The Theory and Practice of Integrating Invertible Counterpoint into Classical Theme-Types

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1 Document généré le 0 mars :17 Intersections Canadian Journal o Music The Theor and Practice o Integrating Invertible Counteroint into Classical Theme-Tes Peter Franck Volume 2, numéro 1-2, 2012 URI : id.erudit.org/iderudit/10188ar htts://doi.org/ /10188ar Aller au sommaire du numéro Éditeur(s) Canadian Universit Music Societ / Société de musique des universités canadiennes Résumé de l'article Cet article eamine l utilisation du contreoint réversible dans le cadre d oeuvres thématiques conventionnelles de la tradition classique. Alors que de récentes recherches ont étudié comment cette technique contrauntique eut créer une continuité, cet article contribue à cette question en montrant comment cette technique onctionne de concert avec l écriture thématique et les ormes organisées ar les cadences, et qui ont le rore d interromre la continuité. Un modèle de base sert de cadre théorique ermettant l analse d etraits tirés d une sélection d oeuvres de Hadn, Mozart et Beethoven. Les analses montrent que certains tes d écriture thématique intègrent mieu que d autres l utilisation du contreoint réversible dans leur organisation ormelle. De lus, ces analses mettent en lumière les divers rôles du contreoint inversé dans les diérentes ormes thématiques. ISSN (imrimé) X (numérique) Découvrir la revue Citer cet article Franck, P. (2012). The Theor and Practice o Integrating Invertible Counteroint into Classical Theme-Tes. Intersections, 2(1-2), htts://doi.org/ /10188ar Coright Canadian Universit Music Societ / Société de musique des universités canadiennes, 201 Ce document est rotégé ar la loi sur le droit d'auteur. L'utilisation des services d'érudit ( comris la reroduction) est assujettie à sa olitique d'utilisation que vous ouvez consulter en ligne. [htts://aroos.erudit.org/r/usagers/olitique-dutilisation/] Cet article est diusé et réservé ar Érudit. Érudit est un consortium interuniversitaire sans but lucrati comosé de l Université de Montréal, l Université Laval et l Université du Québec à Montréal. Il a our mission la romotion et la valorisation de la recherche.

2 THE THEORY AND PRACTICE OF INTEGRATING IBLE COUNTERPOINT INTO CLASSICAL THEME-TYPES Peter Franck Within some Classical-stle works, the technique o invertible counteroint enables the simultaneous resentation o multile melodies, or arts. 1 In such a contet, what was the lower art in one assage becomes the uer in a later one. Nowhere is such a technique more revalent than in ugal writing, where ugal subjects are osited above and below accomaning counter-subjects. And within the Classical reertor, ride o lace is given to the ugal inale, where the contrauntal rowess o the comoser is ut to the test. 2 But invertible counteroint need not require ugal rocedures or its use. Moreover, the alication o invertible counteroint, which can hel to acilitate dialogue between dierent arts within a teture not onl in smhonies, but also concertos, string quartets, and iano sonatas is not restricted to inal movements o works within the Classical reertor. Indeed, man non-ugal movements within this reertor contain theme-tes that eature invertible counteroint and can be comrehended using William E. Calin s analtical aroach to Classical orm; this methodolog, however, does not elicitl address how invertible counteroint interacts with musical orm. The resent essa thus elains not onl technical asects o this interaction, but also the urose o integrating invertible counteroint into Classical theme-tes. There are man non-ugal movements in the Classical reertor that emlo invertible counteroint as a sohisticated means o reetition. For instance, in reerence to the increased stlization o the minuet that took lace over the course o the late eighteenth centur, James Heokoski and Warren Darc write, It became a musical genre subjected to the comositional crat o stle-variation, something to be maniulated with wit and skill (200, 1). The continue, Thus arose some subtes o the minuet: the canonic, ugal, or otherwise learn- 1 Following the ractice o William E. Calin, Classical stle denotes the music o the high Viennese classical stle, comosed within the eriod ca (Calin 1998, ). Although some authors resist calling this music Classical or instance, Robert O. Gjerdingen reers galant (2007, ), and James Webster dislikes this term, since it conlates meanings associated with time eriod, value, and stle (1991, 8) this article emlos Calin s analtical methodolog, thus reerring to Classical stle throughout is entirel aroriate. 2 See Brown 200; Grier 2010; Horton 200; and Kirkendale 1979, 7 and Keee 200,. Calin In this regard, see Grier 2010, 7 82.

