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Perciballi, Adam C.
Analytical perspectives of thematic unity :
b applications of reductive analysis to selected fugues by J.S. Bach and G.F. Handel
h [electronic resource] /
by Adam C. Perciballi.
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University of South Florida,
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Thesis (M.M.)--University of South Florida, 2008.
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ABSTRACT: Thematic unity in music occurs when elements from a musical idea appear frequently, in significant places and their presence is recognized or experienced on or beneath the surface. In fugal compositions, thematic unity is evident in the opening statement of the subject and it permeates each layer of its texture. Three analytical perspectives are used to investigate the degree to which local thematic material anticipates later structural features in Johan Sebastian Bach's Fugue in G minor WTC II, and Georg Frederic Handel's Fuga II in G Major. The analytical perspectives identify: (1) cohesive relationships between motivic fragments, (2) underlying motives and their relationships to keys and harmonic progressions, and (3) voice leading reductions relative to linear and tonal prolongation. Arnold Schoenberg, Hans Keller, and Rudolph Reti provide valuable insights concerning the organic nature of thematic material. The voice leading reductions of Heinrich Schenker and William Renwick offer procedures that reveal underlying thematic relationships. The cohesive elements of the selected fugues will be explained with reference to immediate and long-range relationships.
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t USF Electronic Theses and Dissertations.
Analytical Perspectives of Thematic Unity : Applications of Reductive Analysis to Selected Fugues by J.S. Bach and G.F. Handel by Adam C. Perciballi A thesis submitted in partial fulfillment of the requirements for the degree of Master of Music College of Visual and Performing Arts University of South Florida Major Professor: Ann Hawkins, M.A. David Williams, Ph.D. Chichun Lee, D.M.A. Jill Brasky, Ph.D. Date of Approval: February 1, 2008 Keywords: basic idea, fugal structure, developing variation, hierarch ical levels, voice-leading Copyright 2008, Adam C. Perciballi
ii Table of Contents List of Figures iii Abstract viii Introduction 1 Chapter Two: Theoretical and Philos ophical Views of Thematic Unity 5 Arnold Schoenberg 5 Rudolph Reti 11 Hans Keller 16 Chapter Three: Reductive Analytical Approaches to Fugal Structure 22 Heinrich Schenker 22 William Renwick 28 Chapter Four: Three Analytical Pe rspectives in Selected Fugues 38 Stage One: Foreground Perspective of Fugue in G minor 39 Stage Two: Middleground Perspective of Fugue in G minor 43 Stage Three: Background Perspective of Fugue in G minor 46 Stage One: Foreground Perspective of Fuga II in G Major 48 Stage Two: Middleground Perspective of Fuga II in G Major 50 Stage Three: Background Perspective of Fuga II in G Major 52 Chapter Five: The Relationship of Philo sophical and Theoretical Views to the Analytical Perspectives of this Study 56 Conclusion 65 List of References 69
iii List of Figures Figure 2.1 Technique of Inversion 13 Figure 2.2 Technique of Reversion 13 Figure 2.3 Technique of Interversion 14 Figure 2.4 Augmentation in tempo change in Sonata in G Major Op. 14, No. 2 by Beethoven 14 Figure 2.5 Transposed variation in Pathetique Sonata Op. 13 by Beethoven 15 Figure 2.6 Thematic transformation in Rondo in G Major by Beethoven 16 Figure 2.7 Theme from Piano Concerto in C Major K. 503 by Mozart 17 Figure 2.8 Reduction of structural pitches from mm. 4-7 from Piano Concerto in C Major K. 503 by Mozart 18 Figure 2.9 Flute, mm. 62-63 from Piano Concerto in C Major K. 503 by Mozart 19 Figure 2.10 Violin, mm.70-71 from Piano Concerto in C Major K. 503 by Mozart 19 Figure 2.11 Bassoon and violin, mm.18-20 from Piano Concerto in C Major K. 503 by Mozart 20 Figure 2.12 Oboe, mm.1-3 from Piano Concerto in C Major K. 503 by Mozart 20 Figure 2.13 Violin, mm. 50-52 from Piano Concerto in C Major K. 503 by Mozart 20
iv Figure 2.14 Flute, mm. 63-64 from Piano Concerto in C Major K. 503 by Mozart 21 Figure 2.15 Strings and piano, mm. 91-94 from Piano Concerto in C Major K. 503 by Mozart 21 Figure 3.1 Foreground of Fugue in C minor by Bach 24 Figure 3.2 Background of Fugue in C minor by Bach 25 Figure 3.3 Table of Thematic Entries of Fugue in C minor by Bach 26 Figure 3.4 Reductions of subject of Fugue in C minor by Bach 27 Figure 3.5 Mm. 3-5 of Fugue in C minor by Bach 27 Figure 3.6 Countersubject I of Fugue in C minor by Bach 28 Figure 3.7 Countersubject II of Fugue in C minor by Bach 28 Figure 3.8 Thoroughbass compositional process 30 Figure 3.9 French Suite 1 in D minor BWV 812, Allemande mm. 1-5 by Bach 31 Figure 3.10 Prolongation of inner voices 33 Figure 3.11 Invertible counterpoint in Fugue in G minor by Bach 34 Figure 3.12 Mm. 12-14 of Fugue in D minor by Bach 35 Figure 3.13 Mm. 7-10 of Fugue in D minor by Bach 36 Figure 3.14 Mm. 52-56 of Fugue in D-sharp minor by Bach 37 Figure 4.1 Motives of subject a nd countersubject as stated in Fugue in G minor by Bach 39 Figure 4.2 Mm. 1-12 of Fugue in G minor by Bach 40 Figure 4.3 Mm. 3-5 of Fugue in G minor by Bach 41
v Figure 4.4 Mm. 8-12 of Fugue in G minor by Bach 42 Figure 4.5 Mm. 24-28 of Fugue in G minor by Bach 42 Figure 4.6 M. 5 of Fugue in G minor by Bach 43 Figure 4.7 M. 20 of Fugue in G minor by Bach 43 Figure 4.8 Underlying pitch groups in the subject and countersubject of Fugue in G minor by Bach 44 Figure 4.9 Key Chart of Fugue in G minor by Bach 45 Figure 4.10 Mm. 18-20 of Fugue in G minor by Bach 46 Figure 4.11 Reduction of subj ect and countersubject of Fugue in G minor by Bach 46 Figure 4.12 Motivic segments of su bject, answer and countersubject of Fugue in G minor by Bach 48 Figure 4.13 Reduction of subject, answer and countersubject of Fugue in G minor by Bach 48 Figure 4.14 Motives of subject as stated in Fuga II in G Major by Handel 48 Figure 4.15 Mm. 1-11 of Fuga II in G Major by Handel 50 Figure 4.16 Underlying pitch groups in the subject of Fuga II in G Major by Handel 51 Figure 4.17 Key chart of Fuga II in G Major by Handel 51 Figure 4.18 Cadence on middl e entry, mm. 38-39 of Fuga II in G Major by Handel 52 Figure 4.19 Cadence on episode, mm. 78-79 of Fuga II in G Major by Handel 52
vi Figure 4.20 Cadence on middl e entry, mm. 96-97 of Fuga II in G Major by Handel 52 Figure 4.21 Cadence at the e nd of piece, mm. 123-124 of Fuga II in G Major by Handel 52 Figure 4.22 Reduction of subject of Fuga II in G Major by Handel 53 Figure 4.23 Reduction of countersubject of Fuga II in G Major by Handel 53 Figure 4.24 Motivic outlines of subj ect, answer, and countersubject of Fuga II in G Major by Handel 54 Figure 4.25 Reduction of subject answer, and countersubject Fuga II in G Major by Handel 55 Figure 4.26 Further reduction of subj ect, answer, and countersubject of Fuga II in G Major by Handel 55 Figure 5.1 Motives of subject and basic idea as stated in Fuga II in G Major by Handel 58 Figure 5.2 Motives of subj ect and countersubject of Fugue in G minor by Bach 58 Figure 5.3 Flute, mm. 62-63 from Piano Concerto in C Major K. 503 by Mozart 59 Figure 5.4 Violin, mm.70-71 from Piano Concerto in C Major K. 503 by Mozart 59 Figure 5.5 Underlying pitch groups in the subject of Fuga II in G Major by Handel 60 Figure 5.6 Mm. 1-19 of Fugue in C minor by Bach 61
vii Figure 5.7 Background of Fugue in C minor by Bach 62 Figure 5.8 Invertible counterpoint in Fugue in G minor by Bach 63 Figure 5.9 Reduction of subj ect and countersubject of Fugue in G minor by Bach 64
viii Analytical Perspectives of Thematic Unity : Applications of Reductive Analysis to Selected Fugues by J.S. Bach and G.F. Handel Adam C. Perciballi ABSTRACT Thematic unity in music occurs when elements from a musical idea appear frequently, in significant pl aces and their presence is recognized or experienced on or beneath the surface. In fugal compositions, thematic unity is evident in the opening statement of the subj ect and it permeates each laye r of its texture. Three analytical perspectives are used to investigate the degree to which local thematic material anticipates later structural features in Johan Sebastian BachÂ’s Fugue in G minor WTC II and Georg Frederic HandelÂ’s Fuga II in G Major The analytical perspectives identify: (1) cohesive rela tionships between motivic fragments, (2) underlying motives and their relationship s to keys and harmonic progressions, and (3) voice leading reductions relative to linear and tonal prolongation. Arnold Schoenberg, Hans Keller, and Rudolph Reti provide valuable insights concerning the organic nature of thematic material. The voice leading reductions of Heinrich Schenker and William Renwick offer procedures that reveal underlying thematic relationships. The cohesive elements of th e selected fugues will be explained with reference to immediate and long-range relationships.
