution of that dissonant seventh would violate (Rameau 1722, 213; see also Rousseau 1768). So just as that six-five chord over the seventh scale degree is actually a perfect triad, then conversely the six chord over the sixth scale degree is actually,in a functional sense, a dissonant seventh chord. Alreadywe can clearlymake out that tendency towardformalisticabstracand tion espritdu systèmethat in the late writingsof Rameau often takes on such abstruse manifestations.24In the Traité,however, Rameau's complex operations still have a recognizable basis in experience and in the musical features themselves. The thesis that the fundamental principle of modern (Rule of the Octave) harmony was the dogmatization of the cadence, understood as the transition from a dissonant sonority to a consonant one (and vice versa), actually grasps an essential aspect of the new chordal basis of composition in the style of Corelli's trio sonatas. But one can also clearly distinguish in Rameau's bassefondamentalethe difficulties and problems of a one-dimensional systemization of the Rule of the Octave. In concert with his theory of inversion, Rameau's consonance-dissonance dichotomy eliminates the concept of imperfect consonance. It may still be present as a phenomenon in compositional technique, but as a music-theoretical category it disappears completely.25The consequences are far reaching. As imperfect consonances merge with perfect consonances in the concept of chord, the concept of harmonic movement is tied exclusively to dissonance. Beyond dissonance, Rameau's system reaches an impasse. Thus it is literally impossible for two accordsparfaits(each with a different bassefondamentale)to follow one another. At their core, the labored constructions of the cadenceirregulière(sixte ajoutée),the later sous-dominante, and the infamous doubleemploionly serve the purpose of maintaining the rigid logic of progression, which enforces the exclusion of imperfect consonances and the dogmatization of dissonance. Rameau's music theory does not engage the dialectical tension between the old interval progressions and the "new" cadential harmony of the Corelli style, which was worked out as a central factor in the Rule of the Octave. With a revolutionarygesture he simplywiped the centuries-old and autonomous theory of intervallic qualities off the table. Toward an "Italian" concept of chord No music-theoretical theorem of the eighteenth century did more to imple- "inversion" ment a break with tradition than Rameau's theory of renversement 24 In the Traité, Rameau himself points repeatedly to the fact that the basse fondamentale is "of little use in practical music" (inutile à la pratique; Rameau 1722, 381).

25 Christensen refers to the difference between a concept of inversion based on "inversional derivation," which was already common before Rameau, and one based on this new "inversional equivalence" (1993, 70f.).



23

sealed the fate of the old intervallic qualities. No other concept of Ramellian theory would have a comparablywide diffusion. Even traditions of musictheory teaching that took themselves to be anti-Rameau and rejected in particular his theory of chord progression26nevertheless adopted as self-evident the concept of inversion. By the end of the eighteenth century it had already gained acceptance across all of Europe, and by the middle of the nineteenth century it finally achieved a position where it had almost no competition. Even today, it still holds sway so naturally, so unchallenged that it is worthwhile drawing attention to what a radical break it once represented from a centuries-old tradition. According to Rameau, a chord of the sixth is no longer an independent sonority in its own right, but becomes a "derivative" chord, an "inversion"of a "fundamental"triad. The old pivotal distinction between fifth and sixth, between a sonority of rest and one of motion, was not only completely leveled, but perfect and imperfect consonances became, in Rameau's thoughts on inversion, nearly "identical."His new principle of the stacking of thirds takes the place of the old intervallic qualities. From it Rameau derives both of his "root chords":the triad {parfait)and the seventh He even bases the essential opposition between chord (dominante-tonique). consonant and dissonant chords- between consonance and dissonance- on his principle of the stacking of thirds. The partisansand interpreters of Rameau have alwaysinvoked the idea that his theory was the first to actually develop a precise concept of harmonic dynamism (Christensen 1993, 132). That would be correct if one has in mind his attempt to trace harmonic process back to the "basic units" of tension and release, to the dominant-to-tonic progression, and his efforts to develop a holistic concept of harmonic space. Yet one could as easily argue the opposite- that in its schematized ideas of inversion and the stacking of thirds, Rameau's theory leads to a complete antidynamic enervation of harmonic process. Forjust as the difference between perfect and imperfect consonance vanishes, so does any factor of linearity in the concept of chord.27 One can unproblematically ascribe the sonorities of the Rule of the Octave to a series of cadencesparfaiteson the notes of the bassefondamentale as long as it behaves like forms of cadenzedi grado,thus as long as there is a soprano or tenor clausula in the bass. The fifth degree of the ascending Rule of the Octave- as the penultimate tone in a bass clausula- properly requires a leap and so becomes a problematic case for Ramellian theory, a problem whose elaborate solution has been discussed in detail above. 26 In the eighteenth century, Rameau's theory of chord progressions - the actual heart of his theory - only plays a subordinate role, and even German scale-degree theory of the early nineteenth century only marginally takes up this aspect of it. Only with the "neo-Ramellian turn" of fundamental bass in Vienna (Sechter) and of functions theory in Leipzig (Hauptman) does Rameau's theory of progression finally become relevant for musical practice.

27 In the early twentieth century, it was Heinrich Schenker who time and again pointed out Rameau's "overemphasis on the vertical" (1930, 11). As much as he was unconsciously bound to an understanding of tonality that was Ramellian at its core, it is his undisputed historical achievement to have highlighted the significance of the compositional framework and its figuration for "classical" tonality.


24

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The cadential effect of the fifth degree is actuallysuperior in the Rule of the Octave, even if in a sense different from the one Rameau thought of. The triad (Example 10a), but especially the seventh chord (Example 10b), on the fifth degree almost compels a cadential resolution, thus a drop of a fifth or third following it. The example makes it clear that in the Rule of the Octave, degrees 6 and 7 following the dominant (Example lOd) should be understood as merely a stepwise filling out of the ascending cadential leap of a fourth, and are treated as "passingchords" (Schulz [Kirnberger] 1773, 36). If one considers m. 2 in Example 4a, one will see that the rising scalar passage from D3 to G3 in the bass actually presents the figuration of a doppiabass clausula. One can glean from this and other examples that Rameau's interpretation of the Rule of the Octave is doomed to failure because it does not respect the functional differences and the functional variabilityof the individual degrees and their sonorities. For Rameau, cadenzedoppie,cadenzesemplici,passing chords, chords resulting from figurations- in short, everything- must conform to the unitary mechanism of the consonance-dissonance succession of the cadence parfaite.To be sure, the Rule of the Octave also isolates individual sonorities from their originally linear contexts. Nonetheless, one can still document within it a contrapuntal provenance from three-voice compositional and cadential models. In Rameau's theory of chords, however, chordal sonorities become radically equalized. Chordal relationships that extend beyond the simple two-stage progression from consonance to dissonance fall completely outside the system. The functional variabilityof chordal scale degrees (Stuferi)can be clearly demonstrated by the chord of the sixth on the third degree, one of the outwardly most stable harmonic constellations within the Rule of the Octave (Example 11). On the one hand, the chord of the sixth on the third degree can essentially serve, in Rameau'ssense, the function of a tonic chord in inversion (Example lia). But given its placement on a mi-degree, it can also be part of a cadenzasempliceand exercise the function of a "local"dominant to the fourth degree, which in turn will be treated like a Mitteltonika(Riepel 1996,


