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ARS COMBINATORIA IN SELECTED WORKS OF C.P.E. BACH: AN ANALYTIC INVESTIGATION by @ Nancy Wilson Thesis submitted to The Faculty of Graduate Studies and Research in Partial Fulfillment of the Requirements for the degree of Master of Arts < Faculty of Music McGill University Montreal, Quebec November 1988 Short title: ARS C011BINATORIA IN SELECTED WORKS OF C. P. E. BACH c ABSTRACT This thesis combinatoria, permutation explores the of some technique musical implications of ars of material, eighteenth-century music, using combination for ideas and analysis of of Leonard B. Ratner as a starting point. Examined here are solo Bach: several pieces from leichte Clavierstücke keyboard works by C.P.E. the two sets of Kurze und (H. 193-203 and H. 228-238) and a longer, more serious work, the Freye Fantasie minor (H. 300). The analyses demonstrate in F# that Ratner's ideas can provide analytic insight into these contrasting works by Bach and that the selected works suggest extensions to these manifestations of ars ideas as weIl combinatoria. several questions worthy of further study most notably relating chroma tic-enharmonie syotem. ( to as other In addition, are raised, C.P.E. Bach's handling of resources within the tonal 'G " ,1'; 1 1 ABREGE Cette l'~ thèse explore combinatoria, soit la de permuter implications technique de de combiner et la matière musicale, pour l'analyse de la musique du dix-huitième nous quelques servirons des siècle. idées debuter nous " Pour pertinentes de Leonard B. Ratner. Sont revues ici quelques solos pour clavier de C.P.E. Bach: plusieurs piéces des deux sèries de Kurze und leichte Clavierstficke (H. 193-203 and et une pièce Fantasie en démontrent plus F# que longue, (H. mineur les H. 228-238) plus sérieuse, la Freye Ces 300) . analyses idées de Ratner peuvent suggérer une perception analytique de ces oeuvres contrastantes de Bach et que les oeuvres choisies suggèrent des extensions de ces idées, d'autres manifestations quelques questions approfondie fa~on don t sont de qu'elles suggèrent d'ars combinatoria. qui méritent soulevées, C.P.E. 1\ meme Bach en une En plus, étude particulier traite des plus sur la ressources chromatiques et enharmoniques dans le système tonal. c TABLE OF CONTENTS Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v CHAPTER 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 INTRODUCT l ON CHAPTER 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 A MECHANISTIC APPROACH TO WORKS FROM THE KURZE UND LEICHTE CLAVIERSTÜCKE Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 CHAPTER 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 A DIFFERENT CONTEXT: THE FANTASIA IN F# MINOR Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Bach's Writings on the Free Fantasia ....... 40 Form in the Free Fantasia in F# Minor ...... 45 Analysis of the Sections . . . . . . . . . . . . . . . . . . . 49 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 APPEND IX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Scores of Compositions Analyzed in Chapters 2 and 3 (H. 193, 196, 228, 231, and 300) c t f PREFACE The idea ~ for an analytic investigation involving combinatoria originated in a theory Haydn's early keyboard music led by Dr. McGill University. awareness on This my part seminar of seminar on Bo Alphonce at fueled phenomena a such growing as ars combinatoria and rhetoric, both of which can be sensed as influential factors construction and acknowledged in perhaps for design, typical the following discussions and geared toward guiding analysis. distinction in but which are rarely classroom theory analyses, reasons. Firstly, written explanations applications occurring were in eighteelh-century musical in of their musical eighteenth-century sources teaching composition rather than Secondly, owing to an all-too-clear North American music education between the content of music history and theory classes, phenomena may these be considered by theorists as belonging to the domain of the former. Leonard B. Ratner crossed concerns. several ~s lines Besides applying one scholar dividing aspects whose work has these of differing rhetoric and vi ( other issues derived from eighteenth-century sources to ana1ysis in Form, and his book Style (New Classic York: Schirmer Books, 1980), he has suggested the importance our understanding Music: Expression, of of ars combinatoria for eighteenth-century short, fascinating article to be music in a discussed in this thesis. The music of Carl Philipp Emanuel fascinating for reasons to be discussed and l have thus chosen Bach is a1so in Chapter 1, to use several of his solo keyboard works in the analytic portions of this study. There is a growing interest in his music, as the bibliography to sorne extent indicates, a will no doubt accelerate in light growth which of 1988 being the bicentennial anniversary of his death. Given aIl of the abcve considerations, of this thesis begins by reminding interesting factors surrounding C.P.E. music, ars and then introduces discussing Ratner's Chapter 2 seminal then offers article Chapter 1 the reader of Bach and his combinatoria on by this topic. a preliminary attempt to apply concepts of ars combinatoria to the analysis of solo keyboard works by Bach in a popu1ar idiom, after which Chapter 3 expands the scope of the analytic inquiry to inc1ude ( one serious works. of Bach's A brief least conventional and most conclusion then discusses 1 vii several issues arising from this study which could be further pursued. Concerning the edition music, l have taken used in studying Bach's advantage of the recent publication of Bach's entire solo keyboard output in a facsimile edition of which Darrell Berg is the editor. This edition, as weIl as a useful review of it by George Barth, are listed in the bibliography. At this proofreading time and constant support l wish copying Bo profound have Alphonce, inception. who se understanding helped examples, and encouragement. to express my appreciation Dr. to thank David Judah for motivate of and to my and for his Finally, l wish thesis supervisor, insightful comments eighteenth-century and music guide this study from its ( CHAPTER 1 INTRODUCTION Not only was Carl Philipp Emanuel Bach one of the most influential composers, authors, teachers, and performers in the musical world of the eighteenth ~entury. He was, of course, the son--indeed, the most renowned of the five musically active sons--of the greatest of aIl composers.<l> As the above citation suggests, there is little cause to wonder why the music of ) should (1714-1788) Carl Philipp generate Emanuel Bach considerable interest within historical and analytic music scholarship. addition to music, the intrinsic there contextual compose r . exists factors Firstly, an positive qualities of this int:iguing relating it In is to assortment Bach's weIl known ljfe that of as a Bach acknowledged his father, Johann Sebastian Bach, as his only teacher,<2> and that training and the Baroque the roots of his musical compositional craft thus may be found in tradition of a figured bass approach to <1>William S. Newman, "Emanuel Bach' s Autobiography," Musical Quarterly 51/2 (1965): 363. ( <2>In 1773, at age 59, Bach stated in his Autobiography that " • in composi tion and keyboard playing l never had any other teacher than my father." (Ibid. ~ p. 366.) 2 composition.<3> upon future Secondly, composition extensive, as is reflected C.P.E. and Bach's influence keyboard esteem musicians in as which Haydn, his is in the wide dissemination of his treatise on keyboard playing<4> the playing music Beethoven, German composers of Bach's time.<5> was and as weIl held by such various Thildly, as by North 3ach was <3>Wri ting to Forkel in 1775, Emanuel Bach summarized Sebastian Bach' s method: "Sirice he himself had composed the most instructive pieces for the clavier, he brought up his pupils on them. In composition he started his pupil~ right in with what was practical, and omitted aIl the dry species of counterpoint that are given in Fux and others. His pupils had to begin their studies by learning pure four-part thorough basse From this he went to chorales; first he added the basses to them himself, and they had to invent the alto and tenor. Then he taught them to devise the basses themselves. He particularly insisted on the writing out of the thorough bass in [four real] parts. In teûching fugues, he began with the two-part CInes, and so on." Translated by Hans R. David and Arthur Mendel, ~ Bach Reader (New York: W. W. Norton & Company, 1945), 279. <4>Carl Philip~ Emanuel Bach, Versuch über die wahre l l i .ill. ClavieJ. ~ spie1en, (Berlin, 1753 and 1762). Facs. reprint ed. Lother Hoffmann-Erbrecht (Leipzig: Breitkopf und Harte1, 1976). Translated and edited by William J. Mitchell as Essay ~ the True ~ of Playing Kevboard Instruments, (New York: W. W. Norton & Compdny, 1949). <5>ln his introduction to the English translation of Bach's Versuch (see previous note), William J. Mitchell discusses the spread of Bach's ideas, which occurred directly via his students, and indirectly via widespread sale of the treatise itself. See "C.P.E. Bach' s Essay; An Introduction," Musical Quarterly, 33 (1947): 460-80. As well, a chapter is devç;t:ed to interest in Bach and his music from the eighteenth century to the present in Hans-Günter Ottenberg's recent biography Carl Philipp Emanuel ~ (Leipzig: c 3 involved in various intellectual and artistic circles-music whic~ latter theoretical, were half literary, philosophical, etc.-- flourishing in Northern Germany during the of the eighteenth century, and was concerned with fundamental aesthetic issues pertaining to musical expression.<6> displayed a practical, pragmatic perf ormance , and pedagogy relatively comfortable material Nonetheless he also si de in composition, which ensured existence.<7> him a These Verlag Philipp Reclam jun., 1982), which is translated by Philip J. Whitmore (London: Oxford University Press, 1987); see pp. 185-217 of the English translation. For an account of the influence of Bach's style on contemporaneous composers of North Germany see Darrell Berg, "The Keyboard Sonatas of C.P.E. Bnch: An Expression of the Mannerist Principle" (Ph.D. dissertation, State University of New York at Buffalo, 1975), 66ff. <6>Significant discussions of Bach's involvement in theoretical, literary, and aesthetic circles appear in the following, among others: E. Eugene Helm, "The Hamlet Fantasy and the Literary Element in C.P.E. Bach' s Music," Musical Quarter1.I. 58/2 (1972): 277-96; David Schulenberg, The Instrumental Music 21 Carl Philipp Emanuel Bach, (Ann Arbor: UMI Research Press, 1984), esp. pp. 17-29; Berg, "Keyboard Sonatas," pp. 58ff, and, perhaps MOSt notably, Ottenberg's biography of Bach (see note 5), which focuses throughout on the rich cultural and intellectual milieu surrounding the composer. c <7>This practical side of Bach is revealed in the fo1lowing excerpt from his autobiography: "Because l have had to compose most of my works for specific individuals and for the public, l have always been more restrained in them than in the few pieces that l have written merely for myself. At times l even have had to follow ridiculous instructions, although it could be that such not exactly pleasant conditions have led my talents to certain discoveries that l might not otherwise have come upon. 4 and other facets of Bach's musical personality and activities make his life a fascinating topic of study. There is a correspondjng be sensed in his keyboard music, light, popular pieces limits of musical subsequent analyses to those several of of the of Bach's diversity to which ranges from tbat expression chapters of degree of chal1enged the his present era.