1 Chapter One Introduction Thematic unity in music occurs wh en similar relationships appear in various dimensions of the musical fa bric and provide cohesive elements throughout the composition. While these rela tionships are often more prominent in melodic features, they al so provide significant points of reference when they anticipate later harmonic pr ogressions, key schemes, and rhythmic patterns. Arnold Schoenberg, in his discussion of Grundgestalt (basic shape) creates an appropriate framework for understanding th ematic unity. A musical idea or basic motive contains the seeds of its development and as the composition progresses, it continuously evolves through a process he calls "developing variation". A description by Josef Rufer, an assistant to Schoenberg at the Prussian Academy of Arts in the 1920Â’s, adds furt her clarity to the concept. Everything else is derived from this Â– in music of all kinds, not only twelve-not e music; and it is not derived merely from the basic series which is contained in the basic shape, but also from all the elements which together with the series as the melodic element, give it its actual shape, that is, rhythm, phrasing, harmony, subsidiary parts, etc.1 Thematic unity in the structure of a fugue is ev ident through the continuous development of the theme a nd is reinforced by imitative treatment throughout the composition. In recent anal ytical discussions about the fugue, 1 David Epstein. Beyond Orpheus: Studies in Musical Structure (Oxford: Oxford University Press, 1987), 18.
2 features of thematic unity are identified in linear dimensions that occur within the smallest thematic units and that also b ecome significant within broader segments. These relationships create underlying c onnections through various techniques of prolongations that mirror similar surface material. A primary objective of analysis is to identify structural elements and perspectives within a composition that may enhance our musical understanding and provide insight into th e way we experience unity. Michael Rogers describes characteristics of analysis as explanat ions, connections, relationships, patterns, hierarchies, and comparisons.2 Traditional and innovative approaches to the analysis of tonal music contribute a variety of perspectives to structural relationships. Many of the traditional approaches are used to identify unique characteristics and explain connections between elements of melody, harmony, rhythm and form. An innovative approach to analysis by Heinri ch Schenker, reveals elements of tonal unity that are revealed through a proce ss of voice-leading re duction. The concept of tonal unity is expressed in the Urlinie (fundamental line) and its prolongation through successive stages of embellishmen ts. The technique of reductive analysis provides an opportunity to observe the underlying stru ctural features of the Urlinie and its relationships on hierar chical levels of the foreground, middleground and background. In this thesis, concepts of thematic unity are explored in the philosophical and practical applications of Arnold Schoenberg, Hans Keller and Rudolph Reti. 2 Michael R. Rogers. Teaching Approaches in Music Theory (Southern Illinois University Press, 1984), 75-76.
3 These theorists discuss the embryonic and generative nature of a basic idea and the compositional techniques that contri bute to a series of continuously developing patterns. The resu lt of this process provide s a unifying framework for immediate and more remote relationships. The analytical approaches of Heinrich Schenker and William Renwick are used to observe thematic unity in hierarchical relationships that appear on the surface and beyond. The use of reductive analysis to clarify structural patterns and pitche s on one level and to anticipate others on a broader level offers a valuable dime nsion to the study of thematic unity. Traditional and contemporary procedures are used to identify features of thematic unity in two selected fugues by Johan Sebastian Bach and Georg Frederic Handel. In addition, modifications to these procedures are made to add further insight concerning the concept of thematic unity. Analytical procedures of Schenker and Renwick are used as a point of reference for relevant innovative procedures and as points of departure for the modified techniques in this thesis. Traditional procedures indi cate significant motivic material that occurs at the beginning of the composition and that defi ne other structural sections of the fugue. Three analytical perspectives in chap ter four are given by the author of this thesis and they incorporate many ideas of the theorists discussed in earlier chapters. These perspectives are expa nded to offer additional explanations concerning various dimensions of thema tic unity. The subject and countersubject in the fugue provide the s ource of thematic material and consequently they are used as the musical source for these an alytical perspectives. In the first perspective, cohesive rela tionships between motivic fragments are identified
4 within the fugal subject and counters ubject. The second perspective contains structural pitches that implicate later ha rmonic functions and key schemes. In the third perspective, voice-leading redu ctions are used to indicate broader dimensions of tonal unity through various stages of struct ural prolongations.
5 Chapter Two Theoretical and Philosophical Views of Thematic Unity In the late 19th and early 20th centuries, there were significant theoretical discussions related to the function of thematic material and its relationship to structure on many levels of a compositi on. Arnold Schoenberg, Hans Keller, and Rudolph Reti provide interesting perspectives of cohesive elements that evolve from thematic material and that appear throughout the composition. In a prefatory note written by Donald Mitchell to The Thematic Process in Music by Rudolph Reti, the statement below comments on the concept of thematic unity in relationship to these theorists: Dr. Reti, I am sure, would not have claimed that his book provided all the answers to so fundamental a question; nor would he ha ve failed to acknowledge the influential work already accomplished in the analytic field by two renown ed seekers after musical unity, Arnold Schoenberg and Heinrich Schenker. I know that he was pleased that a most significant later development in musical analysis, Mr. Hans KellerÂ’s Functional Analysis owed something to his brilliant pioneering.3 In this chapter, the theoretical philos ophies and specific concepts of Schoenberg, Keller, and Reti are discussed as they relate to the compositional techniques that appear on and beneath the surface. Arnold Schoenberg One of the most detailed discussions of concepts relating to thematic unity 3 Rudolph Reti. The Thematic Process in Music (Faber and Faber Limited, 1961), v.
6 is given by Arnold Schoenberg in Style and Idea In this discussion, he describes Grundgestalt as a 'basic idea' or the source that generates fragments of thematic material in order to create unity within a composition. A real composer does not compose merely one or more themes, but a whole piece. In an apple treeÂ’s blossoms, even in the bud, the whole future apple is present in all its detailsÂ–they have only to mature, to grow, to become the apple, the apple tree, and its power of reproduction. Similarly, a real composerÂ’s musical conception, like the physical, is one single act, comprising the totality of the product. The form in its outline, characteri stics of tempo, dynamics, moods of the main and subordinate ideas, their relations, derivati ons, their contrast s and deviationsÂ– all these are there at once, though in embryonic state. The ultimate formulation of the melodies, themes, rhythms, and many details will subsequently develop through the generating power of the germs.4 The Grundgestalt (motive ) is primarily a pitch-oriented feature, however its influence may be observed in other areas of musical structure. As a point of departure, it contains the seeds of its own growth and its various contexts provide a means of continuous development. This basic idea becomes a unifying feature in that its reappearances provide connectiv e tissue for related ideas. The unifying features that result from varied transformation of the idea is evident in many of the compositions of the Baroque and Cla ssical-Romantic period. The concept of the Grundgestalt as the original source of pitc h content is also evident as a generative force in twelve tone music. In th e analysis of pitch structure in selected compositions of Mozart, Schoenberg observes similarities in his conception of 4 Arnold Schoenberg. Style And Idea: Selected Writings Of Arnold Schoenberg (University of California Press, 1975), 165.
7 patterns within the 12-tone procedure.5 Josef Rufer, an assistant to Schoenberg at the Prussian Academy of Arts in the 1920Â’s, states that the basic shape refers to a configuration of pitches, however the driving forces inherent in this sh ape also extends to motivic rhythm and harmony.6 One of these forces in tonal music is the union of melodic and rhythmic material within the motivic a nd thematic character of the composition. Another force is the tension that arises from the harmonic material with reference to chordal content and diffe rent harmonic progressions. The motive ( Gestalt ) according to David Ep stein, author of Beyond Orpheus assumes a significant role as it gra dually unfolds during the process of developing variations. This process of development in later passages of a composition may give the impression on the surface that the motive is in contrast to previous material, however, there ar e underlying features that also reflect earlier themes. In the development of the Grundgestalt, variations that contribute to the formal and structural represen tation of a compositi on include inversion, retrograde, transposition, augmentation and diminution as well as other forms.7 The topic of variation in context to motive, motive-forms and developing variation, is described by Schoenberg in three of his pe dagogical books: (1) Models for beginners in Composition (2) Preliminary Exercises in Counterpoint and (3) Fundamentals of Musical Composition This topic is also discussed in various essays from Style and Idea The purpose of these books is to inform 5 David Epstein. Beyond Orpheus: Studies in Musical Structure (Oxford: Oxford University Press, 1987), 17. 6 Ibid ., 18. 7 Ibid ., 19.
8 students about the compositional methods and concepts of the common-practice era.8 Motivic and variation techniques are important features described in Models for Beginners in Composition by Schoenberg. Motives are identified by their use in strict and vari ed repetitions that contai n rhythmic and intervallic alterations. During the process of de velopment, these motives produce new motive-forms that are used as continuati ons, contrasting sections, new segments, and new themes of a composition. During the process of development, motives acquire new characteristics while they re tain enough distingu ishing features to assure a sense of coherence. A motive may contain a characteristic feature that has the potential to develop in one way, however this potential may be replaced with a different variation. Schoenbe rg refers to this departure from the expected developmental treatment as a means of developing new segments.9 In the construction of phrases, the motive provides unity by establishing relationships in different sections. In Fundamentals of Musical Composition Schoenberg states that the intervals a nd rhythm of a motive are combined to produce a memorable shape and harmony. The motive is a part of everything that follows within a phrase and it generates the rest of the material within the composition. The subject, a longer thematic statement provides the basic motivic material for a large number of phrases within a com position. In some instances, motivic material may contain secondary pitc hes while retaining all of the original ones. Further variations of phrases are created when both rhythmic and intervallic 8 David Epstein. Beyond Orpheus: Studies in Musical Structure (Oxford: Oxford University Press, 1987), 207. 9 Arnold Schoenberg. Models for Beginners in Composition (G. Schirmer, 1943), 15.
9 material is changed during the compositional process and they provide extended and contrasting themes. The result of these changes through variation is the development of new motive-forms wh ich are further changed throughout a composition.10 In Style and Idea Schoenberg describes the t echnique of variation and repetition as a method of generating related features that link thematic material on various levels of musical structure. Schoenberg defines variation as changing some features while others are preserve d. When some features are taken out of context their original func tion decreases and allows for variations of those features. The author provides insight into the way these passages are connected in order to create a cohesive bond.11 Schoenberg associates the technique of developing variation with homophonic-melodic music and the techni que of unraveling to contrapuntal compositions. In homophonic-melodic music, a main theme is supported by harmonic material, and the technique of developing variati on provides fluency, contrast, variety, logic and unity duri ng the elaboration of the basic idea. Schoenberg makes a distinction between the artistic result of continuously varying a basic idea and the occasional addition of repeated notes within new material. He refers to contrast, vari ety, logic and fluency as a method of achieving configurations, combinations and varian ts of the theme of the musical idea.12 In contrapuntal compositions, the initial organization of the 'basic idea' is 10 Arnold Schoenberg. Fundamentals of Musical Composition (St. MartinÂ’s Press, 1967), 8-9. 11 Arnold Schoenberg. Style And Idea: Selected Writings Of Arnold Schoenberg (University of California Press, 1975), 256. 12 Ibid ., 397.