3 18 Intersections ed minuet (a disla o comositional or contrauntal ingenuit in the manner o a scholastic game). Part o this contrauntal ingenuit involves integrating invertible counteroint into the contet o conventional theme-tes, such as the eriod or sentence. Although scholars generall agree that this is a learned ractice, little research has been devoted to show how this ractice interacts with the orm o such theme-tes. To be sure, James Grier convincingl demonstrates how Hadn summons invertible counteroint within the inales o the o. /1 and o. 7/1 string quartets as a means o creating rhthmicall continuous assage[s] in which the voices constantl overla without strong cadences and rhthmic articulations (2010, 7). But the contet he describes involves sections that normall eress continuit, as in the develoment section o a sonata orm (such is the case with the inale o o. 7/1), not a standard theme-te, which requires the sstematic deloment o cadences a means o quashing continuit or its articulation. And although Simon P. Keee keenl demonstrates how dialogue inorms Mozart s late iano sonatas (200,, 7) a ractice arguabl inherited rom his concerto writing aart rom acknowledging the back-and-orth la between the right and let hands that some o these sonatas engender, little is said concerning the elicit use o invertible counteroint and the seciic theme-tes through which this dialogue is eressed. Finall, desite the wealth o recent research concerning Classical orm, little o it has been devoted to studing the concet o injecting invertible counteroint into conventional eight-measure and siteen-measure themetes a ractice observed within man works o Beethoven, Hadn, and Mozart. Moreover, more needs to be investigated as to the unction and urose o invertible counteroint within such contets. This essa addresses this lacuna o knowledge b initiating a stud that shows how invertible counteroint works in concert with these amiliar themetes. The essa contains our sections. The irst section establishes a contet in which to understand the use o invertible counteroint within the Classical stle. Here, I contrast the use o invertible counteroint as it is commonl emloed within Baroque ractice to that within Classical ractice, elucidating the kinds o arts contained within the invertible tetures emloed within the latter; additionall, I elain the urose o using invertible counteroint within Classical themes. The second section resents analtical models that encasulate conditions b which theme-tes using invertible counteroint must abide; the models rovide general temlates with which to analze seciic eamles. The net two sections rovide analses o ecerts o works b Beethoven, Hadn, and Mozart, which involve a variet o theme-tes, including sentences, eriods, hbrids, and comound themes, and combine the roosed models rom the second section with Calin s orm-unctional aroach to thematic analsis (1998, 70). The third section ocuses on themetes involving two invertible arts, whereas the ourth section ocuses on Ecetions within current research include Calin 2009, 10 11; and Schmaleldt 2011, 8. Concerning orms o the learned stle, Leonard G. Ratner ocuses on the use o canon, ugato, and ugue within Classical-stle works (1980, 20 71); and Elaine R. Sisman eands the dierent meanings that the learned stle can take (199, 21 8).

4 2/1 2 (2011) 19 theme-tes involving three or more invertible arts. Given the analses, it becomes clear that theme-tes containing onl one cadence, such as the sentence, are more amenable to alications o invertible counteroint than those that contain two or more cadences. Invertible counteroint within the Classical stle Invertible counteroint entails switching the registral disosition o at least two musical arts such that lower arts can echange registral ositions with uer ones, and vice versa. Within such contets, theorists, ast and resent, have emhasized the distinctness and autonom that each art should conve. That is, each art is understood as indeendent rom the others in that the roject a distinct melodic contour and a unique rhthmic attern. In this regard, Luigi Cherubini writes, In double counteroint the arts must be distinguished rom one another as much as ossible b the value o the notes (18, 1); Ebenezer Prout states that the subject and counteroint should be contrasted as much as ossible, both in melod and rhthm (1891, 8; italics original); and Kent Kennan elains that there must be suicient indeendence between the voices in terms o direction and rhthmic motion (1999, 19). Related to the notion o distinctness is the view that each art should be autonomous and able to stand alone. For instance, according to Perc Goetschius, Each line, sung or laed alone, must roduce a satisactor melodic imression (1910, ); and or Kennan, Each line must be good in itsel (1999, 19). Thus, according to the descritions rovided above, distinctness and autonom are characteristics one would eect musical arts to conve when set in invertible counteroint with each other. Although these characteristics work well or describing musical arts as the occur within works in the Baroque stle or in earlier stles, the work less well or later, more homohonic works, such as those within the Classical stle. The earlier stles call to mind equal-voiced tetures, whereas works in the Classical stle oten roject tetures consisting o rimar (melodic) and secondar (accomanimental) arts. Desite this tetural division o labour, invertible counteroint still revails within some Classical-stle works. To this eect, Imogene Horsle, in the reace to her edition o Augustus Frederic Christoher Kollmann s An Essa on Practical Musical Comosition, writes, Scholars investigating the contrauntal usages o the late eighteenth and nineteenth centuries have tended to stress their [comosers ] use o ugue and canon, et the most requentl used contrauntal device in these times is invertible counteroint. Mozart uses it constantl. Though Beethoven was slow at learning the conventions o ugue in his studies with Albrechtsberger, he mastered invertible counteroint quickl and began using it right awa in his comositions in act, it is an ideal device or a stle which stresses one redominant melod, since it makes ossible the shiting about o the main melod and the comonent melodies o its accomaniment. (Kollmann 1799/197, i)

