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2017 Score Reduction and Simplification as a Learning Tool in J.S. Bach's Allemande from Partita No. 6 in E Minor, BWV 830 Brooks Ryder Hafey
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COLLEGE OF MUSIC
SCORE REDUCTION AND SIMPLIFICATION
AS A LEARNING TOOL IN J.S. BACH’S
ALLEMANDE FROM PARTITA NO. 6 IN E MINOR, BWV 830
By
BROOKS RYDER HAFEY
A Treatise submitted to the College of Music in partial fulfillment of the requirements for the degree of Doctor of Music
2017 Brooks Hafey defended this treatise on March 8, 2017. The members of the supervisory committee were:
Read Gainsford Professor Directing Treatise
Evan Jones University Representative
David Kalhous Committee Member
Gregory Sauer Committee Member
The Graduate School has verified and approved the above-named committee members, and certifies that the treatise has been approved in accordance with university requirements.
ii This treatise is dedicated to the memories of Carolyn Bridger and Kent Conrad.
iii ACKNOWLEDGMENTS
I would like to express my sincere gratitude to Read Gainsford for his support, expertise, and especially his patience throughout the writing of this treatise and through the many years leading up to it.
I would also like to thank the members of my committee, Dr. Evan Jones, Dr. David Kalhous, and Prof. Greg Sauer, for their assistance, kindness, and encouragement.
My friends from Florida State University have been a constant source of motivation and inspiration and for that I am grateful.
Finally, I would like to thank the incomparable Bobby Pace for his undying love, support, and understanding as I wrote this treatise.
iv TABLE OF CONTENTS
List of Tables ...... vi List of Figures ...... vii Abstract ...... viii INTRODUCTION ...... 1 Background and Significance ...... 1 Purpose ...... 2 Survey of Literature ...... 3 On the Benefits of Using Reductions as a Learning Tool ...... 6 ALLEMANCE FROM PARTITA NO. 6 IN E MINOR, BWV 830 ...... 9 MELODIC REDUCTIONS ...... 13 Melodic Reduction Set 1 ...... 14 Melodic Reduction Set 2 ...... 20 Combined Original and Reduction ...... 31 Summary ...... 33 HARMONIC REDUCTIONS ...... 37 Harmonic Reduction Set 1 – Keyboard Style ...... 38 Harmonic Reduction Set 2 – Block Chords ...... 39 Harmonic Reduction Set 3 – Closest Position Chords ...... 41 STRUCTURAL REDUCTION ...... 46 CONCLUSION ...... 48 APPENDIX: ALLEMANDE WITH ROMAN NUMERAL ANALYSIS ...... 49 Bibliography ...... 52 Biographical Sketch ...... 54
v LIST OF TABLES
Table 3.1: Creating a Melodic Reduction ...... 36 Table 4.1: Creating a Harmonic Reduction ...... 45 Table 5.1: Creating a Structural Reduction ...... 47
vi LIST OF FIGURES
Figure 2.1: Form Diagram of Allemande, BWV 830 ...... 12 Fig. 3.1: Melodic Reduction Set 1, RH, mm. 1-8 ...... 15 Fig. 3.2: Melodic Reduction Set 1, RH mm. 9-20 ...... 17 Fig. 3.3: Melodic Reduction Set 1, LH, mm. 1-8 ...... 19 Fig. 3.4: Melodic Reduction Set 1, LH, mm. 9-20 ...... 21 Fig. 3.5: Combined Melodic Reduction Set 1...... 23 Fig. 3.6: Melodic Reduction Set 2, RH, mm. 1-8 ...... 25 Fig. 3.7: Melodic Reduction Set 2, RH, mm. 9-20 ...... 27 Fig. 3.8: Melodic Reduction Set 2, LH, mm. 1-8 ...... 29 Fig. 3.9: Melodic Reduction Set 2, LH, mm. 9-20 ...... 30 Fig. 3.10: Combined Melodic Reduction Set 2...... 32 Fig. 3.11: Combined Original and Reduction ...... 34 Fig. 4.1: Harmonic Reduction, Keyboard Style, mm. 1-8 ...... 39 Fig. 4.2: Harmonic Reduction, Keyboard Style, mm. 9-20 ...... 40 Fig. 4.3: Harmonic Reduction, Block Chords, mm. 1-8 ...... 41 Fig. 4.4: Harmonic Reduction, Block Chords, mm. 9-20 ...... 42 Fig. 4.5: Harmonic Reduction, Closest Position Chords, mm. 1-8 ...... 43 Fig. 4.6: Harmonic Reduction, Closest Position Chords, mm. 9-20 ...... 44 Fig. 5.1: Structural Reduction ...... 47
vii ABSTRACT
This treatise examines the use of reductions and simplifications as learning tools. These tools are applied to the study of J.S. Bach’s Allemande from Partita No. 6 in E Minor, BWV 830.
There are three types of reductions explored in this treatise: melodic, harmonic, and structural.
There are two levels of melodic reductions, the first of which is the simple melodic framework and the second of which is a mid-level reduction. The harmonic reductions are in three different voicing styles: keyboard style, blocked chords, and closest position chords. The structural reduction at the end aims to provide a playable structural framework for the entire composition.
These reductions are inspired by analytical methods such as Schenkerian analysis but are meant to remain idiomatic to the keyboard and practical for the pianist. The benefits of utilizing reductions and simplifications are numerous and include increased understanding of the score, decreasing the risk of memorization mistakes in performance, bridging the gap between analysis and performance, and decreasing the pianist’s reliance on visual and kinesthetic components of the music.
viii INTRODUCTION
Background and Significance
During my years as a Piano Performance undergraduate student at the University of
Missouri-Columbia, I took several music theory courses beyond the required theory sequence.