10 re-assembled through the technique of unraveling. A contrapuntal composition contains a brief statement that has th e potential for development by regrouping, reshaping and reordering various motivic patterns.13 Schoenberg uses the statement below to describe the variations of basic shapes within contrapuntal compositions. Whatever happens in a piece of music is nothing but the endless reshaping of a basic shape. Or, in other words, there is nothing in a piece of music but what comes from the theme, springs from it and can be traced back to it; to put it still more severely, nothing but the theme itself.14 The pitches and pitch groups in a contra puntal composition, which initially occur in the Grundgestalt are presented both simu ltaneously and successively throughout the composition.15 In The Musical Idea Schoenberg includes the characteristics of the musical idea, along with the c oncepts of logic, technique and artistic presentation. The logical order within a musical idea gui des the listener towa rd a predetermined point or goal within a com position. An artistic presentati on of an idea affects the coherence and comprehensibility throughout the composition. He explains that the effectiveness of a composition is influen ced by forces of the basic idea, and the ways in which they are realized and transformed into new motive forms within a systematic and artistic framework. Coherence in music may be achieved by exact or varied repetitions of a 13 Arnold Schoenberg. Style And Idea: Selected Writings Of Arnold Schoenberg (University of California Press, 1975), 397. 14 Ibid ., 290. 15 Arnold Schoenberg. The Musical Idea and the Logic, Technique, and Art of its Presentation (Columbia University Press, 1995), 400.
11 basic idea. The technique of exact repetiti on contributes significan tly to the clarity of a coherent statement. In slightly varied statements the coherence is retained, however elaborative features provide a sense of development. Techniques of variety may also be applied when ha rmony, basic pulse, and accompaniment are changed for the purpose of variety.16 Rudolph Reti Rudolph Reti states that thematic or mo tivic structure, as a form building element in music, is almost completely neglected and no real attempt to comprehend the motivic process has been made.17 In his book, The Thematic Process in Music Reti addresses the developmen t of thematic unity from a stylistic perspective of music in the Baroque and Classical eras. He describes the compositional process involve d in thematic unity as that of forming themes from one consistent musical idea. In multi-m ovement compositions, themes may appear to be contrasting on the surface yet simila r in substance. The content of a theme consists of structural pitches that are prevalent in the initial theme and later varied in subsequent statements. Reti empha sizes the importance of maintaining homogeneity within the inte rnal content of a compos ition. The result of inner homogeneity is that the theme may not be recognizable as it progresses, however it remains derivative of one consistent musical idea.18 Reti continues a discussion of the compositional principles that are reflected in the evolution of musical styl es, specifically that of the Baroque and 16 Arnold Schoenberg. The Musical Idea and the Logic, Technique, and Art of its Presentation (Columbia University Press, 1995), 157. 17 Rudolph Reti. The Thematic Process in Music (Faber and Faber Limited, 1961), 3. 18 Ibid ., 3-7.
12 Classical-Romantic period. He associates a significant compositional style of the Baroque period as one of contrapuntal imitation. Compositions such as the canon and fugue are ones in which a motive is de veloped by direct repetition or indirect treatment, techniques that he considers to include i nversion or augmentation. A sense of clarity is achieved in the developmental process when literal statements that are gradually varied duri ng the course of development.19 Reti identifies a significant compositional style of the Cl assical-Romantic period as one that results form thematic transformation. In this period the concept of form, especially in the sonata or symphony is enhanced by elements of contrast. Thematic shapes are transformed so that new themes appear on the surface to be distinctly different. Reti elaborates on this compositional style by explaining that: a thematic transformation must be regarded as most impressive from a structural angle if the identity is rooted strongly and firmly in the depths of the shapes in question and at the same time is as inconspicuous and little tr aceable as possible on the surface.20 There are various compositional devices that are used to add variety to motivic material. Reti, in his discussion of motivic variants such as inversion and reversion (retrograde) clarifies some of the different perspectives that are associated with inversion, contrary motion and reversion. He explains that inversion of interval occurs when a fifth becomes a fourth, however contrary motion or inversion by direction is used to identify an ascending fourth (C up to F) that becomes a descending fifth (C down to F). In musical practice, he shows how these two techniques might be comb ined. Figure 2.1 contains two treatments 19 Rudolph Reti. The Thematic Process in Music (Faber and Faber Limited, 1961), 57. 20 Ibid ., 58.
13 of a motive, the first statement (a) consis ts of a skip upward of a fourth from E-A followed by a stepwise descent to D. The second statement (b) is an inversion of the first statement and consists of a skip downward from E-A followed by a stepwise ascent to F. Figure 2.1. Technique of Inversion (Cited from RetiÂ’s Book on p. 68). Reversion (also referred to as retrogr ade) occurs when the last note of a segment is used at the beginning of th e transformation and the second to last follows, and so forth, until the first pitc h of the original is reached. Figure 2.2 contains a C minor triad (a) that is follo wed by its reversion or retrograde (b). Figure 2.2. Technique of Reversion (Cited from RetiÂ’s Book on p. 68). Thematic transformations occur in statements that are further removed from the original theme, however these tr ansformations contain elements that are derived from their earlier theme. An interversion may be considered as a technique that results in a transformation of the theme. In this technique, the notes of the transformed statement have been reordered from its original source. Reti states the following c oncerning interversion: It consists of interchangi ng the notes of a thematic shape in order to produce a new one. Since the current theory is so una ware of this type of transformation that not even a name has been designated for it, we are compelled to invent a new term and may call in an interversion .21 21 Rudolph Reti. The Thematic Process in Music (Faber and Faber Limited, 1961), 72.
14 In Figure 2.3 there are two examples, (a) an ascent of three pitches followed by a downward skip of a third, and (b) a reordering (interversio n) of the material which yields a descent of the same notes from highest to lowest. Figure 2.3. Technique of Interversion (Cited from RetiÂ’s Book on p. 73). Other techniques that contri bute to transformation of a statement consist of a change in tempo, and changes in rhyt hm and accent. In contrapuntal music, tempo changes are achieved by augmentati ons and diminutions which lengthen or shorten the motivic idea. In Figure 2.4, motive a occurs at the begging of the Allegro movement and motive b its augmentation, the re sult of a tempo change occurs at the beginning of the Andante movement.22 Figure 2.4. Augmentation in tempo change in Sonata in G Major Op. 14, No. 2 by Beethoven (Cited from RetiÂ’s Book on p. 76). Rhythm and accent changes are other ways in which a theme can appear to be disguised by developmental procedures. In Figure 2.5, motive a and b share similar contours, and the circled pitches in motive b may be described as a transposition that begins on the pitch D. The changes in rhythm and the shift in 22 Rudolph Reti. The Thematic Process in Music (Faber and Faber Limited, 1961), 75.
15 accent that is initiated by the pitch E-natural create a transformed version of motive a Figure 2.5. Transposed variation in Pathetique Sonata Op. 13 by Beethoven (Cited from RetiÂ’s Book on p. 77). In another discussion of thematic transformation, Reti relates two significant themes from the BeethovenÂ’s Rondo in G Major In Figure 2.7, the first four measures of each theme are given and are identif ied as (a) and (b) respectively. An immediate relationshi p can be made between the first two measures of each theme, by recognizing that the rhythmic version of an ascending triad in theme (a) is replaced in theme (b) by a descending triad with only a slight rhythmic feature. The thema tic fragment in the next two measures of theme (b) however, is further removed from the co rresponding measures in theme (a). For example, notice that in theme (a), the fragment in mm. 3-4 contain a neighboring treatment of the pitch D before it skips dow n to the pitch A. The interval of the outer pitches (D down to A) creates an interval of a perfect fourth. In the corresponding measures of theme (b), an interval of a perf ect fourth (D up to G) is filled in stepwise and followed by a similar treatment of another perfect fourth (A up to D). While the relationship between the two themes may be most noticeable in their qualities of inversion, theme (b), in the last two measures provides a transformation of th e earlier statement.
16 Figure 2.6. Thematic transformation in Rondo in G Major by Beethoven (Cited from RetiÂ’s Book on p. 69) Hans Keller Thematic unity is directly related to the presence of motivic material throughout a composition. In his article, Unity of Contrasting Themes and Movements Hans Keller discusses similarities between passages in the Piano Concerto K. 503 by, Wolfgang Amadeus Mozart that have previously been identified as contrasting material. The author describes specific compositional techniques that gradually provide elements of variety during the developmental process. Keller defines and explains techni ques that are used to modify the initial idea and to combine it with other fragment s in a variety of musical contexts. The concept of unity is demonstrated in passa ges that contain obvi ous relationships as well as those where thematic materi al is hidden and might otherwise be identified as contrasting material. In order to reveal relationships that contribute to thematic unity, the author raises ques tions that should be consid ered during the analytical process. The analysis which here follows is based on the tenet that a great work can be demonstrated to grow from an all-embracing basic idea, and that the essential, if never-as ked questions of why contrasting motifs and them es belong together, why a particular second subject necessarily belongs to a particular first, why a contrasting middle section belongs to its principl e section, why a slow movement belongs to a first movement, and so
17 forth, must be answered if an Â“analysisÂ” is to deserve its name.23 In the following paragraphs, a disc ussion of specific techniques and musical examples from his book will be given to demons trate his concepts of melodic and harmonic interversion, simultaneous suppression, augmentation, diminution, and accumulated motives. It shoul d also be noted that terms used by Keller to describe some of these variati on techniques may not coincide with ones that are in current use. The opening theme of the concerto (F igure 2.7) contains three significant motives: (1) a triadic passage (x) that a ppears in the character of a march-like fanfare, (2) a retrograde version (y) th at has the character of a three note anacrusis, and (3) a short lega to passage (z) that begins with a dotted-note rhythm and continues with stepwise motion within an interval of a th ird. The author also uses the letters a, b and c (Figure 2.8) to describe the compositional manipulations of a three-note pattern that emerges betw een measure four and five (see the first slur below) and becomes the three-note pa ttern that he labels as motive (z). An explanation of technique he calls interversion will be discussed in figure 2.8. Figure 2.7. Theme from Piano Concerto in C Major K. 503 by Mozart. 23 Keller, Hans. 1956. Â“K.503: The Unity of contrasting Themes and MovementsÂ–I.Â” MusicReview Vol. 17, No. 1 (February), 48.