<8> study The offer solo keyboard works exemplifying this diversity. A approaches are the analysis of Bach's music, analysis well-suited to approaches of form such and investigation of various to one or more as number Schenkerian phrase structure, stylistic genres.<9> of ana1ytic reduction, and the issues pertaining In the present study, Since l have never liked excessive uniformity in composi tion and taste, since l have heard such a quantity and variety of good [things], since l have always been of the opinion that one could derive sorne good, whatever it may be, even if it is on1y a matter of minute detai1s in a piece, probably from such [considerations] and my natural, God-given ability arises the variety that has been observed in my works." Newman, "Autobiography," p. 371. <8>This diversity i5 reflected in the following set of distinctions suggested by William S. Newman wi th respect to Bach' s solo keyboard music: " music written to order as against music written to taste," and works written "in the interest of sure sales" as against those other works, again, wri tten for his own artistic satisfaction. See William S. Newm~n, The Sonata in the C1assic Era, 2nd ed., (New York: W.~ N~;;-&-Compa;y, 1972),~3. <9>See for example Darrell Berg, "Keyboard Sonatas;" Suzanne C1erx, "La forme du rondo chez Carl Philipp Emanuel Bach," Revue de Musicologie 19 (1935): c 5 however, the focus which, because these other of is on a different point of view its flexible approaches while perspective on certain issues. nature, complements offering This a point unique of view will now be introduced. * In a broad * sense, * dll western music can be considered to be constructed from various combinations and permutations century, eighteenth and combin'ation expli,:i tl y used technique may seem the has little the were teaching come While its pre-designed combinatoria c however, permutation in which combinatoria. various of the twelve pitch classes. to of be nonetheless notions of quite often composition, a known as ~ most trivial manifestations, compositional more In the than quaint games of chance, pastimes, ars reflects broader scientific 148-67; Pamela Ruth Fox, "Melodie Nonconstancy in the Keyboard Works of C.P.E. Bach," (Ph. D. dissertation, University of Cincinnati, 1983); Nancy Barnes Hager, "Rhythm and Voice-Leading as a Facet of Style: Keyboard Works of J.S. Bach, C.P.E. Bach, and Mozart," (Ph.D. dissertation, City University of New York, 1978); Heinrich Schenker, "Ph. Em. Bach: Kurze und leichte Klavierstückc mit verànderten Reprisen (176~ Nr. 1, Allegro," in Der Tonwille 4 (1923): 10-11 (translated by Steve -rBrson in lu Theory Only 10:4 (1987): 5-10); David Schulenberg, Instrumental Music, esp. pp. 147-60. ~---------- ------------------------- 6 and philosophical views of the which may be subsumed under the eighteenth century concept of mechanism. Briefly, mechanism is a doctrine of eighteenth-century thought which states that aIl phenomena, both animate and inanimate, may be explained in terms of principles by which machines derived from operate, that is, by principles the ordering and arranging of components according ta physics and chemistry.<lO> Many of the combinatoria and composition together in in an basic issues mechanism as the by Combinatoria: Chance and Choice in ars they relate ta musical eighteenth article in vol ved century are brought Leonard B. Ratner, "Ars in Eighteenth-Century <10>Based on the definition provided by the Concise ùxford Dictionarv of Current English, 6th ed., s.v. "mechanism." Discussion of this biologicalphilosophical concept appears in various standard sources on philosophy and ideas; see e.g. Morton O. Beckner, "Mechp-nism in Biology," in lli Encyclopedia of Philosoph y (vol. 5). In mus il" , as is the case wi th science and philosophy, mechanism may be understood as being antithetical to the concept of organicism, which is currently receiving attention in light of the widespread influence of HeInrich Schenker's theory of music. The following recent sources address the topics of organicism and, more implicitly, mechanism: Jamie Croy Kassler, "Heinrich Schenker's Epistemology and Philosophy of Music: An Essay on the Relations Between Evolutionary Theory and Music Theory," in The Wider Domain of Evolutionary Thought, eds. D. Oldroyd éind K. Langham. (Australia: D. Reidel Publishing Company, 1983), 221-60; William A. Pastille, "Heinrich Schenker, Anti-Organicist," 19th Century MUb_c 7/1 (Summer 1984): 29-36; Ruth A. Solie, "The Living WC'rk: Organicism and Musical Analysis," 19th Cent ury Music 4/2 (Fall 1980): 147-56. c 7 Music. "(11) For this reason a contents is presented in article focuses the brief summary of its following pages. The on the various discrete components of composition which are susceptible to combinations and orderings, short components rhythmic figures, such as melodic and phrases, key schemes, and even whole movements. Ratner begins aforementioned short the article by referring to the eighteenth-century movements, primarily pastimes dance in which types, were 'composed' by randomly selecting the components from a pre-determined reservoir of appropriate musical figures, using such means as throwing dice to make the selec tions. He then suggests that such games are a clue to more serious compositional issues of the time: The amusement afforded by these musical games of chance bespeaks pure dilettantism and, perhaps, decadence. Yet, the proces5 by which the games were put together reflects a substantial view of musical construction, one that permeates the seventeenth and eighteenth centurj es. In this view, the play of musical elements is controlled 50 as to achieve a coherent and persuasive flow of rhetoric. At this time in musical history, it was possible to codify the mechanical elements of musical composition more clearly than at any other time. Arrangements of such elements, though uncountable in practice, were intelligible ( <11>Found in Studies in Eighteenth-Century Music: A rribute ~ Karl Geiringer. H. C. Robbins Landon, ed., in collaboration with R. E. Chapman (London: Oxford University Press, 1970), 343-63. 8 and limited.<12> Ratner subsequently serious issues in turn. goes on into four These to organize these more categories, discussing each discussions form the bulk of the article. Ratner uses reference to according to alone, term of objects a fixed are may be set of determined in arranged or placed conditions."<13> by whether These combination permutation alone, or both together are invoked in a given situation. The permutations, Ratner as mathematics.<14> Taking starting we point, can unordered selection of r r combinatoria "the number of different ways in which a given quantity conditions the n. phrases, For we a combinations and notes, set of define belongs n objects to as a a combination as an objects from this set where example, given a set of four muslcal can containing from topic of select one to the fol10wing combinations four of these phrases without regard to order: [1] [3,4] [2] [3] [1,2,3] A permutation, ..,.. , . .... , [4 ] [ 1 , 2] [1,2,4] [1,3] [1,3.4] [1,4] [2,3.4] [2,3] [2,4] [1,2,3,4] conversely. is an ordered selection of <12>Ibid., p. 345 • 1 <13>Ibid., p. 345 . <14>Ibid., p. 345. ( 9 r objects from a set of n objects !: n. where r In other words, whereas [1,2,3,4] is the same combination as [4,3,2,1], the two represent different permutations of this combination of four phrases. In some aspects permutation is fixed of while For example, possible. composition several a single combinations are given two phrases we can fix tha following permutation in keeping with tonal and formaI function closing phrase opening phrase and then provide n Where, for example, n optional realizations for each. = 2, the following combinat ions would then be possible: opening phrase closing phrase C-l 0-1 0-1 0-2 0-2 C-2 C-l C-2 Conversely, some aspects of composition consist of a single combination and the possibility for different permutations--for example, arrangements vertical of a major arrangements the triad, of three possible or the lines linear possible in triple counterpoint with each other. Each of the four wide-ranging categories into discussion of the which Ratner's influence of ars - 10 combinatoria is divided concerns a different The musical construction. the most basic units A figures. compositional Galeazzi both permutation generate the by the of by that and rhythmic conditions line.<15> of treatises indicate first of these deals with of musical variety a design, motives and different examples from Ziegler, Riepel, either and permutation alone or combination and level of may be used to diastematic motives which fit given 'slot' melodic in a From these, one possibility may be selected student. As an aid to composition this procedure can generate short ideas and phrases which a student or even professional composer might use as the basis for a composition. Ratner places this procedure in a broader perspective: AlI the theorists who treat of permutation, from Mersenne to Galeazzi, do so for a practical reason--to unlock the imagination of the student. The method is mechanical; the materials are few and simple; but the possibi1ities are unthinkably vast. If we think of the device as a way of obtaining a 'prius factus,' then it does not diffcr essential1y from taking an ostinato, a cantus firmus, a motto, or a known melody as a point of departure for composition. As such it need not be spurned even by the experienced composer.<16> The second level of musical construction to which Ratr.er suggests the possibility <15>Ibid., pp. 346-50. <16>Ibid., p. 350. of applying ars ( 11 combinatoria is that Combinat ion alone of is the phrase basic source this level since permutation, phrases or the periods, is syntactical and or the pe riod.(17) of options at re-ordering of not especially relevant given constraints phrases governing in combination; for example, a 4-measure cadential phrase and a 4-measure sequential places within the temporal Ratner cites examp1es applications of per-:ods. Harmonie form, both f10w of a musical work. harmonie combinp.tion, the three for how a composer binary of not exehange and melodie combination applLed to phrases and/or exemp1ified by J phrase eould of aIl, is options set forth by Riepe1 might begin name1y, first the second half of a an aseending sequential phrase (monte), a phrase emphasizing the dominant (ponte), or a deseending sequential phrase (fonte).