Analyzing and Reinterpreting Dimensions of Bach's Harmonic Rhythm by F. C. Zuke

The University of Nebraskaâ&#x20AC;&#x201C;Lincoln

Analyzing and Reinterpreting Dimensions of Bachâ&#x20AC;&#x2122;s Harmonic Rhythm

A Senior Honors Thesis Project Submitted to the Hixon-Lied College of Fine and Performing Arts

F. C. Zuke

CONTENTS

LIST OF FIGURES

ACKNOWLEDGEMENTS

vii

ABSTRACT

PART I: A DIMENSIONAL ANALYSIS HOW DO WE ANALYZE HARMONIC RHYTHM?

A DIMENSIONAL ANLAYSIS OF HARMONIC RHYTHM

Composite Rhythm

Phenomenal Rhythm

Bass Pitch Rhythm

Root/Quality Rhythm

Harmonic Density

Rhythm of Harmonic Function

“HERR, UNSER HERRSCHER”: THE RHYTHMS OF THE DIMENSIONS

CONCLUSION TO PART I

PART II: REINTERPRETATION A REINTERPRETATION OF BACH’S HARMONIC RHYTHM

A Reinterpretation of the Root/Quality Dimension

A Reinterpretation of Harmonic Density

FINAL REMARKS

BIBLIOGRAPHY

35 Click here to go to appendices

APPENDICES

LIST OF FIGURES

Figure 1: Traditional analysis of harmonic rhythm

Figure 2: Ignored bass activity in Piston’s analysis

Figure 3: First two cadences in Nun lob’ mein’ Seel’, den Herzen

Figure 4: Analysis of composite rhythm

Figure 5: Comparison of composite and phenomenal rhythms

Figure 6: Distinguishing differences in bass activity

Figure 7: Harmonic density in Nun lob’ mein’ Seel’, den Herzen

Figure 8: Analysis of harmonic density

Figure 9: A different perspective of harmonic density

Figure 10: Notation of hard and soft changes of harmonic density

Figure 11: Primary patterns of bass rhythm throughout “Herr, unser Herrscher”

Figure 12: Guidelines for designating new pitches as hard or soft

Figure 13: Level of harmonic density throughout “Herr, unser Herrscher”

Figure 14: “Herr, unser Herrscher” root/quality rhythm, mm. 19-23

Figure 15: Analysis of unordered pitch class intervals in “Herr, unser Herrscher” 29 Figure 16: New bass line reinterpreted from Bach’s series of chord roots

Acknowledgements

Thank you to Dr. Kurt Knecht for his guidance, expertise, and encouragement throughout the course of this project and in the study composition.

Thank you also to Dr. Stanley Kleppinger for his willingness to serve as the second reader and for the knowledge gained from his theory courses.

ABSTRACT (Updated February 2, 2016)

The primary part of this thesis project analyzes the harmonic rhythm of J. S. Bach’s “Herr, unser Herrscher”, the opening chorus from St. John Passion. While several theorists from the 20th century have addressed harmonic rhythm in terms of the metrical position of chord changes, some more recent publications have explored ways to analyze harmonic rhythm in greater detail. This paper explains these methods of analysis as well as the differences and additions made to those methods. Furthermore, the project provides a modernized transcription of Bach’s work, an analysis underneath the score, and a commentary that illuminates some important aspects of this work in respect to harmonic rhythm. An additional part of this project involves new musical material. Explanations of compositional processes will be provided for reinterpreting the analysis from “Herr, unser Herrscher”. Elements from Bach’s music will govern the procedure, but these elements are used in different ways so that they may no longer be recognizable. The author’s personal goal for this project is to demonstrate how tradition can be filtered through a 21st century lens and how music from our history can inspire new works.

PART I A DIMENSIONAL ANALYSIS

HOW DO WE ANALYZE HARMONIC RHYTHM?

Harmonic rhythm has often been an underexplored area of study. Usually, harmony textbooks only superficially explore the factors that contribute to harmonic rhythm. Authors provide the reader with a rudimentary definition, such as “the frequency of harmonic change in a composition”1 or “the rate of chord change”.2 Walter Piston’s Harmony, which was once the most popular textbook used by the National Association of Schools of Music,3 devotes a significant number pages to harmonic rhythm. Piston refers to harmonic rhythm routinely throughout his book, stating that it “should be the subject of extensive research during the study of harmony.” But, like other authors, he simplifies the study of harmonic rhythm as “the distribution of chord changes in a phrase”.4 Figure 1 exemplifies this simplistic analysis of harmonic rhythm used by Piston (and others). Analyzing “Herr, unser Herrscher” with the traditional one-line method only results in a series of half notes and whole notes. While this procedure might serve as a fundamental starting point for harmonic rhythm, there is room for much more insight.

1. Gary White, The Harmonic Dimension (Dubuqe, IA: Wm. C. Brown, 1991), 112. 2. Robert Gauldin, Harmonic Practice in Tonal Music (New York: W.W. Norton, 1997), 171. 3. In 1963, a survey found that 91 of 228 schools used Piston’s Harmony as their principle theory textbook. This data can be found in George Thaddeus Jones, Symbols Used in Music Analysis: Cooperative research project no. 2049 (Washington: Catholic University of America, 1964), 9-11. 4. Walter Piston, Harmony, rev. by Mark Devoto, 4th edn. (New York: W.W. Norton, 1978), 140.

Figure 1: Traditional analysis of harmonic rhythm â&#x20AC;&#x153;Herr, unser Herrscherâ&#x20AC;?, mm. 1-4

When the study of harmonic rhythm is limited to notating the mere metrical positions of chord changes, the analyst must group the activity of each harmonic element (chord quality, chord function, bass activity, etc.) into one single analytical line. In many cases, it is beneficial to study a stratification of different musical elements in order to learn how they complement one another or work against one another in respect to harmonic rhythm. It is possible for these to elements change at different times and to move at different speeds. Take, for example, the harmonic progressions found in Figure 2. By Pistonâ&#x20AC;&#x2122;s method, each passage would receive the exact same analysis (chord changes at each quarter note). Notice, however, that the second passage contains a much more active bass line. It is reasonable to assume that the listener may hear a

more pronounced harmonic rhythm in the second example. There is no way to graph this difference if we use the superficial single-line analysis.

Figure 2: Ignored bass activity in Pistonâ&#x20AC;&#x2122;s analysis

Furthermore, the simplistic, â&#x20AC;&#x153;merely quantitativeâ&#x20AC;?5 methods discussed above ignore the means by which harmonies change. In the study of functional harmony, students learn not only the order of progressions, but also the means by which each chord changes (e.g. the proper resolutions of the leading tone and fourth scale degrees in a V7 chord). Like a harmony textbook demonstrating the importance of voice leading, this paper will demonstrate the benefits of analyzing harmonic rhythm at a deeper level. The following example further demonstrates how a single-line analysis fails to distinguish between different means or strengths of harmonic change.

5. Piston, 202.

Figure 3: First two cadences in Nun lob’ mein’ Seel’, den Herzen6

The two cadences above (Figure 3) are excerpted from a Bach chorale harmonization. Notice that the progressions are nearly identical. The only difference is the way in which the chords are voiced. As a result of this difference, only three voices move to a new pitch at the first cadence, while all four voices move from the V chord to the I chord at the second cadence. Surely the connectedness of individual voices plays a role in the listener’s perception of harmonic rhythm.7 The system of analysis used in this project is primarily based on a system developed by Joseph P. Swain, which is outlined in his book entitled Harmonic Rhythm: Analysis and Interpretation.8 His method compensates for some of the insufficiencies found in the single-line methods of Piston and others. The following pages will contain an explanation of Swain’s philosophies in addition to the changes and additions made to that system for the purposes of this project. Although this paper is not a survey of analytical methods, it is necessary to briefly describe the method used in this paper so that the reader will better comprehend the analysis and reinterpretation. 6. Johann Sebastian Bach, 371 Harmonized Chorales and 69 Chorale Melodies, ed. Albert Riemenschneider (New York: G. Schirmer, Inc., 1941), 2. 7. Further elaboration on this idea can be found in the Harmonic Density section of this paper. 8. Joseph P. Swain, Harmonic Rhythm: Analysis and Interpretation (Oxford, New York: Oxford University Press, 2002). An eBook is also available, accessible through the World Wide Web.

A DIMENSIONAL ANALYSIS OF HARMONIC RHYTHM Swain refers to his graphical analysis of harmonic rhythm as a â&#x20AC;&#x153;dimensional analysisâ&#x20AC;?9. This references the graphâ&#x20AC;&#x2122;s ability to separate the elements of harmonic rhythm, which Swain labels as dimensions. He says that this system â&#x20AC;&#x153;isolates each of the components of harmonic rhythm, each aspect that changes, so that all may be evaluated separately yet seen together at a glance.â&#x20AC;?10 In essence, this system is like a microscope that allows us to view the inner workings of a simplistic, one-line representation of harmonic rhythm. It stratifies harmonic elements and puts them on a graph so that we can study the activity of each one and how they relate to one another. The following pages contain brief descriptions of Swainâ&#x20AC;&#x2122;s dimensions of harmonic rhythm. This paper does not cover Swainâ&#x20AC;&#x2122;s theory in its entirety. Swainâ&#x20AC;&#x2122;s philosophies that are not relevant to the analysis and reinterpretation of Bach are excluded. Further information can be found in his book. An abridged version of Swainâ&#x20AC;&#x2122;s method is also available in a short article that preceded the primary text.11 The modifications and additions to his system are designed to specifically assist in the analysis of the work in question.

9. Swain, Harmonic Rhythm, v. 10. Ibid. 11. Joseph P. Swain, â&#x20AC;&#x153;Dimensions of Harmonic Rhythmâ&#x20AC;?, Music Theory Spectrum 20, no. 1 (Spring, 1998), 48-71. Available on JSTOR (doi:10.2307/746156).

Composite Rhythm The first dimension analyzes what Swain refers to as â&#x20AC;&#x153;textural rhythmâ&#x20AC;?.12 This part of the graph notates each moment that a voice is articulated within a polyphonic texture. Other theorists have referred to this as â&#x20AC;&#x153;composite rhythmâ&#x20AC;?, a term which will be used in place of â&#x20AC;&#x153;textural rhythmâ&#x20AC;? henceforth.13 This first dimension introduces an important principle of Swainâ&#x20AC;&#x2122;s ideology: elements that might not immediately be recognized as pertinent to harmony might still reveal information relative to the rhythm of harmony. Swain puts forth the following justification for the presence of composite rhythm in his graph:

â&#x20AC;&#x153;Having the [composite] rhythm at the top of the graph gives an absolute standard, a theoretical limit to the harmonic rhythm of the passage under analysis: no dimension of harmonic rhythm can possibly move faster than the textural rhythm at any moment. When it comes to judging how fast any particular dimension of harmonic rhythm moves, it is often useful to know exactly how fast it could move, if the composer so desired, within that texture.â&#x20AC;?14 Composite rhythm also provides an abstract view of activity within a polyphonic

texture as chords are prolonged. We are able to see the busyness of the texture in between each harmonic entrance. As with all dimensions, this initial one will prove more useful as we compare it to the others. Figure 4 shows the graphical representation of composite rhythm.

12. Swain, Harmonic Rhythm, 16. 13. The author of this paper has found â&#x20AC;&#x153;composite rhythmâ&#x20AC;? to be a more popular and intelligible term among his peers. 14. Swain, Harmonic Rhythm, 17.

Figure 4: Analysis of composite rhythm15 J. S. Bach, Prelude in A Major from The Well-Tempered Clavier, vol. 2, mm. 1-2

Phenomenal Rhythm The dimension of phenomenal harmonic rhythm addresses the occurrences of new pitches. It is almost identical to composite rhythm. The only difference is that repeated pitches do not register on the phenomenal rhythm graph. Changes of an octave are considered new pitches.16 Figure 5 contains two analyses of composite and phenomenal rhythm. Why analyze phenomenal rhythm? Like composite rhythm, it may give the analyst an idea as to what the fastest harmonic rhythm could be (each time a new pitch occurs, there is an opportunity for a new chord). This, however, is not the most important use of the phenomenal rhythm dimension. 15. Transcription and analysis taken from Swain, Harmonic Rhythm, 23. 16. Swain elaborates on the justifications for considering octave changes as new pitches. See Swain, Harmonic Rhythm, 24.