18 The term interversion, originally associat ed with Reti Keller refers to a regrouping or reordering of pitc hes in which some of the pitch classes are retained.24 In addition to the retention of a few pitches, the process of regrouping might substitute a new pitch for the remaining notes while reordering might result in a new succession of pitches. Keller adopts th is terminology in his article and uses it to explain the process of motivic manipul ations of melodic as well as harmonic patterns. Melodic interversion involves the reor dering of at least two consecutive pitches and when it contains notes of the same pitch class, it provides a point of reference to the earlier motiv e. Figure 2.8 contains a seri es of three-note patterns that appear in the opening measures of the Mozart theme from K. 503. In measure four, the first pattern (a) in the violin and the second pattern (b) in the flute, later yield the derived motive (c) th at occurs in bassoon at measure seven, A reference to the figure below will show that the pitch classes g and e of the patterns (a and b) in measure four have been reversed. The later pattern (c) that occurs in measure seven has been further re orderd as a stepwise pattern within an interval of a third. Figure 2.8. Reduction of structural pitches from mm. 4-7 from Piano Concerto in C Major K. 503 by Mozart (Cited from KellerÂ’s article on p. 51). Keller associates harmonic interversi on with a re-ordering of harmonic progressions. In Figure 2.9 the circled pitc hes F, E, and C are re-ordered in the 24 Rudolph Reti. The Thematic Process in Music (Faber and Faber Limited, 1961), 72.
19 later musical example of Figure 2.10. The re-ordering of pitches in these two examples is also accompanied by a re-ordering of the chord progression. Figure 2.9. Flute, mm. 62-63 from Piano Concerto in C Major K. 503 by Mozart (Cited from KellerÂ’s article on p. 53). Figure 2.10. Violin, mm.70-71 from Piano Concerto in C Major K. 503 by Mozart (Cited from KellerÂ’s article on p. 54). Simultaneous suppression is a technique in which a fragment of the thematic material is omitted during the initial conception of the idea, however, it appears during the process of its developm ent. This later use implies that the composer is aware of the significance of this fragment and its unifying function in relationship to other thematic material. In a further explanation of this process, Keller hypothetically impersonates Mozart by saying that the composer's response might be Â“don't letÂ’s say it, but vary it immediatelyÂ”.25 Keller continues by identifying this technique of simultaneous suppression as Â“defin ite implication of the self-evidentÂ”. A traditional definition of augmenta tion and diminution is the lengthening and shortening respectively by half the orig inal value of the rhythmic statement. Keller's treatment of these techniques relate in a general way to the expansion and contraction of the statement that might o ccur with the addition or subtraction of notes. In the Keller article, the examples of augmentation refer to an extension or 25 Keller, Hans. 1956. Â“K.503: The Unity of contrasting Themes and MovementsÂ–I.Â” MusicReview Vol. 17, No. 1 (February), 51.
20 compression of time and they are not always in relationship to the duration of note values in the original rhythmic st atement. In Figure 2.11, the example of augmentation is related to the pitches C, D and Eb in the lower bracket ( motive c ) and their extended appearance as longer structural pitches in the upper bracket (see the circled pitches). Figure 2.11. Bassoon and violin, mm.18-20 from Piano Concerto in C Major K. 503 by Mozart (Cited from KellerÂ’s article on p. 52). The example of diminution in Figure 2.12 illustra tes that the thematic statement occurs in the first two measures and is di rectly followed by a shorter version that has been condensed within one measure. In the diminuted version of measure three, a slight modification is achieved by the absence of rests between the last two pitches. Figure 2.12. Oboe, mm.1-3 from Piano Concerto in C Major K. 503 by Mozart (Cited from KellerÂ’s article on p. 54). Keller illustrates motivic variants th at result from a combination of motives. In Figure 2.13, the ascending triad (y1) is indicated in circled notes as a triadic inversion. Motive z1 (a fragment of z), appears in a series of quarter notes. Figure 2.13. Violin, mm. 50-52 from Piano Concerto in C Major K. 503 by Mozart (Cited from KellerÂ’s article on p. 53).
21 A reference to Figure 2.14 will show another version of these combined motives. Following the anacrusis, there is a direct statement of the ascending triad in yet another inversion. Also, in this example motive z (in circled notes) is elaborated by intervening pitches. Figure 2.14. Flute, mm. 63-64 from Piano Concerto in C Major K. 503 by Mozart (Cited from KellerÂ’s article on p. 53). In Figure 2.15, the x and z motives appear with rhythmic and melodic variations. The motives are stated in a reve rsed order from their appearance at the beginning of the movement and these exch anged statements enhance their varied treatment. The neighbor pattern is used to add embellishments to both statements. In motive z3, the circled pitches G-F-E represen t a transposed inversion of the original motive (D-E-F). The pitch f is elaborated by a lower neighbor E. It should be noted that this motive also contains a rhythmic fragment from the original. Motive x2, a version of the descending triad is preceded by a lower neighbor and its rhythmic framework is also varied. In motive x4, the repeated neighbor patterns precede the descending triad and offe r yet another rhythmic variation. Figure 2.15. Strings and piano, mm. 91-94 from Piano Concerto in C Major K. 503 by Mozart (Cited from KellerÂ’s article on p. 53).
22 Chapter Three Reductive Analytical Appro aches to Fugal Structure In reductive approaches, surface elabor ations of musical patterns are gradually replaced by structural pitches in larger segments of the composition. In the fugue, motivic material is recogni zed by relationships within and between patterns, as well as the underlying pitche s that preserve the structure of the prominent tonality. The procedure for re ductive analysis developed by Heinrich Schenker offers a method for defining and accessing relationships on various structural levels of the composition. Schenker's method is based primarily on the significance of outer voices, however W illiam Renwick has expanded this method to include, where appropriate the structure of inner voices. In this chapter a series of Heinrich SchenkerÂ’s reductive analytical procedures for the fugue are discussed as they appear in Volume 2 of The Masterwork in Music In addition, analytical procedures by William Renwick are taken from his book Analyzing Fugue: A Schenkerian Approach Heinrich Schenker The analytical method of Schenker is based on structural levels which consist of a hierarchy of tones, and structural voice-leading that occurs at these successive levels.26 The perception of musical structure on the foreground, middleground, and background create a format for the comparison of hidden 26 William Renwick. Analyzing Fugue: A Schenkerian Apporach (Pendragon Press 1995), vii.
23 relationships. In the statement below, Schenker compares the traditional methods of fugal analysis with his approach. The difference between this study and all of the textbooks on the fugue as well as all other analysis is readily apparent. Th e textbooks and analysis always describe the orga nization of the fugue in terms of exposition, restatement, episode, and every other device imaginable: eg. contrary motion, retrograde motion, augmentation, diminution, stretto, etc. The only thing they never mention is the most important of all: the fundamental hidden relationships that bind th e fugue into an organic whole, into a true work of art.27 An application of his approach to tona l structure in the fugue is evident in the C minor fugue from BachÂ’s Well-tempered Clavier Book I. In this analysis from The Masterwork in Music his concept of tonal unity is expressed on each structural level with reference to the way that musical patterns coincide with the broader structures of the Urlinie and its complimentary Bassbrechung In Figure 3.1 from this book, the foreground contains gr aphic representations of structural melodic and harmonic patterns. In this firs t stage of analysis, the pitches from the fugue appear with rhythmic notation a nd other analytical groupings that are unrelated to the original notation. This foreground representation is also a composite of middleground and background relationships. A reference to this example will show that certain pitches have gained more structural significance while various embellishing patterns prolong these pitches over longer periods of time. The structural pitches are indicated by scale degree numbers with carets to indicate the eventual ba ckground structure of the Urlinie Harmonic progressions 27 Heinrich Schenker. The Masterwork in Music Vol. 2 (Cambridge University Press 1996), 42.
24 are also summarized to show the structural harmony of the ultimate Bassbrechung are considered to have an embellishing structural pitches from melodic patterns of the original composition are indicated. Figure 3.1. Foreground of Fugue in C minor by Bach (Cited from SchenkerÂ’s book on p. 33) A further reduction of the foreground is contained in the background of Figure 3.2. The surface elaborations in the previous figure have now been removed and the long range connection of the Urlinie is more evident. Note that
25 within each section of this fugue a separate Urlinie provides the tonal unity. A reference to Figure 3.2 indicates that the Urlinie of the exposition (5-1), the development (5-1), and the recapitulation (8 -1) are self contained in each section. In addition, a larger Urlinie (5-1) unifies the sections. Figure 3.2. Background of Fugue in C minor by Bach (Cited from SchenkerÂ’s book on p. 32). Schenker discusses the entrances of the subject, answer, and countersubjects in relationship to the Urlinie as well as the linear progressions that occur in the thematic statements of the fugue. The entrances of the subject, answer, countersubjects are provided in the table of entries, shown in Figure 3.3. In this table, the numbers refer to the entrances of thematic material throughout the fugue. Number 1 is designated for ei ther the subject or answer, number 2 indicates the first countersubject, and number 3 is indicative of the second countersubject.28 The keys associated with the thematic entries reinforce the prominent triad of the overall tonality (C-Eb-G). A reference to this chart indicates the relationship of these thematic entrances to the tonality. 28 Heinrich Schenker. The Masterwork in Music Vol. 2 (Cambridge University Press 1996), 33.
26 Figure 3.3. Table of Thematic Entries of Fugue in C minor by Bach (Cited from SchenkerÂ’s book on p. 33). Figure 3.4 contains reductions of the fugue subject, each containing the linear progression of the third (G-F-Eb). These reductions provide a sense of unity over the changing bass progressions that cr eate harmonic variety. In the first two examples of Figure 3.4, the 3d progression (G-F-Eb) occurs, each supported by two versions of dominant support. In the next two examples, the linear progression in the upper voice is elaborated by extended neighbor patterns and the bass line is expanded by the inclusion of the subdominant that precedes the dominant. In the last example, the pitc h C accompanies the linear progression (GF-Eb) with a neighbor pattern, culminating in the structural pitches of the C minor tonality.