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585) (Examplelib). Moreover,it is alsofrequentlypartof a dominantpreparation,one that preparesthe dissonantsix-fivechord on the fourth degree (Examplelie). Such fine differentiationsfind no resonancein the mechanismof the bassefondamentale. Hence, the vanishingof the distinctionbetween perfect and imperfectconsonanceultimatelyleadsto an impoverishmentin the concept of harmonicfunctionality.Giventhe disappearanceof all linearfactors, harmonicdynamismappearsin the form of a monotonous,basically"undynamic"logic of progressions. Johann David Heinichen and the systematization of the Rule of the Octave

To speak of a concept of chord in the Italianthoroughbasstraditionraises its own problems.On the one hand, the notion is hardlymore than a rough summaryof certaintraditionsof instruction,whicheach ought to be historicallyand geographicallydifferentiated.The readermayhavenotedwithsome confusionthat the partimentotradition,the Italianthoroughbasstradition, and the Ruleof the Octaveare not clearlyset apartfrom one anotherin this text. In fact,it is scarcelypossibleto drawclearboundariesbetweenthem. If one refersto partimentias the didacticalthoroughbassexercisesthemselves, it is not difficultto showa continuoustraditionalcontextthroughoutEurope, extendingfarinto the twentiethcentury,in whichthe differencebetweenItalian, French,or even Germantheoreticalapproaches,betweenthe Ruleof the or scale-degree(Roman-numeral)theory (StufenOctave,bassefondamentale, theorie)are of secondarysignificance.If one takes partimentias a didactic tradition,however,in whichthe accompanimentof unfiguredbassesis of fundamentalimportance,then "partimento" alsocontainsa theoreticalapproach that is inseparablytied to the principlesof the Rule of the Octaveand the compositionalmodels.If I referhere alsoto an Italianthoroughbasstradition, it is becausethis theoreticalapproachis not bound to the didacticismof the


25

26


partimenti, even if it developed from them. Manyschools of thoroughbass are certainly in the partimento tradition, even if they do not make use of actual partimenti (e.g., Kellner 1732). What they have in common is the central concept of the Rule of the Octave. On the other hand, as alreadypointed out, there was no explicitly articulated theory and comprehension of chord that, in the sense that one might contrast "Italianmusic theory versus French music theory,"one could set in opposition to the Ramellian bassefondamentale.The singular and indeed puzzling success of Ramellian theory can substantially be attributed to the fact that Rameau never fledged a real theoretical opponent, someone who could have confronted his bassefondamentalewith a competing concept. Thus, in the course of the eighteenth century the Rule of the Octave took on ever more clearly the role of conservative, "old Catholic," and pretheoretical teachings that shut themselves off from contemporary Enlightenment innovations, even before their subversiveprogressive potential, the basis for Rameau's own basse fondamentale,could have penetrated at all into the general consciousness. It would be incorrect, however, to state absolutely that no theoretical counterproposals to Rameau came forward.The attempts made seem to have found neither the language nor the form of presentation that would have been recognized as "theoretical"in the discourse of the early Enlightenment, nor did they develop in a sociocultural environment that would have facilitated a broad European impact transcending their narrowerregional and linguistic borders.28 If one wished to nominate one such counterproposal to Rameau's theory, then first and foremost the monumental second edition (1728) of Johann David Heinichen's Der General-Bassin der Composition(Thoroughbassin Composi-

tion) comes to mind. The second part of this work, "On the Complete Science of Thoroughbass" ("Von der vollkommenen Wissenschaft des GeneralBasses"), explicitly represents the unique attempt of its time to systematize and theoretically substantiate the music theory of the Italian partimento tradition (Horn 2000). No other eighteenth-century author made the Rule of the Octave the basis of his theory to such a degree (Horn 2001, 2002). A digression on Heinichen

The modern functionality of the Rule of the Octave, which Heinichen develops in his thoroughbass treatise of 1728, stands at the top of a hierarchy.The "natural"harmonies of unfigured basses "permit themselves to be discovered in three ways**(Heinichen 1728,726-27): 28 Heinichen's work was therefore unable to find an international audience because German, in contrast to French and Italian, was not a "European" cultural language. His influence on composition teaching in German was, however, considerable. See, for instance, Carl Philipp Emanuel Bach's very similar concept of chord (C. R E. Bach, 1753/62).


Ludwig Holtmeier ~ Heinichen, Rameau, and Italian Thoroughbass I. II. II.

From the vocal or instrumental voice written over the bass. From some easy general rules, or from characteristic intervals of the modes. From some special rules, or from the ambitus of the modes themselves.

On the one hand, this acts like a systematic hierarchy. In order "to guess at" (erraten; Heinichen 1728, 731) the missing voices from the intervallic relationships between the upper and lower voices, only a knowledge and mechanical application of chord theory is required. To move to the second hierarchical level where one applies "generalrules," however,already calls for a clearly higher understanding and level of knowledge. Here (rules for chord progressions) derived "general rules" mean the old Klangschrittregeln from the tabulanaturalis.Hardly any treatise of the seventeenth and early eighteenth centuries lacks these rules for standardized chord combinations, for example, 1. The 5th [scale degree] in the major and minor modes naturally has a major 3rd above itself, and in the system of modes it may or may not be notated. 2. The 4th [scale degree] in the minor modes naturally has a minor 3rd above itself, and in the system of modes it may or may not be notated. 3. The semitone [leading tone] beneath the major and minor mode, by which one modulates, naturally has a "6"over itself. . . . (Heinichen 1728, 739) "He who acquaints himself with these general rules," continues Heinichen, "willfrequently acquire great facility in the practice of an unfigured thoroughbass" (738). Attaining the highest hierarchical level, however, requires "the solid understanding of the musical ambitus"(731) - by this is meant nothing else than the Rule of the Octave. It is "the main source from which flow the aforesaid general rules" (738). The Klangschrittregeln give rules for chord progressions, but they are based on a mere intervallic relationship. Only the Rule of the Octave gives a precise place to those free intervallic relations in the harmonic space of the scale. It is obvious that this hierarchical order of precedence is also a didactic order ("the easiest comes first";Heinichen 1728, 727). That Heinichen 's course of study to follow begins quite traditionallywith chord theory and then leaves Klangschrittregeln means that it represents, at the same time, a historical order of precedence. Klangschrittegeln,especially as explicated in the German tradition (compare, e.g., the treatises of Matthâus Gugl 1719 and Johann Baptist Samber 1704, 1707) is, as it were, a historical prehistory (Christensen 1992, 113), now surpassed and nullified by the new functionality of the Rule of the Octave. One can perceive the same relationship between Heinichen's later treatise and his own earlier one (1711; see Gjerdingen 2007, 15-16). Although in 1728 Heinichen asserts that he had already explicated the Rule of the Octave "in the year 1710 during the preparation of my old edition of this treatise" (763), that is not really the case. Had his 1711 Klangschrittsequence extended across all eight tones of the scale, it would take on just as little of the obligatory form of the Rule of the Octave as with the treatises of Samber, Gugl, and Spiridionis- a qualitative and the Rule of the Octave (Gjerdingen difference exists between the Klangschrittregeln 2007, 15-16).