Figure 5: Comparison of composite and phenomenal rhythms17

J. S. Bach, Prelude in A Major from The Well-Tempered Clavier, vol. 2, mm. 1-2

Vivaldi, Concerto op. 8, no. 4, â&#x20AC;&#x153;Winterâ&#x20AC;?, I, mm. 1-4

Some music can be explained by the congruence or incongruence between the composite and phenomenal dimensions. If we analyze two pieces that have the same composite rhythm, but different phenomenal rhythms, we might be able to explain the musical effect that is created by disagreement between the two dimensions.18 Swain compares the Bach and Vivaldi excerpts above in order to exemplify this principle. While the phenomenal rhythm moves at the same speed as the composite rhythm in the 17. Transcriptions and analyses taken from Swain, Harmonic Rhythm, 23. 18. Swain, Harmonic Rhythm, 23.

Bach, there is an obvious disagreement between the two dimensions in the Vivaldi. Notice how the whole note phenomenal rhythm conflicts with the straight eighth note pace of the composite rhythm. Swain finds that the phenomenal rhythm’s “resistance” to the speed of the composite rhythm is what creates interest (a “terrific strain”19 as he calls it).

Bass Pitch Rhythm The third dimension of Swain’s graph marks changes in pitch of the bass voice. Like phenomenal rhythm, octave changes are also considered new bass pitches.20 The importance of notating changes in bass pitch is fairly straightforward. Swain points to the importance of the bass voice throughout the common practice period as it relates to harmony: “Throughout the so-called common practice period, when musical languages assigned specific syntactic roles or functions to different triads within the context of a key, music theorists, analysts, and critics have pointed to the bass voice of a texture as the one that has the most effect on harmonic articulation and movement. German writers have called it Harmonieträger, the harmony carrier. Since Rameau, harmonic analysis has focused on triad identities, but many thinkers before him said nothing of triads but instead wrote very useful books on how to build compositions on a bass line.”21 Figure 2 demonstrated the failure of Piston’s method to show important differences in bass pitch rhythm. The same passages appear here (Figure 6) with bass 19. Swain, Harmonic Rhythm, 23. 20. Notating octave changes may be appropriate in the analysis of bass pitch rhythm due to the importance of the bass voice in respect to chord changes. For a musical example demonstrating why octave changes are considered new pitches, see Swain, Harmonic Rhythm, 30-31. 21. Swain, Harmonic Rhythm, 29.

pitch rhythm analysis included). Although both passages contain chord changes at every quarter note, the bass lines are much different. The graph provides us with a clear representation of bass activity.

Figure 6 : Distinguishing differences in bass activity

This dimension may be beneficial in itself, but when it appears alongside the other dimensions, it can reveal more detailed information regarding the music as a whole. This is discussed in the analysis section.

Root/Quality Rhythm No dimension of Swainâ&#x20AC;&#x2122;s system has hitherto addressed actual harmonies. The root/quality dimension is the first to involve the analysis of simultaneous pitches as chords. This dimension only addresses the root and quality of chordsâ&#x20AC;&#x201C;function is ignored. The reason for this separation echoes the original flaw of Pistonâ&#x20AC;&#x2122;s one-line

analytical method: harmonic elements move at different speeds and one analytical line is (at times) not sufficient. Therefor, Roman numerals are not used. Swain states, “Roman numeral analysis summarizes three different harmonic features [root, quality and rhythm] that are to some extent independent of one another”.22 Take, for example, a D7 chord followed by an F# diminished chord in the key of G. This progression may contain two separate chords, but both chords are nested within an event of dominant harmonic function. In this dimensional system, the analyst can graphically represent how the rhythm of individual chords may be nested within the rhythm of a broader harmonic function. This dimension inevitably requires more subjective analytical decisions to be made. Another benefit of separating function from root/quality, however, is that fewer decisions need to be made at once. In the case of the root/quality dimension, problems related to functional ambiguity are ignored for the moment. The following chord symbols will be used for root/quality identification in “Herr, unser Herrscher”.

Major: G Dominant Seventh: G7 Augmented: G+ Half-Diminished Seventh: gJ

22. Swain, Harmonic Rhythm, 41.

Minor: g Dominant Ninth: G9 Diminished: gdim. Diminished Seventh: gdim7

Harmonic Density Density of harmonic rhythm addresses the means or strength with which chords change. The density graph counts the number of voices that move to a new pitch when a new chord is formed. Voices that repeat the same pitch between two chords are not counted on the graph (e.g. anticipations, common tones). Tones that do not contribute to the new chord (e.g. suspensions, accented passing tones) are not counted on the graph either. Voices that enter after a rest are considered new pitches and are thus counted on the density graph. Swain refers to harmonic density as a sort of “volume control” on harmonic rhythm.23 The logic behind this dimension is simple: more voices moving to a new chord results in a more pronounced harmonic change. Perhaps “accentuation control” of harmonic rhythm would be a better descriptor. The notation used in this paper is slightly different from Swain’s. His graphical representation of density involves markings that extend upwards, intersecting the horizontal lines of the graph. The number of lines that each marking touches symbolizes the number of voices that move to a new pitch at a new chord. This paper uses stacked squares. Each square represents one voice contributing to the density of the new chord. This “counting squares” method might be a more intuitive representation of harmonic density than Swain’s method.24

23. Swain, Harmonic Rhythm, 61. 24. To see Swain’s graphing system, refer to Swain, Harmonic Rhythm, 58-59.

Recall the two Bach cadences discussed earlier in this paper (Figure 3). The single-line analysis of harmonic rhythm did not convey any information related to differences in harmonic density. If we were to graph the density of these two cadences, the analysis would be as follows (Figure 7).

Figure 7: Harmonic density in Nun lob’ mein’ Seel’, den Herzen25

The density graph can reveal significant musical events. Swain mentions the endings of some Bach fugues in which the composer uses less fluid voice leading (a higher harmonic density) in order to create a more climactic conclusion.26 He has also found that some works gradually increase in density as a climax is approached.27 “Herr, unser Herrscher” contains some very explicit patterns of harmonic density, which are discussed later in this paper. Just as the first two dimensions connected harmony to contrapuntal activity, it appears that density can connect harmony to another musical element—form. Other uses of the density graph are discussed in the analysis of “Herr, unser Herrscher”. 25. Johann Sebastian Bach, 371 Harmonized Chorales and 69 Chorale Melodies, ed. Albert Riemenschneider (New York: G. Schirmer, Inc., 1941), 2. 26. Swain, Harmonic Rhythm, 67. 27. Swain, “Dimensions of Harmonic Rhythm”, 62-64 (Music Theory Spectrum page numbers).

The analysis of harmonic density can be problematic and misleading at times. As a hypothetical example, turn to the following passage (Figure 8).

Figure 8: Analysis of harmonic density

By the strict definition of harmonic density, the above analysis is correct. Each member of the three-voice texture changes to a new pitch at each chord, resulting in maximum harmonic density throughout. If we study the top voice, however, we find that a D4 pitch is repeated in the first two measures with neighboring tone embellishments in between. Is this voice actually moving to a new pitch at each chord change? Could each set of four sixteenth notes be instead considered as single events of the D4 pitch? Other problems arise if we analyze from an even more abstract perspective. What about the neighboring tone in the middle voice between the first and second chord? What about the eighth note figure in the first measure? Does the anticipation of the upcoming F3 take away from its appearance in the d/A chord? Further problems arise if we address tempo, articulation, etc. The previous analysis considers the passage to contain maximum harmonic density throughout, but another analysis might be equally valid (see Figure 9).

Figure 9: A different perspective of harmonic density

Because of the prevalence of this problem in â&#x20AC;&#x153;Herr, unser Herrscherâ&#x20AC;?, the density graph will receive one addition. The terms â&#x20AC;&#x153;soft changesâ&#x20AC;? and â&#x20AC;&#x153;hard changesâ&#x20AC;? will be used to refer to the following types of voice change: 1. Voices that technically move to a new pitch at a chord change, but whose structural pitch remains the same, are considered soft changes. These voices are parenthesized on the density graph. 2. Voices that structurally move from one chord tone to a new chord tone are considered hard changes. Blocks without parentheses symbolize hard changes. Figure 10 shows how this addition to Swainâ&#x20AC;&#x2122;s system can reconcile (some) ambiguities.

Figure 10: Notation of hard and soft changes of harmonic density

Of course, this system still does not provide an answer of what constitutes soft and hard changes. The analyst must make a subjective decision and choose the level of abstraction. In the upcoming pages, a set of guidelines will be explained for the density analysis of â&#x20AC;&#x153;Herr, unser Herrscherâ&#x20AC;?, but other perspectives may be equally as valid.

Rhythm of Harmonic Function This final dimension simply declares the â&#x20AC;&#x153;key in forceâ&#x20AC;? 28 at any given moment and notates how chords function within that key or take us to new ones. For the analysis of common-practice music, Swain uses the three functions declared by Hugo Riemann: tonic, subdominant, and dominant.29 While Swain uses Riemannâ&#x20AC;&#x2122;s Roman numerals to represent function, this paper will instead use a straightforward lettering system. This system is based on the method of theorist Ian Quinn.30 The lettering system is diagramed below. Quinnâ&#x20AC;&#x2122;s system also involves the analysis of the bass scale degree, but this paper will take a less aggressive approach. Only root position chords are specially marked (with a square around the functional symbol) in order to reveal where strong, root-position sonorities sound.

T â&#x20AC;&#x201C; Tonic

S â&#x20AC;&#x201C; Subdominant

D - Dominant

P - Parallel and counter parallel chords (e.g. III and VI) 28. Swain, Harmonic Rhythm, 70. 29. Ibid., 69. 30. Ian Quinn, â&#x20AC;&#x153;Harmonic Function Without Primary Triadsâ&#x20AC;? (paper delivered at the annual meeting of the Society for Music Theory, Boston, November 2005).

“HERR, UNSER HERRSCHER”: THE RHYTHMS OF THE DIMENSIONS The dimensions of harmonic rhythm can be analyzed to reveal the character of Bach’s music. This includes studying the dimensions individually and in combination with one another. While the analysis31 itself is highly detailed and provides a glance at many of the qualities that define “Herr, unser Herrscher”, the following pages will briefly address some of the more noteworthy findings. If we restrict our analysis to the rhythm of the bass pitch, we can derive some interesting information in regards to form. Notice that there are three primary patterns of bass activity throughout the entire piece (Figure 11). With a few brief exceptions, these patterns permeate the entire work.

Figure 11: Primary patterns of bass rhythm throughout “Herr, unser Herrscher” a) long pedal tone (e.g. mm. 1-9)

b) whole note and half note changes (e.g. mm. 10-18)

c) repeated sixteenth note figures (e.g. mm. 34-36)

This reduction exemplifies Bach’s ability to compose a considerable amount of music with only a few recurring bass patterns. Each pattern has certain idiosyncrasies. Moments of long pedal tones (a) are always met with a tonic or dominant tonal center. 31. Please see Appendix A for the transcription and analysis of “Herr, unser Herrscher”.

During these moments, the bass pitch rhythm is often the only element preventing all dimensions from agreeing on a change. Perhaps this creates a “terrific strain” like the Vivaldi excerpt earlier. The rhythm of whole notes and half notes (b) is often paired with the circle of fifths progression or other patterns containing several modulations. The sixteenth note bass pitch rhythm (c) contains several instances of quick tonicizations. This figure also acts as a trigger for episodes of canonic choral activity.32 This bird’s eye view of the bass activity provides the analyst with a simplified perspective of overall structure. The root/quality dimension has received a “surface-level” analysis. Swain states that certain passages may require different levels of analysis (a surface-level and a more abstract level) in order to differentiate between chords that are essential to the harmonic structure and those that merely pass by for a fleeting moment.33 This paper suggests that a multilevel analysis might be avoided by using a surface-level analysis of the root/quality dimension in combination with an abstract analysis of function. This method is rather effective in that it offers a compromise between presenting just one level of analysis and splattering the pages with several levels. In the analysis of “Herr, unser Herrscher”, analysts can find different levels of activity by comparing the surface-level root/quality dimension with the more abstract function dimension. An abstract analysis of function may be most appropriate for this particular piece: the chords seem to be, at times, an ambiguous result of Bach’s contrapuntal complexity (e.g. pedal tones, decorated suspensions, etc.). Pairing these 32. See measures 33, 58, and 78 for examples. 33. Swain, 43-57.

two analyses is rather efficient, and it is surely more successful than one line of Roman numerals that must either ignore certain chords or represent all chords as equally significant. During the course of this project, a significant amount of time has been devoted to the study of harmonic density. This dimension provides a great amount of information relative to harmonic changes and textural changes. Before Bach’s music is addressed, however, recall the problem discussed earlier in regards to “hard” or “soft” changes of harmonic density. Due to considerations of tempo, rhythm, and meter, the following system has been devised to help designate voice changes as hard or soft when new chords are formed. Soft changes are restricted to a one beat proximity. In other words, the new chord tone must be anticipated within one beat of the new chord. One exception exists (see below). Figure 12 shows various sixteenth note patterns that permeate Bach’s chorus. Most of the problems surrounding hard vs. soft changes of harmonic density involve these figures. This diagram is intended to represent the general approach to determining whether pitch changes are hard or soft. Assume that a chord is formed on each downbeat of Figure 12.