(18> me10die options in phrases and periods, discussed by Ratner: given two-bar idea aIte~native and alternative As for two types are continuations to a melodies over a fixed bass line.(19) (17)Ibid., pp.350-53. (18)Joseph Riepel, Grundregeln ~ Tonordnung insgemein, (Frankfurt, 1755), 45-47. Riepel's theories are diseussed in Nola Reed, "The Theories of Joseph Riepel as Expressed in his Anfangsgründe ~ musikalischen Setzkunst," (Ph. D. dissertation, University of Rochester, 1983). ( 1 9 >Rat n e r, ,~ Ars Co mb i na t 0 ria," pp. 35 2 - 5 3 . 12 Moving to yet larger the third category emphasis concerns Despite keys.<20> on dominant in components of composition, the overall the increasingly relationship the tonal arrangements of widespread between scheme of tonic and compositions as the eighteenth-century progressed, other combinat ions and permutations of from modal influences, keys, derived never became entirely obsolete.<2l> Riepel's discussion of the Here Ratner cites options in tonal a fixed relationships which combination of keys being ordered according to any of its permutations. arrangement must can The result restrictions begin and derived must from present study category to As discusses those kcys The third chapter and permutations of related keys. the four th ways compositioual of broadens the discussion of this include combinations chromati~ally that the which permutations comprised be diatonically related to the tonic. of the 3re end with the home key and that intervening combination are from in and final which procedures as category, several they apply Ratner important to entire <20>Ibid., pp. 343-44. <21>A genre that continued to exploit numerous key relationships was the free fantasy, an example of which by C.P.E. Bach is discussed in the present study (see Chapter 3). c 13 movements cou1d a broad conceivably be understood in terms of notion explains, many variation, century of ~ when music, are used in usually thus combinatoria techniques variable compatible many interesting perspective numerous actual thinking that in and texture, aspects of variation have composers the gave been over the lending an construction of facet rise of to the the mechanistic games of ~ Types of paraphrase and variation which associates parody, counterpoint. with ~ rescoring, and In addition to these combinat6r~ adaptation, multiple also hints at the applicability of invertible techniques Ratner ~ combinatoria to formaI designs: c ~ Since discussed. effect, to :::ranscription, pasticcio, eighteenth- works by suggesting that they reflect loosely include and is, serious, comb~natoria. Ratner with respected Ratner to melody being centuries, more reference paraphrase by another, he r.onsist of a fixed harmonic- presently of practised As procedures involving paraphrase and/or rhythmic structure and and combinatoria.<22> There is no way to assess the extent co which ~ combinatoria might have el. tared into the composition of music in the eighteenth century. Dice games and instructions from music theory are specific; <22>Ratner, "Ars Combinatoria," pp. 354-57. 14 we can follow the process, step by step. But this is not the case with the composer's imagination •.. who is to say that the principal structural layout in classic music, the I~V, X-I plan, which shapes the two-reprise dance form and its larger sibling, the sonata form, is not a framework within which composers were constantly creating fresh music by means of melodic combinatorial play?<23> In summary, 1) the then, Ratner's generation and four categories are: combination of musical motives and figures, (2) melodic and harmonic variables within a fixed ord~ring phrase structure, of keys, and movements based (4) the on sorne Ratn~r which that approach pedagogy which arrangement of of the to permutations in the substitution of en tire sort of common procedure, or basic scheme, or form, etc. from (3) derives In general, these four categories is eighteenth-century emphasizes the musical components time.<24> the context Because the compositional construction and into popular forms goal of this approach <23>Ibid., pp. 358-359. <24>It is for this reason that Riepel figures so prominently in Ratner's discussion, for Riepel's approach to compositton, innovative in its time, avoids emphasizing iigured bass and harmony and foc uses instead on a style-conscious handling of phrase structure, rhythm, melody, and forme Ratner's sources for Riepel are the Grundregeln ~ Tonordnung insgemein (Frankfur~ 1755) and the GrUndliche Erklàrung ~ Tonordnung insbesondere (Frankfurt, 1757), which form the second and third chapters in Riepel's magnum opus Anfangsgründe ~ musikalischen Setzkunst. Ratner's other sources are too numerous to Tist in entirety, but include the following: Christian Gottlob Ziegler, Anleitung zur musikalischen ---~~ ~~~~~- ( 15 was presumably to rely less and less on pre-determined formulas and clichés and increasingly on original and subtle handling of musical materials, it to detect the consciously modern extent practised scholars we to which ars combinatoria was by advanced cannot phenomenon to the finest in the was to ) model scholars. However, this compositions written students and lesser was compositional pedagogy in the eighteenth century does not anal y tic link As simply on the basis of how taught composers--for what composers. conclusively of the eighteenth century composition is difficult necessarily constitute an available the to twentieth organization of century this topic into four clear categories by Ratner may weIl serve as a workable involving The starting ~ point analytic inqujry ~n combinatoria. following two chapters analytic inquiry undertaken keyboard compositions ( for with represent respect by C.P.E. Bach. in the present chapter, Bach's gifts encompassed ability to both the su ch an to several As noted early as a composer compose deeply Composi t ion (Quedl inbur g, MS. 1739) ; Francesco Galeazzi, ~lementi teorico-pratici di musica (Rome: Puccinelli, 1791-6); Honore F. Langl~, Traité de la basse ~ le chant, precedé de toutes ~ r~glëS la composition (Paris: Naderman, 1798); William Crotch, Elements Qi Musical Composition (London: Longmans, 1812). E 16 artistic works and the to lighter, more publication.(25) Chapter Two, ~ popular turn his attention styles for court use and The wQrks to be examined include, in short pieces from the two sets of Kurze leichte Clavierstùcka ~ verandE~ Reprisen (H. 193-203 and H. 228-238),<26> and, in Chapter Three, FR the Free Fantasia in different works: reasons led Kurze und the intended for a pragmatic intended to minor to the leichte (H. 300).(27) Very composition of these Clavierstficke were students at the early stages of keyboard studies; in contrast, with ability to ex~ress using Ratner's the function Fantasia was not written in mind, and was instead Bach's most personal :~elings. In four categories as a basis of inquiry, we shall be interested in (1) whether they can provide (25)Bach himself even indulged in the aforementioned games of ~ comb!natoria. His "Einfall" is discussed on pp. 357-58 of the article by Ratner in question. As weIl, E. Eugene Helm provides a translation of it along with commentary in nSix Random Measures of C.P.E. Bach," Journal .2i Music Theory 10:1 (1966): 139-51. (26)The Helm numbers for Bach's w0rks are found in various recent sources including New Grove (s.v. "Bach, Carl Philipp Emanuel") and the Whitmore translation of Ottenberg, Carl Philip Emanuel Bach, pp. 225-43 and 245-48. These numbers will be used in the present study. For reference, the older Wotquenne numbers for the Kurze und leichte Clavierstücke are as follows: for the' firstSet (H. 193:'203): Wq. 113 #1-11 and for the second set (H. 228-238): Wq. 114 #1-11. (27)Wq. 67. Background information regarding this work is provided on pp. 38-39 of the present stuny. 17 analytic insight into these contrasting works by Bach, and (2) whether the to these extensions manifestations encompass~ng questions than the simply to selected works by Bach suggest categories of combinatoria. and comprehensive would require one presently provide a with which to century music. answers to other Since these two a much more extensive study undertaken, the sample, Bach's keyboard output and ars combinatoria and/or goal here is both of the diversity in of the potential value of as one of a number of analytic tools approach this and other eighteenth- CHAPTER 2 A MECHANISTIC APPROACH TO WORKS FROM THE , KJRZE UND LEICHTE CLAVIERSTUCKE Bach's two sets of leichte Kurze Clavierstücke mit veranderten Reprisen und beygefügter Fingersetzung für Anfanger Berlin in 1766 and indicates, were f.irst published in As 1768 respectively. fingerjngs as weIl as varied repeats are provided for the beginner, the varied as introductory and diminution student of master. models which for in the keyboard assorted pieces, repeats serving the art of ornamentation the eighteenth would have Each of the t*o The design each of the two - phrases. first work in 'Allegro di Molto' in F major, H. 228. of H. 228 is a binary form in which sections con tains followed by its varied repetition. 8-measure units eleven short, the sever al to be considered in this chapter we shall begin with the the second set, century a been expected to sets contains and of the title consists In terms in of issues turn an 8-measure unit Each of these four of two 4-measure raised in the previous chapter we can view this formaI design as a series of ------- --------.----~-~------- C 19 phrase slots whose specifie permutation is determined by within function establishes the the tonie overall by 1 work: phrase to authentic moving an cadence, phrase 2 moves to the dominant, phrases 3 and 4 repeat 1 and 2 with variations, phrase 5 focuses on the dominant with a ponte,<l> phrase 6 returns tonie and closes with the strongest to the cadence, and phrases 7 and 8 repeat 5 and 6 wita variations. The following diagram summarizes this view of the work:<2> \~~ SQ.c:t'~ ,.- lM .• 1 lM.$' r t. X"c:. 1: -......... 1 1_.1\ 1 1H\. '3 X 1: "t. 'Io.C"\d. ",~\s." ~ M • \~ 1"va.' % t·t'· .....") • 'r .~~ a 1M. 1.,\ ft\. '\S "V:. 1 galant 1 ) 1: p~~ ~ .. ~~"eQ.•• ) conven tional, "1.t,. ........ ".. ""'"' 1 1 1 %4-1 1:,,<- ~c. ".". Isolating ",....,. OZ'-.1 l: 'l1\~ s.u.'t:'o~ I",.,~ '1."". n.,,",~ ~ ..n.\-' ...... 1 style formaI <l>This term is discussed on page Il. <2>1n the following example and throughout the remainder of this study, HC, PAC, and lAC refer to half cadence, perfect authentic cadence, and imperfect authentic cadence respectively. These labels are used here in accordance with Edward Aldwell and Carl Schachter, Harmony ~ Voice Leading l (New York: Harcourt Brece Jovanovich, Inc., 1978), 76. 