Rameau'sschematized thoughts on inversion and the stacking of thirds break with a further core aspect of the traditions of music theory and the history of composition: one of the oldest elements in European compositional


27

28


SchemataModorum,

4

Example 12. Heinichen's

Schema (Rule of the Octave)

teaching is the distinction between step and leap. The notion that stepwise progression is, as it were, the prototype of all harmonic and melodic motion hearkens back to a centuries-old tradition. Thus, in a sense the leap is the exception to the norm of regular stepwise motion. In Rameau's music theory, based on the prototypical falling fifth of the cadenceparfaite,the leap not only takes the place hierarchically of the step progression, but the step progression, as an independent music-theoretical category, became completely meaningless: in Rameau's theory every step is based on a leap. Heinichen's music theory, as we will see, retains the old distinction between gradus and saltus (step and leap). If the Rule of the Octave is to become the basis of a music-theoretical systhen two central questions must be answered: (1) what happens when the tem, bass moves by leap, and (2) how does one explain and categorize sonorities that do not reside in the model of the classic Rule of the Octave?The Rule of the Octave must become both a comprehensive theory of chord progression and a theory of the chord morphology. Example 12 shows Heinichen's version of the Rule of the Octave.Though Heinichen also understands the Rule of the Octave as a practical aid to improvisation, it is primarilythe representation of a harmonic system in itself: it represents a comprehensive "schema."The systematic character of Heinichen's Rule of the Octave is immediately apparent, for it differs conspicuously from its Italian and French precursors. Aside from the obligatory passing six-fourtwo chord on the fourth scale degree, Heinichen does not present any (dissoand imperfect nant) four-note chords- only the "pure"perfect (vollkommene) chords. The absence of the six-five chord on the ascend(unvottkommene) fourth scale ing degree (l'accordde la grandesixte) is especially conspicuous. a "Through complete omission of certain figures" ("durch gânzliche Hinweglassung einiger Ziffern";Heinichen 1728, 765), Heinichen here establishes something like a "PrimaryRule of the Octave" made up of the most simple



«

4

4

Example 13. Gasparini's Rule of the Octave after Heinichen

chordalelements:as in a modularsystem,all more complex and dissonant variantscan be derivedfrom this prototype,as I showlateron. The form of representationis also noteworthy:Heinichen's Ruleof the Octavedoes not move throughthe entire octave,as is the case with Rameau andin manysourcesfromthe Italianpartimentotradition;instead,his schema ends on the sixth scale degree and then changesdirection.The similarityto versionof the Ruleof the Octaveis deceptive,however, FrancescoGasparini's for Gasparinidirecdyfollowshis Rule of the Octavein majorwith a harmonizationof the descendingscale degrees 8-7-6-5, in order to make it clear thaton the descendingsixthdegree the chordwiththe majorsixthshouldbe placed (Example13) .29 For Heinichen, this is unacceptable:he stressesthat he "omittedthe majorsixth over the sixth scale degree becauseit addsa new Itthat does not belong to the mode"("die6. maj.uberdie 6tamodi maj.deswegengarweggelassen,weilsie ein neues I angiebet,welchesgarnichtzu dem Modogehôret"; 1728,765). He considerswhatGasparinidoes "alreadyhalf a cadence and a digressioninto D major"("schoneine halbe Cadenzund Ausschweifungin das D.dur";765). For Heinichen,however,the unityof the mode is an inescapableprerequisiteof the "schema,"of the "naturlicheAmbitus."Thus, he lets his Ruleof the Octaveascendto the sixth scale degree in order to make it particularlyclearthat its functiondoes not fundamentallychangewhether its motionis ascendingor descending.The fact thathe retainsthe traditional representationof the modes, and first lets his nottetoniquedescend to the leading tone, also stems from this strictunderstandingof mode: being the 29 Gasparini admittedly notes that "the sixth can be major or minor" whether ascending or descending {la Sesta porrà essere, o maggiore, o minore) (Gasparini 1722, 61), but he leaves no doubt that major sixths on the descending sixth degree "are necessary for their cadential effect" ("necessarie per esser specie di Cadenze") but do not constitute a modulation to a different note {non fanno mutare il tono; 57).


29

30


"inseparablecharacteristic of all modes" ("dasunzertrennliche Kennzeichen aller Modorum") he has "placed the leading tone next to the tonic at the very outset" ("dasSemitonium modi . . . gleich Anfangs neben sein 8vam lociret"; 764). For our topic, however, something else is far more decisive: Heinichen repeatedly emphasizes that his "schema"is "much more universaland applicable" ("vielmehr universalerund applicabler";1728, 765) than Gasparini'sand Rameau'sversions of the Rule of the Octave. According to him, they introduce "manyspecial signatures that only pertain for as long as the notes march along nicely in the order in which they were written down" ("vielspéciale Signaturen, die nicht langer gelten, als die Noten fein in der Ordnung marschieren, wie sie hingeschrieben worden";765) , that is, for as long as the bass moves in stepwise motion. For the main purpose of Heinichen's reduction to the basic (perfect and imperfect) chords is to turn the Rule of the Octave into an explanatory model that also encompasses "leaping"bass progressions. One sees that Heinichen sets the figures 5 and 6 one after the other over the second degree (and the sixth degree) of the F-majorscale. The intention is by no means a model-bound progression like, for instance, a sequence of 5-6 motions, as is sometimes maintained ("thatyou are not allowed to play the signatures one after another, as is usually done in thoroughbass" ["daBman also nicht beyde Ziffern nacheinander (wie sonst im General-Bassgebrâuchlich) anschlagen darff"]; 1728, 750]). Instead Heinichen explains the deeper sense of this double figuring as follows: Butconcerningthe majormode one shouldparticularlyobservethat because its seconddegree supportsa perfectfifth, one is thusfree to use eithera 5 or a 6 overthe said seconddegree.The 6 soundsmore naturalif [the bass]should risestepwiseto the thirddegree or go backward[downto the firstdegree] If, however,one is at the second degree midsta leap, then the 5 seems more natural.(743)30 Here one can still clearly recognize the persistence of the old differentiation between perfect and imperfect consonance. Particular types of motion are assigned to particular sonorities: the leap is assigned to the perfect consonance of the five-three chord; the step, to the imperfect consonance of the six-three chord. The chord of the sixth is placed "more naturally,"namely, in a stepwise progression, on the second degree. But if a sonority made from stacked-up thirds (a triad or even a seventh chord) takes the place of the