One of those courses was Schenkerian Analysis. I recall having numerous discussions with my instructor at the time, Dr. Neil Minturn, about how a performer could use this sort of reductive analysis to aid in the learning process and to help convey compositional structure in performance. Though at the time he and I never reached any particularly satisfactory answers, the concept of using reduction and simplification as a practice tool has occupied my mind since then. In my subsequent studies, I have come to develop processes of reduction and simplification in my own practice that have greatly improved my practice efficiency and effectiveness. These methods are inspired by, but not identical to, Schenkerian analysis. In my practice, the rigor of the theory is diluted for practical purposes and is more basic in nature. For example, a full
Schenkerian analysis is not meant to be played but rather used as a visual and analytical guide to the structures of a composition. A practical reduction or simplification remains idiomatic to the keyboard and may contain part-writing errors and/or chords or voicings that are important to the changing positions of the hands, but not necessarily to the structure of the composition. Like
Schenkerian analysis, however, there are multiple levels of practical reduction and simplification. The goal of these reductions is not necessarily to convey the underlying structure to an audience in performance, but rather to encourage the pianist to find and understand these structures during the learning process, strengthen his or her confidence and deepen his or her knowledge of the score.
1 Another source of inspiration for this treatise has been my role as a collaborative pianist, particularly in opera. Reading and performing orchestral reductions has taught me to look for the essential framework, to understand what is necessary to play and what can safely be left out, how to reduce at sight, and how to convey the musical meaning of a score as efficiently as possible.
Many orchestral reductions are not playable as written and must be adjusted, simplified, and reduced further by the performer. The pianist must be able to look at the full reduction and decipher what must be played. The pianist therefore does not play exactly what is on the page in front of him or her, but rather makes constant adaptations to the score. The adaptation of this process to the learning of a piece of solo piano repertoire yields significant benefits for the pianist.
Purpose
The purpose of this treatise is to provide a case study for employing reduction and simplification during the learning process of a piece of advanced piano music. I will examine the
Allemande from J.S. Bach’s Partita No. 6 in E Minor, BWV 830 in order to help piano students understand how to use reduction and simplification in their practicing. I selected this composition because it has clearly identifiable harmonies and melodic contours, but whose melodic content is highly ornamented. Pianists use multiple learning styles when approaching a new piece of music. For many pianists, the analytical style of learning is intimidating and underexplored. Though the process of analyzing the music at the piano takes time, in the end the learning process is accelerated. Creating reductions while learning a piece of music is in fact a time saver. In writing this treatise I seek to aid in the transference of knowledge acquired in theory classes to the application of that knowledge in the practice room.
2 Survey of Literature
There is a vast amount of literature devoted to the subject of analysis and performance.
Though this treatise is not on analysis and performance specifically, the derived concepts are valuable contributions to the subject of utilizing analysis as a practice tool. Early examinations by music theorists placed a strong emphasis on analysis as a precedent to what they would consider a good performance (Berry, 1988). For Berry, the analysis of the score led to a single successful performance possibility. Performers such as Arthur Schnabel insisted on both score study but allowed for the possibility of spontaneous reactions to the musical details during performance (Wolff, 1979).
That score analysis is valuable is not contested, but differences of opinion exist among multiple authors on the application of analysis to performance practices. This tension between performers and analysts (theorists) has been noted and explored by several authors (Fisk, 1996;
Nolan, 1993/1994; Swinkin, 2007; Yih, 2013). Performers may feel intimidated by the austerity of abstract analysis and feel at a loss to apply the knowledge gained from a graphic reduction.
Several authors encourage a happy medium of sorts between the two camps. Swinkin (2007, p.
79) encourages a “metaphorical, rather than explanatory” approach to analysis. Here, Swinkin attempts to understand how the musical surface, what the pianist plays, relates to the long structural lines discovered via analysis. Howell’s work (1992) reflects attempts to bridge the gap between academics and performers by looking at the attributes of intuition and rigor found in both analysis and performance.
Howat (1995) examines the philosophical and practical questions raised by relating sounds that we hear to the notes on the page. He determines that every musical work has many
3 possible performances, but that analysis provides performers with a strong framework on which to base their interpretations.
Rothstein (1995) encourages performers to utilize analysis as a means to create a narrative, much as actors use the text of a play to create a drama on stage. He emphasizes that analysis has the potential to lead the performer astray, for instance by causing a pianist to highlight each and every fugue subject in a Bach fugue, even though Bach sometimes took great pains to conceal the subject.
Literature on the use of reduction and simplification as a practice tool is not rigorous and is often mentioned in passing when examining other topics. There exists no specific research that
I have encountered on the subject. That being said, there are numerous studies that touch on aspects of analysis as practice tools.
Duke et al. (2009) observed a selection of students learning a short yet difficult excerpt of music and determined that the time spent practicing the excerpt was not indicative of a successful performance, but rather the methods and determination of the students proved to be more important. The more successful students utilized their time efficiently and effectively.
Chaffin et al. (2002 and 2003) looked at the process used by a concert pianist to learn a piece of music, namely the third movement of Bach’s Italian Concerto. They determined that the pianist worked very diligently to improve conceptual memory in addition to motor and auditory memory.
Byo (2014) seeks to draw connections between score analysis in rehearsal and the expressive potential unlocked by its discoveries. His techniques and vocabulary are specific to ensemble rehearsal, but can be useful for the pianist as well.
4 Ericsson et al. (1993) did a multidisciplinary study in which they examined what types of practicing lead to expert performance, be it in sport, music, or another field. They found that experts in many fields focused deliberately on skills that they could not already do well and persevered until the weaknesses were eliminated. For many pianists, the analytical component of learning a piece of music is the most difficult, yet many pianists avoid confronting the difficulty.
Mishra (2008) looked at a number of studies in an effort to determine and summarize how compositional characteristics affected the learning process and memorization of a piece of music. She found that the number of notes was the number one predictor of memorization efficiency; the more notes there were to memorize, the longer it took the student to do so. In addition to the number of notes, she looked at the number of bars, number of beats, density, tonality, number of sharps/flats in key signature, number of chromatic tones, meter, tempo, number of repeating bars, and rhythmic complexity.
Shockley (2001) transfers analysis to a highly visual representation in her book on mapping. The diagrams created via her method require close scrutiny of the score and aid in confidence in memory.