20 design such permits as this from clearer a other view The also model a comparison of structure is relevant successi ve phrase determined by the functions of thus many works created. to fill each imagination composer s, accepted slot in the or musical composers. Before we shall put this each options is slot. Many phrases fulfilling the the in the of a lively most inventive of currently body case of lesser the music of a composer former turning handling of the indi vi dual for reservoirs of phrases of When considering applicable. that consist of the of phrase slats may be generated, and might clichés it, and to regard: actual case of C.P.E. Bach's rank of These perhaps on apr lied reservoir a these based this function of individual between several such works. in slot different combinations the work combinatoria ~ the of idiosync racies of any single thus musical parameters to is certainly more Bach's imaginative idiosyncracies of H. 228, concept of different options for a phrase slot to work in the following comparison. Of the eleven pieces contained in each of the sets of Kur?~ fourth und derive leichte from namely that which was ....... (see page 19). Clavierstücke, the first and a common formaI-harmonie design, illustrated These works are: above for H. 228 ................ _ ; ~ =11 «0::1111""4. zœXll 53 _ c kU;;, 21 No. 1 No. 4 1766: Allegro in G H.193 Minuet in F H. 196 1768: Allegro di Molto in F H. 228 Minuet in G H. 231 There are several minor differences such as the use of PACs in H. 193 interpolation in into the rather these individual The each of aspects is the se works come the manner and of each work influences function of the half. recall page the chart on the 8.<3> leading These repetition in tone goals in are In 19 ponte f is to tonicize <3>The music for reproduced on page 31. H. ponte 228, we that an lAC is with an arrivaI the upper voice in measure reiterated in measures 9 through 16. the specifie option which the exact respective reached in measure 4 followed by a HC on in which the specifie progressions and cadential goals phrase beginning each second from general design, case in point regarding comparison of in the first half realization a 2-measure the same, and provides a backdrop against A strength of and H. 231; the se will enter shortly. which individual aspects of into focus. lACs the minuet discussion however, is than Bach uses the varied Following this, to realize the the dominant for two measures the se eight measures is = n LA. 22 before reverting to V7 of the home key. 1 M.\ ~ . - . :1!: • J"\ .. w 1: f ~ y~ ..... 1..- ~, ..... '"Z~ ~ ~ _ .. '( -- x: The two lACs, with melodic 4-3 suspensions (measures 4 and 8), result in reiatively inconclusive scale degrees 3 and 7 respectively, with the move to dominant harmony in measure half cadence tonicizing therefore, in the is arrivaIs on the 8 home dominant in being expressed key. The the subsequent as a effect of ponte, to strengthen the role of the dominant, providing more tonal contrast before the Lonic is reconfirmed in the final phrase. By contrast, following: (2) a H. 193 in G major con tains the (1) a PAC in measure 4 rather correspondingly strong than an lAC; tonicization of the dominant with a PAC in V in measure 8 rather than just a HC in I; and (3) tonicizing V as in H. th~ home measures. key and a ponte which, 228, rather than first moves immediately back to simply states V7-1 throughout its 4 c 23 '"'- ..... 1 .::-- - ;.j .... + "" - /l , • . -' ..,O'l\~·· 1 M.I':\- " I~ ==bl±:·: I~· • J ~'-r • :bQ l -f:- A :Ét= ... - . f-f -- -F r Given the tonicization of function ~t"-= :E::= :r r tne -- ./"\ of the in mea&~re 8, the dominant ponte, therefore, rather than being to further strengthen and intensif y the dominant as in the above case, i3 to direction by immediately turning home key, ensuring that the stabilize the tonal back to dominant V7 of the area is n~t overly prominent in such a short work. A further case is the G major Minuet H. 231; - 24 . r weIl, the components cohere in a unique way. here, as A slightly more extravagant of the two works ii chord and a tonal palette than those just mentioned includes a tonicized chromatic bass motiorr into the He in measure 8: -M. f oJ .. ,... • . :a . .fA. . .. . ,. - 1 , IJ .. !: . r.T ,...-~ . " . ...: " .. yS" ~'I Seemingly as a result, the ponte is that much more adventuresome as weIl, remaining four measures. Subsequently, in V the concluding phrase is expanded from four to six measures: ---.. , ~, throughout aIl 25 - -'on.+t." ri------------~~~------------~Ir___------- m.'~ ,J ~ ..... ~ " ... - .. . . ~ !~ .. • ":! -= .. ..J -. y- This playful alteration of the 32-measure norm clearly destabilizes the regular phrase structure; at the same time, though, it balances the strong emphasis placed upon the dominant a few measures earlier by providing extra breadth to the return of the home tonic. The 196) reader would find in the other minuet (H. another interesting example to considere In aIl four cases, the specific weight of cadences (IAC, PAC, HC) and strength of harmonic direction (whether or not a tonicization occurs) in the first section imposes conditions for the specific content of ( for what function it tonal coherence of the the ponte, and will fulfill within the overall work. Thus the choice of 26 content for eaeh phrase slot in these pieees fulfills not only general requirements of style and form as 19, but also specifie desire for coherence and were diseussed on page conditions arising from the ~dch correspondenee of aIl material within each work. Of the mentioned four ie categories previous the discussion relates to the and periods, and, by movements based of the above second, options in phrases extension, to the fourth, whole on a common design. combinatoria combinatoria chapter, drawing attention to component ~ ~ lends an By isolating and phrases in the form, analytic framework derived from a meehanistic perspective to what might be termed a 'generie' approaeh to phrase and form analysis. may weIl be, though, practice ~rs eombinatoria ubiquitous to the isolated models; language and point ~ construction in of phrase preeluding compositional structure is clearcut and proeess may weIl be Ratner hints at this when he notes combinatoria characteristic terms of compositional the whole eighteenth-eentury musical saturated with it. that that in It of often at this level "points eighteenth-century practised by to a musical eomposers and frequently sensed by listeners--the interchangeability of melodie components."<4> <4>Ratner, "Ars Combinatoria," p. 353. c 27 We turn first now to work rather generic analysis, thorough analysis of the H. discussed, combinatoria, on the a more than offers 228, simply its own musical construction. in which amplifying !!.!.§. more ur.ique perspective The lively contours and rhythms of this piece derive from four basic motives, two of which are melodic and two rhythmic: x ;~ 1+ ~ -4 1- J'J The way '/ • • J: i • • • % are built out ~f mechanistic procedures JJ/J JjJ J -41. phrases in these both halves of the work motives calls to mind the of!!.!.§. combinatoria. AlI four combinations of rhythm and melody, X+S, Y+R (see above) are .. R dl J J' in which • X+R, Y+S, and systematically explored in the upper line at the entrance of the respective 4-measure phrases. The following chart summarizes (omitting the 8-measure repeats in each half): this ....". 28 ~ Upper Line Measur.e ~ 1-4 X+S 5-8 Y+R 17-20 Y+S 21-24 X+R thus combinatoria generating plays contrasting yet an important related role melodic in ideas for different phrases. Since this work texture throughout, combinatorial we in can In X+S, X+R, doing two-voice contrapuntal consider what the are for two contrapuntal Y+S, and Y+R as composite we find that there are ten combinations, including those four which use the same composite motive so a further possibilities lines involving motives. is in both combinations which use voices. For each of the six different composite motives in each voice, there are two vertical permutations depending upon which material is which in the lower. possibilities. If placed in the upper voice and In aIl, therefore, there are sixteen one wished to consider melodie or rhythmic components alone, they are embedded within these possibilities as S ) R R S for rhythm and v.. y '1 ,) X for melody. -..... With these possible motivic combinations in mind we r 1. can expand the ------~---------------- formaI ------ diagram shown on page 19 to ( 29 incorpora te those Bach uses in this work. Some of the more 'creative' and less 'systematic' details, which will be discussed later, are not taken into account by the following diagramj it does, however, provide of how rhythmic and diastematic an overview figures interact systematically with the phrase structure and form: 's.,\" "C.~'Of\ IM I~.~ .\ R" X+,. \.M ~+. ",.-- 'M&.' y'." ~+& 1: 1: ~.~ 1: ~ 1:"(, "'" \.M "t+R "-+S 1: 'J: 1: ,,<. 1 I~.U' .'1.\ ~""tt '-'c:. .., ..... '11: ) \,. tcw\~") T ~~c.. ~.\~-1.4 CIÇ. l ""'. "'f'~" ~~s 'E4 - J l: ,... ........ l "'" ..., .. ft. ..,'.R 'lA"'• ...-..n- ~ ...,.~~ 1M.\!. 'Ii. + '-'(. '1~ su.~O~ "~.\~ """."'IQ. CIÇ. M. '-Il.......,. 'JG."'~ -... ",,- '1, ........ 1 "'...s lC.+.s. 'te • J: ~" .. o~.. ) In this diagram, y' indicates that leaps are ~"c:. embedded in the overall stepwise linear motion derived from Y for the purpose of gaining a higher register. Sever al of these instances are discussed further along. Bach ( also plays direction of the individual general possibilities with long-range lines in this contour and work. Two are relevant here: contrary motion 30 (including oblique motion as a spe~ific type) and similar motion (including parallel motion as a specifie type).<5> By considering upward and downward directions separately, four possibilities are generated: 2) 1) 3) With these in mind, we note measures 1 ~ to 3 hands: .---, to coyer 4) that the consists of contrary motion between the This gesture is inverted aIl of measures 17 32) Bach and eX1;ended through 20. phrase in measures 21 through 24 29 through opening gesture in (and its provides contrast In the final repetition in to this contrary motion: both lin es make their way in simi1ar to the cadence. In a1l, three combinations are used to provide overt begins the first section, ~ --.. motion down of the above four contrast: -.... ~ begins the second, and :::::::: is found in the closing phrase, as though in answer to the other two. Ars combinatoria is thus used prominently in interrelated parameters and variation. In to provide addition, more s~veral systematic contrast subtly fashioned details add vitality and finesse to the above mechanistic features. l In comparing the first and second phrases, for ,t <S>More specifie distinctions are not necessary in order to capture this aspect of the work. ( 31 example, we note not only the 'mechanical' exchange of the motivic material X+S and Y+R but also the changes in between the melodic two hands, contour material undergoes when it is transferred which Y+R from the lower part in the first phrase to the upper part in the second: H.l.l!a M.