30 Wegen des modi maj. aber ist besonders zu mercken, daft weil seine 2da modi allerdings eine 5te perfect, in ambitu hat, so stehet auch frey, ob man uber besagter 2da modi die 5te oder die 6te gebrauchen will. Naturlicher lautet die 6. wenn man gradatim in die 3e auff oder ruckwerts gehet. . . . Kômt aber die 2da modi mitten im Sprung zu stehen, so fallet die 5te naturlicher aus. . . .



six-three chord on the second degree, then a leap ensues. (In case the leap does not happen, as with the "tonic-like"[Riepel] triad on the fourth degree, the five-three sonority has the effect of a caesura.) Even if Heinichen does not fully work out all the consequences of these central ideas of his theory, it nevertheless becomes clear that one functionally differentiates between a degree's stepfunction and leapfunction. Of course a three- or four-note stackof-thirdssonority can occur on any scale degree on which a chord of the sixth occurs in the classic Rule of the Octave. Such a sonority would only require a - from step to leap.31 change in the modusmovendi A digression on trainingmanuals In structure and organization, partimento textbooks follow popular training manuals like Oratio Scaletta'sfrequently reissued solfège textbook Scaladi musicamoltonecessaria perprincipianti(1595). In these solmization manuals, the first things taught were the Scaletta 1595, ascending and descending scales (portarla voceascendendo,et descendendo; 9). Then followed- likewise ascending and descending - diatonic patterns with leaps tables of a third, fourth, fifth, sixth, and octave. In the seventeenth century, Klangschritt of the so-called tabulanaturalis(Christensen 2008, 113; Dahlhaus 1990, 108; Heimann 1973, 55f.) were arranged according to the same paradigm. The compositional models in the partimento tradition were imparted according to the identical paradigm:harmonization models of the scale ascending (principallychains of 5-6, 7-6, and 9-8 suspensions and progressions of alternating sixths and thirds), the scale descending (chains of 7-6 suspensions and progressions of alternating seconds and sixths), leaping thirds ascending and descending, and so forth. Neapolitan composition manuals, above all the exercises in style found in Francesco Durante's partimentibassi diminuiti (2003), follow this organization, and many German training manuals are similarlystructured. Examples would be Friederich Erhardt Niedt's Handleitungzur Variation(Musicalische (1930), and also Handel's (1978) Handleitung,vol. 2, 1721), as well as Bach's Vorschriften cultivates the teaching of comFenaroli Fedele exercises. systematically thoroughbass s.v. "Satzmodelle"). Holtmeier Partimenti in his models 2007, (1978; positional

Renversement versus Verwechslung This puts in sharp relief one of the central distinctions between the functionality of the Rule of the Octave and that of Rameau's bassefondamentale the former is totally aligned with movement. Rule-of-the-Octavefunctionality not only distinguishes between a degree's meaning in the context of a step or a leap, but also differentiates the meaning of a degree according to the direction of the motion, whether ascending or descending. Thus, the fourth degree in ascent takes the six-three or six-fivechord, but in descent the "dominant"six-four-twochord; the seventh degree in ascent takes the six-fivechord

31 Riepel (1996, 580f.) and Kellner (1732) follow Heinichen's conception relatively faithfully and even expand it.


31

32


but in descent the plain six-three chord, and so forth. For its reception history, one thus encounters a problem with Rule-of-the-Octavefunctionality. Its "animate"dynamics elude being fixed by a "physicalist"systematization that permits the derivation of more complex structures from simple basic axioms. For Rameau's supporters, one of the central arguments in favor of the basse fondamentaleis that it can explain the basic principles of harmonic tonality in the shortest time and, as it were, free of presumptions. As has often been stressed, the principle of inversion adapted by Rameau was not new (Christensen 1993, 67f.; Barbieri 1991). The interchangeability of the voices was one of the elementary assumptions of three-voice models for sixteenth- and seventeenth-century cadences, sequences, and the "contrapuntal"orientation of teaching composition. Heinichen was well acquainted with Rameau's Traitédel'Harmonie.Above all the concept of renversement (inversion) left lasting traces in his own theory. But an approach can be observed here that is typical for the history of the French, Italian, and also Viennese thoroughbass tradition: though Ramellian bassefondamentalefinds an entry into the teachings, it still cannot displace (or only very slowly) the old theorems. For Heinichen, a six-three chord can be regarded as being the inverted form of a five-three chord. But the long commentary in footnotes that he dedicates to notions of inversion (1728, 146-51) stands surprisinglydetached from the received thinking in terms of intervallic qualities which unfolds in the main text. Heinichen, however, completely distances himself from the procedure of systematic third-stacking,and thus from the basic principle of bassefondamentale.His term Verwechslung (recombination) designates a concrete procedure of compositional technique - the regrouping of a sonority (usually with an eventual return to its starting position; Heinichen 1728, 624-25). 32Thus, each chord can become "recombined":if a six-four-twochord is followed by a seventh chord, built with the same notes (Kellner describes this concept of inversion as based on a relation of "pitch classes"; 1732, 32), then this later chord represents the "firstinversion" ( Verwechslung) of the first, and so forth. To speak in Ramellian terms, every type of chord can be considered as a "root chord." Rameau's idea of inversion, however, is theoretically an a priorievery sonority has to be reduced to its stack-of-thirdsprototype. Beyond third-stacking: Toward an Italian morphology of chords For Heinichen, the functional meaning of a chord is not determined by the principle of third-stacking.Just as he brings leaping bass motions under the interpretive authority of the Rule of the Octave by falling back on traditional categories, so too he explains the complex chord morphology of the advanced, 32 In this regard, Daube follows Heinichen (see Diergarten 2008).