5 170 Intersections Desite her correct observation concerning the use o invertible counteroint within the works o Beethoven and Mozart, she downlas its resence within Kollmann s works, largel or the simlicit o the secondar arts. Concerning a assage o quadrule counteroint contained within a smhon o Kollmann s, she comments, It shows the stlistic simlicit o much o the invertible counteroint used in homohonic music and illustrates wh this device is so seldom recognized the secondar arts are so simle that one siml does not think o it as being contrauntal, let alone being in invertible counteroint. It is in shar contrast to Baroque usage where there is a tendenc to combine subjects o near equalit. Here it is siml a ractical device, not an ehibition o skill (Kollmann 1799/197, i). Setting aside or now Horsle s ambivalence concerning the signiicance o invertible counteroint within late eighteenth-centur and earl nineteenthcentur ractice, she makes it clear that the music rom this eriod includes tetures consisting o rimar and secondar musical arts, an observation conirmed b Kollmann himsel and his contemoraries. For instance, he writes, There is a great dierence between the rincial art or arts o a iece, and those called accomaniments; and even the latter must be divided into necessar and voluntar, or obligato [sic] and ad libitum ones. Concerning the obbligato arts, he writes, Accomaniments o this sort ma be set to a iece in two dierent manners, viz: irst, so that the rincial art and the accomaniment take the chie melod b turns, and orm a sort o concertante (1799/197, 12). 7 The taking o turns here, o course, alludes to the ractice o invertible counteroint. Heinrich Christoh Koch also comments on such matters, eseciall as the ertain to the string quartet: I it reall is to consist o our obbligato voices o which none has riorit over the others, then it must be treated according to ugal method. But because the modern quartets are comosed in the galant stle, there are our main voices which alternatel redominate and sometimes this one, sometimes that one orms the customar bass (Koch 198, 207). Thus the sentiment eressed b Kollmann and Koch, here, is one o comromise: eression o invertible counteroint, but one that actors in a hierarch o musical arts. In addition to the hierarchical role that musical arts oten la within Classical-stle tetures involving invertible counteroint, consideration should also be aid to the toical content that such tetures roject. In some cases, assages o invertible counteroint within Classical works evoke the learned stle, such as through ugal ractice, but in others, the can roject a less elevated stle, such as through non-ugal, motivic imitation, and all under the categor o what Elaine R. Sisman describes as Classical counteroint (199, ). 8 In a comarison o the two stles, learned stle ticall rojects a 7 The second manner involves the accomaniment serving onl as a bass or inner voice. Additionall, Kollmann is reerring to instrumental arts, not voices in the music-theoretic sense. 8 Learned stle, a toic in the music-semiotic sense, connotes the emloment o contrauntal techniques, such as imitation, ugue, and canon. The notion o learned stle originates in the research o Leonard Ratner (1980) and has been eanded urther in Agawu 1991; Allanbrook 198; Balter 2012; Hatten 199; Monelle 200; Sisman 199; Somai 198; and Somai and Ausser 1988.

6 2/1 2 (2011) 171 serious ethos, tical o sacred music, whereas Classical counteroint conves a much more secular one, as would be ound within a minuet. 9 Summoning counteroint in these two was loosel corresonds to the aorementioned tes o musical arts one would eect to ind in contrauntal tetures within Classical works: learned stle involves arts contained within an equal-voiced contet, as ound within sacred, vocal olhon, but Classical counteroint (oten, but not alwas) involves a hierarchical arrangement o arts that are instrumentall oriented. The ormer stle involves arts that one would construe as melodies, ticall to be sung, whereas the latter stle oten emlos arts seciicall tailored or and/or evocative o instrumental reroduction, as suggested b such toics as brilliant stle, Alberti bass, or hunt stle. 10 Regardless o which te o teture a assage ma roject learned stle or Classical counteroint both tes are caable o containing musical arts set in invertible counteroint. (The large majorit o works resented in this essa all into the Classical counteroint categor.) Thus the toical content o a assage does not bear on the invertibilit o its constituent musical arts, but rather on the characteristic qualities o the musical arts themselves. In Classical-stle contets, thereore, since musical arts can la dierent roles (rimar, secondar, rincial, accomanimental, etc.) and be combined into tetures that are either learned or Classical in orientation, we need to eand our notion o what are viable musical constituents within the assages o invertible counteroint that we elore. Thus, reerring to each art as a melod is not entirel reresentative (though in some cases this might be aroriate), since some arts ehibit a lower melodic roile than others. Additionall, research into the scholog o hearing demonstrates that listeners organize musical henomena into discrete ercetual units known as streams. 11 Listeners dierentiate between dierent streams according to reerences or a variet o actors, including stewise motion, avoidance o snchronous onsets, use o dierent rhthms, avoidance o voice-crossing, timbral contrast, avoidance o arallel motion, temo/consecutive melodic-interval combinations suggesting multile voices (olhonic melod), and even satial searation amongst erormers within a concert setting. 12 The allout rom these reerences is that listeners grou musical henomena, not necessaril into dierent melodies or voices in the conventional music-theoretic sense, but rather into more generall deined chunks or streams that occu low, middle, and uer registers o a teture. Thus, because there is a variet o was that musical arts ut into invertible assages can be set and/or erceived, I will reer to each recognizable constituent that articiates within such assages as siml 9 Agawu mentions the notion o secular counteroint, an eression coined b Giorgio Pestelli (Agawu 1991, 1). 10 See ibid., 0, or a uller list o toics. 11 Streams all under the urview o auditor stream segregation and auditor scene analsis, concets associated largel with the ioneering research o Albert S. Bregman (1990). There is a wide bod o literature concerning this research area, a small samle rom which are Be and McAdams 200; Cambourooulos 2008; Deike et al. 200; Deutsch 2010; and Pressnitzer et al Be and McAdams 200, 27; Bregman 1990, 9 02; Deutsch 2010, 2; Pressnitzer et al. 2011,.