27 Figure 3.4. Reductions of subject of Fugue in C minor by Bach (Cited from SchenkerÂ’s book on p. 34). An example of broad tonal relationshi ps is evident in the answer of a fugue. The primary function of the answer is to express the dominant tonality, however it also reinforces the tonality of the tonic. In Figure 3.5 (m.1 b.3) the C minor chord (IV in G minor) provides a c onnecting link to the overall tonality of C minor. The prominence of this domina nt area is achieved by immediate and prolonged neighbor patterns. In the lower voice, the F# (m. 2) assumes a neighboring function that also help s to prolong this dominant area. Figure 3.5. Mm. 3-5 of Fugue in C minor by Bach (Cited from SchenkerÂ’s book on p. 36). In Figure 3.6 and 3.7 respectively, count ersubjects I & II reinforce the
28 tonic tonality through a series of third progressions that are first presented in the subject. In the foreground graph shown ear lier (Figure 3.1), the function of third progressions within the subject wa s discussed. A reference to these countersubjects also indicates the cohesive function of the third progressions. In countersubject I (Figure 3.6), the pitches G down to C are connected by a prolonged pitch Eb that reinforces the significant pitches of the C minor triad. Figure 3.6. Countersubject I of Fugue in C minor by Bach (Cited from SchenkerÂ’s book on p. 37). In countersubject II (Figure 3.7), a series of third progressions end with the pitches G-F-Eb, the same third progression that occurs toward the beginning of countersubject I and the subject The third progression (G-F-Eb) also anticipates two measures later, the key of Eb major. Figure 3.7. Countersubject II of Fugue in C minor by Bach (Cited from SchenkerÂ’s book on p. 39). SchenkerÂ’s analytical approach to th e fugue recognizes th e organic nature that is inherent in thematic material of the subject).29 In selected examples from his analysis, thematic relationships occu r in various dimensions of the musical texture, both in immediate and long range connections. As a result they provide long range connections between thematic and tonal levels. William Renwick In his book Analyzing Fugue: A Schenkerian Apporach William Renwick 29 Heinrich Schenker. The Masterwork in Music Vol. 2 (Cambridge University Press 1996), 42.
29 expands the limitations of SchenkerÂ’s appro ach to reductive analysis of thematic treatment within the fugue. On e of the main challenges that he identifies in fugal analyses is the individual character that each voice assumes in expressing and developing thematic material that is rela tive to the fugal themes. Schenker assigns specific functions for individual voices as they relate to his background tonal structure. For example, the specific desi gnations that he gives to the upper voice as the Urlinie the lower voice as the Bassbrechung and the inner voices as contributing elements. Renwick presents th ese questions in regards to SchenkerÂ’s concept of an ideal tonal structure. Th e reductive analytical approaches that Renwick presents are indicative of compos itional similarities rather than unifying material which Schenker presented. Renwick's account of the historical development of contrapuntal music links the master composers who unified the art of counterpoint and triadic harmony. He notes that a significant cont ribution to this development was the compositional processes and performance pr actices in thorough bass realization in the 18th century. The harmonic implicati ons of the bass line were gradually expanded vertically by chord progressions and linearly by voice-leading strands. Individual lines gradually gained more independence as these strands were interchanged in an imitative-like texture. Figure 3.8 illustrates a three-step process involved in this harmonic realization. The top stave contains the figured bass with harmonic implications. The second system below contains a linear elaboration of the bass line and is supported by chords in the upper stave. The third system consists of periodic elaborations of passing tones and skips in all parts,
30 culminating in an imitative texture. The process of thoroughbass realization allowed the composer to gradually de velop a linear texture with greater independence while retaining the harmonic stability governed by the figured bass. Figure 3.8. Thoroughbass compositional process (Cited from RenwickÂ’s book on p. 4). The process of thoroughbass realizati on reflects a method of creating a composition from the background structure of the figured bass to the foreground textures in imitative counterpoint. A reductive analysis of contra puntal texture is enhanced when observations of structural pitches are made from the composition level of the foreground, and through a series of reduc tions, these pitches are related on a background level. While motivic connectio ns of thematic relationships are observed on the foreground level, it is the st ructural voice-leading that reinforces underlying tonal stability. Johann Philipp Kirnberger, a pupil of J.S. Bach, considered this analytical process, in conjunction with performance, improvisation, composition, and theory to be an essential skill for the baroque
31 musician.30 In Figure 3.9, Renwick provides a redu ctive analysis of this process from foreground to background and relate d underlying voice-leading connections. On the reductive level, the vertical interv als of parallel tent hs contribute to the prolongation of the I and IV chords. This sustained harmonic rhythm helps to preserves the harmonic framework during the active melodic texture. Figure 3.9. French Suite 1 in D minor BWV 812, Allemande mm. 1-5 by Bach (Cited from RenwickÂ’s book on p. 15). The application of reductive analysis to fugal compositions must consider ways to accommodate the presence of thema tic material in all of the voices. From the initial statement of subject and answer thematic material appears either in complete statements such as stretto a nd invertible counterpo int or as motivic 30 William Renwick. Analyzing Fugue: A Schenkerian Apporach (Pendragon Press 1995), 11.
32 fragments in various stages of continuous development. The concept of invertible counter point provides a texture in which thematic material appears simultaneousl y, such as the subj ect along with its countersubject or the treatment of stretto by the delayed entrance of the subject in each voice. In these treatments, the thema tic material serves a dual function, both as a prominent and a subordinate statemen t. A question then arises as to which voice or voices contribute to the organic unity of the passage. Heinrich Schenker addresses this issue by saying the following: The equality of individu al voices of invertible counterpoint is invalid, since in any polyphonic construct one of the se veral linear progressions serves as the leader and represents the underlying linear basis of the passage.31 He explains that the ultimate unity will be displayed in the voice with the Urlinie SchenkerÂ’s concept of Â‘fundamental structureÂ’ refers to the role of outer voices (melody and bass) as the determinants of tonal unity. With invertible counterpoint, these roles are interchangeable during the course of thematic development. Renwick expands the limitations of Schenker's perspective about fundamental structure and he explores ways to acknowledge the structural significance of thematic material when it occurs in any voice. He creates a theoretical construct based on the voice-leadi ng patterns of 8-7-8, 5-4-3, and 3-2-1 along with the bass pattern, 1-5-1. These patt erns can appear in different voices and simultaneously and together they reinfo rce the tonal stability of I V I. In 31 William Renwick. Analyzing Fugue: A Schenkerian Apporach (Pendragon Press 1995), 79.
33 Figure 3.10 (a) these patterns are shown as they appear in a simple form and in 3.10 (b), they are prolonged in time. Figure 3.10. Prolongation of inner voices (Cited from RenwickÂ’s book on p. 84). The treatment of invertible counterpo int occurs when a thematic statement in one voice exchange positions with the previous statement. Renwick uses the theoretical constructs in the paragraph above to demonstrate that a shift in position does not interrupt the function of voice-lea ding patterns to reinforce the tonality. In the fugue, the subject and countersubj ect appear simultane ously in different voices throughout the composition. In Figure 3.11 (a), an excerpt from the Fugue in g minor (WTC I) consists of the subject and countersubjec t in an original and inverted context. Figure 3.11 (b) on the second system, contains reductions in which the scale degrees of voice-leading patterns prolong the tonic and dominant harmony.
34 Figure 3.11. Invertible counterpoint in Fugue in G minor by Bach (Cited from RenwickÂ’s book on p. 89). In episodic passages of fugues, seque ntial patterns provide a connective link between thematic material. Sequentia l patterns contain transposed repetition based on voice-leading patterns, and th eir appearance in episodes prolongs structural harmonies and creates a st rong sense of overall unity. Schenker disregards the topic of sequence because the repetition in motivic development is not embodied in the Urlinie Renwick however recognizes its function of generating voice-leading pa tterns that ultimately prolong basic harmonies. The next two examples are excerpts from Fugue 6 in D minor (WTCII) by J. S. Bach. In Figure 3.12 (a), the motiv e is imitated between the middle and lower voice at the interval of an octave. The reductive analysis in Figure 3.12 (b) indicates the voice-leading patte rns that serve to preserve the stability of the tonic chord in D minor.
35 Figure 3.12. Mm. 12-14 of Fugue in D minor by Bach (Cited from RenwickÂ’s book on p. 143). In figure 3.13 (a), the imitative patterns occur between voices at an interval of a fifth. The voiceleading patterns that are ge nerated from this passage reflect tri-tone reso lutions in various forms of repetition. In the reduction of Figure 3.13 (b), the dominant harmony is prolonged in a passage of tonal instability. The broken line in the upper a nd lower voices indicates pitches of the dominant chord that frame mo st of this passage. Within this transitional passage, voice-leading patterns from the tonality of the tonic (see numbers), appear periodically and may sugg est an anticipation of the later tonic, confirmed.
36 Figure 3.13. Mm. 7-10 of Fugue in D minor by Bach (Cited from RenwickÂ’s book on p. 143). The treatment of stretto occurs when the subject is repeated in different voices, at delayed entrances. In his disc ussion of stretto, Renwick suggests that the underlying structural patterns in stretti are a product of prolonged harmony, linear progressions, the voi ce-leading complex, and sequences. He provides examples from BachÂ’s contra puntal literature and suggest s that Bach was aware of similar underlying voice-leading patterns and that he was able to incorporate their imitative potential in his thematic materi al. In the analysis of a segment from BachÂ’s Fugue in d# minor (WTC I), voice-leading st rands in the key of D# minor appear in various voices to prolong the sub-dominant (G# minor) and the mediant (F# Major) of that key. In Figure 3.14, the voice-leading strands in each prolongation is written once and the im itations of that strand are circled.
37 Figure 3.14. Mm. 52-56 of Fugue in D-sharp minor by Bach (Cited from RenwickÂ’s book on p. 168). RenwickÂ’s study of fugal analysis provides recognition of structural similarities in the fugue whereas Sche nker theory deals with the fundamental structure of the fugue.32 Both styles of reductive an alysis contribute to hidden connections in fugues even though they were presented with different intentions. 32 William Renwick. Analyzing Fugue: A Schenkerian Apporach (Pendragon Press 1995), 209.