"theatrical"harmony of his era- his own focus- with the traditional terms of Italian music theory. To begin with, his concept of chord has an entirely different basis from that of Rameau. For Rameau the chord is its own entity, an inherently closed unit. Even here the ideal of the four-voice texture ( Vierstimmigkeit)stands in the background. Though certain functions and tendencies for linear motion are attributed to individual elements (nottefondamentale,notte sensible,dissonancemajeureand mineure,etc.), these constituents always present themselves in combination and remain functionally invarianteven in the process of inversion, as will be shown. They are subject to a rigid, hierarchical organizing principle. For Rameau, chords are primarilyvertical blocks of stacked-up thirds in which the linear tendencies have been frozen. Heinichen 's way of thinking was shaped by his early "contrapuntal" schooling in Germany,but above all by the Italian tradition of apprenticeship that he got to know so well during his long stay in Italy (Buelow 1994). Yet even though his theory of thoroughbass stands well apart from contemporary sources on account of its high degree of theoretical awareness, neither with him nor with any other contemporary author does one find a comprehensive, systematicallyarticulated theory of chord. In what follows, I have tried to work out the "implicit"systematicsof Heinichen's theory of chord. For Heinichen and traditionalItalianmusic theory,the polyphonic chord heart was alwayssomething put together- a composite. The contrapuntal at pairing of two main voices formed the framework of a composite sonority, which could be supplemented by Neben-Stimmen (secondary voices; Heinichen or more voices. Understood of a texture to create four, five, three, 1728, 171) multivoice controls in this way,a distinct hierarchy sonorities, giving priority to the chordal components, which effectively determines the comprehension and functionality of the chord, and which has consequences for the formation of voice leading, consequences that extend the far beyond the chordtradition. progression, part-writingrules of the modern Harmonielehre A digression on counterpoint

This other concept of chord also presupposes another concept of counterpoint. It is significant thatJohann Joseph Fux's Gradusadparnassum(1725), the founding document of the modern, autonomous teaching of counterpoint, originated and was published in close chronological proximity to Rameau's Traitéde l'Harmonie.In terms of reception history, Fux's treatise plays a role quite comparable to that of the Traité.It much as Rameau's treatise did for that of harmony. monopolized the term counterpoint It is above all the idea of "strict counterpoint" (strengeSatz) or even more so what the Fux reception made of it, that obstructs the view of what, at the beginning of the eighteenth century, "counterpoint" really was. In the nineteenth-century Harmonielehretradition, "strictcounterpoint" changed from a stylistic category (stilo antico,the "Kônigsdisziplin"of counterpoint) to the epitome of counterpoint itself. As a result of this development the intrinsically comprehensive doctrine of counterpoint became


33

34

JOURNAL of MUSIC THEORY bound to a markedlynarrowand invariableconcept of dissonance and resolution. The dissonant intervals are static sizes. Not only are the "false"fifth and "majorfourth," as diminished and augmented intervals, always dissonant, but also the technical voiceleading behavior of the dissonances- second, fourth, seventh, and ninth- is fixed once and for all. With the fourth, seventh, and ninth, the upper note is dissonant. With the second, the lower note. Thus, dissonance completely solidifies into intervallic quality and abandons what it was in the consciousness of the early eighteenth century when it actually represented something more: a rhythmic constellation. Significantly, Berardi treats the dissonances under the heading "Introduction to syncopation or dissonances" ("Introduzione aile legature- owero dissonanze"; 1687, 134). Essential for the contrapuntal concept of dissonance in the late seventeenth or early eighteenth The fourth of strict and supersyncopatio. century is the distinction between subsyncopatio to a third. By which resolves is a , (4ta soprasyncopata) composition quartasupersyncopata contrast a quartasubsyncopata(4ta sottosyncopata;Heinichen 1728, 171), in which the lower note must be "bound,"resolves in the ideal case to the sixth (as in \ to §). In addition, an intrinsicallyconsonant interval can, by virtue of a tie, become a dissonance or be treated like a dissonance. ("Often the quintaperfectais used as a dissonance and a quintasyncopata"[Heinichen 1728, 179], as in f.) In place of rigid intervalliccategories, the early eighteenth century recognized an abundance of intervallic functions (quarta consonans, quarta dissonans [quarta sopra syncopata], Hulffsquarte [quarta sotto syncopata], quarte irregolare[quarta italica], quarta transiens, quarta suavis, quinta perfecta, quinta syn-

copata,sextaperfecta,sextasyncopata,etc.; see Muffat 1699, 8-bis). It is this open concept of interval that allows harmony and counterpoint to be conceived as a unity.

Examples 14 and 15 clarify the differences between Rameau's and Heinichen's concept of chord, using the case of the dominant seventh chord and its inversions. For Rameau, not only the (dominant) six-five chord (Vaccord de la fausse quinte;Example 14b), but also the four-three chord (/ 'accordde la petitesixte-,Example 14c) and the four-two chord (Vaccorddu triton;Example 14c) are nothing but derivativeforms of the stack-of-thirdsdominant seventh chord (dominante-tonique; Example 14a). The functional roles of the chordal are distributed: G is the root (bassefondamentale),the third components clearly B is the leading tone (nottesensible)and must move up a step as a dissonance majeure,the chordal fifth D takes on the role of filler voice, and F is dissonant seventh, which must resolve down a step as dissonancemineure(Example 14e). The structurallycontrolling interval is the seventh. It is, so to speak, the mother of all (chordal) dissonances. For Rameau's thinking about inversion, it is essential that the functional roles of chord tones remain fixed once and for all, and persist in every inversion. Thus, B is alwaysa leading tone, F a dissonant seventh, D alwaysa filler tone,33and G alwaysa root, regardless of the particular constellation in which the tones occur. 33 Significantly, the fact that the chordal fifth in effect fulfilled a dual function- both that of the filler tone and that of the tenor clausula - hardly plays a role in Rameau's idea of inversion.


Ludwig Holtmeier ~

(c)

(b)

(a)

Heinichen,

35


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(d)

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(a)

JB Framework ,

voices

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Example 15

In contrastto this novel, invariantchord morphology,one can posit a concept of chord that clearlyderivesits origin from the contrapuntalthinking of the sixteenthand seventeenthcenturies,and in whose traditionHeinichen also stands.In Example15, one againsees Rameau'sbasicchord and its formsof inversion,but now examinedin light of Heinichen'sconcept of chord (Example15). Eachchordis basedon a two-voiceframework(Example 15, staffI). It is assembledfrom those chord tones most clearlyand unmistakablyable to representeach sonorityin a two-voicesetting.This two-voice frameworkis far more than a systematiccategoryof organization.Rather,it designatesan "idealplacement,"a real aestheticand didacticstandardfor the relationshipbetweenbassand melody.The factthatas a theoryof correct voiceleadingit wasassignedto trainingin counterpointprovidesevidencefor the extensive,stillintactunityof contrapuntaland harmonicthinking.Under or besteLage the termof disposizione (Fôrster1818,1) it wasa central,practical of teaching. composition eighteenth-century topic This compositionalframeworkcan most clearlybe derivedby wayof a reductiveprocess,one that at the same time uncoversthe internalhierarchical structureof the chords.Forinstance,the chordalfifthoccupiesthe lowest level in the hierarchyof Rameau'sbasicdominantchord {dominante-tonique).