Teixeira dos Santos and Gerling (2012) discovered that the more advanced a student, the more likely that student was to rely on dynamic or procedural knowledge, meaning trying to understand “how” whereas less advanced students relied on fixed or “declarative” knowledge.
The more advanced students’ perception of pitch, rhythm, and harmony discrimination aided in their preparations and performances.
Katz (2009) and Moore (1984) both discuss the importance of understanding how to rewrite orchestral reductions in order to make the music more playable. They both provide numerous examples of simplifying textures, awkward passagework, adjusting passages for
5 varying tempi, and other modifications a collaborative pianist must learn in order to be an effective and musical accompanist.
On the Benefits of Using Reductions as a Learning Tool
Classical piano students work diligently to observe all of the details of a score. Emphasis is often placed on learning the correct notes and rhythms, observing all dynamic and articulation indications provided by the composer, understanding the stylistic elements of the genre and composition, and getting the fingers to execute with fidelity the composers written intentions.
Volumes of technical exercises exist for the purposes of aiding students achieve a greater degree of finger dexterity, increased velocity, fuller tone, greater rhythmic flexibility, a large and varied color palette, and other pianistic goals. While a student must work on improving his or her mechanical and aural skills, it is also of great value to improve how the student absorbs the melodic and harmonic content of a composition. This process of understanding the melodies and harmonies is often allowed to happen on its own through hours of repetition and may occur without much depth of understanding. In fact, it is entirely possible for a student to learn a piece of music without being able to name any harmonies at all. The kinesthetic and visual elements of playing the piano are so strongly memorable that a student can choose to rely solely on them. It is a mistake to rely on these elements, however, as most pianists can attest to experiencing mistakes in performance, especially memory slips, as a result of this type of shallow learning.
Improving one’s understanding of the melodies, harmonies, and structure of a composition can help to prevent mistakes and memory slips.
Most pianists are not active readers of theoretical analysis. Catherine Nolan (1993/1994) states that “most of the literature on the relationship between analysis and performance is published by scholars in theory and analysis, and appears in publications that are not routinely
6 read by performers, and, therefore, has little influence on, or even alienates, performing musicians through its often technical and sometimes dogmatic tone” (p. 112). Piano students may feel intimated by analysis and decide not to broach the subject in learning a piece of music unless forced to by a teacher. However, it need not be so. Analysis can occur on many levels and does not need to take hours upon hours to do. A pianist can develop the skills to look at a score and readily find melodic contours and outlines, harmonies hidden among the textures, and structural signposts.
Simplifying a melody or harmonic progression in a composition has multiple benefits other than reducing the risk of memory slips and improving one’s knowledge of the score. It can also help to “detect the tension developments within [a] simplified line” (Bruhn, 1989, p. 31).
Seeing the simplified melody, free of the visual complexity of elaborate figuration, can help to identify how to phrase. In the music of the Baroque, the melismatic writing may obscure a very simple phrase shape, and simplifying it may help to play more musically.
Many pianists rely on the visual element of piano-playing when learning a piece of music. This includes how the music looks on the page, but also how the hands look as they move across the keys, and the visual pattern of the keys themselves. An overreliance on the visual can hinder the other components in the learning process, such as the aural and cognitive components.
Creating a reduction forces a student to de-emphasize the visual element, without abandoning it entirely. The student must look into the score and find what lies beneath the surface.
Finally, creating an idiomatic reduction helps to bridge the gap between analysis and performance. For an instrumentalist, music is often understood via the instrument. In creating a playable reduction, the pianist is able to connect with the piano itself rather than looking at a
7 graph or reduction that may provide a tremendous amount of information, but remains in the abstract.
8 ALLEMANDE FROM PARTITA NO. 6 IN E MINOR, BWV 830
Bach was forty-one years old when he decided to publish his first work. In 1726, he published the Partita No. 1 in B-flat Major and five other Partitas followed, with one appearing each successive year until 1731. The six Partitas together form part I of the Clavierübung which
Bach labeled his Opus 1. Bach’s complete Clavierübung included four parts that were published between 1726 and 1741. It is remarkable that the four parts of the Clavierübung were among
Bach’s few compositions published during his lifetime.
Bach composed his six Partitas during his Leipzig years when he was Kantor at the
Thomaskirche. He had already composed a large number of keyboard suites including the
French and English Suites and had also completed his first book of the Well-Tempered Clavier.
The six Partitas are different from standard Baroque dance suites in that they each begin with a differing and non-dance movement. Thus, the first Partita begins with a Praeludium, the second with a Sinfonia, the third with a Fantasia, the fourth with an Overture, the fifth with
Praeambulum, and the sixth with a Toccata.
The Partita No. 6 in E Minor consists of seven pieces. The opening piece, Toccata, is an extended fugue framed on either side by an improvisatory exploration that emphasizes a two- note sighing figure. This figure becomes an important part of the fugue subject. The second piece, the Allemande, is the subject of the current study. The third piece, Corrente, is a rapid and brilliant dance whose frequent syncopations communicate a mischievous character. The fourth piece, entitled Air, is short in duration and whose fervent drive is in stark opposition to the following Sarabande. The Sarabande is a deeply solemn stylization of the dance form whoe melodic material is elaborately ornamented. The following dance, Tempo di Gavotta, is light-
9 footed and quick whereas the concluding Gigue is a pianistically demanding version of the lively dance.
The allemande as a dance is one of the standard dances in keyboard suites of the Baroque period. Though it appears as the second piece in Bach’s Partita No. 6, it is almost always the first dance of a suite. The other standard dances in order of appearance are the courante, sarabande, and gigue (Schulenberg, 2008, p. 246). Composers would often include another dance, such as a gavotte or bourrée, for variety in between the sarabande and the gigue. According to Little and
Jenne, the allemande had lost its identity as a specific dance by the time of Bach (Little and
Jenne, 2001, p. 34). They excluded the dance from their exhaustive study Dances and the Music of J.S. Bach as they “discovered neither clear choreographic roots nor distinguishable recurring rhythmic patterns; nor did [they] find any choreographies” (p. 34). However, Stewart Gordon
(1996) provides a general description of Bach’s allemandes in A History of Keyboard Literature.