38 Chapter Four Three Analytical Perspec tives in Selected Fugues The analytical pers pectives of selected fugues that are presented in this chapter, offer additional insights relate d to thematic unity. The fugue is a continuously developing process in whic h the subject, answer and countersubject are stated at the beginning of the compos ition and developed in different keys and structural patterns. Concepts of them atic unity are used to explain the developmental process on the surface and approaches to reductive analysis provide explanations concerning underly ing relationships. The approach to different perspectives of thematic unity in previous chapters influenced the conceptual methodology of the analysis in this chapter. The current analytical perspectives reveal surface and hidden rela tionships and their function in small as well as larger structural areas. In this chapter, excerpts from the Fugue in G minor WTC II by J.S. Bach, and the Fuga II in G Major by G.F. Handel are used to illustrate the analytical perspectives. Thematic material from th e subject, answer an d countersubject are analyzed for their motivic references and for the hidden features that anticipate later structural events. A three stage approach provides insight into the compositional treatment of motivic st ructure, key relationships, chord progressions, and thematic unity on re ductive levels. The first stage is a foreground perspective which contains motives in the subject, answer, and
39 countersubject as well as their treatment in significant por tions of the fugal structure. The second stage, a middlegr ound perspective consis ts of structural pitches from the beginning of the composition, defined by the process of reduction. These pitches are placed on a series of hierarchical levels in order to reveal key and chordal relati onships that lie beneath the surface. The third stage or background perspective is a reductive appro ach, similar to the process used in Schenkerian analysis. These voice-leading an alyses are used to reveal structural pitches that prolong basic t onal structure and provide thematic unity and tonal unity. Stage One: Foreground Perspect ive of Fugue in G minor Figure 4.1. Motives of subject an d countersubject as stated in Fugue in G minor by Bach. In the first stage, motives within the subject and countersubject are segmented into motivic fragments. Th e brackets in Figure 4.1 indicate these motives and their modified relationships. Motive a begins on the pitch D, followed by an ascending step (escape tone) which inte rrupts the skip to G and is completed by a lower neighbor pattern. Motive b contains a stepwise as cent that outlines an interval of a third (A-C ) and is followed by a lowe r neighbor on the pitch Bb and a descending skip to G. Motive b1 (the first fragment of the countersubject) represents a modification of the previous motivic fragment. This motive begins with descending stepwise motion that also outlines an interval of a third (A-F), however it is followed by anothe r ascending stepwise third (G-Bb). In motive c
40 the last pitch of the previous motive is also the first pitch of this motive. The pitch Bb becomes a member of a descending e di minished triad that is followed by an ascending step from C#-D. A sense of unity is achi eved between the subject and the countersubject by the modified treatment of motive b1. The overlapping of the two motives in the countersubject enhances this unity so that a combined statement of the subject and countersubj ect could be descri bed as a modulating subject. At this point in th e discussion Figure 4.2, a portion of the Exposition and the first episode is given to illustrate th e frequent use of motivic material and the relationship between motivic fragments. A process of thematic unity is achieved while developmental techniques add a sense of variety. Figure 4.2. Mm. 1-12 of Fugue in G minor by Bach. The technique of motivic developm ent is a successive and modified
41 treatment of fragments which emerge fr om motives and appear in structural positions within the fugue. In the counters ubject, an ascending stepwise interval of a fourth ( motive b1) appears in the lower voice (see first bracket in Figure 4.3). In the next measure, this motivic fragme nt appears at the be ginning of an episode and is followed by a sequence. In m. 5 this interval of a stepwise 4th appears as an ascending skip. This treatment of the 4th and its variations in episodes throughout the fugue are indicative of motivic development. Figure 4.3. Mm. 3-5 of Fugue in G minor by Bach. In Figure 4.4 the motivic fragment related to the 4th is given greater significance when it appears in developmental treatment within the first episode (mm. 8-12). This motivic fragment is transposed, rhythmically altered, and inverted in subsequent statements. The two rhythmically altered patterns in brackets 2 and 3 are used together in th e form of rhythmic counterpoint. The linear stepwise pattern within the interval of a 4th creates a dominant to tonic statement which culminates in deceptive resolutions within brackets 3 and 5. The deceptive treatment in fragment 5 an ticipates the stronger resolution to Bb Major in the next measure.
42 Figure 4.4. Mm. 8-12 of Fugue in G minor by Bach. In Figure 4.5 (mm. 24-28), the developmental treatment of the fragment of a 4th is imitated repeatedly in the upper two voices. In both Figure 4.4 and 4.5, this fragment appears in conjunction with motive b of the countersubject. The fragment is also used to create a domin ant to tonic statement that results in deceptive resolutions in G minor within brackets (4) and (12). Figure 4.5. Mm. 24-28 of Fugue in G minor by Bach. A sense of thematic unity is experi enced with the simultaneous appearance of motivic fragments. These fragments c onsist of motivic statements along with other hidden features. Figure 4.6 represents the second statement of the subject in the Exposition. A fragment from the subject appears on the bottom staff,
43 accompanied by a fragment of the answer on the top staff. On the middle staff, fragments from the answer are embedded in the elaborative textur e. The fugue is a continuously developing process in whic h the subject, answer and countersubject are stated at the beginning of the com position and developed in different key and structural areas. Figure 4.6. M. 5 of Fugue in G minor by Bach. Figure 4.7 represents the beginning of the third middle entry in the key of C minor. Motive a appears on the bottom staff while motive b1 (the first fragment of the countersubject) appears directly a bove on the middle staff. Within the top staff pitches embedded within motive b1 also reflect motive a Figure 4.7. M. 20 of Fugue in G minor by Bach. Stage Two: Middleground Persp ective of Fugue in G minor In the second stage, successive staves beneath the example contain intervals or pitch groups that suggest a link to keys, key areas or other harmonic
44 material throughout the fugue. The exclusion of rhythm allows more attention to be placed on these pitches and the underl ying function they assume in anticipating keys that are defined later in the co mposition. In Figure 4.8, these successive staves (Figures 4.8 (b) to (f )) contain structural pitches that have been abstracted from the subject and countersubject. The st ructural pitches are then assigned the keys of G minor, Bb Major, F Major and D minor th at appear in prominent areas during the developmental process of the fugue. The presence of Eb Major is included because of its prominent appearan ce as a chord of a deceptive resolution in G minor. Figure 4.9 contains a chart of keys and key areas in this fugue. Figure 4.8. Underlying pitch groups in the subject and countersubject of Fugue in G minor by Bach.
45 Figure 4.9. Key Chart of Fugue in G minor by Bach. The motivic and harmonic material stated from the beginning of the Exposition to the first middle entry contains structural implications and statements of keys. Chord progressions reflect these t onal areas and anticipa te other structural appearances later in the fugue. At the beginning of the fugue, the subject and answer are stated in the traditional manner as tonic and dominant, respectively. After the four-voice entrances repeti tion of the subject and answer, an Eb Major chord appears on the last beat of m. 9 is emphasized by the slower motion of eighth notes, surrounded by pa ssing sixteenth notes. This deceleration of motion at the Eb Major chord provides a reference po int, especially when it reappears later in other structural positions. This chord appears as the result of a deceptive resolution before the Recapitulation which begins in m. 27. A traditional harmonic progression (ii Â– V Â– I) provides cadential support as well as modulations to new key areas. The progression later appears sequentially and reflects th e key areas from the chords of the progression in Bb Major. The key areas of the middle entries are Bb Major, F Major and C minor in measures 12, 15 and 20 respectively. In Figure 4.10, mm. 18-20, the ii V Â– I progression occurs sequentia lly in tonal areas of Bb major, Eb Major (not anticipated), F minor and in C minor. The resolution of the V chord in C minor is delayed by the middle entry of the subject in the same key.
46 Figure 4.10. Mm. 18-20 of Fugue in G minor by Bach. Stage Three: Background Perspective of Fugue in G minor In the third stage, underlying relation ships appear within the subject and countersubject. Voice-leading reductions re lated to the analyt ical procedure of Heinrich Schenker are used in order to expose these hidden features. In this analytical perspective linear progressions and other uni fying features will be revealed through reductive analysis. In Figure 4.11, the subject and counters ubject of the fugue appear together with three levels of reduction. The or iginal form of th e fugue subject and countersubject are represented in Figure 4.11 and are followed by three levels of reduction. The reductions on the bottom two staves indicate features which provide a sense of underlying unity to the thematic material. Figure 4.11. Reduction of subject and countersubject of Fugue in G minor by Bach.
47 In Figure 4.11 (b), the first level of re duction indicates a 51 linear progression which unites the subject and countersubj ect. The pedal g provides a unifying feature beneath this linear progression. Within the re duction are other features such as lower neighbors which emphas ize the G minor tonality and a 4th progression which has been discussed ear lier as a motive derived from the countersubject. In the second level of reduction from Fig. 4.11 (c), the linear progression is now represented as an Urlinie Unfoldings of the G minor tonality are expressed within the subject and the count ersubject (see arrows between Bb and G). A reference to G minor is extended in the D minor tonal area of the countersubject and becomes the subdominant to reinforce this area of D minor. In Figure 4.11 (d), the third level of reduction, the neighbor pattern of the tonic lies within motive a while the lower neighbor of the dominant is extended throughout the statement of the subject a nd countersubject. Unity between this thematic material is evident from the nei ghbor pattern of the tonic that is nested within the lower nei ghbor of the dominant. In Figure 4.12 (mm. 1-4) the answer is included with the statement of the subject and countersubject. This example is given here to show the surface unity that occurs between motives within the fugal process.
48 Figure 4.12. Motivic segments of subject, answer and countersubject of Fugue in G minor by Bach. In Figure 4.13 a Schenkerian style reduc tion of this passage is given to indicate the broader unity that is created when the answer enters. When the tonal answer enters it contains, in the area of the dominant, th e lower neighbor (D-C#D) which anticipates the broader neighbor labeled in Figure 4.11 (d). In addition the first two pitches (G-Bb) along with pitches from motive b reinforce G minor through voice exchange. Voice exchange also occurs toward the end of the answer when E-natural and G reinforce the ii0 of the dominant. Figure 4.13. Reduction of subject, answer and countersubject of Fugue in G minor by Bach. Stage One: Foreground Perspect ive of Fuga II in G Major Figure 4.14. Motives of subject as stated in Fuga II in G Major by Handel. In this first analytical perspectiv e, motives within the subject are segmented by their grouping and varied repetition. A reference to Figure 4.14 will indicate these motives and th eir modified relationships. Motive a begins with an
49 anacrusis of repeated pitches, followed by a descending tonic triad. Later in the subject, a descending diminished triad on F# (vii0) is expressed within motive a1 (see circled pitches). Motive b is an ascending fourth fill ed in stepwise, separated from the next motive by an octave skip. Motive c contains a descending octave skip of the pitch C, followed by repeated statements of that pitch. The continuous repetition of this pitch provide s an interesting link between motive b which is suggestive of the subdominant and motive a1 which expresses the diminished triad. Motive d appears at the end of the subj ect with an ascending skip of a seventh followed by a lower neighbor. The treatment of overlapping motives is a unifying technique that is used to generate motivic forms. For example, the pitch G at the end of motive a (see circled note in Figure 4.15), is also the first pitch of motive b The pitch C (the last pitch of motive b) links the beginning of motive a1 by a skip of a descending octave. A reference to Figure 4.15 will show that pitch G in measure 4 links the end of motive a1 with the extension motive. At th is point in the discussion Figure 4.15, a portion of the Exposition is given in order to illustrate the frequent use of motivic material and the relationship between motivic fragments.