36


It is a classic filler voice that enjoys a relative freedom in voice leading. It can and as a tone appear both as a classic "pedal"or "common tone" (Liegestimme) free to leap; it can (in the sense of a tenor clausula) be treated like a voice in parallel upper thirds with the chordal third (the leading tone) or even like a voice in parallel lower thirds with the chordal seventh. The chordal third (leading tone) is one hierarchical level below the frameworktones, which are formed here by the mandatory bass note and the "characteristic"dissonance of the seventh. The chordal third thus supplements the two-voice framework to achieve the ideal three-voice setting. In Example 15a, I, square bracketsindicate frameworktones of the dominant seventh chords that form a diminished fifth between the tones B and F. This alternative framework refers to the alleged "root"tone G being at times able to appear as a secondary voice, as a lower third to the leading tone. That is especially the case when the dominant seventh chord does not progress with a genuine root progression (i.e., by leap) to a (cadential) chord of resolution, but almost appears in transituitself, that is, appears to be a passing chord (see Example lOd). In the six-five chord (Example 15b) the framework is formed by the framing interval of the diminished fifth. The sixth (G), as bearer of the dissonance, is an important but nevertheless hierarchically subordinate voice. Functionally, it can appear upper sixth to the bass note (B). Here, the third (D) takes over the role of the supplementary, filler voice. In the four-three chord (Example 15c), the frameworkset is formed by the majorsixth between the bass note and the leading tone. The third (F) , as a voice in parallel thirds with the bass, supplements the two-voiceframeworkto form a three-voice setting. The fourth (G) is, however,pure filler- a dissonant common tone that received special attention from contemporary theorists due to its special dissonance treatment. It was called quantairregolaris,quanta (Heinichen 1728, 151), or quartaitalica(Muffat 1699, 8). The special irregolare position of this fourth highlights the fact that for many eighteenth-century theorists- thus also for Heinichen - the four-three chord did not appear as an independent chordal category, but was treated as a special form of the sixoften not marked even in a figured bass ("The three chord. Quartairregolaris, not is fourth alwaysexpressly indicated above the notes" ["Eswird irregular aber . . . diese irregulaire 4 ... nicht iederzeit ûber denen Noten ausdrûcklich angedeutet"]; Heinichen 1728, 151), was a quasi-"improvisational"addition to the basic three voices of a six-three chord. The French term petitesixte testifies to this origin.34 34 Riepel perceived the quarta irregolaris as a fashionable aberration. He labeled such intervals pejoratively as "Turkish fourths" since they reminded him of Turkish"fifes" blowing "a loud series of fourths one after the other," which he had heard "in the year 1737 near Banja Luka" (1757, 39).



6 4 3

6

Example 16. Two of the examples for the 3a syncopata

6 14 3

15 I

Heinichen gives

Naturally,that is not the only form in which the four-threechord can occur.It can alsoappearas a terzasyncopata as shownin some examplesbyHeinichen (see Example16) (Heinichen 1728, 163). The four-threechordwith terzasyncopata most closelyresemblesa Ramellianchord of inversion.Yetin the improvisatory and compositionalpracticeof the eighteenthcentury,this is just chord, when comparedto the four-threechord with quartairregolaris, four-threechord is the exception. Heinichen stressesthat the "syncopated" properlyunderstoodas a variantof the four-twochord ("relatedto the syncoHeinichen 1728, 163). pated second"["der2da syncopata. . . anverwandt"]; And in factthe chordis alsomostoften utilizedin thisform (see Arnold1931, 632, his example9). chord (Example15d) restson the frameworkof Finally,the six-four-two the augmentedfourth (F-B). Heinichendescribesthisfourth,whichresolves to the sixth,asa "helper-fourth" , as ancilla2dae(handmaidento the (Hulffs-4te) second) (Heinichen1728,171). Here,one can clearlyrecognizehowthe hierarchicalconcept of chord also impliesa hierarchicalconcept of dissonance. The notion of the ancilla2daeis basedon the centraldistinctionbetweendissonantiadominansand dissonantiaconcomitans(Heinichen 1728, 186), between

a "controlling" and an "accompanying" dissonance.ForHeinichen,the dissonantfourthis an "accompanying" dissonance,an upperthirdto the "controlling"dissonantsecond.In the musicalpracticeof the eighteenthcentury,however,the circumstancesseem to be just the reverse:the seventhscale degree is the "ideal"uppervoice for the fourthscaledegree in the bass,and only the chord in a augmentedfourthcan unambiguouslyrepresentthe six-four-two two-voicesetting.Yetfor Heinichenthis fourth (B) is, accordingto its inner nature,an upperthirdto the second (G). Converselythe G becomesthe lower thirdto the leadingtone (B). The sixth (D) appearsas its upperthirdor as a "free"secondaryvoice. In the specialcase of this chordone can hardlyspeak of a hierarchicalprioritybetweenthe twosecondaryvoices. In orderto makethis hierarchicalconcept of chord still clearer,Exam1 7 ple constructsa few chords not from the perspectiveof Ramellianinversion, but ratheron the basisof the relationshipbetweena two-voicecomposi-


38


(I)

(ID

(a) |(fo éfl3LXT ^

(HI)

J

|

I J

<\

|j

l[g U |.w]

J^

[ j 1 bjg

[ j 1 -f]g

[rfTzz

® -Ô-W^J

-«J.I

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M^

«J

»J-

r il N

r

...

il

*J

r ji

«L

TfJi

i^| .J, \f\4m^

Example 17

frameworkvoices tionalframeworkand secondaryvoices.The "leading-tone" determinethe functionof chordson the ascendingand descendingsecond degree in majorand minor,on the descendingsixthdegree in minor,and on the descendingfourthdegree in majorand minor (Example17, col. I). They markthe invariants of the functionalconcept of chord.The obligatorythird in as the first joins secondaryvoice added to the sixth on the second degree and to the augmentedsixthon the sixthdegree (Example17, col. II, stavesa andb) andeithera sixth(Example17,col. II,stafFd)or a second (Example17, col. II,staffe) can be addedwithequaleffectas a thirdvoice to the tritoneon the fourthdegree.Forthe fourth,"filler"voice,even more tonesare possible. Not only the fourthbut also the diminishedor perfectfifth can supplement the sixthon the seconddegree (Example17, col. Ill, 8taffa). A fourthor fifth can be added to the augmentedsixth on the sixth degree (Example17, col. Ill, staffb). And if a sixth is addedas thirdvoice to the tritoneon the fourth degree, the second, the minor third,or the majorthirdcan enter as a filler voice (Example17, col. Ill, staffe). Differentchords (with"stepfunction") can thus representthe scaledegree.Though the choice of the fillertone can cruciallyshape the auraand color of a chord,the functionof thatcbord- its dynamictendency- is exclusivelyassignedby the frameworkvoices. The function of chord tones