He states that they “exhibit typical characteristics of the dance as it evolved from the seventeenth century: figural writing in broken counterpoint, the use of duple meter to be played at a moderate tempo, each section opening with an upbeat” (p. 60). The roots of the dance date back to
Renaissance and it became popular as a dance form among the French aristocracy. It was one of a number of moderate tempo dances to be “composed and likewise danced in a grave and ceremonious manner” (Walther, 1732, p. 28). As with most dances of the era, it is in binary form, with two sections, each repeating.
The Allemande from Bach’s Partita No. 6 in E Minor is in simple continuous binary form. It consists of two sections, A and A’, both of which are repeated. As Clendinning and
Marvin (2005) explain in their chapter on binary form, the form is continuous because it modulates to the dominant at the end of the first section and the second section begins in the
10 dominant. The two sections of the form are balanced, meaning that material from the end of the first section is brought back at the end of the second section. Indeed, the second section varies and develops material from the first section, hence the designation A’ (p. 473-476).
The first two measures of the dance establish E Minor as the tonic key. In measure 3, an ascending seconds sequence leads to a brief tonicization of the iv chord, A Minor. This presages a modulation to iv in the second section. From the middle of measure 5 into measure 6 there is a descending seconds (alternating 6/3) sequence which prepares for the modulation to the dominant. In measures 6 and 7, the minor v chord is prevalent, though the modulation to v is completed with a Picardy third in a Perfect Authentic Cadence (PAC) in measure 8.
The second section begins in the dominant but quickly returns to the minor mode with a modulation to iv, A Minor, in measure 11. In measures 11 and 12 there is a descending seconds
(alternating 6/3) sequence, similar to but lengthier than the descending seconds sequence in measures 5 and 6. In measures 13 and 14 there is a PAC in iv. This strong cadence indicates that there has been a modulation to iv, rather than a brief tonicization. In measures 15 and 16 there is a descending fifths sequence whose function is to return to the dominant of E Minor. The dominant is prolonged in measures 17-19 and the piece ends with a PAC in E Minor.
The form is diagrammed in on the following page in Figure 2.1.
11 ||: ------A------:|| e: i - i Ascending Tonicization Descending Modulation PAC V 2nds of iv 2nds to v Sequence Sequence mm 1-2 3 4 5 7 8
||: ------A’------:|| e: V Modulation Descending PAC iv Descending PAC to iv 2nds 5ths V - I Sequence Sequence mm 9 10 11-12 14 15-16 17-20
Figure 2.1 Form Diagram of Allemande, BWV 830
12 MELODIC REDUCTIONS
Underlying the highly ornamented melodic line of the Allemande is a simple melodic contour. Though the floridity of the ornamentation masks the simple nature of the contour, finding this fundamental melody may help the pianist memorize and execute the passage. In her study of how compositional characteristics affect the learning process, Mishra (2008) discovered that the number of notes was the number one predictor of memorization efficiency. The more notes a student had to learn, the longer it took the student to memorize the music. By simplifying the melody, one of the goals is to decrease the number of events to memorize during the learning phase. Eventually, of course, the pianist must bring back the full ornamentation, but understanding the melodic skeleton will make that memorization more secure in the end.
Another goal is to understand the voice leading, and how Bach subsequently manipulates it with ornamentation.
There is no single right answer as to what the underlying melody is. As in many reductions, there are multiple levels and those levels are somewhat subjective. In the figures that follow are two possible sets of reductions. In the first set of reductions (Figures 3.1, 3.2. 3.3, 3.4,
3.5) all note values smaller than eighth notes are eliminated and most of the rhythmic motion is at the level of the quarter note. The second set of reductions (Figures 3.6, 3.7, 3.8, 3.9) is a middle ground between the first reduction and Bach’s full ornamentation. Both sets of reductions are discussed in detail below.
13 Melodic Reduction Set No. 1
The goal of this first set of reductions is to pare down the right-hand melodic line to its bare essentials, while maintaining a pianistically idiomatic shape. Figure 3.1 contains measures
1-8 and Figure 3.2 contains measures 9-20. Sixteenth and thirty-second note values are eliminated, and most eighth note activity is also eliminated. Passing tones, non-harmonic tones, and neighboring tones are discarded and only the main pitches of the melodic line are retained.
The resulting rhythmic motion is slow and moves almost entirely in quarter notes.
In measure one, the melody traces a diatonic descending third pattern from G down an
11th to D-sharp. Bach’s octave displacement of the following F-sharp on beat two of measure 2 is transposed down an octave to illustrate the gentle contour of the underlying melodic structure and its stepwise resolution to G. Measure 3 contains a brief sequence moving up stepwise from B to D on the downbeat of measure 4. The E on beat four of measure 4 may be considered as the melodic goal of this ascending pattern. Upon reaching this goal, the E moves down to D-sharp and then leaps up to A and the beginning of another sequence. Measures 5-6 contain a descending fifths sequence in which the melody moves downwards stepwise from G to D. The following modulation to the dominant begins in the melody on beat three in measure 6 as an arpeggiation of the diminished leading tone seventh chord and then dominant seventh chord. The ascent through these chords arrives at B on beat two of measure 7, and then leaps down to a 3-2-
1 cadential pattern.
14 Figure 3.1 Melodic Reduction Set 1, RH, mm. 1-8
Figure 3.2 includes measures 9-20 and follows the same process as the reduction in
Figure 3.1. Measure 9 begins with a downward arpeggiation of B Major, the newly established key, and then leaps up to A, which is scale degree 7. This chordal seventh resolves down to G on the downbeat of measure 10. The melody then ascends to B, then down to a leading tone G-sharp
15 and finally landing on A on the downbeat of measure 11. Bach has modulated to A Minor in this passage. A lengthy sequence follows, beginning with the F-natural on beat three of measure 11.