7 172 Intersections a art. Parts, thereore, can take on man dierent guises: distinct melodies, doubled melodies in thirds or siths, Alberti basses, chordal accomaniment, and even edals. Additionall, when arts echange ositions with each other, the sometimes undergo subtle changes once in their new inverted contet; desite these changes, we can still regard the inverted assage as a case o invertible counteroint. In this sense, we, as listeners, would be resonding more to the rhetoric o invertible counteroint, rather than the recise ath that each art ollows. Although I am levelling the laing ield concerning labelling the mriad tes o arts that can enter into an invertible contet, this siml rovides an initial stage o analsis; once the constituent arts have been identiied, we can then elore the dierent roles and characters the la and ehibit. Finall, we must address, i onl rovisionall, the rationale o setting such arts in invertible counteroint within the contet o a Classical theme. One ossible urose would be to rovide a means o varied reetition. Reetition is a rimar eature o all the themes we will discuss; indeed, it is a rimar eature o music, in general (Huron 200, 228 1). For instance, a consequent hrase is generall understood as a varied reetition o an antecedent hrase, with variation coming b wa o the unique cadences that close and distinguish the one hrase rom the other. Similarl, in other ormal contets, varied reetition can result, though not necessaril so, through the alication o invertible counteroint. Indeed, in recent literature on the irst movement o Beethoven s Temest sonata (Calin 2009, 10 11; and Schmaleldt 2011, 8), some o the reasons roosed or the use o invertible counteroint include summoning dierent ormal unctions, inhibiting or modiing cadential articulation, and obscuring ormal boundaries. To this we add other reasons, such as orestalling monoton within assages containing or between assages that undergo numerous reetitions (Huron 200, 7), and delineating musical atterns b making contiguous events containing the same material more noticeabl searable, or distinct (Meer 197, 8). On the ace o it, eliminating monotonous musical assages ma seem to be rather trivial; but uon urther consideration, it allows more reetitions within a assage to occur a means o ormal eansion than would normall be the case. Thus relieving monoton via invertible counteroint becomes not just an end in itsel, but also a ormal strateg. Basic model o invertible counteroint within theme-tes The ractice o aling invertible counteroint within theme-tes is highl constrained b the cadences that hel to articulate their orm. Consider eamle 1, which rewrites the oening theme rom Mozart s Piano Sonata in B b Major, K., iii. Measures 1 show Mozart s original music (though the end o m. is altered), whereb the sorano is labelled and the bass ; and mm. 8 contain m rewriting o the irst our measures b inverting both arts such that art now aears above art. Although the entire theme gives the

8 2/1 2 (2011) 17 antecedent c.i. intervals: 8 B : 2 HC consequent c.i. intervals: 8? (no cadence)? Eamle 1. Rewritten version o theme rom Mozart, Piano Sonata in B b Major, K., iii Figure 1. Basic model o ormal units that include cadences and invertible counteroint outward aearance o being in eriod orm, the lack o a cadence and tonic harmon in m. 8 renders the theme incomlete. (Moreover, the erect ith searating both arts at the outset o the antecedent inverts into a dissonant ourth at the beginning o the consequent.) Thus m recomosition demonstrates that integrating invertible counteroint into theme-tes involves more than just uending arts one over the other; indeed, it shows that a comromise must be made between registrall echanging arts, on the one hand, and articulating cadences, on the other.

9 17 Intersections We can encasulate such a comromise in the orm o a basic model (igure 1). At (a), the basic model mas out two zones that generall revail in an comlete ormal unit (such as a resentation or antecedent) that incororates invertible counteroint: invertible and cadential. 1 The invertible zone reers to an area where arts that are intended to invert with each other ma aear above or below each other. The cadential zone demarcates the sace in which the cadence occurs, thus closing o an ossibilit or invertible counteroint to revail. A variant o the basic model, shown at (b), inherits the two zones rom the one at (a) but also includes a transitional zone that searates the invertible rom cadential zones. This additional zone contains neither invertible nor cadential content. The invertible zone (in either version o the model) can start at the ver beginning o a theme, such as in a resentation o a sentence, or it can begin midstream, such as in a continuation. 1 Additionall, sometimes an invertible zone will graduall diminish as a theme rogresses towards the transitional or cadential zone. Such a scenario occurs when, ater arts have inverted ositions with each other and the music gets closer to the end o the invertible zone, at least one o the arts starts to undergo changes suicient to render it as being altered rom its earlier aearance in its original registral osition. Similarl, this situation can also work in reverse, where the invertible zone graduall comes into being near the beginning o a ormal unit containing an inverted reetition o an earlier assage (as could haen within a consequent hrase) due to changes evinced b one o the arts articiating within the inversion. The two versions o the basic model shown in igure 1 ma be simle and abstract, but this allows us to make the ollowing inerence: theme-tes with ewer cadences ermit more oortunities or invertible counteroint to lourish. 1 For instance, a sentence is more likel to include invertible counteroint than a eriod, since the ormer theme-te contains onl one cadence and the latter two. On the basis o this notion, we can create a table o theme-tes listing the number o cadences the contain (table 1). 1 1 Although zones are emloed within sonata theor (Heokoski and Darc 200), their use throughout this article is not meant to deliberatel reerence that theor nor detract rom Calin s. Rather, zones here demarcate saces within which articular ormal unctions ma reside. 1 A continuation a shortened orm o continuation hrase is the second o two hrases within a sentence that combines continuation and cadential unctions. According to Calin, Continuation unction destabilizes the revailing hrase-structural, rhthmic, and harmonic contet (as deined b the resentation) and eatures a breaking down o the structural units (ragmentation), an increase in rhthmic activit (acceleration o harmonic change and shorter surace durations), and a weakening o harmonic unctionalit (sequential rogression). Cadential unction brings closure to the theme and is characterized b tonal conirmation (cadential rogression) and the conversion o characteristic motives into conventional ones (liquidation) (1998, 0). 1 See Grier 2010, 7 (cited above), which comments on the lack o cadences within assages involving invertible counteroint. 1 The table ecludes rounded binar, since this orm would alread have embedded within it the theme-tes currentl listed in the table. Although Calin reers small ternar to rounded binar (1998, 71 7), he states that the must be understood, nonetheless, as essentiall the same orm. I have chosen to use rounded binar throughout because this eression is more amiliar.