In Rameau'stheory,chord tones retainthe same functionalqualitiesin varichord. The ous inversionthat had accrued to them in the "root-position" In the Italin all inversions. dissonance remains the same function-defining ian thoroughbasstraditionas systematizedby Heinichen, however,chordal



39

elements are subjectto a great degree of functionalvariability.(The interconnected circlesin Example15 tryto clarifythis point.) Not only do these elements belong to differenthierarchicalchord levels, thus havinga different structuralsignificancein differentchords,but theyalso altertheirvoiceleadingpropertiesin the context of differentchords.Only the leadingtone maintainsitsfunction,evenfor Heinichen,in allformsof Ramellianinversion. The seventh,however,appearsin three functionallydistinctforms (Example 18): (1) as prototypeof the (suspendedor passing)dissonance,it appearsonly in the basic,root-positionchord itself (Example18, 1) and in the six-four-two chord (Example18, II); (2) in the six-fivechord, it formsa "semiconsonant" diminishedfifthwiththe bass,whichdoes not requirepreparation(Example 18, III);and (3) in the four-threechord it appearsas a parallelupper-third voice to the bass,consequentlyas an imperfectconsonancenot subjectto the need to resolveand thus free to move stepwiseup (Example18, FVa),down (Example18, IVb),or even to leap (Example18, IVc). WithRameau,the chordalfifth takesover the functionof a fillervoice. It approachesthis functionwith Heinichen too, but in the four-threechord it lies in the bassvoice and there its functionchanges.It becomesthe penultimatetone of a tenor clausulaand is thereforesubjectto a need to progress stepwise(Example18, IV). The second scale stage (the chord fifth) is functionallyambiguous.It can be understoodas a componentof a tenor clausula or as a pure "patchtone"(Riepel),as so to speaka variantof an alto clausula.

(la)

(b)

ifj >n

!r

F

\h'j

.1

If

(b)

(c)

lA-J I'll-]

(lia)

rli

(b)

|iljdi|d Hr r (Va)

jiH Irr'r

I"'

si

f F liUd

r

r r

1-^^

(Via)

(b)

L'l IIi P lj

(IVa)

(III)

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IJ J IJ J Ile g le Ë II

Example 18


40


Also with the six-three, six-five-three,and six-four-twochords they mostly progress stepwise, in the sense of a tenor clausula. This voice leading is not, however, mandatory. The fifth of the root chord can likewise leap to the fifth of the chord of resolution, even if it should result in consecutive fifths (Example 18, Va) or if a fifth in the outer voices is reached by direct motion (motusrectusr,Example 18, Vb). If the chordal fifth of the six-four-twochord lies in the upper voice, then a leap is actually the rule: it is necessary to avoid the empty cadential perfect consonance of the octave in the outer voices of the chord of resolution (Example 18, Via) and to go instead to the imperfect tenth in the outer voices (Example 18, VIb). The difference, however,with Rameau's static functionality shows itself most clearly when one regards the functional variabilityof the very voice that, in Rameau's theory, represents the foundation of the chord. For Heinichen as well, the "root"appears in three distinct forms. In the six-five and six-four-twochords it is the lower third or upper sixth of the leading tone, and thus simply a secondary voice. In the four-three chord, it actually takes the lowest place in the chordal hierarchy. as quartairregolaris, Only in the basic, root-position chord is it what Rameau saw in it- the centre of the Klang. harmonique If one allows a "contrast-enhanced"formulation of Heinichen 's theory of chord, then there are two basic chords from which all other chord forms are derived- the five-three sonority and the six-three chord. One sees the old opposition of perfect and imperfect consonance that alreadydetermined Heinichen's concept of the Rule of the Octave, seamlessly brought forward into modern chord theory. In harmonic discourse, the third, on which the whole Ramellian system is based, had long become an unmarked filler interval that indiscriminately characterized the pattern of all chords, whether consonant or dissonant. And so there are essentially two intervals that determine the nature of chords: a fifth or sixth distinguishes the basic functional orientation of a sonority. The crucial difference between Rameau's basic chord and its inverted forms can be viewed from the perspective that while the basic chord is determined by "static"fifth, the inversions are characterizedby the "mobile"interval of the sixth. This difference is categorical in nature and cannot be waived by a simple process of derivation, in the sense of Rameau's idea of inversion. For Rameau, dissonance connects the basic chord with its inversional forms and makesobsolete the differentiation between perfect and imperfect consonance. In this understanding of chord, however,the dissonant character of a sonority replicates the distinction between fifth and sixth, since it is these intervals that determine the fundamental dynamic nature of sonorities. Rameau's inversion forms are first and foremost sixth chords and require stepwise motion (a "varietyof sixth chords";Christensen 1993, 172). The fifth of the basic chord, by contrast, requires a leap. Dissonance is added to the sixth or the fifth, as it were, externally.To the sixth one can add a fifth (Example 19, la), or a fourth


Ludwig Holtmeier ~

(Ilia)

(b)

Heinichen,

(c)

(Via)

(a)\

Step a

(b)

A6* ascending 5

6

(IVa)

(b)

v'

(c)

(b)

7

\

(I)

41


(c)

6 4 ¥cendiPS descending 3

(II) .. , 4Ç descending

lâP

/

(b)

2

(Va)

'

r^t

nï

6

5

/

(a)

7

i

//

Example 19

and third (Example19, Ib), or a fourthand second (Example19, Ic). To the fifthone can add a seventhas its upperthird (Example19, Ha). In so doing,the originaltendenciesfor motionareonlystrengthenedby the requirementfor dissonanceresolution.It is as if dissonancerepresentsan autonomouscontrapuntalelementwithinthe chord.The dissonant"auxiliary note"does not changethe fundamentalfunctionalcharacterof the chord,but ratherintensifiesitstendencyformotionandspécifiesitsdirectionof motion.35 The added fifth lends a risingtendencyto the six-threechord (Example19, la) becausemovingdownwardstepwiseeasilyleadsto parallelfifths(Example fourth"or as an accompanying 19, Ilia), an addedfourth(whethera "Turkish note to the terzasyncopata) permitsmotion in either direction (Example19, IV), and an added second forces the sixth downward(Example19, V). The chords are not strictlybound to these forms of motion. The six-fivechord can resolvedowna step into a six-foursuspension(Example19, IIIc),;andin certainharmonicformulasthe dominantsix-four-two chordcan moveup stepwise (Example19, Vb). Notwithstandingthe inganno(deceptivecadence), a 35 "Vonder Sextenkette, die zur Oktave strebt unterscheidet sich Rameaus Septakkordfolge deren Ziel ein Dreiklang, ein Accord parfait' bildet, zwar graduell, aber nicht prinzipiell" (Dahlhaus 1990, 27).