Figure 12: Guidelines for designating new pitches as hard or soft

Chord 1

Chord 2 The new chord tone is the same pitch and occurs at precisely the same metrical position as the previous chord tone. The fundamental structure is the same. This is considered a soft change.

The new chord tone (Bb) appears in the previous beat but only as a decoration of the previous chord tone (C). Furthermore, the new chord tone is slightly more accented because it is approached by a skip as opposed to a step. Therefor, this is considered a hard change.

The new chord tone occurs just one half beat prior and is only separated by a neighboring tone. This is considered a soft change.

The new chord tone appears immediately before the chord is formed. This does not register on the density graph.

At the beginning of â&#x20AC;&#x153;Herr, unser Herrscherâ&#x20AC;?, a rather consistent density level of four can be found. Notice how the top two voices weave in and out of one another. These two voices move exclusively by oblique motion until the contrary motion in measure 7. This contrapuntal event gives us our first density level five. Notice that this moment also involves the retonicization of our home key (albeit weakened by the pedal tone). Density level five occurs regularly leading up to the choral entrance at measure 19. Finding trends in harmonic density becomes more challenging after the choir enters. Irregular plunges to density level three or four can often be explained by weak beat choral

exclamations in which the choir echoes a sonority that has already arrived. Turn to mm. 40-41 to see this exemplified. The Eb chord is particularly weak, with only 1 hard change. The density graph can assist in making hierarchical decisions. Notice that the Eb chord in measure 40 is nested alongside the preceding G minor chord within a tonic function. The modest density level of this chord furthers the evidence for this analysis. The density graph has proved to be a useful â&#x20AC;&#x153;analytical bridgeâ&#x20AC;? for making these decisions in this project. Its position between the root/quality and function dimensions seems most appropriate.34 The improvement on Swainâ&#x20AC;&#x2122;s system of distinguishing between hard and soft changes has also proved useful for revealing the superficiality of certain chords in the surface-level analysis. Turn, for example, to the second half of measure 21. The F#dim7 chord contains a density level of 8, of which only 1 pitch is a hard change. This raises the question as to whether there are actually two chords present. Perhaps the single hard change is simply the resolution of a suspension. Of course, the density analysis itself does bring us to a definite conclusion, but it may serve as a caution flag for further inspection.

34. Swain also touches on the usefulness of the density graph in revealing more significant chord changes and higher-level harmonic activity. See Swain, Harmonic Rhythm, 60-63.

Figure 13 plots the harmonic density of every chord in â&#x20AC;&#x153;Herr, unser Herrscherâ&#x20AC;?. We find quite a variety of peaks and valleys throughout, but general observations can be made. Notice the (somewhat) gradual increase in density during the first 30 measures. From there, the density level gradually decreases before it starts another process of growth to the maximum density level at measure 83.

Bach achieves maximum harmonic density in this work by dividing the flute and oboe just a few measures prior to measure 83. Notice that the rhythms of all dimensions change at this moment. This is a noteworthy event in regards to harmonic rhythm. This is also the only moment in the entire piece that the composite and phenomenal dimensions stray from the motor rhythm of straight sixteenth notes. These subtle, yet peculiar, phenomena mark the beginning of the melismatic surge to the da capo.

CONCLUSION TO PART I

Part I of this project has accomplished several objectives:

1) It has exposed some inadequacies of one-line analyses of harmonic rhythm. 2) It has outlined a system that compensates for some of these flaws. 3) It has provided some improvements to Swainâ&#x20AC;&#x2122;s method in order to illuminate harmonic changes in greater detail. 4) It has shown how the analysis process might be streamlined by analyzing the root/quality and function dimensions from different perspectives in order to avoid multilevel analyses. 5) It has provided a transcription and highly detailed analysis of the opening movement from a very important musical work.

Throughout the course of this project it became increasingly apparent that an analysis of harmonic rhythm must welcome not only the study of rhythm but of contrapuntal motion as well. Perhaps an important lesson from this paper is that music theory often requires an awareness of several (or all) elements of music in order to understand even a single aspect.

PART II REINTERPRETATION

A REINTERPRETATION OF BACH’S HARMONIC RHYTHM

For the purposes of this project, “reinterpretation” refers to the process by which musical elements are isolated and used to inspire new musical passages. While the ideas expressed in this section may very well lead to new compositions, a complete step-bystep description of compositional processes is beyond the scope of this paper. The following pages are simply intended to exemplify how musical elements can be recycled in order to provide a starting point for new works.

A Reinterpretation of the Root/Quality Dimension

Figure 14: “Herr, unser Herrscher” root/quality rhythm, mm. 19-23

One goal of the reinterpretation of Bach is to create new musical ideas that are not recognized as having been inspired by Baroque music. Figure 14 graphs the rhythm of the root/quality dimension at the first choral entrance. The harmonic progression is quite conventional at this point. One method of reinterpreting this passage begins with an analysis of intervals formed between the roots of each chord.

Figure 15: Analysis of unordered pitch class intervals in “Herr, unser Herrscher”

Unordered Pitch-Class Intervals

Figure 15 shows an analysis of unordered pitch-class intervals formed between the roots of each chord. Through trial and error, that interval series has resulted in the following new bass line, with precisely the same UPCI series (Figure 16).

Figure 16: New bass line reinterpreted from Bach’s series of chord roots

Unordered Pitch-Class Intervals

The excerpt entitled “Harmonic Prototype”35 represents the harmonic structure of a new piece. The bass line above has been harmonized using a quasi-functional harmonic vocabulary. The only difference is the third to last bass pitch. The A natural from Figure 16 has been replaced with an Eb, resulting in an augmented sixth chord (an operation referred to as tritone substitution in jazz terminology). This harmonic

35. See Appendix B.

structure might now be “reverse engineered” in order to work out motivic and rhythmic ideas for a full composition.

A Reinterpretation of the Density Dimension The excerpt entitled “Interlude No. 1”36 exemplifies one reinterpretation of the harmonic density of “Herr, unser Herrscher” (mm. 1-18). In this excerpt, the density graph has been labeled “polyphonic density”, because the compositional processes of this excerpt are constructed by linear operations, as opposed to harmonically inspired ones. In the Bach analysis, each density level signified the number of voices contributing to a new chord. In this reinterpretation, each density level signifies the number of new pitches that occur, at any point, before a new density marking occurs. Appendix B also includes an analysis of the first page of “Interlude No. 1” which may most clearly demonstrate how the music fits the density graph. The analysis counts new pitches from top to bottom over each density marking. Musical events that involve voice doublings (e.g. the tritone doublings on beat 1 and 2 of measure 2) are counted as single events. Recurring ideas, such as the repeated Eb-A diad in the first measures of the “Ee-A-Ee-Ee” (electronic instrument) are not counted on the density graph. This short excerpt demonstrates the general procedures for one reinterpretation of Bach’s harmonic density into the “polyphonic density” of a new work.

36. See Appendix B.

FINAL REMARKS Although Part I alone would have comprised a significant thesis project, it is appropriate that Part II serves as the conclusion. It is the authorâ&#x20AC;&#x2122;s interest in the study of music composition, and in the cycle of analysis and reinterpretation, that justified the addition of Part II. There are several other ways for concealing or disguising the music of the masters in new music. Bachâ&#x20AC;&#x2122;s sonorities might be transformed via set theory operations, hard and soft changes in the density graph might have other contrapuntal implications, harmonic function might influence timbrel changes, the bass pitch rhythm might be used in a retrograde, etc. Part II has served as a small demonstration for what else may be possible. But why is this important? What is the purpose of isolating musical elements and putting them in another context? For one, it pays homage to the great composers who came before and creates opportunities for theorists and those who study music to unravel the mysteries of a composition. In addition, the process of reinterpretation opens up new doors that composers may not have considered by mere intuition or experimentation at a keyboard. Music theory offers an escape from instinctual musical decisions and can be used to overcome redundant impulses. Hopefully, the reinterpretations of Bachâ&#x20AC;&#x2122;s harmonic rhythm contained in this paper might point towards other creative paths which students of music composition might pursue.

BIBLIOGRAPHY

Bach, Johann Sebastian. 371 Harmonized Chorales and 69 Chorale Melodies. Edited by Albert Riemenschneider. New York: G. Schirmer, Inc., 1941.

Bach, Johann Sebastian. Johannespassion. Composer’s manuscript. Revised in 1749.

Bach, Johann Sebastian. St. John Passion. Edited by Arthur Mendel. Kassel: Bärenreiter, 1974.

Bach, Johann Sebastian. St. John Passion. Edited by Herman Roth. Vienna: Wiener Philharmonischer Verlag, 1920.

Bach, Johann Sebastian. St John Passion. Edited by Wilhelm Rust. New York: Dover, 1993.

Dürr, Alfred. Johann Sebastian Bach St. John Passion: Genesis, Transmission, and Meaning. Translated by Alfred Clayton. Oxford; New York: Oxford University Press, 2000.

Forte, Allen. Tonal Harmony in Concept and Practice. Third Edition. New York: Holt, Rinehart and Winston, 1979.

Gauldin, Robert. Harmonic Practice in Tonal Music. New York: W.W. Norton, 1997.

Jaffe, Andy. Jazz Harmony. N.p.: Advance Music, 1996.

Jones, George Thaddeus. Symbols Used in Music Analysis: Cooperative Research Project no. 2049. N.p.: Catholic University of America, 1964.

Ottman, Robert W. Elementary Harmony: Theory and Practice. Englewood Cliffs, N.J.: Prentice-Hall, 1961.

Piston, Walter. Harmony. Revised by Mark Devoto. Fourth Edition. New York: W.W. Norton, 1978.

Pratt, George. The Dynamics of Harmony: Principles & Practice. Milton Keynes, England; Philadelphia, PA: Open University Press, 1984.

Quinn, Ian. “Harmonic Function Without Primary Triads”. Paper delivered at the annual meeting of the Society for Music Theory in Boston, November 2005.

Richter, Ernst Friedrich. Richter’s Manual of Harmony: A Practical Guide to Its Study, Prepared Especially for the Conservatory of Music at Leipsic. Translated by John P. Morgan. New York: G. Schirmer, 1867.

Sadai, Yizhak. Harmony in Its Systematic and Phenomenological Aspects. Translated by J. Davis and M Shlesinger. Jerusalem: Yanetz, 1980.

Schenker, Heinrich. Harmony. Edited and annotated by Oswald Jonas. Translated by Elisabeth Mann Borgese. Chicago: University of Chicago Press, 1954.

Schoenberg, Arnold. Theory of Harmony (Harmonielehre). Translated by Roy E. Carter. Berkeley: University of California Press, 1978.

Swain, Joseph P. “Dimensions of Harmonic Rhythm”. Music Theory Spectrum 20, no. 1 (Spring, 1998), 48-71. Available on JSTOR, doi:10.2307/746156.

Swain, Joseph P. Harmonic Rhythm: Analysis and Interpretation. Oxford, New York: Oxford University Press, 2002.

White, Gary. The Harmonic Dimension. Dubuqe, IA: Wm. C. Brown, 1991.

APPENDICES to

Analyzing and Reinterpreting Dimensions of Bachâ&#x20AC;&#x2122;s Harmonic Rhythm

F. C. Zuke

APPENDIX A

J. S. Bach “Herr, unser Herrscher” From St. John Passion

A Dimensional Analysis of Harmonic Rhythm

Appendix to Part I of Analyzing and Reinterpreting Dimensions of Bach’s Harmonic Rhythm

Transcription Notes The following score and analysis is a modernized transcription of J.S. Bach’s “Herr, unser

•

Herrscher” chorus from St. John Passion. Listed to the right are the modifications made to earlier editions of the score. Several editions of the score (including Bach’s original manuscript) have been consulted in order to produce a score that is more intelligible to

21st

century readers, while

breaking beams according to syllables of the text. •

Slurs have been corrected so that they also encompass tied notes (e.g. mm. 56-57 Violin II).

•

Slurs have been added over text that is not set syllabically (e.g. the melismas at mm. 21).

maintaining the integrity of Bach’s work. Most of the modifications have been made in accordance with guidelines found in Elaine Gould’s Behind Bars, an in-depth 21st century treatise on music notation.

Vocal lines are beamed according to modern day practice as opposed to the tradition of

Other slurs related to phrasing have not been added or altered. •

Dashes and line extensions (___) have been added to the text where appropriate.