10 2/1 2 (2011) 17 Table 1. Number o cadences within eight-measure and siteen-measure theme-tes Sentence Period Theme-te 1 cadence 2 cadences cadences Hbrid 1 (antecedent + continuation) Hbrid 2 (antecedent + cadential) Hbrid (c.* + continuation) Hbrid (c. + consequent) Siteen-measure eriod (resentation + continuation) Siteen-measure eriod (c. + continuation) Siteen-measure eriod (antecedent + continuation) Siteen-measure sentence * Comound basic idea. Formal unctions in arentheses o each siteen-measure eriod reer to content within both the antecedent and consequent. The theme-tes with onl one cadence reresent the most likel choices or emloing invertible counteroint, those with two cadences less likel, and those with our the least. One caveat must be made concerning the siteenmeasure eriods containing resentation or comound basic idea (c.) within their eight-measure antecedents and consequents; since both these eight-measure units contain onl one cadence, the larger eriods o which the are a art are also some o the more likel candidates to contain invertible counteroint within their conines. Equied with the basic model and our understanding o which theme-tes are more likel to contain invertible counteroint than others, we will now investigate relevant eamles rom the literature. Analses o ieces involving two invertible arts We begin b looking at a sentence rom Mozart s Piano Sonata in C Major, K., i (eamle 2). The ocus here is the continuation, which undergoes a varied reetition through the alication o invertible counteroint. Concerning the analsis, orm-unctional labels occu the laer directl above the sta, whereas the labels relating to the basic model, abbreviated and resented in caital letters, occu the to laer. As shown, the invertible zone consists o the continuation and its reetition; the cadential zone covers the last our measures o the theme, where no invertible content obtains. The overall urose o using invertible counteroint within the theme is to avoid monoton, eand the orm, and clearl demarcate a modulation rom the subdominant to the tonic ke. Here, brilliant assage-work that irst aears in the uer register (art ), starting in m., moves to the lower register in m. 0. Meanwhile, this assage-work is accomanied (mostl) b chords (art ) that irst aear beneath and then above art. The assage-work takes on the rimar role while the accomaning chords take on a secondar

11 17 Intersections resentation 2 [Allegro] tr F: ( ) continuation 7, contd. continuation, reeated 0 7 C: CAD cadential /V HC ( ) ( ) Eamle 2. Analsis o Mozart, Piano Sonata in C Major, K., i, mm. 2 7 one. The switching o arts recludes tedium rom setting in b reventing the eight-old scalar run contained in art rom aearing in the right hand onl. Additionall, invertible counteroint eands the dimensions o the continuation hrase here within the recaitulator main theme rom that within its eositional counterart, intensiing the drive to the hal cadence that closes the theme. 17 Moreover, the eansion rovides room in which to modulate back to the home ke. Seciicall, with ormal sace now allocated, the inversion o arts serves to highlight the return to the home ke within this sonata-orm movement. The recaitulator main theme in which these arts are laced occurs within the unconventional non-tonic ke o F major, IV; a modulation to the home 17 The eansion could all under the rubric o additional model-sequence technique, one method o altering recaitulator main themes and transitions. See Calin 1998, 1.

12 2/1 2 (2011) 177 ke, however, evinces itsel b the end o the theme in the orm o a I:HC. 18 The modulation itsel involves the inversion o arts and within the continuation. In the irst our measures o the continuation, both arts create outervoice arallel tenths and articulate the harmonic rogression IV I VII I in F major; in the net our measures (mm. 0 ), the arts switch hands but still articulate the outer-voice tenths and the same harmonic rogression, though this time in C major. The nature o the inversion here involves invertible counteroint at the twelth, which enables outer-voice thirds (or tenths) articulated b over to invert to tenths when both arts echange ositions with each other. Because the outer-voice counteroint is reserved, Mozart is able to maintain the same harmonic rogression rom the one assage to the net, desite the inversion o arts. In contrast to this invariance, the inversion o arts hels to dramatize the modulation back to C major. Thus in this sense, inversion hels to articulate orm, ointing u the return to the home ke within the recaitulator main theme through an elicit change in teture. More subtl, it also smoothes out the seam that connects both kes. That is, had there been no inversion, the transition rom m. 9 (the last measure o the continuation) to m. 0 (the irst measure o its reetition) would sound reetitive, static, and somewhat clunk, or lack o harmonic rogression and virtuall no change in melodic design. Thus the inversion imarts a sense o motion, not onl o arts and moving to oosite hands, but also that between kes. The reasons or using invertible counteroint within Mozart s Rondo in F Major, K. 9, minore, are somewhat dierent rom those suorting its use in K.. Shown in eamle, invertible counteroint summons dierent ormal unctions and inhibits cadential articulation with the reetition o reviousl heard material. The uer and inner voices are labelled as and, resectivel, at (a), and invert ositions with each other later within the minore (shown at [b]), which is in rounded binar orm. 19 In both themes, arts and are clearl on an equal ooting neither las a secondar role since much o their resective melodic content is structurall identical, though resented canonicall and under transosition. As shown at (a), the irst our measures articulate an antecedent hrase, concluding with a I:IAC. 20 Ater the cadence in m. 98, a continuation ensues rom the ollowing measure, leading to a III:PAC (A b major). The orm that mm take is Calin s hbrid 1 (antecedent + 18 Ater this cadence, the subordinate theme takes over. Thus the main theme uses with the transition, a scenario that sometimes las out within a recaitulation. Within this articular work, however, the same usion also transires within the eosition, an event that rarel occurs within a sonata-orm movement. For more on this toic, see Calin 1998, 1 7 and Heokoski and Darc 200, Dotted lines in brackets outlining invertible zones, such as those at (a) and (b), indicate that at least one o the arts articiating within the inversion has undergone slight changes; this method o indicating such changes within the invertible zone will be maintained throughout the article. 20 Although the boundar between the basic idea and contrasting idea is located midstream within a descending iths sequence, the latter idea is distinguished rom the ormer through the authentic cadence it articulates. Moreover, in some cases, a contrasting idea can sometimes borrow motivic ideas rom the basic idea (as is done here), desite the nomenclature used to dierentiate them. For more on this issue, see Calin 1998, 9.