This is another descending fifths sequence in which the melodic line traces a diatonic stepwise motion downward. The downbeat of measure 13 is the end of the sequence. The remainder of measure 13 and downbeat of measure 14 is a descending 4-3-2-1 motion in the key of A Minor.
The key of A Minor is weakened in measure 14 by the presence of the G-natural, scale degree 7 in A Minor, and its resolution downward to F-sharp. The melody outlines a B7 chord into measure 16, highlighting a return to the key of E Minor. Beginning on beat three of measure 16, a descending fifths sequence appears which cements the return to E Minor. The melodic line also moves in descending fifths in the order of G-C-F-sharp-B-E-A-D-sharp. The D-sharp on the downbeat of measure 17 is displaced by an octave in Bach’s original and restored in the reduction to the simpler contour. The melody then climbs slowly from F-sharp up to the B on beat four of measure 18. The perfect authentic cadence in measures 18 and 19 includes a descending 3-2-1 melodic motion, though displaced an octave by Bach, and restored in the reduction.
Figures 3.3 and 3.4 apply the same processes illustrated above to the left hand part.
Figure 3.3 includes measures 1-8 and Figure 3.4 includes measures 9-20. The bass clef part in general is not nearly as ornamented as the melodic line in the right hand, but it can still be simplified to show the underlying simple structure.
The left-hand line begins in measure 1 on E and follows a chordal outline going through the i, iv, and V chords in E Minor over measures 1 and 2. Starting on E, the line ascends to G, A, and C before descending back to E via an F-sharp and D-sharp. The brief sequence in measure 3 is an ascending seconds sequence with passing chords, shown as notes in parentheses, and the
16 Figure 3.2 Melodic Reduction Set 1, RH, mm. 9-20
17 Figure 3.2 – continued resulting left hand line moves up from C to E. A minor is briefly tonicized by this sequence, but a passing chordal seventh leads back to a B7 chord and the left hand line traces that motion and arrives back on E on beat three of measure 5. The simplified bass line of the ensuing descending fifths sequence moves stepwise downward from E to B and initiates the modulation to B Major.
18 Measure 7 could be reduced in more than one way. Here I have chosen to highlight the root movement, but another option is to highlight the leading tone movement from A-sharp to B on beats one and two.
Figure 3.3 Melodic Reduction Set 1, LH, mm. 1-8
19 Figure 3.4 shows the left hand line for measures 9-20 and begins with an arpeggiation of a B7 chord. Measure 10 begins the modulation to A Minor and the bass line highlights the leading tone G-sharp on beat three. The C on the downbeat of measure 11 weakens the cadential feel of the modulation but the ensuing sequence strengthens it. The descending fifths sequence begins on beat three of measure 11. The bass line descends stepwise from D to its goal pitch, E, on the downbeat of measure 13. The modulation to A Minor is highlighted by the bass line movement A-E-A into measure 14. Before arriving at the sequence in measure 15, the bass line moves up from D through D-sharp to E. On beat three of measure 15 the descending fifths sequence begins and the bass line follows the pattern of root position motion and settles on
B in measure 17. The bass line then climbs stepwise from E to A before ending the piece in a cadential pattern.
The results of combining the right and left hands of the previous reductions can be found in Figure 3.5. A common practice tool used by many pianists is to practice hands separately and then to bring the hands together after developing a sense of ease in playing hands alone. It is for this reason that the figures in this treatise are published first hands separately and then hands together. Combining the two parts increases the chance to observe and absorb elements such as parallel motion, contrary motion, linear intervallic patterns in sequences, and voice exchanges.
Melodic Reduction Set No. 2
The reductions in this section bridge the gap between the simplification of the previous reductions and the full ornamentation composed by Bach. These four reductions follow closely the contour of the piano part, the kinesthetic components of the passage, maintain octave displacements, include passing tones, and strive to provide a slightly fuller texture. Thirty-second
20 Figure 3.4 Melodic Reduction Set 1, LH, mm. 9-20
21 Figure 3.4 continued
notes are absent but occasional sixteenth notes appear in certain situations such as when Bach accelerates an arpeggiation. There is a great deal of subjectivity in this level of reduction. One pianist may choose to certain emphasize elements of the melodic content and another may not.
Figures 3.6 and 3.7 show these middle-level reductions for the right hand in measures 1-8 and 9-20 respectively. In measure 1 of Figure 3.6, the simplified melody displays the descending scalar pattern that begins on G and ends an 11th below on D-sharp. Alternatively, this descending melodic line could be reduced to highlight the semitone neighboring movement while maintaining the descending thirds pattern discovered in the first melodic reduction in Figure 3.1.
In this case, the first eighth note pitches would be G, D-sharp, E, B, C, G-sharp, and A. Again, this is subjective and will depend on how an individual hears and processes the melodic content.
22 Figure 3.5 Combined Melodic Reduction Set 1
In exploring the melodic content in this way, the student determines what the essential identifying characteristics of the melody are. Bach’s octave displacement in measure 2 is evident in the disjunct motion that outlines the B7 chord. The ascending triadic outlines of measure 3 continue into measure 4 though with Bach’s octave displacement intact. In fact, the upper B in
23 measure 4 begins a long stepwise octave descent to the B in measure eight. These are the circled tones in the figure. In Figure 3.1, this descending scalar figure was not evident because the octave displacement was removed. Continuing in measure 5 is the descending fifths sequence.
Here the simplified melody in Figure 3.6 follows more closely the motion of the hand and this passage’s characteristic span of a seventh. In the middle of measure 6 through beat two of measure 7, Bach reaches back up to the high B by means of a rapid arpeggiation of a leading tone diminished seventh chord. Though Bach then arpeggiates down through a B Minor triad which is minor v. Measure 8’s ending arpeggiation through the dominant chord, V, is marked with the octave leap in the reduction.