•

Figured bass symbols involving altered notes originally represented by a (nearly invisible) vertical line are represented instead with a slash through the digit. (For example, 4Ι has been replaced with

•

Soprano, alto and tenor clefs in the choir have been replaced with their modern equivalents.

•

Instrument names have been translated to English.

•

Unnecessary courtesy accidentals have been removed.

•

Some earlier transcriptions beam eighth note octaves together with opposite stem directions. These are awkward and have been replaced with stems in the same direction.

"Herr, unser Herrscher" Flute I Oboe I Flute II Oboe II

Violin I

Violin II

Viola

Soprano

Alto

Tenor

Bass

b & b 44 Ó b & b 44 Œ

Johann Sebastian Bach

Opening chorus from St. John Passion

Modernized Score

˙ ˙

œ œ

#˙

˙. ˙

b˙.

Transcribed and Analyzed by Bryce Heesacker

w œ

w ˙

nœ

˙ #œ

˙ ˙

Nœ

b & b 44 œ œ œ œ œ œ œ œ œ œ œ œ œ œ bœ œ œ œ œ œ #œ œ nœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ #œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ nœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ nœ œ b 4 &b 4

œ œ œ bœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ #œ nœ œ œ nœ bœ œ œ œ bœ nœ œ œ bœ nœ œ œ œ œ œ œ œ œ œ œœœœœœœœœœœœœœœœ œœœœœœœœœœœœœœœœ œœœ œœœ œœœœœœœœ œ œœœœœœœœœœœœœœœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ bœ œ œ œ œ œ œ œ œ œ œ #œ œ œ œ œ œ œ œ B b b 44 œ œœœœœœœœ œ œœœ œ œ œ Nœ nœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ b & b 44

∑

b V b 44

∑

œ œ œ œ œ œ œ œ Œ Œ ^4 S&4™

œ œ œ œ œ œ œ œ Œ Œ %4 3

b 4 &b 4 ? b b 44

? b b 44 œ œ œ œ œ œ œ œ Œ Œ Celli and Bassoons

Basso Continuo

Organ and Basses

œ ,(8§`Z ¢

œ œ œ œ œ œ œ Œ Œ (7¢`Z

œ &n

œ œ œ œ œ œ Œ Œ

œ œ ^5

œ œ œ Œ ^4

œ œ Œ

œ œ œ œ Œ ™

S&6¢

(s7∞

œ ¢

œ Œ

œ 9

œ œ Œ

œ 8

œ œ œ œ Œ 7`z

œœœœœœœœœœœœœœœœ œœœœœœœœœœœœœœœœ œœœœœœœœœœœœœœœœ œ œœœœœœœœœœœœœœœ œ œ œ œœœœœœœœœœœœ œ œœœ œœœœœœ œœ œœœœœ œœœœœœœœ œ œœœ œ œœ œ œ œ œœœ œ œ œœœœœœœœœ

Composite Phenomenal

Bass Pitch

Root/Quality (Surface Level)

Density

Function

(g:)

(tutti to measure 83)

w g

˙ f

w c

f#dim7

–– ––

– (( –– ))

–– ––

( –– ) (( –– ))

–– ––

( ––– )

–– ––

w T

(c:)

( ) T= S

f#dim7

–– (( –– ))

– ( –– ) ( –– )

–– ––

(g:) D

w T

2 Fl. I Ob. I

Fl. II Ob. II

b œ

b n˙

nœ

#˙

n˙

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

n˙

b˙

nœ

B.C.

9 Comp./Phen.

Bass Pitch

Root/Quality

? bb ? bb

œ ^S4sΩ

œ Œ

œ œ œ œ œ œ œ œ bœ œ œ œ œ œ œ œ nœ Nœ œ œ œ bœ œ œ œ nœ bœ œ œ œ œ œ œ

∑

∑ œ

œ Œ

œ &x

œ S@

œ Œ

œ œ œ œ œ œ œ nœ œ œ œ bœ œ œ œ œ

œ Aœ œ œ œ œ œ œ œ œ œ œ œ œ Aœ œ œ œ œ œ nœ #œ œ œ œ œ œ #œ nœ œ œ œ œ œ œ œ bœ nœ œ œ œ œ œ bœ B bb œ N œ œ œ œ

Vla.

œ &x

œ Œ

n˙

b˙

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ bœ œ œ œ œ bœ œ œ œ œ œ œ œ nœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ Aœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ bœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ #œ œ Nœ œ œ œ œ œ œ Nœ œ œ œ œ œ œ œ bœ œ œ œ œ œ œ œ #œ œ œ œ œ œ nœ œ œ œ œ œ œ œ ∑

∑

œ n^S˜

œ Œ

œ ^Sz

œ Œ

#œ

œ &

œ Œ

œ ^z

œ Œ

œ &`Z

œ Œ

œ ^z

œ Œ

&3`Z

œ Œ

œ ^

œ Œ

œ œœœ œœœœ œœœœœœœœ œ œœ œœœœœœ œ œœœœœœ œœœœœœœœœœœœœœœœ œ œœœœ œœ œœ œ œœ œœœœ œœ œœœœœœ œœœœœœœœ œœœœœœœœœœœœœœœœ œ œœœœœœ œœ œœ œœœœœ w

˙ D

(D7)

–– ( –– )

–– –– –

– ( –– ) ((–– ))

c#dim.7

Function

#œ

b & b nœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

Vln. II II

Density

N˙

#˙

b nœ œ œ œ œ œ œ œ Nœ œ Aœ œ œ œ œ œ œ œ œ œ œ œ œ & b #œ nœ œ œ œ œ œ œ œ

Vln. I I

D/D

w D

bdim7

edim

adim

œ c

ddim.

œ f

Bb7

œ g

Bb+

– ( ––– ) –

( ––– ) ( –)

( ––– ) ––

–– ( ––– )

–– –– –

– ( ––– ) –

–– ––

–– –– –

–– – ( –– )

–– ( –– )

–– –– –

( ––– ) –

–– ––

* This circle of fifths (fourths) progression demonstrates Bach's ability to inject his creativity into a widely popular harmonic device.The intervening diminished and minor chords are simply a result of chromatic motion and anticipations of new chord tones. Since the root/quality analysis is a very "surface level" analysis, some of the diminished and minor chords might be excluded from a more abstract analytical level.

(

)

D/S= D

(c:)

( D/S= ) D

(F:)

( D/S= ) D

(Bb:)

( T=P )

(D:)

˙ S

*The Bb chord takes on a momentary dominant role as an F# appears just before the G minor chord. Bach's inventive counterpoint is often responsible for unusual function analyses and modulations.

b &b

Fl. I Ob. I

b & b #˙

Fl. II Ob. II

Vln. I I

Vln. II II

w n˙

n˙

˙ b˙

œ œ

#˙

#œ

œ œ

#œ

b˙.

˙ œ

œ nœ œ œ #œ œ œ œ œ œ œ œ Aœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ b œ œœœ œœ œ œ œ œ œ œ œ œ œ œœœ œœœœœ œœœ œœœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ #œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ nœ œ œ œ œ œ œ œ œ œ œ œ œ œ b

∑

? b b

Comp./Phen.

Bass Pitch

Root/Quality

∑

œ œ œ bœ œ Œ ^4£`Z

œ œ Œ

œ œ œ œ #œ Œ S^4 &5`Z

∑ œ

œ œ Œ

œ %4

œ œ œ œ œ œ Œ Œ X

#œ

Herr,

œ œ œ œ œ œ œ Œ Œ

#œ œ

un - ser

Herr,

^S5`z

Herr,

? b b nœ

B.C.

Herr,

œœ œœœœœœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ #œ œ œ œ œ œ œ

Herr

œ œ

Herr

œ œ

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ #œ

œ œ

Herr

un - ser

Herr

œ œ œ œ œ œ œ œ Œ Œ ^4

un - ser

œ œ #œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

S&4™

œ *5¢

œ œ œ œ œ #œ

*4™

œ œ œ œ œ œ Œ Œ S&

scher, un - ser

œ œ œ œ œ œ œ

scher, un - ser

œ œ œ œ œ œ œ Œ Œ ^5

^4™

&S5¢ ™

scher,

Herr,

scher,

œ œ

*5£

bœ

Herr,

œ œ œ œ œ œ Œ Œ

Herr,

nœ

Herr - scher,

œ œ

Herr,

Herr - scher,

Herr,

œ œ œ œ œ œ œ œ Œ Œ (8§`Z ¢

(7¢`Z

œ œœœœœœœœœœ œœœœœ œœœœœœœœ œ œœ œ œœœœ œ œ œ œœœœœœœœœœœœœ œ œœœœœœœœœœœœœœœ œ œœœœœœœœœœœœœœœ œ œœ œœœœœœœœœœœœœ œ œœœœœœœœœœœœœœœ œœœ œœœœœ œœœœœœœœ œ œœœœœœœœœœœœœœœ ˙

˙ G

c#dim7

˙ g

–– –– ––

–– –– –

–– ––

–– –– –– –– –

((––– )) ( ––– ) –

c#dim7

Function

œ œœœœœœœœœœœœœœœ œ #œ œ œ œ œ œ œ œ œ œ œ œ œ nœ œ œ œ œ œ œ œ œ #œ œ œ bœ œ œ œ œ nœ #œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ #œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ #œ nœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ Aœ œ œ œ œ œ œ œ œ œ œ œ œ œ #œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ nœ œ œ œ œ œ œ œ œ œ œ œ Aœ œ œ œ œ œ œ œ #œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ #œ œ œ œ #œ œ nœ œ œ œ œ œ œ œ œ bœ œ œ œ œ œ Aœ œ Nœ œ œ œ œ œ œ œ œ nœ œ œ œ œ œ B bb œ œ œ œ œ œœœœœœœœ œ œœœœœœœœ œ œ œ œ œ œ œ œ

Vla.

Density

#˙

w D

a j

( T= ) D

(g:)

w T

˙.

f#dim7

–– –– –– ––

w D

˙ g

((–– )) ( –– ) –– –

–– –– –– –

w T

adim

f#dim7

–– –– –– ––

(( ––– )) (– ) ((–– )) (( –– ))

–– –– –– –– –

–– ((( ––– ))) (–– )

–– –– –– –

˙ g

Eb+

–– ((––– )) ((–– )) ––

–– –– –– ––

( ––– ) (– )

( ––– ) –– –

(

)

D/S= D

(c:)

–– ––

( ––– )

((––– )) –– –– –

b ˙

˙.

b & b n˙

Fl. I Ob. I Fl. II Ob. II

Vln. I I

Vln. II II

Vla.

b œ œ œ bœ nœ œ œ Nœ œ œ œ bœ œ œ œ œ œ

b Œ

? bb

B.C.

œ *7

25 Comp./Phen.

Bass Pitch

Root/Quality

ser

œ œ œ bœ œ œ œ œ bœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ bœ

œ un

œ Œ

Herr

œ œ œ œ œœœ œ

ser

Herr

ser

Herr

œ ^4

œ œ Œ

œ œ

œ œ œ œ œ œ œ bœ œ nœ

nœ

œ Œ

scher,

œ ^5

un - ser

œ scher,

un - ser

œ Œ

˙ ˙

#œ

n˙ œ

n˙

scher,

œ nœ

Herr - scher,

un - ser

des - sen

Herr - scher,

&6¢

™`Ω

œ Œ

œ ^5

scher,

des - sen

Herr - scher,

un - ser

scher,

œœœœœœœœœ

Herr

œ œ œ ‰

Ruhm

œ J

#œ

‰

j œ

des - sen

Ruhm

al - len

œ Œ

S&6¢

al - len

™

œ Nœ J

œ Aœ œ

Ruhm

œ Œ6¢

#œ nœ œ œ œ œ œ œ œ #œ œ œ œ œ œ œ œ

Ruhm

des - sen

al - len

Land - en

Lan - den

#œ

Lan

den

œ Œ

œ ™

(7s∞

œ œ œ œ œ œ œ œ œJ

herr

œ #œ œ œ œ œ œ œ œ

herr

œ œœœœœœœœ

herr

œ Œ

(

œ -

œ *

œ œ œr R

œ œ

lich, in al - len

œ œ œ

lich, in al - len

den

œ bœ

herr - lich

œ nœ œ œ Nœ œ œ œ œ

den

herr - lich

œ Œ

Lan

œ œ œ œ nœ

lich, in al - len

Lan

den

lich, in al - len

Lan

den

œ œ œ œ

œ Œ

œœ œ

œ œ œ œ nœ œ œ œ #œ

S^s4£`Ω

œ Œ

herr - lich

œ Nœ œ Aœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ #œ œ œ nœ nœ œ œ

nœ œ œ œ œ #œ œ œ œ œ œ œ #œ nœ œ œ œ

#œ nœ œ œ œ œ œ œ nœ Lan

œ Aœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ nœ œ œ Nœ œ œ œ œ œ œ œ œ œ œ œ œ œ

#œ

œ œ œ bœ œ œ œ œ

ist!