\-~ - X+S ~ ".., ... ~ ........ ..J • - -~ ~ '1+4\ ... ... .. "'l . ,- • - 11 ......, oJ Besides the obvious .... --overall -.,. ... f: --- ----' I.J ~ ~ .. ~. ~ ... change descending motion, the stepwise from ascending to bass line through 4, when transferred to become th~ in measures 1 upper part in 5 through 8, now contains a leap of a seventh from and, instead of (corresponding to sixth to D. an the bass octave leap in measure in 3), a C to Bb measure 7 leap of a These changes add a more melodic character 32 to what was originally a simple bass line, as weIl as providing embedded repetitions of materiai from the first phrase, as shown below: fO\." "".S J Jg lb,It1r t 1tri r tir e j t 11 '--_---', , 1 1 --1 J..'_ _ ~'-- The varied repetition in measures follows the same procedure of exchangir.g 9 ~~per ~hrough 16 and lower parts for its second phrase and reaches the same harmonie goals. to The following example shows those noted above occur that changes similar with regard to these t«o phrases: "'. '!o-'~ Si r t 1 t ----:"1-, 11 r 1, ~ ........ embedding CT of X stepwise contrary motion. through 28 then 1 r measures 17 In the ponte in similar !: focuses Î t '7 1 through 20 there is a contours within predominantely Its repetition in measures 25 on an arpeggio figure deri ved ( 33 from measures 19 20. and The following example summarizes these points: '"'. 1. '1.8 M. x \1·-1.0 ... r 1 ... _a -' '..(1 <.J ~ .... ~ 1 r . • :.f;~~ .. ~. \ The underlying counterpoint relating aIl material in both of these phrases to parallel tenths with a the Y motive consists of stepwise sixth move to a higher register: ( interspersed to effect a 34 ---- - ~, ... .... \0 \0 \0 \0 \0 \0 \0 III. 1 '" 1 \J ~ .. t • le) manifestation of last phrase, upper part \0 • ta ... lua) \. \0 ~ The final in the . - • measures 29 embeds Y+R within humorous summary of the ~+S, previous embedded motives occurs through 32. Here th( as though to provide a combinatorial play of motives: )(+s ........ This and the preceding type ~ of presumably examples of combinatoria because it is not ~mbedding suggest explored by Ratner a J not related ta compositional & c 35 pedagogy or main musical games of the eighteenth century (his sources), embedding one namely within other. This type and more a hierarchy--and the combination the overriding of combination encompassing th us motives by framework of the requires both context--in relates of to other a local words, hierarchical a analysis involving concern for the interaction of middleground and foreground motives. Besides this, the form ~ of Ratner's combinatoria in H. first category with the generation of composite motives from a fixed set of rhythmic 228 also takes figures. As weIl, his diastematic and second category is relevant to the extent that musical content at the phrase level was seen to exhibit some use of combinations. scope here is broader however, because than that this The of Ratner's discussion, content includes not only diastematic and rhythmic material, but also such features as the switching of material between hands, different combinations of ascending and descending lines, etc. of these uses of ~ combinatoria result in an aurally tangible motivic coherence within this work combinatorial listener. c aspects are readily AlI in which the apparent to the 36 Conclusion In comparing the works chapter we noted that Bach model to generate aIl emphasis and considered uses of them. strategy, giving balance between the used in point each work analysis. made phrases and basic formaI its own unique tonie and dominant areas, were discussed different options was same Differences in harmonie as an example of how the mode! of variety of early in this In this periods and design with a for filling it in might be section of ~ that a fixed the chapter the combinatoria to whole as applied to movements (Ratner's second and fourth categories) reiterates from a different perspective, but does not necessarily of fer insights into, new analytic a more basic or generic 3pproach to these pieces. Much more however, before it investigation could be would be determined needed, whether this observation holds true in more general contexts. We saw as weIl, in H. constructed to a large combined and arranged ~ inter-related parameters. example at We but from of a work systematically gestures, cornbinatoria combinatione an extent motives, demonstrating rnechanical 228, and contours, work in a nurnber of considered also sorne not only of Bach's more artistic finishing touches involving surface details. Within procedures these of ~ short pieces cornbinatoria by Bach, rnechanistic can thus be considered 37 ( constructive compositional tools into which inventiveness and artistry of detail resource reflecting are one injected. or an analytic more parameters within the inherent structure or these works, flexible--capable providing a different way of both of thinking about more standard modes offering its own unique insights. (~ As ~ of combinatoria is analysis and of CHAPTER 3 A DIFFERENT CONTEXT: THE FANTASIA IN F# MINOR Introduction In the previous broad description of relevant to chapter, ~ several of galant-style compositional handling models, Bach's which clarity and models such aIl relate to style. In the examine the Bach's works inventiveness important ~ in factorG. combinatoria outside this 1ight, popular present chapter, therefore, we shall of G~t~n~ion conception 'mechanicé\l' pragmatic and balance, simple Bach's are more accessibility to Nothing was shown, however, about how might of Ratner's combinatoria were shown to be compositions--compositions in beginners, aspects of of mechanistic principles to the genres in most free and his oeuvre, the 1east free fantasia. The work to be considered, Bach's Free Fantasia in F# minor (H. 300), was written in 1787, and had not been pub1ished by the time of his death - 1' later. The title commonly ascribed "C.P.E. to thia just one year Bach's Empfindungen" is work, although in fact it ( 39 actually appears on the made by Bach for clavier and manuscript of manuscript of an arrangement violin, and the original solo clavier version which is the subject of this chapter.<l> differ very little in and thus the William S. vhich we title may seems the safely for applicable two versions to both. As this is one of the few works assume its product The essential content,<2> however, Newman notes, consideration instead not on the was written without world1y success, and which is of Bach's own inner feelings (nEmpfindungen").<3> In this considering fantasia the aspects procedure of ~ combinatoria in will be as follows: Firstly we shall examine mechanistic aspects of Bach's concept of the free fantasia genre Versuch. the Secondly, as stated in his overa11 form of the F# minor Fantasia will be discussed, fol10wed thirdly by a more detailed analysis then conclude of its with a sections. summary The chapter will of observations concerning ~ combinatoria in this free fantasia. <l>Elinor Goertz EIder, "Carl Philipp Emanuel Bach's Concept of the Free Fantasia," CM.A. Thesis, University of Rochester, 1980), 92. <2>Ibid., p. 93. <3>Newman, Sonata, 423. This relates to Chapter l, footnote 8 (page 4) of the present study. 40 Bach's Writings on the Free Fantasia In the ~ wahre final chapter das Clavie~ of Bach's Versuch über die ~ SpieIen,<4> the topic of improvisation in the free fantasia genre is addressed, with prescriptions being given for how diatonic and to the former, chromatic fantasias. diatonie type may to crea te both Those which apply be summarized as follows:(5) 1) assume 4/4 meter 2) begin with an aseending or descending major or minor scale 3) determine (or select from options provided in the examples) an appropriate figured bass for the scale 4) interpolate half steps and their where desired figured bass 5) arrange the scale degrees between the upper and lower tonie in a desired permutation; i.e. these need not be in stepwise order 6) realize the progression with a mixture of arpeggiated and sustained textures To these are added the with a tonie pedal suggestion as weIl as to pedal just prior to the final tonie. these guidelines with to begin and end use as a dominant Bach accompanies a variety of exampIes--scales (4)References in this chapter will be to page numbers in the English translation by William J. Mitchell, Essay ~ the True Art 2i Playing Keyboard Instruments (New York: W. W. Norton & Co., 1949). <5>The following Essay, pp. 430-33. summary is condensed from Bach, ( 41 with figured bass, interpolated half figured bass, varied orderings of bass and pedal points with dimension of by selecting ~ figured bass. may with scale degrees, The pedagogical combinatoria is clearly in evidence: acceptable combinations and permutations from the options given in the student steps fashion a examples the uninspired reasonably correct diatonic fantasia of short duration. When a greater amount of time is available to the performer, Bach considers a chromatic, rather than a diatonic, fantasia to be more appropriate.<6> suggests, in addit~on Here he to the basic instructions for a diatonic fantasia (see above), the following:<7> 1) subject to nos. 2 and 3 below, any combination may be selected from the twenty-four major and minor keys and may be permuted as desired 2) one should not simply move systematically through a cycle of fifth-related keys as part of the basic plan but should instead use a non-systematic permutation 3) a number of keys distantly related to the tonic should be included 4) a minimum of two formaI cadences should occur in the fantasia: one somewhere in the middle and one at the end 5) for moving to closely related keys and for brief forays to distant keys it is sufficient merely to reach the leading tone <6>Ibid., p. 434. ( <7>The following Essay, pp. 434-38. summary is condensed from Bach, 42 6) when planning to remain in a distant key for more than a brief time this key should be reached via an extended harmonie progression 7) surprise changes in tonal direction are essential but should not appear too frequently 8) options for quick motion to distant keys are afforded by the three diminished seventh chords and their enharmonie equivalents In student addition with to two the above, The aIl minor.<8> other set contains III, iv, v, VI, and The second contains progressions to keys possess varying first each of the closely related keys: ii, iii, IV, V, and vi in major, and VII in provides the sets of modulating progressions in the accompanying examples. progressions to Bach which, because degrees of their tonie triads chromatic inflection with respect to the main tonality, are defined as distantIy related to it.