As in the opening of the dance, measure 9 begins with a descending stepwise motion, this time in the dominant (Figure 3.7). The C-natural passing tone is maintained as its physical impact is an important part of playing this passage. The reach upwards to the chordal seventh, A, is followed by its resolution pitch, G. In measure 10, the E Minor triad of the reduction replaces
Bach’s full descending scale. The octave span at the beginning of measure 11 is maintained and the A Minor triad is highlighted in place of the busy figuration. The sequence beginning on beat three of measure 11 again follows the shape of the hand while reducing the number of notes. The sequence’s characteristic interval of a seventh is made apparent in the simplification. In measure
13 the emphasis is on the modulation to A Minor. The leaps and hand position shifts through the harmonies are evident in the reduction and follow Bach’s original contour. The Amin7 chord in measure 14, expressed as an ascending scale in Bach’s original, is arpeggiated in the reduction to highlight its harmonic function of leading to the D Major triad at the end of the measure. In measure 16, the arpeggiated B7 chord leads to a descending fifths sequence, here expressed as a melodic broken chord pattern that repeats every two beats.
24 Figure 3.6 Melodic Reduction Set 2, RH, mm. 1-8
At the end of the sequence, downbeat of measure 17, the melody reaches up a tenth through a B7 chord and then climbs stepwise up. Bach’s melodic figuration in measure 18 is reduced to show the principle tones and the octave span of the hand whereas measure 19 reduces the scalar patterns to arpeggiations, following closely the melodic contour.
25 `The middle-level reductions for the left hand are in Figures 3.8 and 3.9. Because the left-hand part does not include nearly as much ornamentation as the right hand, these reductions are even closer, and in some cases, identical, to Bach’s original notes and rhythms. At the beginning of the reduction, for example, the first nine tones are identical to the original. This is because the motion is already in a simple stepwise pattern. In measure 2, however, the left-hand part can be simplified to outline the harmonies and hand positions. The V chord can be reduced to an arpeggiation leading down to the low E on beat three. The sequence beginning in measure 3 can be reduced in a number of ways, but to illustrate how Bach changes hand position frequently, I have chosen a linear simplification that outlines the harmonies and keeps an element of the hand movement. Over the span of five beats, from the last beat of measure 3 to the last beat of measure 4, the range in the left hand spans over two octaves, from F#2 to A4. This is a significant change in register and is reflected in the reduction. From the A on the last beat of measure 4 the line descends back down stepwise and then in broken thirds during the descending fifths sequence. The descending fifths sequence ends in measure 6 and the left hand plunges back down to the same low F-sharp, F#2, from measure 3. Again Bach covers a wide range of the bass clef range in a few short beats in measure 7. Just as in the treble part, the B Major arpeggiation that closes the section is reduced to an octave leap.
Figure 3.9 contains the middle level reduction for measures 9-20. It begins identically to
Bach’s original and measure 10 highlights the two-octave leap and the modulation to iv. The outlines of the choral inversions on the first two beats of measure 11 lead to the descending second sequence, here again with Bach’s original notation. The change in the sequence figuration changes on beat three of measure 12, and this is emphasized in the reduction with a quarter note G. The arpeggiation of the V of A Minor is reduced to its octave outline and the
26 following broken chords emphasize the rapid movement across the keyboard. Bach’s left hand figuration in the second half of measure 14 is an elaboration of a descending arpeggio, first through a D Major triad and then through a fully diminished seventh chord. The frequent register shifts in the descending fifths sequence of measure 15 are not eliminated in the reduction,
Figure 3.7 Melodic Reduction Set 2, RH, mm. 9-20
27 Figure 3.7 continued
but rather made more pronounced with the disjunct intervallic motion. This may be one instance in which Bach’s original is simpler to play than the reduction. The winding left-hand figure in measure 17 is made simple with a descending scalar movement and the similar figuration in
28 measure 18 is truncated to a broken chord figure. The final two measures outline the chords of the cadence and follow the basic contour of the left-hand movements.
Figure 3.8 Melodic Reduction Set 2, LH, mm. 1-8
29 Figure 3.9 Melodic Reduction Set 2, LH, mm. 9-20
30 Figure 3.9 continued
The individual parts of this second set of reductions are combined in Figure 3.10 to create a playable two-hand version. The resulting form is a two-part invention that approximates the original enough to be recognizable as Bach’s Allemande but simplified enough to eliminate the pianistic difficulties of realizing all of the ornamentation.
Combined Original and Reduction
Once the student has found a reasonable reduction for the melodic line, it may be helpful to combine that reduction with Bach’s original writing for the opposite hand. Figure 3.11 combines the first set of melodic reductions with Bach’s original left hand in measures 1 through
8, and the second set right hand melodic reduction with the original left hand part in measures 9-
20. Combining a reduction in one hand and the original writing in the other creates a bridge from
31 Figure 3.10 Combined Melodic Reduction Set 2
32 Figure 3.10 continued
the reduction to the full original composition. Also, when combining the parts in such a way, the student may discover that his first inclinations for the melodic reduction do or do not align well with the original. Ideally this type of combined reduction is done at sight at the keyboard.
However, as this type of combined reduction is difficult, writing this out will prove helpful until the student develops the skills to reduce the melody at sight.
Summary
The steps to create a melodic reduction are few and simple. Table 1.1 enumerates the steps to take in the creation of a melodic reduction of the sort in the first set of reductions. This process will help to discover the underlying skeleton of the melody and the development and release of tension of its tones.
33 Figure 3.11 Combined Original and Reduction
34 Figure 3.11 continued
35 Table 1.1: Creating a Melodic Reduction
Step 1 Decrease rhythmic activity
Remove fast subdivisions of beat
Step 2 Remove all ornaments
Step 3 Remove non-harmonic tones
Passing tones
Neighboring tones
Suspensions
Appoggiaturas
Step 4 Remove octave displacements
36 HARMONIC REDUCTIONS
Understanding the harmonic structure of a tonal composition is vital to developing security in performance. The visual elements of a composition such as Bach’s Allemande are highly detailed, linear in appearance, and may obscure the harmonic foundation. Simplifying the melodic lines and reducing them to their essential elements helps to understand the counterpoint whereas simplifying the harmonic structure helps to understand the vertical elements and the functions of the harmonies.