œ ist!

œ X

œ Œ

œ ^4

œ Œ

œ œœ œ œ œœœœ œœ œœœœœ œœœœœœœœœœœœœœœœ œœœœœœœœœœœœœœœœ œ œœ œœœœ œœ œœœœœœ œ œ œœœœœœœœ œœ œ œœœœ œ œœ œ œœœœ œ œœ œœœœœ œ œœ œœœœœœ œœ œ œ œœœ w ˙

Function

Herr

#œ

œ œ œ œ œ œ œ bœ œ

œœœœœœœ œœœœ œœœœœ

œ œ œ œ œœœ œ

ser

œœœœœœœ œ œ œ œ œ œ œ œ œ œ œ bœ œ œ œ œ bœ œ œ œ œ œ œ œ nœ œ œ œ œ œ œ œ œ bœ œ œ œ œ œ œ œ œ œ œ œ œ nœ œ œ œ œ œ œ œ œ

œ œ œ œ œ œ œ œ œ bœ œ œ œ œ œ#œ œ œ #œ œ œ Nœ œ œ Aœ #œ œ œ œ œ œ œ œ œ œ #œ œ œ œ œ œ œ œ œ œ #œ œ œ œ œ #œ nœ œ œ œ œ œ œ nœ œ œ œ œ œ

? bb Œ

Density

nœ

œœœœœœœ œœœœ œœœœœ

b œ œ œ œ œ œ œ œ œ nœ œ œ œ œ œ œ

nœ Nœ œ œ œ B bb

nœ

–– ––

–– –– –– ––

–– –– ––

(S) T=

Eb+

–– –– ––

f#dim7

–– –– –– ––

((––– )) ( ––– ) –

(g:)

w D

˙ D

–– –– –– –– –

– ( ––– ) –– –

–– ( ––– ) –– –

–– –– –– –– ––

–– ––

w g

c#dim7

D/D

b &b

Fl. I Ob. I

Fl. II Ob. II

Vln. I I

Vln. II II

b ˙. b b

B bb

Vla.

? bb

B.C.

? bb

Comp./Phen.

Bass Pitch

Root/Quality

Function

#œ

j œ. ‰

œ J

j j œ. ‰ œ. ‰

∑

∑ ∑

Herr,

&S6¢ ™ß

œ œ Œ

œ œ n œ # œJ

un - ser

Herr

j #œ œ

œ nœ

un - ser

œœ

Herr

œ œ J

^4™ß

Herr

j œœœ œ

œœœ

scher,

un - ser

œ œ J

‰ œj ‰ n œ ‰ œJ ‰ J

œœ œ

#œ œ

nœ J

œ œ j œ œ ‰ J ‰ J ‰ J ‰

œœ œ

œ œ œ n œJ

un - ser

Herr

œœ œ J

scher,

Herr

scher,

œ œ

Herr,

œ Œ

un - ser

nœ J

Herr

nœ

bœ œ ‰ J ‰ J ‰

un - ser

scher,

œœœ œ J

&5≈

œ œ Œ Herr - scher

œœ œ œ Œ

∑

‰ œ œ œ Herr,

un - ser

scher,

Herr,

scher,

Herr,

œœ œ œ Œ

Herr - scher,

un - ser

Herr

œœ œœœ œ œœ œœœ œ

Herr

scher,

Herr,

œœœœ œ œ œœœœ œ œ

scher,

œ œ &

un - ser

Herr,

Herr

œ œ œ &

œ œ œœ œ

œœœ œ œ

nœ

Herr

œ œ &

œœœœ

œ œ

scher,

Herr,

scher,

œ œ

œœœœ

‰ #œ ‰

Herr,

≈ #œ œ œ œ

œ œ œ Aœ œ Nœ nœ œ #œ

œ œ œ œ œ œ œ œ #œ œ œ

un - ser

œ œ œœ œ

Herr,

#˙

œœœœ œ œ #œ ≈ œ œ œ œ œ œ œ nœ œ #œ œ œ œ œ œ

œ œœœ œ ‰ œ œ œ œœœ œ œ Herr,

™

œ œœœœœ œ ≈œœœ

un - ser

Herr

œ œ œœœœœ œ œœœœ œ œ

œ ‰ J

œ œ n œJ œ

œ œ œœœœœ œ œœœœ œ œ

‰ œ ‰ œJ ‰ œJ ‰ J œ œ œ œ œ nœ œ -

œ J ‰

‰ œJ ‰ œJ ‰

œ Œ

œ J

nœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ nœ #œ œ œ œ œ #œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ #œ œ œ œ œ œ œ œ œ œ œ œ œ *6¢ &5 ^4 & ^4 & ^5 &

tutti

œœœœœœœœœœœœœœœœ

un - ser

‰ œJ ‰ œJ ‰ œJ ‰

Herr,

j œ nœ #œ œ

Herr,

œ J

j œ. ‰

œ. ‰ J

∑

œ. ‰ J

j œ. ‰

œ. ‰ J œ. J ‰

j # œ. ‰ œ. J ‰

œ. ‰ J

j œ. ‰

œ. ‰ œ. ‰ J J

∑

œ œ œ œ œ Œ

œ. ‰ J

œ. ‰ # œj ‰ J .

∑

Herr,

un - ser

œ œ

un - ser

œ œ

un - ser

œ œ œ nœ #œ œ

ser

Herr

œ &x

œ œ

œœœœœœœœœ œœ œ œœœœ œœœœœœœœœœœœœœœœ œœœœœœœœœœœ œ œœœœ œ œœœœœœœœœœœœœœœ œ œœœœœœœœœœœ œœœœ œœœœœœœœœœœœœœœœ œœœœ œœ œœœœœœ œœœœ œœœ œœ œ œœ œœ œ œ œœœœ w ˙ e

Density

Ÿ œ

œ œ œ œ œ œ œ œ œ œ œ # œ n œ œ œ œ # œ. j ‰ j n œ œ œ œ œ œ œ œ œ # œ œ œ œ œ œ œ œ. ‰ œ œ. ‰ œœœœœœœœœ œ œ J

^4™ß

#˙

–– ––

S/D

œœœœœœœœœœœœœœœœ œœœœœœœœœœœ œ œœœœ œ œœœœœœœœœœœœœœœ œ œœœœœœœœœœœ œœœœ ˙

–– ( –– )

–– –– ––

–– ( ––– ) ( –)

c#dim7

D/D

œ g

œ c

˙ c

–– (––– ) ( –– )

–– –– ( –– ) ( –)

–– –– –– – (( –– ))

–– –– – ( –– )

–– –– – ((––– )) ( –)

– ( ––– ) –– (( ––– )) –

–– –– ( –– )

–– –– – ( –– )

–– – ( ––– ) ( –)

–– –– ( ––– ) ( –– )

–– –– ( –– )

–– –– – ( –– ) (( –– ))

– ( ––– ) – ((––– )) –

–– –– –– –

– ( ––– ) –– ––

–– –– –– –

– ( ––– ) –– ––

–– –– ––

˙ T

(

)

D/S= D/S

(Bb:)

( PS= )

j a

(g:)

Fl. I Ob. I

b œ

b &b œ

Fl. II Ob. II

#˙

#œ

œ œ

N˙

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ #œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ nœ œ œ œ bœ œ œ œ œ œ #œ œ nœ œ œ œ œ

Vla.

b &b œ

b &b

Herr - scher,

Herr,

b Vb œ

? bb œ

? bb

B.C.

scher,

Comp./Phen.

Bass Pitch

Root/Quality

Herr,

œ Herr,

#œ

Herr,

Herr

œ œ œ

un - ser

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ #œ œ œ œ œ œ œ œ œ œ œ œ

un - ser

œ œ œ #œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

un - ser

Herr,

#œ

Herr,

Herr

œ -

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ -

œ #œ

œ scher,

#œ

un - ser

œ Nœ œ œ

œ nœ

des - sen

scher,

Herr - scher,

un - ser

Herr - scher,

des - sen

‰

Ruhm

‰

Ruhm

œ Ruhm

j œ

len

‰ nœ J

‰

Ruhm

len

œ Œ

œ J

Lan

œ œ

len

œ bœ

des - sen

œ J

Lan

œ -

den

œ œ œ œ œ œ œ œ #œ nœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

herr

œ #œ

lich

herr

Lan

den,

al - len

œ Œ

#œ

lich

ist!

herr

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ #œ

Herr,

ist!

Lan - den

herr

œ -

lich

Celli and Bassoons

œ Œ

Organ and Basses

Herr,

Herr

Herr - scher,

#œ

b œ & b œ#œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ #œ nœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ Aœ œ œ œ œ œ œ œ œ œ œ œ œ œ #œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ nœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ #œ œ œ œ nœ bœ nœ B bb œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ # œ œ œ œ œ œ œ œ œ œ

Vln. II II

œ ^5

œ Œ

œ ^4™

œ Œ

œ S&4™

œ Œ

œ %4

œ Œ 3

œ *4™

œ Œ &S

œ *5

œ Œ 6

œ *6¢

œ Œ &S5™

™

œ 4

œ *5£

œ Œ

œ &5

™nΩ

œ Œ

^5•

œ ^4™

&S6¢ ™

œ Œ

œ &S5™

œ Œ 4

œœœœœœœœœœœœœœœœ œœœœœœœœœœœœœœœœ œ œœ œœœœœœœœœœœœœ œœœœœœœœœœœœœœœœ œœœœœœœœœœœœœœœœ œœœœœœœœœœœœœœœœ œœœœœœœœœœœœœœœœ w ˙ g

Function

b &b œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

Vln. I I

Density

–– –– –– –– –

w T

((––– ))

˙.

f#dim7

–– ––

w D

((–– )) (–– ) –– –

˙ g

–– –– –– –

w T

–– –– –– ––

f#dim7

(( ––– )) (( –– )) (( –– )) (– )

–– –– –– –– –

– (( ––– )) (( –– )) –

–– –– –– –

–– ((––– )) (( –– )) ––

–– –– –– ––

– ( ––– ) ( –– ) –

–– –– –– –

(( ––– )) ( –– ) –– –

D/S

f#dim7

– (( ––– )) – ( –– ) –

– ( ––– ) ( –– ) ––

w D

b &b ˙

Fl. I Ob. I

Fl. II Ob. II

b ˙

Vla.

b &b Œ

b &b œ

œ œ œ œ œ

un - ser

b Vb Œ

? b œ b

ist!

? bb

B.C.

47 Comp./Phen.

Bass Pitch

Root/Quality

œ (

œ Œ

œ *

‰ n œJ # œ .

nœ

‰

Herr,

œ Œ &

œ œ œ œ œ

œ ^S5

Herr,

‰

Herr - scher,

œ Œ

^S4£`Ω

œ œ

ser

#œ

un - ser

œ Œ

nœ

#˙

n˙

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

des - sen

Ruhm

al - len

Ruhm

al - len

des - sen

Lan

Ruhm

al - len

n˙

b˙

nœ

n˙

b˙

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

œ &x

œ 2s

œ Œ

den,

des - sen

œ Œ

Lan

des - sen

Ruhm

œ ^S n

œ Œ %

Ruhm

al - len

Lan

tutti

des - sen

Ruhm

al - len

œ œ ^Sz

den,

Lan

des - sen

Ruhm

al - len

bœ

œ œ œ œ œ œ œ œ bœ œ œ œ œ œ œ œ

Lan

den,

des - sen

œ ^z

den,

des - sen

Ruhm

al - len

Lan

œ œ

den,

al - len

des - sen

œ œ œ œ œ œ œ œ

œ -

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

Lan

œ œ œ œ œ œ œ œ Aœ œ œ œ œ œ œ œ œ

al - len

den,

œ œ œ nœ œ œ œ œ œ

œ œ œ œ œ œ œ œ nœ œ œ œ œ œ œ œ œ

œ œ

b˙

œ œ œ œ œ œ œ œ œ Aœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ bœ œ œ œ œ

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ bœ œ œ œ œ

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

œ œ œ œ œ œ œ œ nœ œ œ œ œ œ œ œ œ

Lan

Herr - scher,

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

Herr - scher,

des - sen

Herr - scher

Herr - scher,

œ œ

ser

un - ser

Herr,

j œ œ.

