Levels of Harmony
English Grammar and Tonal Harmony
Reviewing a little English Grammar will help us make a point about tonal harmony. Consider this sentence:
Much of the meaning of the sentence is conveyed by its most essential parts—the subject and the predicate—which would appear in unmodified form as follows:
While this telegraphic style is not elegant, it does get the idea of the sentence across, just as would a I–V–I progression. The other words in the sentence flesh it out and help describe the subject and predicate. The whole sentence can be diagramed to show the function of each word:
The grammar of tonal harmony has some similarities to spoken language, but it is not quite so well understood. While we might draw an analogy between chord functions and parts of speech, no one has designed a system of diagraming harmony as precisely as English sentences.
Levels of HarmonyPlay this phrase (Ex. 1) slowly.
Example 1. Haydn, Sonata No. 33, II.
The basic tonal motion of the phrase—the skeletal subject and predicate—is made up of the i–V progression formed by the chords that begin and end the phrase. But how do the other chords function? How do we evaluate their relative importance? The roman numerals give us a hint, but more analysis is required. One way to approach such an analysis is to try to hear the chords as originating at different levels: some levels are rather fundamental to the structure, while others are more ornamental.
Play the first two measures again. One way to hear this fragment is as an arpeggiation from i to i6 that is filled in by the vii0r (or vii06–). We might diagram these relationships on different levels as follows.
The second part of the phrase is more involved. The V chord predominates, but the iv is an important dominant preparation. The root position i serves not as the goal of the phrase but as part of the prolongation of the V chord. Least important of all is the Vq, which is an arpeggiation of the more fundamental root position V chord that precedes it. These relationships might be summarized in this way.
When we put the two halves of the phrase together, the diagram should show i and V as the most significant chords, with the iv coming in at the next level. The function of every other chord in the phrase must also be made clear.
Are there other ways to hear this phrase? Certainly. But we have gone a step beyond mere chord labeling by showing how a listener or performer might interpret this passage.
While Example 1 is incomplete in the sense that it ends with a HC, Example 2 contains a parallel period with complete harmonic motion away from I and back again.
Example 2. Haydn, Sonata No. 35, III.
This excerpt can be seen as an elaboration of the progression presented in Example 3.Example 3.
The other chords in Example 2 include a dominant preparation (IV), arpeggiations (I6), and chords that embellish the arpeggiations ( and ). The chord functions might be diagramed as follows.
This kind of analysis is much more subjective than sentence diagraming is, but it is important that the analyst consider the function of each chord, even if several interpretations are possible. In a levels analysis of a single phrase, the highest level will usually include only the I chord that begins the phrase and the V or the V–I that ends it. The next level will often include the ii or IV preceding the last V. Other chords that sometimes seem to be more significant than those surrounding them include these.
Arpeggiations of important chords
Root position I and V chords
Goals of stepwise bass lines
Tonicized chords (to be discussed in Chapters 16-17)
Chords of longer duration
Various methods are used to expand upon the simple progression that serves as the background of a passage. Some of them have been seen in Examples 1 and 2. The simplest of all is octave displacement (see m. 6 of Ex. 2, soprano and bass). More interesting is arpeggiation (mm. 1-2 of Exx. 1 and 2), which can itself be embellished. Most often used to embellish arpeggiations are passing chords (mm. 1-2 of Ex. 1), although appoggiatura chords (m. 1 of Ex. 2) are also used. Another method is the neighbor chord, two of which are illustrated in Example 4.Example 4.
A familiar form of harmonic embellishment is the six-four chord (review Chapter 9). You will recall that many triads in second inversion serve as passing chords or as embellishments of tonic or dominant chords, while others come about as arpeggiations. Strong dominant preparation chords (usually ii or IV) are in a class by themselves. They often occur at metrically stressed points, and they are frequently embellished. In many cases you may feel that they rank with or just below the fundamental I and V chords in significance. The importance of these chords is reflected in their early appearance in the levels diagrams we have presented so far in this chapter.'
Examples from a Chorale
The chorale harmonization is a good source for the study of levels of harmony because it presents a large number of chords in a short space of time. Since most chorales modulate (change key) or contain tonicizations (see Chapters 16-17), we will have to restrict ourselves in this chapter, for the most part, to excerpts. The remainder of the examples in this chapter are drawn from Bach’s harmonization of "Nun ruhen alle Wälder."