In order to create a harmonic reduction, it is necessary to consider each harmony carefully, whether it is fully realized or only implied. The Allemande is largely in two voices, so the harmonies are not readily placed in vertical arrangements, easy for the eye to pick out as is the case in a chorale. However, the two voices are often simply arpeggiated triads or broken chords, and thus the difficulty in finding the harmonies is easily manageable. Non-harmonic tones such as melodic embellishments, passing and neighboring tones, appoggiaturas, and suspensions must be removed from the texture when creating a harmonic reduction.
In the following reductions are three strategies for creating harmonic reductions. The first set of reductions is based on the “keyboard style” suggested by Hilley and Olson in their book
Piano for the Developing Musician. In this style, often used as an accompanimental figure in that text, the left hand plays one tone while the right hand fills out the chord with three or four voices.
This is a pianistically idiomatic arrangement of chord tones and will be familiar to many students who practice keyboard harmonization exercises. Voice-leading rules are not strictly followed and the focus is more on the overall harmonies rather than correct part-writing. The second set of reductions is centered on block chords in both hands. Both hands play most chord tones and the basic contour of the keyboard geography is maintained. Despite numerous errors in doubling and
37 voice leading, this is a valuable harmonic reduction in that it helps the student to develop a kinesthetic and cognitive understanding of the harmonies in both hands at the same time. The final strategy in the harmonic reductions is based on closest position chords. The goal in this type of reduction is to move from one harmony to the next while moving the hand as little as possible.
Therefore, many chords will be in inversions not found in the original score. Understanding this type of reduction will help a student stretch aural skills, listening for harmonic quality rather than the specific voicing found in the original composition.
Throughout the harmonic reductions, the Roman Numeral analysis found in Appendix 1 serves as the basis. Appendix 1 is the original score of the Allemande as published in the
Breitkopf und Härtel edition of 1853, reset for legibility using Finale notation software.
Harmonic Reduction Set 1 – Keyboard Style
In this first harmonic reduction, the left hand part is nearly identical to Figure 3.3. The blocked chords in the right hand follow the approximate contour and hand position shape of the melody. The ascending seconds sequential motion in measure 3 is made evident with the voice leading and the brief tonicization of iv in measure 4 is readily apparent. The descending seconds sequence in measure 5 can be reduced in more than one way. I have chosen to include the passing 6/3 chords and to keep the descending chromatic line in the alto voice. The descending seconds sequence in the second half of the piece will be reduced in an alternative manner in
Figure 4.2.
This pattern of reduction continues in Figure 4.2 which contains measures 9-20. In the descending seconds sequence starting in measure 11, I use an alternative to the tactic employed
38 Figure 4.1 Harmonic Reduction, Keyboard Style, mm. 1-8
in the previous figure. Here the emphasis is on the descending second root movement and the chromatic line created by the passing 6/3 chords is eliminated. The strong cadence in A
Minor is clear in measures 13 and 14 with the cadential 3-2-1 soprano motion and the 5-1 motion in the bass line. The reduction of the descending fifths sequence starting in measure 15 observes a simple and smooth voice-leading pattern in the right hand at the expense of Bach’s florid figuration. Bach’s emphasis of the dominant is clearly visible in this reduction in measures 17 to
19.
Harmonic Reduction Set 2 – Block Chords
There is no effort in the block chord reductions of Figures 4.3 and 4.4 to be elegant. Indeed, the aesthetic result of playing this type of reduction is not particularly pleasing to the ear. The idea behind this reduction is to play most of the harmonic tones in both hands to increase
39 Figure 4.2 Harmonic Reduction, Keyboard Style, mm. 9-20 one’s bilateral awareness and coordination. There is also no determined effort to be correct in terms of voice leading. It is a sort of brute force reduction that tests the pianist’s ability to find the chord shapes in both hands at the same time. However, there is an attempt to maintain the basic melodic contour in the right hand. Because of the intensity and density of the sound in this type of reduction, I suggest that students elect to reduce small passages in this manner. The student may find blocking all chords to be laborious and should not be pressed to play the complete piece in block chords. The sequences in particular do not reduce well in this kind of reduction. In fact, it is preferable to reduce the sequences using a quicker rhythm as
40 demonstrated in Figure 4.1. However, I complete the sequences in the manner of block chords to demonstrate that applying a single set of criteria to a reduction does not always produce the desired effect.
Figure 4.3 Harmonic Reduction, Block Chords, mm. 1-8
Harmonic Reduction Set 3 – Closest Position Chords
The block chord strategy is slightly adjusted in the closest position chord reductions found in Figures 4.5 and 4.6. Here both hands play the full chords, but the hands move as little as possible from one harmony to the next. The individual chords do not match the inversions indicated by the original Roman numeral analysis. The inversions are instead dictated by the position of the previous chord. The motion from one chord to the next is as efficient as is reasonable. As with the block chord reductions, most voice leading rules are broken, such as parallel fifths and octaves, and forbidden voice doublings and resolutions. The relaxation of the rules here is for the sake of the keyboard exercise of finding efficient hand movements through the harmonies.
41 Figure 4.4 Harmonic Reduction, Block Chords, mm. 9-20
Finding closest position chords is common practice in class piano method books such as Piano for the Developing Musician and it is an essential pianistic skill in the jazz idiom. Jazz comping often includes closest position chords in the left hand. This texture aids in permitting the pianist to focus on improvisation in the right hand. Classical pianists are often intimidated by improvisation, but this type of reduction could help a student broach the subject. Improvisation, often in the form of additional ornamentation, was once an essential element of the Baroque style, though few modern pianists include it in their interpretations. It would be a good exercise,
42 for instance, to take the left hand closest position chord reduction of the Bach, and improvise a simple melodic line above it with the right hand.
Table 4.1 describes the process of creating a harmonic reduction using the original score as a guide.