Herr,

Herr - scher

un - ser

Herr,

un - ser

œ œ œ œ œ œ nœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ bœ œ œ œ œ œ œ nœ Nœ œ œ œ œ œ œ œ œ bœ œ œ œ œ œ œ Nœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ nœ #œ œ œ œ œ œ #œ nœ œ œ œ œ œ bœ nœ œ œ œ œ œ bœ œ œ œ œ œ œ œ œ

Herr - scher,

œ œ œ œ

Herr

Herr,

œ œ œ œ œ

N˙

#˙

œ œ œ œ #œ nœ œ œ nœ œ œ œ œ œ œ œ œ œ œ Aœ œ œ œ œ œ œ œ œ œ œ œ œ

Herr - scher,

Herr,

n˙

b & b œ #œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ B bb œ œ œ œ œ œ œ œ œ # œ œ œ œ œ œ

Vln. II II

œ %

œœœœœœœœœœœœœœœœ œœœœ œ œœœ œœœœœœœœ œœœ œœœœœœ œ œœœœœœ œœœœœœœœœœœœœœœœ œ œœœœœœœœœ œœœœœœ œœ œœœœœœ œœœœœœœœ œœœœœœœœœœœœœœœœ w

˙ ej

c#dim7

˙ D

(D7)

–– –– –

(–– ) ( ––– ) (–– )

–– – ( ––– )

–– –– –– –

– (( ––– )) ( –– )

Function

Nœ

b &b œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

Vln. I I

Density

w T

S/D

D/D

œ d

edim.

adim.

œ c

ddim.

– ( ––– ) ––

( ––– ) (–– ) ((–– ))

– ( –– ) –– ––

–– –– –– ––

– ( ––– ) –– ––

–– –– (( –– ))

–– –– –– ––

–– – ( ––– ) ––

–– – (((––– )))

( ) D/S= D

bdim7

w ˙

(c:)

(

)

D/S= D

(F:)

(

D/S= D

)

b &b

Fl. I Ob. I

#œ

b &b w

Fl. II Ob. II

b œ & b œ bœ œ œ œ œ œ œ œ nœ œ œ œ œ œ

Vln. I I

b & b œ œ œ œ œ œ œ œ œ #œ œ œ œ œ œ œ œ œ œ œ B bb œ œ œ œ œ œ œ # œ

Vln. II II

Vla.

b &b œ

den,

des - sen

Ruhm

al - len

? b b œ &`Z

54 Comp./Phen.

Bass Pitch

Root/Quality

œ œ œ œ œ œ œ œ

Lan

œ œ œ œ œ œ œ œ œ

Lan

œ den

Function

(Bb:)

œ ^

den

nœ

den

herr - lich,

^S5`z

herr - lich,

bœ

^4£` n

herr - lich

œ Aœ œ

nœ

œ #œ

œ nœ

œ.

Ruhm

al - len

Lan

#œ

^S4

&5`Z

herr - lich

œ J

œ nœ

œ.

œ œ œ œ œ

herr

herr - lich

œ nœ #œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

#œ -

herr

lich,

herr

œ %4

lich

ist!

U œ

lich

ist!

U œ

œ X

w ˙

œ g

Bb+

–– –– –– ––

( ––– ) –– ––

–– – ((––– )) –

(P ) T=

(g:)

Œ Œ Œ

j j œ. ‰ b œ. ‰ œ. J œ. J

‰ ‰

œ. J œ. J

‰ ‰

œ. J

‰

œ. J

‰

bœ

œ. J

. ‰ b œJ

œ. J

‰

j j œ. ‰ b œ. ‰

∑

œ. J

‰

j . œ. ‰ œJ . œ. J ‰ b œJ

bœ

œ. J

‰

œ. J

‰

b œ. J

‰

∑

œ. J

‰

œ ‰

œ J

‰

j ‰ œ

j œ. ‰

œ J

‰

œ J

j œ. ‰

‰ ‰

j œ ‰

∑

Zeig'

∑ Œ

œ Zeig'

Zeig'

uns durch

œœœœœœœœ ^4`z

œ J

dei

uns

œ -

uns

j œ œ

durch

dei

Pas

œ bœ œ J

durch

œ bœ

&5`Z

dei

œ bœ J

Pas

bœ œ bœ

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ &`Z

j œ œ

^4`z

œ -

j j bœ œ œ ne

Pas

œ œ œ si

œ nœ

&5`Z

˙ G

c#dim7

œ g

Eb7

–– –– –– ––

–– –– –– –

–– –– ––

–– –– –– –

–– –– –

–– – ( –– ) ( –)

–– (––– ) ( –– )

–– –– ( –– ) ( –)

–– –– –– – (( –– ))

–– –– – ( –– )

–– –– – ((–– )) (– )

–– (–– ) – ( ––– ) –

S/D

D/D

(Ab:)

Œ Œ

œœœœœœœœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œœ œ œ œ œ œ œœ œ œœ œ œ œ

œ œ

œ œ œ œ œ œ œ œ nœ œ œ œ œ œ œ œ

durch

on,

D/D

uns

‰

on,

c#dim7

j œ ‰

j a

Zeig'

ist!

bœ

∑

lich

U œ

˙ -

œ J

˙ ˙

œ #œ

herr

den

herr - lich

herr - lich,

des - sen

U œ

œ œ œ œ œ œ œ œ n œ œ œ # œ œ œ œ œ œ œ œ A œ œ œ œ œ œ œ œ œ œ œ œ œ Uœ

herr - lich,

œ nœ

œ œ

herr - lich,

Fine

#˙

œœœœœœœœœœœœœœœœ œ œœœœœœœœœœ œœœœœ œœœœœœœœœ œœ œ œœœœ œœ œ œœœœœœœœœœœœœ œ

Bb7

Density

b˙

œ #œ œ œ œ œ œ œ œ œ œ œ œ œ nœ œ œ œ œ œ œ œ œ #œ œ œ Nœ œ œ œ œ œ N œ Aœ œ œ œ œ œ œ œ œ œ œ Aœ œ œ œ œ nœ œ œ œ

œ #œ œ œ œ œ œ nœ œ

n˙

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

b Vb œ

? bb œ œ œ œ œ œ œ œ œ

B.C.

n˙

Ruhm

#˙

b &b œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ Lan

œœœœœœœœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œœ œ œ œ œ œ œœ œ œœ œ œ œ œ

(f:) D

* A few of the following modulations can be described as common tone modulations. Relationships of a third can often be found.

61 Fl. I Ob. I

Fl. II Ob. II

b &b œ

bœ

nœ

bœ

Vln. I I

b Œ

j j œ ‰ bœ ‰

b & b n œj ‰

Vln. II II

B bb œ J

Vla.

dei

b œ

œ J

‰

œ J

‰

œ J

‰

j j œ ‰ bœ ‰

‰

j œ œ œ œ ne

Pas

zeig'

uns

61 Comp./Phen.

Bass Pitch

Root/Quality

*6¢`z

j œ ‰

j nœ œ

œ J

‰

dei

œ œ -

^4`Z

œ J

Pas

‰

Pas

dass

bœ œ œ -

Density

œ J

‰ N œJ

Nœ

‰

œ J

‰

œ œ -

du,

der

œ J

dass

du,

j Nœ Nœ wah

j Nœ œ Nœ

der

œ œ œ J re

Got

œ J

‰

œ J

‰

j œ ‰

‰

œ J

‰

du,

œ J Got

j œ œ

der

wah

œ œ -

∑

œ J

‰

œ J

j œ œ Got

œ #œ -

™

œ nœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ & n

*6s

Fl. II

œ J

j œ ‰ œ J

œ J

‰

j œ ‰

‰

Œ œ œ tes

œ nœ der

#œ J

wah

œ J

‰

œ J

j œ ‰

‰

œ nœ #œ œ

der

œ nœ

du,

j œ œ nœ #œ

œ -

der

wah

œ œ œ J re

Got

‰

wah - re

dass

du,

‰

œ J œ J

sohn,

dass

‰

du,

œ -

œ J

dass

du,

‰

j #œ ‰

œ J

œ œ

der

œ œ

*6¢

&5≈

™ß

œ J

‰

œ J

‰

Ob. II

œ J

œ ‰

j œ ‰ # œj ‰ j œ ‰

œ #œ

Got

wah

j œ œ

Got

œ J

j #œ œ

œ œ œ Aœ œ œ œ œ œ œ œ œ œ œ œ œ &x

#œ

tes

œ -

œœ a œœ œœ œœ œœ œœ œœ œœ œœ # œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œ ‰ œJ ‰ œ ‰ œ ‰ œj ‰ œ ‰ J J J J j œ

‰

j œ

‰

œ J œ J

sohn,

j œ œ œ

Got

al - ler

Zeit,

‰

j œ

œ ‰

j œ ‰ œ J œp

‰

‰ œ

j ‰ œ j œ ‰ œ

auch

al - ler

tes - sohn,

œ œ œ œ œ œ œ œ œ

‰

tes - sohn,

œ œ œ

‰

œ œ œ -

œ œ œ

‰

œ J œ J

Zeit,

œp

der

- ler

al - ler

Zeit,

œ Œ

Zeit,

‰

auch

œ J œ

j œ alœ

j œ ‰

‰

pœ J

auch

Celli and Bassoons

&5≈

œ Œ

Organ and Basses

–– – (––– ) ( –)

–– –– ( ––– ) ( –– )

–– –– – ( –– )

–– –– ( ––– ) (( –– ))

– ( –– ) (( ––– )) ––– –

–– –– ( –– )

–– (––– ) (–) ( –– )

–– – ( –– ) ( –– )

–– –– –– – (( –– ))

–– –– ( –– )

–– –– (( ––– )) ( –– )

– ( ––– ) ( –– ) –– –

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

œœœœœœœœœœœœœœœœ œœœœœœœœœœœœœœœœ œœœ œœœœœœœœ œœœœœ œœœœœœœœ ˙

œ Œ

œœœœœœœœœœœœœœœœ œœœœœœœœœœœœœœœœ œœœ œœœœœœœœ œœœœœ œœœœœœœœ œ œœœœœœœ œœœœœœœœœœœœœœœœ

œ nœ œ œ œ œ œ œ #œ œ œ œ œ œ œ œ

sohn,

dass

*6¢`z

‰

œ J

tes

‰

œ œ œ

j œ ‰ œ J

‰

j ‰ œ j œ ‰

tes - sohn,

œ -

‰

on,

‰

œ œ

wah

dass

œ J

‰

j œ ‰ N œJ œ J ‰ œJ

‰

on,

œœœœœœœœœœœœœœœœ œœœœœœœœœœœœœœœœ œ

‰

œœœœœœœœœœœœœœœœ œœœœœœœœœœœœœœœœ

œ J

œ œ œ bœ œ œ bœ œ œ œ œ œ œ œ nœ œ

j Nœ ‰

on,

j bœ œ œ œ

‰

j bœ œ ‰ J

‰

œ œ bœ si

œ J

j j œ ‰ bœ ‰

dei

bœ

j œ ‰ n œj ‰

durch

œ J

‰

œ bœ J

? b œ œ bœ œ œ œ œ œ œ œ œ œ b œ œ œ œ

B.C.

bœ J

œ n œJ b œ

durch

œ œ

∑

zeig'

Function

œ J

on,

? bb œ

‰

j œ ‰

‰

b & b n œj b œ

œ J

(D/S=) (Bb:)T D

(g:) D

–– –– –– –

–– –– –– – ((––– ))

–– –– –– ( –– )

–– –– –– –– ((( ––)))

( ––– ) – (––– ) –– –

( T= ) S

b &b œ

Fl. I Ob. I

b & b œœ

Fl. II Ob. II

Vln. I I

∑

#œ

nœ

∑

tutti

#˙

˙.

N˙

#œ

nœ

˙.

#œ ˙

b & b œ œ œ œ œ œ œ œ œ œ œ œ œ #œ œ nœ

œ œ œ œ œ œ œ œ œ Aœ œ œ œ #œ œ œ œ œ œ œ œ œ #œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ #œ nœ œ œ œ œ œ œ œ œ œ œ œ œ œ nœ œ #œ œ nœ œ œ œ œ œ œ œ œ œ œ œ œ œ nœ œ œ œ œ œ œ œ œ œ œ œ

b &b œ

#˙

Aœ œ œ œ œ œ #œ œ œ œ œ nœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œœœœœœœ œœœœœœœœ œ bœ œ œ œ œ œ œ œ nœ œ œ œ œ œ œ Nœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ #œ nœ œ nœ œ #œ œ nœ œ œ œ œ œ œ œ œ œ œ nœ œ œ œ #œ œ #œ nœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ B bb œ œ b œ œ œ œ œ œ n œ Nœ œ œ œ œ œ œ œ nœ œ œ nœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ #œ œ nœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ #œ œ œ &b

Vln. II II

Vla.

groess

der

b j Vb œ œ

der

? b œ b

B.C.