<9> In order to gain the facility wit~ modulation required to improvise a chromatic fantasia the select student is encouraged progressions and combine transposing the to thew one progressions as after a number of the other, required in or der to move from key to key with smooth voice-leading. These guidelines for chromatic fantasia somewhat more the harmonie design of a are less directIy prescriptive and complex than those for the diatonic <8>Ibid., p. 435. Upper and lower case Roman numerals indicate major and minor keys respectiveIy. <9>Ibid., p. 436-37. ( 43 fantasia, thus requiring more taste and discretion on the part of the performer. teaching of ~ attitude in the both types, however, is clearly allied to combinatoria--to and Bach's stating setting available combinations and basic plan, options This fixed conditions from which to select permutations iD this fantasia. forth of components for a case the figured bass plan for a chapter from Bach's Versuch could therefore be added to Ratner's long list of sources on compositional pedagogy which demonstrate a certain degree of mechanistic thinking in how they explain the manipulation of compositions. category, keys in musical It ~ cûmponents furthermore in enhances combinatoria applied to the a composition, creating his ordering of since Bach discusses not only the possibility of different permutations of combination Ratner, but combination, of diatonically also and that any third of related keys choosing permutation a single as did almost any thereof, from the entire set of twenty-four major and minor keys. These possible possibilities arrangements guidance for how to permit of make keys, artistic a large but number of provide little choices regarding such arrangements; for example, little mention is made of the different functions ( tonal structure--a topic of keys more within an overal! in keeping with .. 'C N .' 44 Schenker's organicist mechanistic view. setting forth view Instead of it than music a more is available options, with a matter of following which the good taste of the composer-performer must decide which combination of Bach selects in the F# analysis. of options is best. and arranges minor The means by which chromatically related keys fantasia will be considered in our These means, as we shall see, include a set inter-related chroma tic voice-leading operations that determine certain combinations of keys as weIl as their possible permutations. linear coherence and These operations provide to direction sorne of the modulatory sections of the work while at the same time creating a sense surprise they conventional of spontaneity engender harmonic and surprise aesthetic and stylistic which to sound the point This syntaXe coherence is from is in goal of because of view of duality accordance of the of with the Bach's fantasias, improvised--to "come as close to incoherence as possible," states.<10> Form is anothar achieving this goal, dnd it is as important to this writer one factor in topic that we turn as we begin the analysis of H. 300. <10)Schulenberg, Instrumental Music, 161. ( 45 Form .il!. lli Free Fantasia i.!!. Playing with FI Minor the listener's expectation of form, as Sehleuning notes in his study of the free fantasia genre, is a resource of which Baeh made increasing use in his late fantasias.<11> This work is no exception. It is based on two contrasting but motivieally related themes both of which on. The largest entire work, tonie being are presented relatively early level of tonal motion, spanning the is i-iv iv-i, with the return to the preeeded hy what May properly be called a development section in which both themes are explored in various keys, as we1l as by a loose recapitulation, in the key of iv, of much earlier material. The overall formaI effect, as the diagram below indicates, is that of a three-part design with both strange and familiar aspects: <ll>Peter Schleuning, Die Freie Fantasie: Ein Beitrag ~ Erforsehung ~ klassischen KlaviermusIk7 (Goppingen: Alfred Kümmerle, 1973), 264. 46 ," P~'lT P"'T \ 1. ~~,+iA ~ r.\ob.\- Mo4..\- S~\&""'C4. ~ ---____-r---__ ~~-+ 1Th,,,,,, , ~'q.u4f1~ ~"MII. 1. I--...- _______ ...__-'., ~~ l'A~ 1ft i -- E",,~,o .. CIj. 'A_"" \ A"~o. The familiar aspects, notes Schleuning, suggest sonata form influences<12>: two contrasting of free passage transi tions, reflecting and an work three themes, sections functioning primarily large-seale as divisions exposition-development-recapitulation <12>Ibid., p. 263. Sehleuning ineludes a diagram of the form similar to the one presented here, but whereas his indicates harmonie motion within each of the ten subsections (without distinguishing eadential from non-eadential arrivaIs), the present diagram foeuses on the long-range tonal motion of the three main sections. 47 design. familiar These coun tered by a subordinate aspects, key unconventional recapitulation area of i v, different meters far as the form of elements of the final for themes 1 and 2, and Schleuning even by other easily discernible factors. goes so to suggest a three-way ambivalence in this a work, single which, sonata he notes, combines form movement, movements of a sonata, and a free fantasia.<13> such a by an in which theme 2 is not heard until a brief statement just prior to cadence, by are ho~ever, large-scale application combining aspects of different of ~ t~o While combinatoria-- forms--may or may not have been Bach's deliberate intention, the main point, J it seems, i s tha t the use various conventional 0 f fami liar componen ts 0 f forms in unfamiliar arrangements and combinations engages and deceives the expectations of the listener as part of the overall strategy of projecting a sense of formaI spontaneity. The clever design of the two themes goes hand with elements this strategy. of the first contrasting, yet a very The second transforms many so as a slow tempo. The to important intact: both themes begin with an at hand in sound thoroughly feature remains open fifth sonority result is that as the work unfolds Llere are moments at which the listener is not ( Il <13>Ibid., p. 264. l 48 sure wh1ch each has Schleun1ng of the two themes been established indicates 1s about as an to enter, as option.<14> these transformed and preserved features in an example which 1s reproduced here ta illustrate the above po1nt:<15) AlI of these aspects of the form--the design of the themes, discernible sonata form elements, combination of differen t combinatoria applied on a Ratner's because categories the sense of an number of variables. genres--reflect broader scale original form and the than any of these aspects relate ta emerging from a large In other words, Ratner's fourth <14>When the performer recognizes this built-in source of formaI uncertainty and reinforces it by not rushing the beginnings of theme entries, the effect is that much more successfully achieved. <15>Schleuning, Freie Fantasie, 265. The heading in this example reads: Adagio III (chosen instead of Adagio l in order for correspondence of key with Largo 1). . 49 category goes different on!y as realizations far of ~ as a combinatoria in pre-determined forma! design, a small sample of which we saw in the previous chapter with the comparison the same binary design. of different works from In this and other fantasias, however, the forma! design itse!f is susceptible to being changed depending upon how forma! components are ordered and combined. Thus the listening process includes such questions, conscious or unconscious, as: Which of the themes is about event be to recur? prolongational? Transitional? Developmental? What kind of form is emerging? ~ Will the next combinatoria This broad concept of thus helps to explain how a sense of 1 formaI spontaneity is achieved in this work. Analysis of the Sections We turn now to main goal resources is to Bach relationship to a more detailed elucidate uses ~ in this sorne analysis whose of fantasia f.2mbinatoria.<16> the chromatic and their Although a <16>The reader should note that in this analysis such terms as 'modulation' and 'key' will not necessarily be reserved for more long-range events, as in a Schenkerian analysis, since we shall be focusing on technical voice-Ieading aspects of various passages rather than on their function within the hierarchical tonal structure of the work. As is weIl known, concepts such as modulation, tonicization, tonality, and key tend to vary in meaning depending upon historical era and analytic approach. These issues are addressed in Richard Bruce Nelson, "Theories of 50 comprehensive analysis shall by Italian may through the work, turn each of the ten sections indicated tempo markings, consider the intention here, we sequentially proceed discussing in is not not only in order that the reader chromatic areas but also the broader formaI context into which they fit.<17> Since the 1 (as three opening sections comprising Part indicated by the chart on page 46) offer only a slight introduction to later chromatic activity, the topic of ~ combinatoria resurfaces only discussion of Parts 2 and 3. in introduce order to the in conjunction with Part 1 is included here first instances of chromatic-enharmonic progressions in their context. PART 1: Adagio The theme opening 1, in respectively. Adagio the presents tonie Unlike theme two and statements of subdominant 2 which keys enters later in the work, theme 1 does not possess a regular, perioaic phrase structure, being instead more aptly Harmonie Modulation in Selected German Treatises of the Eighteenth Century," (Ph.D. dissertation, University of Rochester, 1983) and in William J. Mitchell, "Modulation in C.P.E. Bach's Versuch," in Studies ~ Eighteenth-Century Music: A Tribute to Karl Geiringer, ed. H.C. Robbins Landon in ccllaboration with R.E. Chapman (London: Oxford University Press, 1970),517-25. <17)Also, in light of the fact that there exist long spans of music without bar lines, it will facilitate discussion to refer in turn to each of these ten sections. ( 51 characterized as a thematic continuation and elaboration. receives a with rather free The second statement different continuation moves to D minor, P~!r idea from the first and vi of the home key. \ • A~!2 • \:.t 'l'Ig.\.;. "\ """fWL \ (f'\"u.a c:.oW\Ti f\U~~D'"~ -tc.M"I\"\f'\\ao.:t - ----"QI'--lr-----ll ------------1 Th\.M." , \'1 ~ '-------------~-\-----------'-~~,~----~----=-~~~-------~-V\ It is subsequent to this D minor ar~ival that we get the first inkling of the chroma tic breadth of this fantasia. Here the bass note D is retained and a fully diminished seventh chord unfolded over it: • • " This minor ( vii7 both vi promises a in spelling figuration (not shown in return and to the home key of F# in the right-hand the above reduction). The tonie is not reached, however, as the vii7 of F# minor ..