*

42


in transitu) stepwiseascendingseventhchordis often a passingchord (septima or an 7-6 a unresolved suspension "retarded" sixthchord (Example19,Via) so to saythat finds its resolutionin the followingconsonanceor dissonance (Example19,VIb,c). Butaccordingto theirbasictendenciesthe six-fiveis a is a fallingchord,and the four-threechord can risingchord,the six-four-two eitherriseor fall. *

*

*

The idea of chord and sonority(Klang)dealtwithhere is fundamentallydifferentfromthatof Rameau.His rigidsystem,madeup of a fewbasicelements and basedon a logic of chordderivation,is set againsta sophisticatedframeworkof variationand relationalcomplexity. It is perhapsthisveryrichnessthatspelleddoom for thisunderstanding of chord:as is well knownhistorically,it wasto succumbto Rameau's theory. It could raisescantoppositionto the manifestlogic of Rameau'sprincipleof inversion.We can assumethat Rameau'stheorywasable to gain such popularityonly becausehis concept of chord filled a widelyperceivedvacuum.It seems self-evidentthat the modern harmoniclanguageof the seventeenth and eighteenthcenturiescraveda new explanatorymodel that transcended the old counterpointinstructionof the sixteenthand seventeenthcenturies. Rameauoffereda clearand at the same time simple responseto a question that had neverbeen put quite so explicitlybefore,but that had clearlybeen hangingin the air:whatis Klang} Heinichen also offers a resoundingresponse- in favorof the Italian reconstructedin tradition,as it were.But much of whathas been "implicitly" this essayremainsunspokenby Heinichen,as in the entire Italianthoroughbass tradition:he neither developsthe concept of frameworkvoices in any consistent manner nor systematizesthe functionalityof steps and leaps conclusively. No modernapproachcan remedythis alleged lackof systematicthinkand this text, too, bearswitnessto the difficultyof coming closer to a ing, of concept chordand tonality(dealtwithhere in a verylimitedway)thatlies The internal beyondthe Ramellianconcept of inversionand third-stacking. contradictionsof an account that describesa four-voicechord, on the one hand, as being a five-threeor sixthchord supplementedby a "contrapuntal" auxiliarynote, and on the other hand, as a compositesonoritymade up of a two-voiceframeworkand secondaryvoices,are obvious:followingthe first interpretation,the dominantsix-four-twochord on the descendingfourth degreeis a variantof a sixthchord,withthe sixthbeing the function-defining interval.Followingthe second interpretation,the tritoneappearsas the censubordinatenote tralbasisand the sixthas a secondaryvoice,a hierarchically thatcould easilybe omittedfroma three-voicetexture.



Upon closerinspection,however,we mustconcede thatit is not so much a contradictionas ratherone and the same phenomenonviewedfrom different perspectives.If the idea of chord progressionsis basedon the dichotandimperfect{unvollkommeri) chords,dissonance omyof perfect(vollkommeri) becomesa subordinateparameter.But if the movementof the dissonances itselfis the focusof consideration,the distinctionbetweenperfectand imperfect consonancebecomesof secondaryimportance. Itis preciselythejuxtapositionof thesedifferentperspectivesthatreflects the historicalsituationaroundthe turnof the century:the modernfunctionality of the Rule of the Octaveand the traditionalcontrapuntaltextureof the trio sonatacompetewitheach other,though the one growsout of the other in an organicfashion,as I haveattemptedto demonstrate. One mightconsiderit a deficitthatthe traditionof Italianthoroughbass does not offera comprehensiveand straightforward systematics,but perhaps thisis preciselywhereits truestrengthlies:thatit does not seek to deduceharmonyand melody,line and sonority(Klang),chordand counterpointfroma single coherentprinciple,as Rameaudoes, but permanentlyworksthrough the tensionbetweenthose poles in a dialecticalway. Heinichenconstantlywaversbetweenthe newchordfunctionalityof the Ruleof the Octaveand the "classical" theoryof counterpointand dissonance treatment.This is not merelya sign of his theoreticalindecision,however, but also revealshis deep-seatedaversionto a certainconcept of natureand sciencethathe sees prevailingin Rameau's theory:he confrontsthis formof that"German,French systematicthinkingwithhis "rulesof art"(Arth-Regeln) of for the use . . . have authors and Italian unfiguredthoroughbass provided a long timeago, whichthe latter[i.e., the Italianauthors]since then brought to the highest perfection"("welchedeutsche,franzôsischeund italienische Autores.... vom General-Bassohne Signaturentheils von langer Zeit her zu geben angefangen,theilsletzterezeitherozurVollkommenheitgebracht"; Heinichen1728,19). Heinichendrawsthe principlesof his theorysolelyfrom musicalpracticeand tradition:for him, "nature"manifestsitselfin the "conventionalschemataof composition"("den gebrâulichenpassibuscompositionis";19), but it cannot be deduced from the physicalnatureof the corps sonore.It is this proximityto compositionalpracticeand musicalexperience in particularthat makesthe Italian(and accordinglythe Italian-influenced) thoroughbasstraditionso interestingfor us today. It goeswithoutsayingthatthe complexconceptof harmonicfunctionalon ity whichthisItaliantraditionof the late seventeenthand earlyeighteenth centuriesis basedwouldalwayshavemeritedour historicalinterest.Another question,however- and perhapsactuallythe crucialone- is whatwe are to makeof thisrenaissanceof Italianmusictheory.It opens up the possibilityof interpretingand analyzingthe compositionaltechniquesof the seventeenth and eighteenthcenturiesin a differentway.Elucidatingthe possiblenatureof


43

44


this different way would exceed the scope of this essay;a study of such a kind is in progress, however, and will appear at a later date.

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Sulzer,Johann Georg. 1771/74. AllgemeineThéoriederschônenKùnste.Leipzig: Wiedmann. Vidal, Paul and Boulanger, Nadia. 2006. A Collectionof Given Basses and Melodies.Ed. Narcis Bonet. Barcelona: Dinsic. Vincent, Heinrich Josef. 1830. Kein Generalbassmehr.Vienna: Wallishauser. Weber, Gottfried.

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Ludwig Holtmeier teaches music theory at the Hochschule fur Musik in Freiburg and historische Satzlehre at the Schola Cantorum in Basel. He is the editor of Musik & Àsthetik and has published widely on the history of music theory, the Second Viennese School, and RichardWagner. U*v


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Heinichen, Rameau, And the Italian Thoroughbass Tradition - Concepts of Tonality and Chord In

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