? b b œ

^`Z

68 Comp./Phen.

Bass Pitch

Root/Quality

groess

œ der

ten

œ œ

groess - ten

Nie

j bœ œ ten

Nie

bœ

groess - ten

œ Œ

Nie

œ #œ

drig

œ-

nœ

drig

œ Œ

‰

keit,

ver

f j œver

‰

keit,

n˙

‰

keit,

œ S^4™

f j œ

ver

‰

f œ J

ver

keit,

f j œ

œ Œ

œ ‰

œ J

œ œ œ œ œ #œ œ nœ œ œ œ œ œ œ œ œ œ œ œ œ œ nœ œ œ œ œ œ œ œ œ œ œ œ

herr

œ œ. œ œ œ œ œ - œ œ œ œ- œ œ œ -œ œ # œ n œ - œ n œ œ #-œ œ n œ œ -œ œ œ œ- œ œ œ- œ œ nœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

herr

œ nœ -

herr tutti

œ ^

œ -

^S5

œ nœ

œ %

œ ^

licht

œ #œ nœ

œ ^4`Z

licht

œ S&6¢ ™ß

licht

œ œ Aœ

œ *5£

œ œ

‰

#œ

‰

herr

j œ

herr

j œ œ J

ver

&5≈

œ œ #œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

ver

bist,

œ J

ver

bist,

den

‰

bist,

den

‰

best,

licht wor - den

œ Nœ

wor

wor - den

wor

œ #œ

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œœœœœœœœœ

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ #œ

j œ œ

herr

œ #œ -

œ %4

wor

œ ^5≈

œ.

licht

œ œ œ -

licht,

œ 4

den

licht

bist,

ver -

œœœœœœœœ

ver - herr

œ &6¢

™`Ω

œ 5

œœœœœœœœœœœœœœœœ

œ œœœ œ œœ œœœ œœœ œœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œœœœœœœœœœœœœœœ œ œœ œ œœ œ œ œœœ œ œœ œ œ œ œœœœ œœ œœœœœœœœœ œœœœœœœœœœœœœœœœ w

˙.

Density

(( ––– )) ––– –– –

Function

– ( –– )

œ –– –– –– –– –

edim.

–– –

( –– ) –– –– –

–– –– –– –– –

( ––– ) (( –– )) ( ––– ) –

(d:) D

Bb7

– ((–––)) ((––)) (–– )

–– –– –– ––

– ((–––)) ((–––)) ––

–– –– –– –– –

–– –– –– ––

(

)

D/S= D

˙ g

–– –– –– ––

–– –– ––

(g:) T

b &b

Fl. I Ob. I

Fl. II Ob. II

Vln. I I

Vla.

œ œ

˙.

nœ

n˙

#œ

n˙ œ

b œ -

wor

b œ

? bb

75 Comp./Phen.

Bass Pitch

licht

œ -

herr - licht

B.C.

j b œ œ œ œ œ #œ œ nœ œ nœ œ œ œ œ œ b œ n œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ # œ œ n œ œ œ œ œ œ # œ œ œ œ œ œ œ n œ œ œ # œ œ œ œ œ œ. ‰ #œ

? bb œ

Function

b ˙.

b &b

Density

#œ

b & b #œ œ œ œ œ œ œ nœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ nœ œ œ œ œ œ nœ œ œ œ œ œ œ œ œ #œ nœ œ œ œ œ œ nœ œ œ œ œ œ œ œ œ œ œ #œ œ nœ œ #œ œ nœ œ nœ œ œ œ œ œ œ nœ œ B bb œ œ œ œ œ œ œ

Vln. II II

Root/Quality

œ ^5≈

wor - den

‰ ‰

œ Nœ nœ

‰

licht

wor - den

bist,

&S4ß™

œ J

ver

bist,

j œ

ver

ver - herr - licht

bist,

wor - den

bist,

œ œ nœ

#œ

den

œ J

ver

œ ^4

#œ nœ

wor

den

œ nœ #œ

herr

licht,

herr

licht,

S&5™ß

licht,

bist,

ver - herr

nœ œ.

œ nœ.

œ œ œ œ œ œ œ œ œ nœ œ œ œ œ œ

ver - herr

œ nœ œ œ œ œ œ œ œ œ œ ver - herr

œ œ œ.

œ # œ œ n œ œ œ œ œ œ. J

œ #œ.

licht

wor

œ œ œ œ œ œ œ œ œ #œ œ nœ œ œ œ œ œ #œ œ œ œ œ œ œ nœ

nœ

herr

j œ n œ œ œ œ œ œ œ œ. ‰

œ (S

licht,

‰

nœ œ œ œ œ œ œ #œ œ

ver - herr - licht

œ 4s£^S

den

œ nœ

licht

wor - den

œ nœ -

j œ œ

^S4s£

bist,

œ #œ œ

wor - den

bist,

# œ. J

nœ

œ œ. J

œ ‰

j n œ. œ. ‰ J

‰

j œ. ‰ œ

œ n œ # œJ

uns

durch

‰

dei

œ. J

# œ. J

nœ œ nœ J ne

durch

j #œ œ dei

nœ œ œ J

œ nœ

Pas

uns

durch

*6¢

œ. ‰ J

‰

&5s

dei

œ nœ -

œ œ J

œ. J

‰

œ. J

œ. J œ. J

‰

œ J

‰

œ J

#œ J

‰

œ J

‰

œ J

‰

œ J

‰

œ œ œ. -

#œ œ si

Pas

j #œ œ

œ nœ

du,

der

wah

nœ Aœ -

on,

œ œ œ nœ œ œ œ œ ^4

œ J

‰

œ J

‰

œ J

‰

du,

Got

dass

du,

œ n œ # œJ der

wah

‰ ‰ ‰

der

œœ

œ nœ #œ

du,

œ nœ

dass

j œœœ œ

dass

on,

œ J

si - on,

œ œ œ nœ #œ œ S%x

#œ nœ J

j œ. ‰

œœœ

Pas

œ œ

œ#œ œ nœ œ œ œ œ œ œ œ œ œ œ œ œ &x

j œ. ‰

‰

œ. J

dass

œ nœ

n œ. ‰ J

‰

zeig,

œ. J

j œ. ‰

∑

uns

‰

œ. J

nœ

œ. J

j œ. ‰

j n œ. ‰

nœ

#œ

œ. J

‰

zeig'

œ #œ œ nœ œ œ œ œ X

œ zeig'

œ. ‰ J p j ‰ œ. j œ. ‰

œ nœ

Œ œ

p Œ

bist,

wor - den

bist,

‰

der

wah - re

œœ -

œ #œ œ nœ œ œ œ œ œ œ œ œ œ œ œ œ &5≈

œœœœœœœœœœœœœœœœ œœœœœœœ œœœœœœ œœœ œœ œœ œ œœ œœ œœ œ œœ œœ œœœœœœœœœœœœœœœœ œœœœœœœœœœœœœœœœ œœœ œ œ œœœœœ œœœœ œ œœœœœœœœœœœœœœœœ w ˙

Bb+

c#dim7

–– –– –

– ( ––– ) –– ––

˙.

–– ––

–– –– –– ––

– ( ––– ) –– –

(S ) T=

(d:) D

g#dim7

œœœœœœœœ œœœœœœœœœœœœœœœœ œœœ œ œ œ œœœ œœœœ œ œœœœœœœœœœœœœœœœ

œ –– –– –– –– –

–– ( ––– ) –– –

D/D

˙ D

–– –– ( –– )

–– ( ––– ) ( –– )

–– ( ––– ) ( –)

–– –– –– – (( ––))

œ d

–– –– – ( –– )

–– –– ( ––– ) (( –– ))

–– ( ––– ) ( –– ) ( –– ) –

–– ( ––– ) ( –)

–– –– –– ( –– )

D/S

œ g

–– ( –––) – ( –– )

–– –– – ( ––– ) ( –– )

–– –– – ( –– )

Fl. I Ob. I

b Fl. II & b #œ

Fl. II Ob. II

œ b J &b

œ J

Ob. II

Vln. I I

‰

œ b &b J

Vln. II II

œ B bb J

Vla.

‰

œ J

‰

#œ J

b & b # œj œ

b &b œ

wah

Got

? b b œJ

Got

‰

#œ

tes

∑

œœ a œ œœ œœ œœ œ œœ œœ œœ# œ œœ œ œ œ œ œ œ J ‰ J ‰ J ‰

∑

œ #œ œ nœ œ œ œ œ œ œ œ œ œ œ œ œ

œ nœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ pœ œ œ. #œ œ

œ nœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ nœ

œ J

‰

œ œ -

82 Comp./Phen.

Bass Pitch

œ sohn,

œ œ œ

œ œ J ‰ œJ ‰ J ‰ œj ‰

‰

sohn,

j œ

al - ler

Zeit,

#`~~~`@`

Zeit,

p œ

auch

al - ler

p œ

auch

Nœ

œ œ ‰ œ œ zu

œ j œ Nœ œ

œ œ œ

tes - sohn,

œ ‰ œj ‰ j ‰ J œ

œ ‰ œ ‰ j ‰ j ‰ J J œ œ

‰

tes

‰

œœ œœ œœ œœ n œ n œœ

œ œ œ

sohn,

al - ler

Zeit,

der

pœ

auch

œ œ œ œ œ œ œ œ ^

Composite

nœ

#œ

tutti

œœœœœœœœ œœœ œœœœœ

nœ

œ œ œ œ œ œ œ œ œ œ œ œ œ Aœ œ œ

der

groess

auch

der

groess

ten

n˙.

groess

ten

Nie

der

œ nœ #œ Nœ

groess

œ ^4™

Nie

œ œ

œ #œ ten

ten

Nie

#œ &5`Z

drig

j œ

Nied

#˙.

œ.

drig

#œ nœ

n œf

keit,

ver

keit,

ver - herr - licht

f n œ œ

herr

j ‰ nœ

Aœ œ œ Nœ Aœ œ œ œ œ

œœœ œœœœœ

‰

f œ

wor - den

keit,

nœ œ œ œ œ œ #œ œ œ nœ œ œ œ œ

bist,

ver

ver - herr - licht

Density

–– –– – ( ––– ) (( –– ))

– ( ––– ) ( –––) –– –

Function

wor

- den

‰

fœ

bist,

ver

–– –– –– –– –– –

–– –– –– –

g#dim7

(––– ) (–– ) –

–– – ( ––– ) –– ––

D/D

Nœ

œ ^S

œ %S

wor - den

bist,

licht

œ nœ

ver - herr

œ Nœ

herr

wor - den

bist,

ver

bist,

licht

herr

œ %

wor - den

œ œ œ œœœœœ œ œœœœœœœ ˙

bdim.

œ d

– ( ––– ) –– –

( ––– ) (( –– )) ( –– )

( ––– ) –– ––

– (––– ) –– ––

–– –– – (( ––– ))

–– –– –– ––

( D/S= ) D

ver - herr

f#dim7

œ œ œ nœ œ œ œ œ nœ œ œ œ œ œ œ œ

œ œ œ œ œ œ œ œ

œ œ œ œ œ œ œ œ Nœ nœ œ œ œ œ œ œ œ

ver - herr - licht

licht

œ nœ Nœ œ œ œ œ œ œ bœ œ œ œ œ œ œ

tutti

œ œ œ nœ œ œ œ œ œ œ œ œ œ œ œ œ

œ œ œ Aœ œ œ œ œ #œ nœ œ œ œ œ œ œ

herr

keit,

œ nœ œ œ œ œ œ bœ œ

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ nœ œ œ #œ œ œ œ œ œ œ œ œ œ œ œ œ nœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ Aœ œ nœ #œ

Zeit,

Nœ

#œ

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œœœœœœœœœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œœ œ œœ œ œœ œ œ œ œ œœœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ Phenomenal œœœœœœœœœ œ œ œ œœ œœ œœœ ˙ ˙ ˙ ˙ ˙ w w ˙ ˙ ˙

Root/Quality

Got

? b œ #œ œ Aœ œ nœ b œ œ œ

B.C.

œ J

‰

j œ œ œ

œ J

‰

œ J

‰

b V b œ #œ

œ œ œ œ œ œ œ œ œœœœœœœœœ

D/S=) (g:)( D

b & b Aw

Fl. I Ob. I

Fl. II Ob. II

nœ

Vln. II II

Aœ

b & b Aœ œ œ œ œ œ œ œ œ

? b b

B.C.