13 Eamle. Analsis o Mozart, Rondo in F Major, K. 9, minore, mm at (a) and mm at (b) (a) TRANS CAD antecedent c.i. continuation cadential : ( ) 8 7 A : IAC (b) TRANS CAD comound basic idea c.i. continuation cadential : ( ) 9 8 PAC 9 8 PAC 9

14 2/1 2 (2011) 179 continuation). When this theme returns at the end o the minore, shown at (b), the inversion o with avoids cadential articulation and rojects a ormal unction dierent rom that shown earlier within the irst our measures at (a). Now at (b), as a result o the resence o in the bass, what had been a cadence at the end o an antecedent becomes no cadence at the end o a comound basic idea; here the dominant tonic motion in m. 112 is substantiall weakened b VҖ resolving to I. Such cadential avoidance ostones tonic cadential closure until the end o the theme. The dela o tonic conirmation here intensiies the conclusion o the binar orm within which the theme articiates, in a strateg that is urther enhanced b the chromaticall inlected bass line in m. 11. Additionall, intensit grows rom the change in harmonic meaning that suorts the theme at (b), most notabl in its oening measure (m. 109), resulting rom the inversion o with. Since begins on ^, lacement o this scale degree into the bass as suort or tonic harmon would be untenable. Thus Mozart changes the harmonic tack at this oint b beginning the theme at (b) with dominant harmon, a bold move, given the hal cadence in the receding measure (not shown). Overall, the changes in orm-unctional and cadential design described here imbue the binar orm in which these themes reside with heightened intensit, the result o which stems largel rom the alication o invertible counteroint. Avoiding monoton (as in eamle 2), delineating ormal atterning, and evading cadential closure (as in the last eamle) are three rimar reasons invertible counteroint is emloed in Beethoven s String Quartet in C Minor, o. 18/, ii (eamle ). Here, a twent-ive measure eriod (eanded rom a siteen-measure model wherein the antecedent hrase consists o a sentence [see table 1]), is shown. In the large-scale antecedent, arts and occur in violins I and II, resectivel, and are resented in imitation; in the large-scale consequent, both arts invert with each other b occuing the viola and violin I, resectivel, at least within the section leading u to the irst attemt at cadential closure (mm. 1 1); art returns to violin I within a reeat o the continuation (mm. 1 7), whereas onl a shadow o art moves to the cello. The invertible zone is clearl evident in the resentations o the large-scale antecedent and consequent. The continuations in both halves o the eriod, however, are slightl more comle, since there are three instances o them, not two, thus allowing more comarisons to be made regarding invertibilit. When comaring the irst two, no discernable content is shared; thus we can sa that the second continuation triggers the onset o the transitional zone. But a case could be made or invertibilit between the second two continuations, since the both contain arts and, desite the weakened resence o the latter. 21 I will irst discuss the urose o using invertible counteroint within the two resentations, ollowed b a discussion o its use in the continuation and its reetition within the large-scale consequent. 21 Changes to art, which roduce such weakening, rovide the rationale or using dotted brackets to outline the invertible zones here.

15 180 Intersections TRANS CAD Antecedent resentation continuation cadential Violin I () [Andante scherzoso quasi Allegretto] Violin II () Viola Violoncello G: HC TRANS (when comared to mm. 1-) CAD Consequent 1 resentation continuation etra cad., evaded s s s s s s continuation, reeated CAD etra cadential 1 cresc. s s cresc. s s cresc. s s? cresc. ( ) s 2 s PAC Eamle. Beethoven, String Quartet in C Minor, o. 18/, ii, mm. 7 Since the motivic organization in both resentations is highl reetitive our statements o the oening siteenth-note motive occur in direct succession introducing variet through invertible counteroint becomes a welcome addition to the ormal scheme. Beethoven achieves this in two was. First, imitation integrates invertible counteroint into the teture. In this vein, art begins with the aorementioned siteenth-note motive and ollows it with a reeated eighth-note motive; art imitates this attern at the time-interval