• 52 is treated to of one its possible many reinterpretations. In addition to reearding each note of a potential leading tone, the most the chord as common means of using vii7 enharmonically, exists to treat any of the the option tones as an appoggiatura and move it down a semitone to become the root of a dominant 7th chord: J ..... In this instance Bach moves the fifth, B, down to Bb, the root of V7 in Eb minor. ~.p. The surprise of this effect is enhanced by transfer from upper part appoggiatura B to Bb as functioning to D. weIl as as Since a by the dissonant D the octave Eb in the ornamental is the only tone not enharmonically reinterpreted or chromatically shifted, - this Eb to D masks the more structural appoggiatura, B to Bb, further ohscuring the true nature of the -------~- ~~--~------ ( 53 progression. Although spelled as V7 of Eb minor, the Bb7 chord in question resolves as a German augmented sixth chord to V6/4 in D minor, reinforcing the importance of D as a common tone through this passage. not resolve but is This V 6/4 does instead followed by a series of secondary V7 chords pointing to G minor, A then B minor, and minor which moves to a weak arrivaI in E minor at the very end of the Adagio. Allegretto The passage work of the above E minor this Allegretto arrivaI to C shifts from major and tonicizes F major, presenling earlier motives the double neighbour and transformed setting. to confirmation one of the of F chromatic A then such as the lower appoggiatura in a long dominant major ls pedal pointing thwarted, however, as possibilities inherent dominant seventh chord is suddenly realized. in the - 54 By chromatical1y contracting the inter val between the root and fifth so that C and G dominant seventh realized, with a of following B minor, which strong authentic become C# a the tritone away, ls Allegretto concludes cadence in B minor.<18> two chromatic voice-Ieading techniques resolution appoggiatura and F#, the in the The seen thus far, vii7 chromatic contraction in the V7 chord, chord and will both play a significant role after the next Largo section (to be mentioned onl] briefly). Largo At this were point, theme 2, whose characteristics with those of theme 1 in an earlier 48), is compared example (see page subdominant key. introduced in G second statement Adagio, which the After a fluctuation between B minor and its relative key D major, the head again stated in minor in 1s of theme 2 is the ninth measure. This interrupted begins the by central, the subsequent developmental section of the work. PART 2: Adagio In the development section Bach explores the themes both of and as weIl plays more systematically with <18>Although Bach introduced the subdominant key ear ly in the work, this is its first cadential confirmation. The approach to this cadence through the tritone-related key injects new interest ioto the arrivaI of this large-scale goal. ~~---- .. ': ~. - -- - -~ - -~--~---------------~------------ 55 chromatic contraction and appoggiatura resolution, beginning in this Adagio with chroma tic contraction of an interval in a dominant seventh earlier, we recall, tritone this substitution the significant those that technique just theme 2 (see page 53). chord. prior When used resulted in the to the entrance of To explain more fully, aIl of applications of this technique, i.e., yield the same chord type (a dominant seventh), are as follows: t.."'f"QPNa.~ C. c.owft~+"Of\ Qf S"1I't\ -, 13J1tft§i t"' ..._.. ~.:c. C.D~"'C.~." Of these, successive ) contraction between the root and fifth results chords related of ~ycle the the in a interval cycle of two by a tritone (the tritone substitution se en earlier), successive contraction between 00+ '!..-& root with roots a of the interval and seventh produces a four-member minor third apart, and successive contraction of the interval between the root and third produces these same four the reverse permutation. dominant seventh chorde in - 56 Nowhere are such cycles indicated in the Versuch. The opening however, model-sequence demonstrates section that successive seventh, a chromatic one-measure sequenced twice in exact this Adagio, Bach is clearly aware of them and the harmonie variety they three of model afford.<19> contractions based form and on Using of theme the 1 is a third time in a varied and expanded form: <19>The author learned of these cycles from Professor Bo Alphonce in the context of his nineteenth-century analysis course at McGill University. To take an example from another work by Bach, the Rondo in E minor H. 272 (Wq. 66, whose full title is "Abschied von meinem Silbermannischen Claviere in einem Rondo" [Farewell to my Silbermann Clavichord in a Rondo]) contains such a cycle in measures 57 through 59, just before the final statement of the refrain, en route from G# minor in measure 5S to A minor, iv of the home key, in measure 60: 1 1 ... ... ~ \ - ... ...... .. • .. ...- \,. • ~ .. • • • ... 1 As indicated, the route is indirect from the first to the second stages, but then direct until the fourth, which subsequently resolves as a functional V7. 57 ...." "'.u.o.",1 "" - .... os. ..t:!:!:f\t."- If r f .m .=n' 11 1 p r'T'l ---,;,.-- - -.;;- ..-. . - f 1 ,....... -- - - - - - - - - - - - - - - - - , ~ ~ 1 1 1 - c.ru - .-..l~'r\oft: ï""'1 ~ u," - cl. .~ ~ • p 1 .. r-------, 1 ft --~--~-- 1 . The pattern four th is broken dominant in the fourth measure, but the seventh of Stated eventually reached. contains its to seventh, F7, cycle, in root cadential six-four, it points arrives the position with a Bb, which pointing are then stated in that key. rather than to make preceding of dominant mentioned, the third chord ( of theme Eb minor,<20> resolving it functionally Bach uses this chord, Ab7, cycle Eb The third measure begins as expected, with V4/2 of vii in but when it to Eb. minor is reached, and the first two measures 1 is a last reference sevenths. in that to the As was just cycle, G#7 (=Ab7) <20>Compare with measure 3 of the opening of the work in which the corresponding chord is V4/2 of yii in the home key. \ ", ; .1, f- ~ 58 led only indirectly to the fourth, F7. Now Bach makes the connection explicit; The F7 chord then Lesolves functionally to initiate a section in Bb minor based on theme 2. In the leading above Adagio operation, chromatic seventh, determines in tae cycle and they will contraction of the both the combinat ion of harmonies the occur. it is clear that the voice- specific permutation In determining in which why Bach began the development with this cycle we can look to the opening Adagio of the work for one reason, specifically to the passage, already discussed appoggiatura resolution in detail, containing an of an arpeggiated vii7 chord. The four pitches of this chord, recalling the example on page E# (=F), and they are 51, are D, B, G# and followed by the V7 of Eb, as mentioned. dominant seventh concludes with chords are chords opening V7 of the same, Eb, and and in The cycle of the development also the roots the same of the four order, as the ( 59 pitches of the earlier vii7 • • The underlying • • linear qnfolding of these four p1tches culminating in V7 of Eb (minor) 1s thus a common structural feature shared by bûth sections, suggesting that the latter madel-sequence section is an expansion of the earlier arpeggiated diminished seventh chord.<21> Largo As vith the based on preceding Adagio, section is madel-sequence behaviour and employs earlier chroma tic linear motions more choice and this ar~angement of fully ta determine the transitory harmonies. The averall direction of the sequence is a stepvise ascent from Bb minor digressions to be to C minor ta D minor discu8sed, ta E minor--a tritone removed from the starting point. a verbatim statement of the first in Bb minor, and, with After beginning with measure of theme 2 the second measure is altered by the use of an arpeggio motive ta move from Bb minor ta C <21>Even the characteristic 4-3 melodic motion (Eb-D) in the upper voice of the earlier instance i8 retained within the latter Bb7 chard. - 60 minor.<22> ~1 \.A"IJ' ... ~p iI~ ~ -- r-ï p ~ f a~ In ~ ,'" ~ "',,,... the second second and ~/.. ~ li " measure, the relationship between the third appoggiatura vi'·~ chords reso1ution: is the again that invo1ving fifth of vii6/5 of iv, Ab, moves to G, thereby creating V7 of C. The move from C simi1ar fashion. different ear1ier is enharmonie chroma tic are used D minor is treated in Once D minor is reached the pattern changes, and E minor circuitous minor to reached changes on1y of voice-1eading here one after severa1 direction. techniques Two seen after the other, as tha examp1e shows: - ! <22>It is interesting to note that this same quick arpeggio figure was first used in another chromatic context, namely the tritone substitution preceding the first occurence of theme 2 (see the examp1e on p. 53). c. 61 -. 1"" .. J.. --- .--.. ,.....,..-, "- .. J.J. ? v .. ~ " of departure iv, G minore of vii7 of j . y ..-- ,- ~ v I~. ~ The point - ,- v .. v l J.. J of ". f 1 ... r of .,• in the first measure above is Beginning in the next measure, the third in G minor, A, is moved down a semitone to produce an Ab dominant seventh chord, thus redirecting motion from Two of the common then G minor maintained are contracted the span of minor, to the (=Gb) and upper occurs: the to yield two itq FI tones, in enharmonie change to its tritone-related key Db. as yet another root and V7 of measures tritone part Eb (=D#) are E minore the harmony relation third of Ab7 Thus within points to G Db, and then up an augmented second (minor third) to E minore Bringing combinatoria discussion, we note that back into the a remarkable aspect of this passage is the fact that these three harmonies, G, Db, and E, were the full cycle of preceding first three dominant Adagio. seventh Whereas order of descending minor (~Db» (see goals pointed to in the the example on contractions there thirds ~age in the they appeared in (V7/G, V7/E, V7/C# 57), here a different , \ .... 62 ' permutation reverses the order of the latter two so that E rather than Db is the last arrivaI. able by to vary the permutation relationship between the techniques seen two thus far. Bach was exploiting the chromatic voice-leading This relationship may be summarized as follows: S:IJI ,1 ;.,. Il As the example indicates, V7 and appoggiatura a itd chromatic contraction resolution in a in its related vii7 form a limited set of operations that allow for direct motion from any given V7 or another V7 a minor third above, or a tritone away. its related vii7 to a minor third below, In the above passage from the development section, as discussed, 'third-appoggiatura' ta Bach first uses a point to the tritone-related key and then a chromatic contraction of the third to point up an augmented second (minor third). The move to E minor enharmonie key changes brings that ends the above the development section c. 63 back into minor. the diatonic realm of the main tonality, F# Within a sh?rt time, with arpeggio passage and the the section pedal point elaborates vii7 of B minor, ~ork following Adagio opening an extended then initiates of a return of the work in the subdominant key. Thus far in the work, we have seen several chroma tic voice-Ieading options for dominant and fully diminished seventh chords their possibilities introduced in Part explored in Part 2. 