Figure 4.5 Harmonic Reduction, Closest Position Chords, mm. 1-8
43 Figure 4.6 Harmonic Reduction, Closest Position Chords, mm. 9-20
44 Table 4.1: Creating a Harmonic Reduction
Step 1 Do a Roman numeral analysis of the original
score
Step 2 Select a keyboard texture
Keyboard style
Block chords
Closest position chords
Step 3 Decide if the hands will follow the contour of
the original or not
Step 4 Use visual cues in the score, such as broken
chords and arpeggiated triads, in addition to
Roman numeral analysis to execute reduction
Step 5 Play the reduction following the harmonic
rhythm of the original score
45 STRUCTURAL REDUCTION
Creating a structural reduction that makes sense as a playable piece presents certain challenges. The highly detailed notation of a Schenkerian analysis chart, though tremendously insightful, is visually distracting to a student. An analysis chart does not have the appearance of a piano piece. A compromise must be made. The reduction must be limited to the largest and most prominent features of the score. Recognizable keyboard features, such as common chord voicings and easily recognizable counterpoint, will help to maintain a connection to idiomatic keyboard writing. Finding these elements in the score is the first task for the student. Doing a
Roman numeral analysis and form diagram are the best places to start.
In Bach’s Allemande, the most prominent musical elements are highlighted in the form diagram in chapter 2, Figure 2.1. These elements include the establishment of tonic, the four sequences and their linear intervallic patterns, the cadences, and the tonicization of iv and modulations to v, iv, and back to i. In the reduction in Figure 5.1, the harmonic events are marked with keyboard style chord progressions with cadences clearly labeled. The sequences are reduced to show the root movement and linear intervallic patterns. The resulting reduction provides an efficient and playable summary of the music structure.
Table 5.1 summarizes the process of creating an idiomatic structural reduction.
46 Figure 5.1 Structural Reduction
Table 5.1: Creating a Structural Reduction
Step 1 Complete a Roman numeral analysis of original Step 2 Create a form diagram of entire piece to highlight major musical events Look for structurally important events such as cadences, tonicizations and modulations, and sequences. Step 3 Write out these events while removing all surface details of the original Eliminate rhythmic and metric notation Use chordal textures to notate significant harmonic events Use linear textures to notate sequences Step 4 Label the musical events in the resulting reduction
47 CONCLUSION
Pianists need not fear using analytical tools when learning a piece of music such as J.S.
Bach’s Allemande from Partita No. 6 in E Minor. The visual surface of the music on the page is complex but not impenetrable. Rather than relying only on the kinesthetic, visual, and aural elements of the music while learning the piece, the piano student can greatly improve his or her understanding and confidence by creating idiomatic melodic, harmonic, and structural reductions. Students can reduce the anxiety associated with theoretical analysis by creating reductions and simplifications that are playable. The processes involved in creating reductions are not complicated, and many pianists already possess the tools to start.
48 APPENDIX
ALLEMANDE WITH ROMAN NUMERAL ANALYSIS
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50 51 BIBLIOGRAPHY
Bach, Johann Sebastian. (1853) Partita No. 6 in E Minor, BWV 830. Bach-Gesellschaft Ausgabe 3. Leipzig: Breitkopf und Härtel.
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Bruhn, Siglind. (1989). Guidelines to Piano Interpretation. Penang, Malaysia: Rhythm Publishing Co. SDN. BHD.
Byo, James L. (2014). Applying Score Analysis to a Rehearsal Pedagogy of Expressive Performance. Music Educators Journal 101(2), 76-82.
Chaffin, Roger, and Gabriela Imreh. (2002). Practicing Perfection: Piano Performance as Expert Memory. Psychological Science, 13(4), 342-349.
Chaffin, Roger., Gabriela Imreh, Anthony Lemieux, and Colleen Chen. (2003). Seeing the Big Picture: Piano Practice as Expert Problem Solving. Music Perception: An Interdisciplinary Journal, 20(4), 465-490.
Clendinning, Jane Piper, and Elizabeth West Marvin. (2005). The Musician’s Guide to Theory and Analysis. New York: W.W. Norton.
Duke, Robert A., Amy L. Simmons, and Carla Davis Cash. (2009). It’s Not How Much; It’s How: Characteristics of Practice Behavior and Retention of Performance Skills. Journal of Research in Music Education, 56(4), 310-321.
Ericsson, K.A., R.T. Krampe, and C. Tesch-Römer. (1993). The role of deliberate practice in the acquisition of expert performance. Psychological Review 100, 363-406.
Fisk, Charles. (1996). Performance, Analysis, and Musical Imagining. College Music Symposium, 36, 59-72.
Gordon, Stewart. (1996). A History of Keyboard Literature: Music for the Piano and its Forerunners. California: Wadsworth.
Hilley, Martha, and Lynn Freeman Olson. (2006). Piano for the Developing Musician. Belmont, CA: Schirmer.
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Howell, Tim. (1992) Analysis and Performance: The Search for a Middleground. In John Payner, Ed. Companion to Contemporary Musical Thought (692-714). London: Routledge.
52 Katz, Martin. (2009). The Complete Collaborator: The Pianist as Partner. New York: Oxford University Press.
Little, Meredith, and Natalie Jenne. (2001). Dance and the Music of J.S. Bach. Indiana: Indiana University Press.
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Teixeira dos Santos, Regina Antunes, and Cristina Capparelli Gerling. (2012). Ways of knowing and types of knowledge: How do students approach a new piece of music? International Journal of Music Education 30(30), 195-210.
Walther, Johann Gottfried. (1732). Musicalisches Lexicon. Leipzig: W. Deer.
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53 BIOGRAPHICAL SKETCH
Brooks Hafey was born in Grand Junction, Colorado, on April 27, 1979. He received his
Bachelor of Music degree from the University of Missouri-Columbia in December 2002, and his
Master of Music degree from Florida State University in May 2006. He has taught at Gulf Coast
State College in Panama City, FL, Sam Houston State University in Huntsville, TX, Chadron
State College in Chadron, NE, and La Musica Lirica in Novafeltria, Italy. His academic interests include piano literature, conducting, vocal and instrumental music, opera, foreign languages, and pedagogy. Outside of the professional realm, he enjoys hiking, camping, traveling, and spending time with his family and dogs. He is an active solo and collaborative performer and educator.
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