16 2/1 2 (2011) 181 o one measure. The result o this imitation scheme is that both motives are inverted with each other, rom one measure to the net. Second, inverting with rovides urther variet b teturall dierentiating the consequent rom the antecedent. Moreover, this dierentiation hels to delineate the overall orm o the theme. In addition to roviding variet, invertible counteroint within the continuation rovides a means o evading cadential closure within the consequent, and thus eanding the dimensions o the theme. As a result o the cadential evasion, the continuation undergoes a reetition (mm. 1 7), within which cadential closure is achieved. 22 In the irst continuation, the viola, carring art, begins a descent rom G in m., irst moving through descending thirds G E C (suorting the rogression I VI IV), and then lummeting towards D in m. 8, suorting V. 2 As a counteroint, art in violin I moves with the viola s descending thirds in arallel tenths b wa o the succession B G E, ending u on F # in m. 8. What ollows are unch, eighth- and quarternote ragments, leading into a cadential rogression starting on II in m. 0. Cadential closure is evaded, however, largel as a result o the inversion o arts and in m. 1, signalling a reetition o the continuation. 2 The major laer in this evasion is art, which now aears in the cello and begins b outlining descending thirds (B G E, suorting the rogression I I VI), a succession onl hinted at b violin I within the revious continuation; art, meanwhile, as stated b violin I, creates arallel tenths with the cello. (Part also eands the register to D, a means o creating intensit.) Uon the arrival on F # in m., the cello deviates rom the ath that violin I had taken in the revious continuation and instead continues descending art in violin I, however, continues to sta the course, and moves uwards ultimatel landing on C in m. and sarking the onset o a second cadential rogression, one that ends successull on a V:PAC in m. 7. The use o invertible counteroint in the continuation thus does more than just rovide tetural variet; it also rovides a technical means o evading cadential articulation and, thereore, eanding and intensiing the orm. Evasion o cadential articulation b invertible counteroint becomes an overriding ormal strateg within the irst movement o Mozart s Piano Sonata in F Major, K., i (eamle ). At irst blush, the motivic organization o the assage takes on a eriodic guise, with two eight-measure sentences seemingl combining to orm a large-scale eriod: what would be the large-scale antecedent eatures art over art, ollowed b a large-scale consequent 22 Reeating the continuation in this manner is an instance o the one more time technique. For a discussion o aling this technique in combination with invertible counteroint, see Schmaleldt 2011, 8. 2 The beginning o this descent, G F n E, actuall aears unadorned in the analogous osition in the large-scale antecedent in violin I in mm. 7 8 (where F # substitutes or F n ). Additionall, this earlier assage eatures an areggiated igure starting on B in violin II (as contained within art ), corresonding to a single instance o the same itch class in violin I in the analogous assage in m., thus rojecting a slight trace o invertible counteroint at the beginning o the transitional zone. 2 The inversion here results rom aling invertible counteroint at the twelth, through which art is transosed u a twelth and art down an octave.

17 182 Intersections Eamle. Analsis o Mozart, Piano Sonata in F Major, K., i, mm. 1 1 Comound basic idea resentation (inner voice) F: Comound basic idea, reeated resentation 9 continuation continuation close a b b I edal close b a b a 2

18 2/1 2 (2011) 18 eaturing an inversion o both arts. (The invertible zone comrises both halves o the assage shown here, albeit with some minor deviations toward the close o each, to be discussed.) Lack o cadential articulation, however, recludes such a reading the tonic edal sitting beneath the V 7 I rogression in mm. 7 8 revents an authentic cadence rom sounding, as does the VҖ I rogression in the analogous osition in mm Although these rogressions do not suort authentic cadences, the still rovide means o closure, just not cadential. 2 Thus, these rogressions close o, not an antecedent and consequent hrase, but rather an eanded comound basic idea and its subsequent reetition, two ormal unctions that articiate within a resentation o a large-scale sentence. 2 What drives the large-scale sentential reading here is the dialogue between the right and let hands. 27 Part, which begins alone, takes on a rimar role within the dialogue, whereas art, as a result o its accomanimental status, takes on a secondar one. The colloqu between these two arts serves two uroses. First, it hels to demarcate orm at multile levels, wherein the oening reorts o art within the small-scale resentation are answered b the areggiated iguration o art, which initiates the continuation; additionall, the beginning solo statements o art clearl highlight the reetition scheme o the large-scale resentation consisting o both comound basic ideas: the irst statement rojects the oening gambit o the comound basic idea, whereas the second one, with its migration to the oosite hand and lower octave, signals that a varied reetition o the comound basic idea is commencing. Dialogue also las into the dearth o cadential content within the large-scale resentation here. Although the tonic edal at the close o the irst comound idea does much o the heav work o quashing cadential articulation, the switching between hands o two motives, labeled a and b, serve the same urose at the close o the second comound basic idea. Both motives irst aear at the start o the irst continuation, with a sitting above b, the latter o which undergoes a reetition within the ensuing close. (In the analsis, the cadential unction has been relaced with a close unction, insired b the ractice ollowed in Richards 2011, 20 10). With the inversion o art over art in the second comound basic idea, motive b now resides above motive a at the start o the continuation. The ollowing close, however, deviates rom what occurs in the analogous osition in the irst comound basic idea; the second close siml swas motives a and b (mm. 1 1) between hands rom their original osition at the beginning o the continuation two bars revious. The result o this swa is such that motive b ushes the seventh o the V chord into the bass, an action that suresses cadential articulation, thus allowing urther dialogue to take lace throughout the rest o the theme (not shown). In sum, invertible counteroint and the 2 In this regard, see Richards 2011, which advocates or a semi-closed sentence, which lacks cadential unction but achieves closure on V or I through the use o a cadence-like rogression (20). 2 Although Calin states that comound basic ideas can be ormed onl through the articulation o a basic idea and contrasting idea lacking a concluding cadence (1998, 1), recent research b Mark Richards demonstrates that sentential structures can also la the role o a comound basic idea (2011, ), as is the case in Mozart s sonata here. 27 Keee (200, 7 9) discusses the use o dialogue within this sonata.