1 and The examples discussed are intriguing clues as to how weIl Bach may have understood sorne of the more systematic properties of the mod-12 pitch ) underlying tonal class world context. regard beyond relates to an In the Versuch discussion summarized earlier in this this a3 it chapter he citing the says little in importance of the diminished seventh and offering several examples whose implications are Ieft to the reader. Appoggiatura motion is indeed included in these examples,<23> as is a strange chromatic progression that contraction of very nearly constitutes the third (with an intervening chord):<24> <23>For example, fifth measure. (~ <24>Bach, Essa!, measure • see p. page 438, 438, figure figure 476 b, 476 b, tenth 64 1 J .; ~ " 1 ) \J ~ .. 1 \ .... t, 4Ft-.,~ 1 Had the ;~ I\-i- 1 final chord retained a C# as its seventh and the intervening chord been omitted, as in paren theses , chromatic this contraction would of in the version indeed the third be in a single a dominant seventh chord. In studying some of the modulatory options used by Bach in this work, we find that the options combinatoria with respect permutations of keys have to gone of combinations weIl ~ and beyond Ratner's original description as discussed in Chapter 1 of this study. with Ratner's categories the general are set stylistic forth in keeping context century musical language; this work by of eighteenth Bach, however, stretches these categories in ways that go weIl beyond typical contexts. seen - daring thus far, chromatic Besides Part the keys and modulations 3 of the work contains another progression for which i } combinatoria offers an insightful explanation. ( 65 PART 3: Adagio Whereas this fantasia began theme 1 (with different respectively, the with two entries of continuations) in i and iv present Adagio does the reverse and moves from an entry in iv to the beginning of an entry in i. The and moves latter entry breaks off after one ffiéasure into a new Allegretto, interrupting the recapitulation process. Allegretto Here ornamental scale spell out a descending including secondary work and broken chords fifths sequential progression dominants. The overall motion until the resumption of the Adagio in the next section is from i in F# minor (at the end of the previous Adagio) to C minor harmony, a tritone away. This loss of the F# minor tonalitj is due to VI7 moving not up a tritone to ii of F# minor, but up a perfect four th to bII, G, and then on to C. As with progressions in interesting harmonies. cycle, Bach ways previously this work, discussed the pattern sequential is varied in involving colourful combinat ions of When VI, D major, is reached in the fifths dwells on this harmony before adding the seven th, C, to make V7 /G. fashions a stepwise linear in the cycle, G7, which in Wi th C in the bass, he then descent to the next chord turn resolves to C minor. G 66 This linear descent con tains model-sequence behaviour and is harmonized in a daring manner, as the example indicates: ifr \~ ~ !I i J: fi 1 ri ;'1 ~~:~ _Ip-} .J Co Mi f\ Recalling evants of the development interesting light on this progression. series of The following examples indicates the new combinations and permutations of these few section sheds development chords. The first direct progression from D7 makes reference material to a condensed into example shows that the cadence in back to the Adagio of the development section by immediately juxtaposing the first that cycle of goal, Eb minore - 1 t, Eb minor dominant sevenths chord of with the eventual 67 ( ~ ~ .... ~ ba - li q- E~ """ The next example indicates that the two first stages in the dominant seventh cycle of the development form the first two steps of the sequence of the progression in question. explore It that is cycle recapitulation as if again, process by Bach but were beginning to instead resumes the returning to Adagio material. Il The final example shows that the progression which was used to usher in the fourth chord of the cycle development progression: ( is transposed here in the to become the model 68 J~ r==;=t r"'"u. - ( V i=F= 1........., 1 1 t s:- 1 I ~ '1. 1 • 1 3 =· ""~ In terms "rn- G of harmonie syntax we could refer to the use to Eb minor and V7 in the goes beyond such move from V7 of E to C minor;(25) an understanding of the role played by however, \."i • of modal mixture in this passage of J • ars combinatoria, a label to show how this instance of modal mixture relates to other sections of the work, summary i.e. that it pro vides an intense and daring of aspects of the development section by recombining them. Concerning the remainder subsequent Adagio continues of the opening Adagio, to of J work, the recapitulate material adding extensions that point more and more ....... , the adjustments to the and home key • (25)In other words, each dominant resolves deceptively to a minor chord on lowered scale degree 6. ( 69 This section concludes on following Allegretto which vii7 of i and arpeggiated then redirects launches motion into an back to elaborate progression. Just final and tonic to enter, however, Bach adds one last surprise. Theme 2, listener we cadential V7/iv, precipitating the expects recall, was recapitulation with one the not of last dominant stated earlier at aIl material; reference to this as during the the Bach concludes theme--its only appearance in the home key. Conclusion This chapter of Bach's began by guidelines for These facets in general conditions and range these of a straightforward, possibilities seemingly noting mechanistic facets improvising free fantasias. consisted of variety options such in endless, as the as of different options, the being when examples, in providing fixed the in Bach some himself listed and, case cases in others, of options for cornbinations and permutations derived from the twentyfour major and minor keys. The detailed analysis of the Fantasia in F# minor focused on this latter case. one ( set of voice-leading chromatic contraction and In doing so, it revealed operations consisting of appoggiatura resolution to 70 be a means used by Bach to determine the possible combinations and permutations of transitory chords and keys in several this analysis, one ~ particularly passages. In the final section of combinatoria daring offered insight into progression derived from earlier materials. In order to approach form was this detailed first of a11 considered. the formaI design itself for different components, Here we noted that is variable and thus allows combinations and permutations of formaI suggesting characterizing ana1ysis the the ~ sense combinatoria as a means of of form experienced by the listener with respect to this work. CONCLUSION This thesis was motivated axploring sorne implications ot by an interest in combinatoria for ~ analysis of eighteenth-century music and used Ratner's exposition of the topic as a point of departure for an examination of several solo Based on Bach. pages, a keyboard works by C.P.E. material presented in the preceding number of intriguing issues could be pursued further. ) Firstly, results of concerning these the analyses approach could be compared second based chapter, on the a rnechanistic with analyses based on an organicist approach such as that of Heinrich Schenker<ù or Rudolph Reti ('l.) in order to determine complementary and contradictory aspects. both At one place in Chapter 2 the issue of hierarchy arose with respect to ars combinatoria in motives.~> An attempt ta (1)Heinrich Schenker, Free Composition (Der freie Satz), translated and edi~by Ernst Os ter (New York: Longman,1979). <~>Rudolph Reti, The Thematic Process III Music (New York: Macmillan, 1962). r . _'" .. ;, (3) See page 35 • 72 clarify mechanistic organicist and treatment, and to between similarities and distinctions of concepts motivic formula te these distinctions in a general manner, would be enlightening. Secondly, an third chapter enharmonie Some interesting issue is Bach's exploration of chromatic and possibilities of sense the within wide music in the technique of dominant seventh chord, means an keys of is system. options in suggested in order to grasp the full which he understood these options and, more importantly, put them to to tonal but it is necessary to analyse Bach's own most expressive extent to the spectrum combination and permutation of the Versuch, arising from the artistic use. chromatic for uncommon practice to contract the seventh With respect contraction example, it was in a by no in the eighteenth century once in moving from a major key to its relative minor: 1]).- 1 Bach's use of the full cycle of such contractions, not as a context theoretical of one demonstration of his MOst but rather in the powerfully expressive 73 " ( .- works, is significant. diminished type of seventh chord mathematical combinatoria but This and are his preoccupation focused more phrases, preoccupation, nineteenth and to related century, properties in the is more with tonal to ~ on the future of tonal manipulation of formal become of the indicative of another language than on the construction and motives, uses units. This widespread symmetric system. With and in the cyclic respect to C.P.E. Bach's contribution, this issue forms part of a larger question: enticipatp. To and/or what extent influence does aspects his music of nineteenth- century composition? Besides eliciting such questions as these, hoped that this thesis has shown that has a music, place and independent in the that, th~ory analysis al though ~ it is combinatoria of eighteenth-century not necessarily an in its own right, it is nonetheless a phenomenon to which the analyst should be sensitive, no matter in what context or style it arises. f BIBLIOGRAPHY Aldwell, Edward and Schachter, Carl. Harmony and Voice Leading 1. New York: Harcourt Brace Jovanovich, 1978. Harmony and Voice Leading 1,. New York: Harcourt Brace Jovanovich, 1979. Alphonce, Bo. "Haydn, Fischer, Bach." Paper presen ted to the Department of Music, Yale University, New Haven, Conn., March 26, 1987. Bach, Carl Philipp Emanuel. The Collee ted Works for Solo Keyboard. 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"The Living Work: Organicism and Musical Analysis." 19th Century Music 4/2 (Faii 1980): 147-56. APPENDIX 1 ~- r 1 ~ l' i t, l, t.fi' f " ll ~,. ,,- ( ::::- ..... +'- T 1"'.) ... ~ .. /l '-- - n ~ ..... --- . --- A ,J \ r\ù- po ...-' 1 ..-#*= ~ a ~-. '. f:~ ~. ..-. ~ - "" 1 l . ...., <"'V ~ c:-M " ..J /1 ~ • • -+1 " ,,~ - '" ,--. _1 -, • .-1- ~ .... rit'< 1 :J -.0.1. 1 - -.. - - -'" J ~ ~ . r -" ~ - . ... ... - .... -,.. -,.. • - -4L r- .. "• ~ • 1 T'" .... ~ 41 .- ..... • l 1 ... P'" . ... ...1 • J () ., c- ~ a - • ~ -... ~. .. , ..... e;-f= ...... ...... , -t.. • -...... 1 I - T .. 1 I ~.~ --.... 1 , -~ 'j!: ... -...... ) • , - n .... ... "lit'. 1 ~ \ a ,.~ 7 -- * ~ T .... .... .,.. ~ 1 ~.p.. ~ ---... C'M ~ - V ~ ( ( . -, \ • - -,.. 1 ... - - H. '" - , 1"!. 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