50 Figure 4.15. Mm. 1-11 of Fuga II in G Major by Handel. Stage Two: Middleground Perspective of Fuga II in G Major The purpose of the second analytical perspective is to identify structural pitches that may indicate prominent keys or key areas in later segments of the fugue. These pitches which are emphasi zed in various mel odic patterns are represented on successive staves without rhythm. This approach offers a perspective of unity that lies beneath th e surface, creating anot her level of tonal cohesion within the composition. These an ticipated keys are labeled throughout Figure 4.16. Figure 4.17 contains a chart of keys and key areas in this fugue.
51 Figure 4.16. Underlying pitch groups in the subject of Fuga II in G Major by Handel. Figure 4.17. Key chart of Fuga II in G Major by Handel. In Figure 4.16, the emphasized pitche s or pitch groups that have been extracted from the subject are given na mes that are suggestive of certain key areas. The keys of B minor, D Major, C Major and G Major are tonicized in cadencial passages at the end of significan t sections. The next four figures (4.18 Â– 4.21) indicate some of the harmonic progr essions that reinforce these keys.
52 Figure 4.18. Cadence on middle entry, mm. 38-39 of Fuga II in G Major by Handel. Figure 4.19. Cadence on episode, mm. 78-79 of Fuga II in G Major by Handel. Figure 4.20. Cadence on middle entry, mm. 96-97 of Fuga II in G Major by Handel. Figure 4.21. Cadence at the end of piece, mm. 123-124 of Fuga II in G Major by Handel. Stage Three: Background Perspective of Fuga II in G Major The third analytical pe rspective reveals underlyi ng stepwise motion that prolongs the prominent tonality within th e subject. A reductive method is used to indicate structural motion from the surf ace or foreground to the background level. These levels are compared with refere nce to the relationship between smaller
53 linear progressions and larger prolongations that retain the prominent tonality. In Figures 4.22 and 4.23, the fugue s ubject and countersubject appear separately with two levels of reduction. Th e original fugue subject is represented on the first staff and is followed by two levels of reduction. The reductions on the bottom two staves indicate the underlyi ng stepwise motion that unifies the motives with the expression of the G major tonality. Figure 4.22. Reduction of subject of Fuga II in G Major by Handel. In Figure 4.23, the countersub ject is also represented on the first staff and is followed by two levels of reduction that are e xpressed in the dominant area. Figure 4.23. Reduction of countersubject of Fuga II in G Major by Handel. In Figure 4.22, the second staff show s that the subject is a polyphonic melody that results in two separate lin es. The third staff indicates that the Urlinie is interrupted in the upper line with a progression from 5-3 (D-B). The lower line
54 on this staff provides a complete Urlinie (5-1). When both upper and lower lines are combined they reinforce the tonal stability of G major. In Figure 4.23 the second and third staves indicate that the Urlinie in D major also contains a descent from 5-3 (A-F#). Figure 4.24 contains the subject, an swer, and countersubject as they appear from mm. 1-11. The indications of motivic fragments within the subject, countersubject, and answer show the wa ys in which these fragments provide a sense of unity within the opening statement. In additi on to the motivic unity, a sense of tonal unity results in the dominant area when the pitch G, the subdominant, is retained as a refe rence to the prominent tonality. Figure 4.24. Motivic outlines of subject, answer, and countersubject of Fuga II in G Major by Handel. Figure 4.25, a voice-leadi ng reduction of Figure 4.24 shows the way in which these thematic statemen ts gradually unfold a broader Urlinie of 5-1 (D-G) within mm. 1-11. There are 3 segments within this example, the polyphonic
55 melody of the subject (mm. 1-5), the answ er and countersubject (mm. 5-9), and a link (mm. 9-11). The interrupted Urlinie on the pitch B that o ccurs at the end of the subject is prolonged while the count ersubject and answer expresses a 5th progression from A-D through the dominant area. In the link that follows the dominant pitch D provides a s upport for the completion of the Urlinie in the upper voice. Figure 4.25. Reduction of subject, answer, and countersubject Fuga II in G Major by Handel. Figure 4.26, a further reduction of Figure 4.25 shows the overall tonal unity that results when the interruption of the Urlinie in G Major generates a 5th progression in D Major. The interrupted Urlinie is completed in the link and a broader sense of unity is achieved because the 5th progression of the dominant area is nested in the Urlinie (G Major). Figure 4.26. Further reduction of subject, answer, and countersubject of Fuga II in G Major by Handel.
56 Chapter Five The Relationship of Philosophical and Th eoretical Views to the Analytical Perspectives of this Study The concept of thematic unity within selected fugues of J.S. Bach, and G.F. Handel is described in the analytical perspectives of this thesis and in the established writings of Arnold Schoenber g, Hans Keller, and Rudolph Reti. The discussion of the topic includes the orig in of a musical id ea and the cohesive elements that contribute to immediate and long range relationships. In addition, Heinrich Schenker and William Renwick offe r analytical discussions that explain relationships on the surfa ce level of the composition as well as underlying relationships revealed by the applicati on of reductive analysis. In the following paragraphs, there will be a discussion concerning their influence on the analytical perspectives in chapter four, presen ted by the author of this thesis. Arnold SchoenbergÂ’s concept of the Grundgestalt (basic idea) which evolves during a series of developing vari ations adds consider able insight to the concept of thematic unity. The embryonic nature of this basic idea generates various permutations with both immediat e and remote relationships. Rudolph Reti reinforces this concept of thematic pro cess when he refers to the technique of forming themes from one consistent musical idea. He identifies the first stage of development in contrapuntal music as one of direct repetition or indirect treatment that appears in techniques such as in version or augmentation. Hans Keller the theoretical contributions of Reti and further dis tinguishes the types of
57 developmental treatment that adds variet y to thematic and motivic material. His discussion further illustrates developmenta l techniques that add variety and that gradually transform the motive into initia lly perceived elements of contrast. The concept of thematic unity in contrapuntal music, especially on the surface is inherent in the compositional pr ocess. The subject of the fugue (basic idea), appears initially in all voices and it is fragmented, manipulated and developed in some form that maintains its presence throughout the composition. The role of the subject in creating thematic unity is dependent on the relationship of motivic fragments that it contains and their relationship to the countersubject. An analytical perspective of motivic stru cture can be effective in revealing these relationships. In the following paragraphs, analytical perspectives from chapter four are summarized to illustrate the relationship of thematic fr agments within the subject of the Handel fugue and the subject and countersubject from the Bach fugue. The significance of motivic fragments by Sc hoenberg, Reti and Keller consider the derivative qualities of these fragments dur ing the course of development. In the first analytical perspectiv e of the Handel fugue from chapter four (Figure 5.1), motivic fragments are identified by thei r frequent appearance throughout the composition. An initial reference to the relationships between motive a and a1 are the repeated pitches followed by a desce nding triad (see circle d notes). It should be noted that motive a1 offers an expansion of motive a with additional repeated notes and a passing tone betw een a member of the triad. Motive b is indicated by ascending stepwise motion within the in terval of a perfect fourth (G-C). Motive b1
58 (C-G) may be interpreted as a retrograde inversion of motive b In this example, both motive a and b as a musical idea generates a variation of that idea to complete the subject. Figure 5.1. Motives of subject and basic idea as stated in Fuga II in G Major by Handel. In the subject and countersubject by Bach (Figure 5.2), motivic fragments have also been bracketed in order to id entify their relationships. One reference to the relationships between motive a and a1 is the progression of a half step relationships at the end of each motive that creates a function of a leading-tone to tonic relationship (F#-G) and (C#-D). Another relationship in these motives is somewhat disguised on the surface. In motive a the pitch Eb implies an escape tone that is dissonant to the tonic triad in g minor. If we consider the Eb as a replacement for the pitch Bb, the descending triad (D-Bb-G) reinforces the tonality of G minor. The motive at the end of the countersubject ( motive a1) a descending triad (Bb-G-E), followed by a half step progression similar to motive a At the beginning of motive b the ascending third filled in stepwise (A-Bb-C) of the subject is reversed at the beginning of motive b1. The two motives ( motive a and b ) of the subject generate the material of the countersubject in a reversed order. Figure 5.2. Motives of subject and countersubject of Fugue in G minor by Bach.