19 18 Intersections dialogue that it engenders serve not onl to delineate orm, but also to rovide a means o eanding the orm o the main theme, thus creating an oen-ended conversation between motives, arts, hands, etc. The use o invertible counteroint shown here within the main theme o K. is in keeing with what Keee describes as a marked increase in dialogue within Mozart s later comositional outut, an asect o design that brings this and other o his late sonatas into close corresondence with the Viennese iano concertos (200, 9). The one concerto that according to Keee (9) reresents the innacle o aling such dialogic organization is the Piano Concerto in C Minor, K. 91, i. As one would eect, dialogue easil evinces itsel throughout the requent echanges between the iano and orchestra, but this is not the onl wa that it does so. Indeed, dialogue here also involves colloquies between arts, not onl erorming orces, which can echange registral ositions with each other. As shown in eamle, one articular dialogue within the concerto is conducted between the two main structural arts within the irst tutti statement o the oening ritornello (mm ): the rimar art as irst stated in violin I and the uer winds () and the accomaning descending art in the lower strings and winds (). 28 Since the ritornello undergoes numerous reetitions throughout the movement, articulating dialogue via invertible counteroint becomes one wa o creating variet throughout. The ocus here is on the ront ortion o the theme (mm. 1 22), which includes a comound basic idea ollowed b a sohisticated series o ragments that initiate the continuation, leading into the cadential unction. (The theme itsel in its entiret rojects Calin s hbrid [comound basic idea + continuation].) The invertible zone begins right rom the start: the tonic edal within boldl asserts the C- based tonalit, whereas the areggiated ascent o dramaticall sets orth the minor-mode basis o the movement. The continuation is characterized b the chromatic descent o, as it charges downward towards F in eighth notes an instance o the characteristic assus duriusculus attern 29 and the graduall descending, undulating motion o, which is unctuated b abrut uward leas o a sith, also making its wa towards F (suorting b II ), situated on the downbeat o m. 22. Although art articulates the rimar melodic content o this assage, art, while not outwardl melodic, contributes to the relativel high level o chromaticism dislaed here, elevating the toos o lament (and erhas traged) that such descending bass lines oten roject. 0 The same tack is taken between both arts near the close o the oening ritornello, but with arts and echanging registral ositions (eamle 7); now takes the lower osition and the uer. Here, however, when and converge on F near the end o the end o the ecert (m. 72), the harmon is II, rather than the Neaolitan. Within both assages ecerted in eamles 28 Heokoski and Darc understand art as an idée ie or motto o which its regular resuracings serve as threads binding together a highl varied discourse (200, 8). 29 According to Christoh Bernhard, such a attern ma rise or all and is not necessaril relegated to the bass voice. See Hilse 197, In this regard, see Rosand 1979.

20 2/1 2 (2011) 18 comound basic idea continuation c.i. 1 [Allegro] Violin I Violin II Viola Violoncello and Contrabass c:, contd. CAD cadential 19 2 ( ) ( ) 2 Eamle. Analsis o Mozart, Piano Concerto in C Minor, K. 91, i, mm. 1 2 (strings onl)

21 18 Intersections Eamle 7. Analsis o Mozart, Piano Concerto in C Minor, K 91, i, mm. 7 (strings onl) comound basic idea continuation c.i. [Allegro] Violin I Violin II Viola Violoncello and Contrabass c:, contd. CAD cadential (evaded) 9 Violoncelli EC 8 7 Bassi and 7, the invertible zone ends just beore the arrival o b II and II, resectivel, since ater this arrival, the continuations o both assages diverge rom each other (not shown): the ormer wends its wa towards a i:hc and the latter a i:pac (which eventuall occurs ater the decetive move to VI in m. 7).

22 2/1 2 (2011) 187 Dialogue, thereore, does not occur onl between the iano and orchestra o K. 91, but more abstractl between arts, which ma reside in an instrument o the orchestra, as well as the iano. For instance, in eamle, art is eatured in the lower strings and bassoon, whereas in eamle 7 it migrates u to violin I and oboe I. O course, the ormal structure o the theme contributes greatl to the orchestral shuling that takes lace between both disositions o arts and. As a result o the scarcit o cadences within both assages, arts and can aear within the uer or lower regions o the orchestra. Since the uward surge articulated b and the driving tonic edal rojected b reside within a comound basic idea, a ormal unction containing no cadence, both ma occur in virtuall an instrument o the orchestra. The same ma said or the irst art o the continuation, which resents a string o diminishedseventh chords in a descending-iths sequence, another means o evading cadential articulation. Thus, the dialogue between and that comes to the ore within the oening ritornello is enabled b the orm that the theme takes, one that rojects an aml sized invertible zone, devoid o cadential closure. This enabling o dialogue rovides a method b which to showcase the instrumental orces o the orchestra and thus rovide welcome variet through the subsequent reetitions o the ritornello. Dialogue can also take lace within the string quartet medium, as we have alread seen in eamle ; Beethoven s String Quartet in F Major, o. 18/1, i, rovides another instance (eamle 8). Here the members o the quartet banter back and orth within the contet o this siteen-measure eriod, consisting o two hbrid (comound basic idea + consequent) themes. Calin, however, discourages such a ormal scheme, because the aearance o the basic idea to signal the lower-level consequent would oorl anticiate the higher-level consequent (1998, 7). But the arallelism dislaed within the large-scale antecedent and consequent strongl suggests that the basic idea aears twice within both hrases. And although the basic idea undergoes more reetitions than is eected according to Calin s theor, the dialogue between dierent members o the quartet hels to demarcate the orm o the theme at dierent levels o structure. Seciicall, the invertible zone corresonds to the comound basic ideas that occur at the beginnings o both halves o the siteen-measure eriod; invertible counteroint thus hels to delineate orm at the siteen-measure level. Within the large-scale antecedent, violin I begins alone with art as art o the basic idea, whereas the viola (which carries art ) and violin II enter the conversation with the onset o the contrasting idea. The arts then echange ositions within the large-scale consequent, where the cello now begins alone b stating art, ollowed b the entr o violin I, carring art, along with the remaining strings. Although the two lower-level consequents reside outside the invertible zone, the still contribute to the conversation b allowing other members o the quartet to sound their voice: the viola, in the irst consequent, and violin II, in the second. Thus, each statement o the basic idea is