89 Comp./Phen.

Bass Pitch

#˙

N˙

licht

wor - den

bist,

ver - herr

œ Aœ licht

œ S^z

ist,

ver

œ Aœ

licht

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

herr

wor - den

bist,

œ œ œ œ œ œ œ œ Aœ œ œ œ œ œ œ œ œ

wor - den

bist,

ver - herr

œ ver œ

licht

œ œ

wor - den

œ ^z

œ %

œ &n

bist,

œ licht

licht

wor - den

œ %S

œ nœ œ œ œ œ œ œ

ver - herr

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ -

bist,

nœ

bist,

ver - herr - licht

nœ

^S5

‰

ver - herr - licht,

‰

licht,

œ œ

Aœ

^4s£ n

œ #œ

‰

#œ

‰

‰ Aœ ver

œ œ ^S4£

ver

œ #œ

- herr

ver

ver - herr - licht,

wor - den,

j œ

ver

verr - herr - licht,

licht,

n˙

#˙

œ œ #œ œ nœ œ œ œ œ œ œ œ œ œ œ œ œ œ #œ œ nœ œ œ œ œ

nœ

œ nœ

œ œ œ œ œ

œ nœ œ #œ œ nœ œ œ #œ œ œ œ œ œ œ œ nœ œ œ œ œ

œ Œ Ó

œ œ œ œ œ #œ

#œ

œ œ J

œ.

licht

wor

den

bist.

œ #œ œ nœ œ œ œ œ œ œ œ œ œ œ œ œ œ #œ œ nœ œ œ œ œ œ.

den

bist.

herr

Nœ nœ œ œ œ œ œ œ œ œ œ #œ œ herr

#œ &5`Z

œ #œ œ licht,

nœ #œ. œ

œ nœ œ œ œ -

œ J

ver - herr

licht

œ.

licht

wor

licht

wor

œ ^4

œ J

den

œ %Sx

œ Œ Ó

#œ

Œ Ó

bist.

œ Œ Ó

den

wor

j œ

Œ Ó

œ Œ Ó

nœ

herr

Da Capo

œ Œ Ó

œ œ œ nœ œ #œ œ œ nœ œ œ #œ œ œ œ œ œ œ œ nœ œ œ œ œ œ œ œ œ œ #œ œ œ #œ Œ Ó

œ œ œ œ œ œ œ œ #œ nœ œ œ œ œ œ œ Nœ nœ œ œ œ œ œ œ œ œ

œ œ #œ œ nœ œ œ œ œ œ œ œ œ œ œ

N˙

œ nœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

œ nœ œ œ œ œ œ œ œ #œ œ Nœ œ œ œ nœ Aœ

- herr

#˙

#œ

œ œ œ œ œ œ Aœ œ œ œ œ œ œ œ œ œ œ œ œ nœ œ œ œ œ œ #œ œ œ œ œ œ œ œ nœ œ œ Aœ œ œ œ œ œ œ œ œ œ œ œ œ

œ œ œ œ œ œ œ œ nœ œ œ œ œ œ œ œ

? b b

bist.

Œ Ó

œœœœœœœœœœœœœœœœ

œœ œœœœœœœœœœœœœœ œœœœœœœœœœœ œœœœœ

œœœœœœœœœœœœœœœœ

œœœœœœœœœœœœœœœœ œœœœœœœœœœœœœœœœ œ Œ Ó w

œ Œ Ó

–– –– –– ––

–– –– –– –

–– –– – –––

–– –– –– –

œ Œ Ó

edim.

Function

A˙

œ œ œ œ œ œ œ œ œ œ œ œ œ Aœ œ nœ

B bb n œ

Vla.

Density

b & b Aœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ Aœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ nœ œ œ œ œ œ œ

Vln. I I

Root/Quality

–– –– –– ––

–– (( ––– )) ––

˙ (c:)

adim.

( ––– ) –– –––

–– –– –– ––

(

D/S= D

)

( ––– ) (––– ) (( –– ))

–– –– –– –– –

–– –– ––

(F:)

(P) T=

(d:)

F+

g#dim7

(( ––– )) ( –– ) (( ––– ))

–– –– –– –– –

œ D

D/D

* The strange order of these functional bass symbols is a result of chromaticism. This creates functional ambiguity before we arrive at a more conventional harmonic progression before the da capo.

˙ D

–– –– –– –

D/S

g#dim7

D/D

œ Œ Ó

( T= D )

APPENDIX B

Reinterpretations of Bach’s Harmonic Rhythm

Appendix to Part II of Analyzing and Reinterpreting Dimensions of Bach’s Harmonic Rhythm

Harmonic Prototype

Reinterpretation of Bach's Series of Chord Roots

& 42 ˙˙

˙˙

˙ ?2 ˙ 4 ˙˙f & ˙ ? b˙

˙ b˙ ˙g b˙ ˙ ˙

b˙ ˙ c

˙ ˙

˙c ˙

˙ b˙

˙ ˙ d

b ˙˙ Eb7 ˙ #˙

b˙ b˙ ^

b˙ ˙

b˙ b˙ #D7˙˙ ˙ ˙

b ˙˙

˙ ˙

(Tritone Substitution)

Method of Reinterpretation "Herr, unser Herrscher", mm. 19-23

Interlude No. 1 (Harmonic Density Reinterpreted) q = 122

Disklavier

Ee-A-Ee-Ee

(Vector Envelope = e )

& 44

? 44 Ó & 44 b ww ? 44

• bœ œ bœ œ‰Œ Ó

∑

ßß ‰Œ Ó r≈‰ Œ bœ bœ œ œ b œœ ß

P Ó b œ. œ. •

˙.

?4 4

∑

Gradual Clarity

4 &4

∑

Bloop

B 44

∑

Deep Cleanse

÷ 44

∑

Glass Saw

?4 4

∑

Virus

? 44

r ‰. Œ j ‰ Œ bœ œ. œ •P ß

–– ––

"Polyphonic Density"

‰ ∑

–– –

•

œ. b œ.

œ.

b˙ P

≈œ

∑

b˙

–– ––

∑

–– ––

œ.

∑ b ww

œ ˙.

∑

∑ ≈bœ œ ‰ j . œ . •

∑

Scrambly Guitarpegiator

˙.

∑

∑ Œ

∑ Ó

∑ w P

‰ ≈ r‰ jÓ œ œ. •

–– ––

–– –

∑ r≈‰ Œ Ó bœ œ • fl ww œ

˙. ∑

∑

b ˘œœ ‰ JŒ Ó

∑

∑ w

∑

Ó œ ˙. ˙ b˙ Œ

bœ Ó Œ

˙œ ˙ ˙ . b˙ Œ

b ˘œ ˘œ œ œ b Œ ‰ œ ‰ ‰ œ̆ Ó J ∑

bœ

Ó ˘ ‰ b œœ Œ J

ww ˙œ

˙. ˙ ∑

œ. . ‰ b œ œ. Ó

∑

b ˙ .. ˙

r≈‰ Œ Ó œ œ

∑

–– ––

–– –– –

–– ––

œœ

œœ Ó

œœ

œ œ ∑

˙ bœ

œ‰Œ œ‰Œ J J • F w F –– –– –

–– –– –

œ.

∑ Ó w ww

˙œ ˙ ˙ .

∑

–– –– –

œ bœ bœ ‰ œ œ

˙œ ˙ ˙ . &

•

j‰ Œ bœ •.

•

˙œ ˙ ˙ . ∑ œ

Œ ‰ jÓ bœ π ˘ b œœ œ b œ œ̆ ‰ œ

∑

bœ œ J

bœ

‰ œj ˙ . www ˙œ

˙. ˙

j‰ Œ j ‰ bœ œ p P œ

w Ó

œœ

∑

P ∑

∑

–– ––

–– –– –

bœ œ œ Œ 5

‰ œ. œ . P œ.

–– –– –

–– ––

14 œ œ

Diskl.

E-A-E-E

Scrambly

Gr. Clarity

Bloop

D. Cleanse

Gl. Saw

Vir.

& ˙. œ ‰ Œ

j œ ˙ œ ˙ • œ œ ˙. w & ww ˙ ˙. ? œ

? ‰

& b œj ‰ Œ & w B Œ ÷ ? Ó ? Ó

–– –– –

Œ Œ

œ œ ˙. b www

˙ j ‰ œ

œ˙

j ‰ Œ bœ

‰

P œbœ œ œ Œ •

–– – ( –– )

–– ( –– )

∑

˙.

Œ œ

‰

–– –– –

∑

œ œ www

˙ œ

j ‰ œ

j ‰ bœ

•

j ‰ œ

œ œ œ

˙ œ Œ

–– –– ––

˙. ˙. Œ

bw œ

j‰ Œ œ

j‰ Œ bœ

‰ ≈ r bœ œ œ bœ ˙ œ Ó

∑ Ó

–– –– –

œ œ ˙. www

b˙

∑

–– ––

j‰ bœ

∑

( ––– ) –

˙.

∑

œ œ www

≈ bœ œ œ ‰ bœ ≈ œ œ œ œ bœ œ R œ

∑ œ bœ œ œ ‰

˙.

rit.

b˙

–– –– –

‰

∑

44ˆ81

∑

44ˆ81

∑

4ˆ 1 b wœ 48

˙. j‰ Œ œ

w bœ œ

4ˆ 1 œw œ ˙ . 4 8 ww ˙.

44ˆ81 j ‰ ‰ j Ó bœ œ 44ˆ81 w

j œ b œ b œœ J j œ œ J

a tempo ∑ ∑

4 w 4 b ww f 4 wœ ˙ . 4 f j 44 ∑ œ j 4 œ 4

∑

œ œ j bœ Œ Œ b œ œ ‰ œ œ 44 œ œ œ œ œ œ œ œ bœ œ œ. œ f 44ˆ81 w w œ 44 w> J f w

44ˆ81

∑

4ˆ 1 48

4ˆ 1 w 48

–– ––

∑

bœ J

∑

4 4

w f 4 w 4 w f –– –– –– –– –

∑ w ww

w œ ˙. ∑

œ w w w w

∑ Œ

Analysis of Interlude No. 1 q = 122

Disklavier

4 &4

∑

? 44 Ó

r≈‰ Œ b œœ ß

& 44 b ww 2

Ee-A-Ee-Ee

(Vector Envelope = e )

Scrambly Guitarpegiator

? 44

1 2

• bœ œ bœ œ‰ Œ Ó ßß b œœ œ bœ

b ww

∑

Bloop

B 44

∑

Deep Cleanse

÷ 44

∑

? 44

∑

"Polyphonic Density"

˙.

∑

b ww

˙.

∑

r ‰. Œ b œœ ß 4

–– ––

j ‰Œ œ. •P 3

–––

–– ––

‰

œ. b œ.

œ.

b˙ P

Ó ∑

≈œ 1

b b ww 1

œ ˙.

∑

2 œ.

Œ ∑

∑

•

b˙

–– ––

∑ Ó

∑

w P

r≈‰ Œ Ó b œœ • fl b b ww 2

˙.

∑ ∑

∑

–– ––

–––

–– ––

∑

b b ww

b ˙˙ ..

b b ww

1 Ó œ ˙. ˙

bœ Ó b˙ Œ 3 Œ

b b ww

˙œ ˙ ˙ .

b ˘œœ 3

˘ Œ ‰ b œœ ‰ ‰ œœ̆ J 4

r≈‰ Œ Ó œ • fl 1

b˙ Œ

∑

˙. ˙

∑

˘ ‰ b œœ Œ J 4

‰

3 œ. b œ.

∑

r≈‰ Œ Ó œ œ

∑

–– ––

–– –– –

–– ––

œ. Ó 4

˙ 3

• 1

œœ 2

bœ bœ 4

‰

œ œ3

∑ Ó w1 b b ww

˙œ ˙ ˙ .

j‰ Œ bœ •. 1

˙œ ˙ ˙ .

œœ 2

3 œ œ 4

∑

∑ bœ

œ4 ‰ Œ œ5 ‰ Œ J J • F 5

w F –– –– –

–– –– –

Œ ‰ b œj Ó 2 π ˘3 b œœ 4 3 4 5 œ̆ œ bœ ‰ œ 2

∑

–– –– –

œ 1

b b ww

˙œ ˙ ˙ .

∑

b b ww

bœ

∑

˙œ

∑

r‰ jÓ œ œ. •

∑

b ˘œœ ‰ JŒ Ó

‰.

∑

≈ bœ œ ‰ j . œ . •

∑

? 44

∑

Œ Ó bœ P . œ. •

b ww

Gradual Clarity

Virus

∑

‰Œ Ó

4 &4

Glass Saw

(Harmonic Density Reinterpreted)

∑

– –––

–– –– –

–– –––

œ 5