59 Hans Keller discusses a motivic transf ormation that may also be related to manipulations of harmonic progressions. He refers to a technique where priches and their harmonic implications are both reordered in another statement. An example of harmonic interversion (Figur es 5.3 and 5.4) is taken from Keller's article, Unity of Contrasting Themes and Movements The circled notes in Figure 5.3 occur in a re-ordered version in Figure 5.4. In addition, the first example implies a harmonic progression that is reversed in the second example. The manipulation of melodic material crea tes a transformation of patterns on the surface, however, the inversion of contour and the underlying harmonic progression retain some of the thematic references. Figure 5.3. Flute, mm. 62-63 from Piano Concerto in C Major K. 503 by Mozart (Cited from KellerÂ’s article on p. 53). Figure 5.4. Violin, mm.70-71 from Piano Concerto in C Major K. 503 by Mozart (Cited from KellerÂ’s article on p. 54). The concept that thematic unity can transcend melodic relationships and implicate harmonic progressions has influen ced analytical perspectives presented by the author of this thesis. While motiv ic manipulations on the surface are allow the listener a gradual perception of thema tic relationships, further associations to harmonic progressions and the implications of key areas further contribute to the experience of understanding underlying rela tionships. In the second analytical perspective from chapter four (Figure 5.5), structural pitches fr om the subject of
60 the Handel fugue have been given on subsequent staves. These pitches are assigned to the keys that appear in signif icant portions of th e fugue. The result of this analytical persp ective is a suggestion th at structural pitches in the subject are used to anticipate later key areas and this procedure may contribute another level of experienced thematic unity. It would be interesting to apply this method to other compositions in order to observe the degree to which it might be applicable. Figure 5.5. Underlying Pitch Groups in the Subject of Fuga II in G Major by Handel. Heinrich Schenker offers a theoretical explanation for the broad dimensions of tonal unity that are prol onged within a composition. This concept is achieved by the voice-leading of structur al pitches from the melodic line ( Urlinie ) and its bass harmonization ( Bassbrechung ) that reinforce pitches of the most prominent tonality. Since the outer voices in Schenker's theory maintain the most
61 prominent role in defining the musical st ructure, his analyt ical approach to imitative texture such as the fugue is limited. However, in volume two of The Masterwork in Music, he does provide an analysis of the C Minor Fugue by J.S. Bach. In the first nine measures of this fugue (Figure 5.6), an analysis of the foreground is given along with a skeletal version of a superimposed background. In this excerpt, structural pitches in whole notes indicate that the first two measures are a prolongation of the tonic pi tch before the stepwise descent of the Urlinie is expressed from scale degrees 5-1. In addition, the ultimate bass progression of I-V-I provides the struct ural harmony for the upper voice. While the significance of the inner voices is reduced to melodic and harmonic elaborations on a local level, the outer voices maintain the tonality on a broader level throughout the excerpt. Example 5.6. Mm. 1-19 of Fugue in C minor by Bach (Cited from SchenkerÂ’s book on p. 33). In the Schenkerian reduction of the background level (Figure 5.7) of the C minor Fugue the melodic patterns that appear on the foreground level have been removed. This reduction, wit hout a rhythmic context, c ontains linear progressions
62 as well as an overall Urlinie SchenkerÂ’s concept of harmonic prolongation has now been further reduced to the chordal st ructure that reinforces the tonic triad. Figure 5.7. Background of Fugue in C minor by Bach (Cited from SchenkerÂ’s book on p. 32). William Renwick expands the limitations of SchenkerÂ’s concept to fugal analysis. He retains the advantages of a reductive approach, however he acknowledges that the imita tive treatment of individua l voices can also contain elements of structural significance. The c ontrapuntal process that creates thematic identity in these voices, such as inve rsion and stretto, are recognized for their separate identity while at the same time they contribute to the overall tonal unity in the passage. In the first two measures of Figure 5.8 (a), a simultaneous version of the subject and countersubject ar e given and immediately followed by an example of invertible counterpoint. Figure 5.8 (b) provides a background reduction of these measures and indicates voice-leading strands that appear in both voices. It should be noticed that these strands are segments of the Urlinie and together they serve the same function in creating tonal unity.
63 Figure 5.8. Invertible counterpoint in Fugue in G minor by Bach (Cited from RenwickÂ’s book on p. 89). The role of the subject and counters ubject in establishing thematic unity on an underlying level is enhanced by th e technique of reduction. In the third analytical perspective from chapter four (F igure 5.9), a series of three reductions from the subject and countersubject app ear on successive staves. In the first reduction, two voices emerge to provide tonal stability. The tonic pitch g is elaborated by a lower neighbor in th e lower voice and maintains a reference throughout this statement. The upper voice connected by descending steps, results in an Urlinie from 5-1. In the second reduction the linear progressions of a third appear as vertical intervals to observe the basic voice-leadi ng. The third and final reduction eliminates the vertical intervals of a third and shows the significance of the neighbor pattern (D-C#-D) in reinforcing the tonality. The immediate lower neighbor of the tonic pitch (G-F#-G) is supported by a pr olonged dominant pitch that is also supported by a lower neig hbor. These prominent pitches together reinforce the tonality of G minor in the expression of the subject and the countersubject.
64 Figure 5.9. Reduction of subject and countersubject of Fugue in G minor by Bach. The analysis in Figure 5. 9 shows the tonal unity of G minor that occurs as the thematic material progresses to the dominant area of D minor. This application of reductive analysis from th e third perspective in chapte r four uses concepts from both Schenker and Renwick. An implied pe dal point G allows two voices to be extracted from the single line of the subj ect and countersubjec t (Figure 5.9b). The Urlinie of 5-1 in SchenkerÂ’s concept unf olds through the third beat of measure 3 and this pitch G becomes a common pivot to ne in the unfolding of a diminished seventh chord in D minor (Figure 5.9 c). RenwickÂ’s use of the neighbor pattern as a voice-leading strand occurs at th e beginning of the subject as G-F#-G and the pitch D is prolonged to later confirm th e dominant in the pattern D-C#-D (5.9d). The motivic fragments that are generated from the subject and countersubject are reflective of a surface thematic unity. The subsequent reductive perspectives provide underlying voice-lea ding relationships that contribute to the broader dimensions of tonal unity.
65 Chapter Six Conclusion Thematic unity in music occurs when elements from a musical idea appear frequently, in significant pl aces and their presence is recognized or experienced on or beneath the surface. In this thesis, the concept of thematic unity has been explored in the philosophical discu ssions of Arnold Schoenberg, Rudolph Reti, and Hans Keller and in the analytical methodologies of Heinrich Schenker and William Renwick. The cohesive elements in music have been described, explained and analyzed by these theorist s and some of their ideas have been incorporated in the analytical perspectives used by the author of this thesis. The theories of Schoenberg have referred to the Grundgestalt (basic shape), its potential to embody the essen ce of the musical idea as well as the techniques of developing va riations that generated di fferent motive forms within the composition. In the book The Musical Idea Schoenberg discussed the driving forces within the basic idea and the ways in which they transformed new motive forms in developmental sections. Schoe nberg explained these techniques using terminology that described their function in creating various permutations of the basic idea. In the discussions by Reti and Kell er, developmental techniques were described and labeled with terminology rela ted specifically to their explanations. In some cases it is difficult to und erstand a particular terminology for
66 developmental techniques when current te rms are more descriptive. For example, RetiÂ’s distinction between interval by i nversion and interval by direction (or contrary motion) was an attempt to add some clarity to his discussion. On the contrary, his concept and explanation of reversion with the same meaning as retrograde may add a degree of ambiguity to the meaning of this concept. Regardless of the terminology, these three theorists have offered valuable insights concerning the relationship of thematic permutations to the basic idea in the composition. The concept of structural unity ben eath the surface was defined in chapter three by the analytical perspectives of Schenker and expanded in further applications by Renwick. The analyti cal approaches of these theorists distinguished prolongational patterns from structural pitches that revealed underlying relationships. A seri es of hierarchical leve ls provided a format to observe the gradual reduc tions of these pitches on foreground, middleground and background levels. The result of these obser vations indicated ba sic voice-leading patterns of the Urlinie that contributed to the ultimate tonal unity within the composition. The methodology in SchenkerÂ’s approach emphasized the structural significance of the outer voices, however, he did not include the thematic material of a fugue's inner voices as part of the ultimate Urlinie Renwick on the other hand, recognized that the imitative textur e of the fugue occasionally transferred thematic material to the inner voices and that they also contributed to the tonal unity at the background level. In chapter four, the analytical pe rspectives for the fugues by Bach and
67 Handel were initially based on the inhere nt concept of thematic unity. In the fugue, the subject as a basic idea is deve loped in its entirety, fragmented and sometimes transformed into derivative statements during the process of development. Traditional an alytical methods have been used to identify many of the surface relationships that have resu lted from the permutation of thematic material. Existing techniques of reductive an alysis have been used to identify underlying relationships in th e fugue and they have been modified in some cases to explain other hidden connections. The analytical approach for the two fugues perspectives was divided into a series of three stages in order to observe the following relationships, (1) motivic fragme nts, (2) underlying motives and their indications of keys and harmonic progre ssions and, (3) linear prolongations of voice-leading in reductiv e levels of foreground, middleground and background levels. The perception of thematic unity within a composition is strongly influenced by the initial clarity of a st atement, the gradual process by which it unfolds in direct and indir ect references and concealed relationships that provide a sense of experienced unity on broader le vels of the composition. Schoenberg, in his discussion of the musical idea, relate d coherence and compre hensibility to the use of logic, technique a nd the art of its presentati on. He emphasized that the logical development of the idea guided the listener toward a predetermined point or goal within a composition. In this thesis, analytical perspectiv es have been developed for the purpose of revealing surface and underlying relations hips in selected fugues. The organic
68 nature of motivic fragments within the fugue subject was observed in developmental treatment that added va riety on an immediate level of the composition and that later transformed them atic material into hidden or suggested references. The research and analytical observations in this thesis have identified elements of thematic unity from the trad itional perspective of motivic unity and it has applied the innovative approaches of reductive analysis to reveal voiceleading relationships of tonal unity. This research may be expanded in many directions that include applic ations of the analytical perspectives in this thesis to more contemporary fugal compositions. In future studies, comparisons of potential structural unity might be made with the fugues of other historical periods.
69 List of References Epstein, David. 1987. Beyond Orpheus: Studies in Musical Structure Oxford: Oxford University Press. Keller, Hans. 1956. Â“K.503: The Unity of c ontrasting Themes and MovementsÂ–I.Â” Music Review Vol. 17, No. 1 (February), pp. 48-58. Renwick, William. 1995. Analyzing Fugue: A Schenkerian Apporach Stuyvesant, New York: Pendragon Press. Reti, Rudolph. 1961. The Thematic Process in Music London: Faber and Faber Limited. Rogers, Michael R. 1984. Teaching Approaches in Music Theory Carbondale: Southern Illinois University Press. Schenker, Heinrich. 1996. The Masterwork in Music Vol. 2 ed. Ian Bent. Cambridge: Cambridge University Press. Schoenberg, Arnold. 1967. Fundamentals of Musical Composition St. MartinÂ’s Press. Schoenberg, Arnold. 1943. Models for Beginners in Composition G. Schirmer. Schoenberg, Arnold. 1975. Style and Idea: Selected Writings of Arnold Schoenberg ed. Leonard Stein. Berkley: Un iversity of California Press. Schoenberg, Arnold. 1995. The Musical Idea and the Logic, Technique, and Art of its Presentation Bloomington, Indiana: Columbia University Press.