Example 5 shows the first phrase of the chorale. This phrase is obviously "about" the I chord, which appears in root position three times and occupies four of the eight beats in the example.
Example 5. Bach, "Nun ruhen alle Wälder"
There is no root position V, a weaker being used at the cadence. It can be heard as a neighbor chord to the I (Ex. 6).
The preparation for the is provided by the that precedes it. So far, our levels might be shown as:
The vii06 that appears early in the phrase is a weak form of dominant harmony. Like the , it can be heard as a neighbor chord (Ex. 7).
The vii06 is preceded by its own dominant preparation—a root position IV—which gives us this reading of the phrase.
The third phrase of the chorale (Ex. 8) is essentially a I-V progression.
Example 8. Bach, "Nun ruhen alle Wälder"
We choose the root position I over the I6 as the "original" version, with the arpeggiations embellishing it, as in Example 9.
Since this phrase has no dominant preparation, the only chords left to account for are the relatively weak and vii06 chords that embellish the tonic harmony.
The last phrase of the chorale (Ex. 10) is an embellished I–V7–I progression.
Example 10. Bach, "Nun ruhen alle Wälder"
The V7 is prepared by a IVM7 and by a weaker IV6, as diagramed below.
The other three chords serve as an anacrusis (upbeat) to the first I chord and are added one at a time to the levels analysis.
The concepts presented in this chapter are by no means original, but this kind of analysis of harmonic levels is not widely used. For this reason it will not be pursued systematically throughout the text. Instead, the idea of harmonic layers is introduced here to encourage the reader to understand that, although each chord may be labeled with its own roman numeral, all chords are not equally important. In fact, not all chords with the same label (all V's, all I's) have identical uses. Some serve as starting points, some as goals, others as connectors, and so on. These fascinating and diverse relationships are what the grammar of tonal harmony is all about.
- Label the chords and do a levels analysis. What kind of NCT is the A4 in the soprano?
Bach, "Ich freue mich in dir"
- This exercise and the next one are two different harmonizations by Handel of the same melody. Label the chords, and do a levels analysis.
Handel, "Wenn mein Stündlein vorhanden est"
- Label the chords, and do a levels analysis. What progression in this excerpt is relatively unusual?
Handel, "Wenn mein Stündlein vorhanden est"
- Label the chords, and do a levels analysis. What is the form of this excerpt? What kind of NCT is the C5 in m. 8?
Answers to Self-Test(All the levels analyses are subject to other interpretations.)
- The A4 is an anticipation.
- Here are two interpretations, the first probably being the better one because it agrees with the meter.
- The progression ii6–vi is relatively unusual. In fact, retrogression would be a better term here because vi usually lies further away from tonic than ii6 does in tonal harmony.
- The form is a parallel period. The C5 is an escape tone.
The Epic and the Intimate: Binary Form in Kyrie I of Bach’s B minor Mass
Bach’s B minor Mass “dominates Bach’s oeuvre as a work reaching well beyond the bounds of its practical and stylistic context.”1 The work is too long, the music too challenging, to be part of a standard church service. That the work was assembled, which scholars agree took place over the last two years of Bach’s life, rather than composed for a specific service helps account for the vastness of the work, which consists of twenty-seven individual movements and usually requires over two hours to perform. The Mass would seem to be a model for the many large scale sacred compositions that followed. The opening Kyrie movement is representative of the work’s scope. Composed for a five-voice choir the piece “impresses us not just with its monumental scale but also with its deeply serious nature.”2
The Kyrie is a lengthy and complex movement, consisting of two fugues for five part choir, but at the same time it is a very intimate piece; Bach avoids virtuosic vocal parts and extravagant orchestration in order to create a deeply penitent (but not dispassionate) plea for mercy. What is normally an intricate formal plan is made simple by limiting thematic material and by the use of binary form. The movement is separated into two sections, each containing an instrumental introduction followed by a choral fugue on the same subject, which is first introduced in the first instrumental section. In this essay, I will examine how Bach adapts binary form for the overall structure of the piece as well as how each individual section shows a binary structure, as a microcosm of the whole. The diagram below shows the structure of the piece as well as the individual sections:
According to Donald Tovey, “the first Kyrie of the B minor Mass is so vast that it seems as if nothing could control its bulk.”3 However, considering that the movement is the opening of a Mass that requires nearly two hours of performance time, its length seems appropriate. Yet, the piece is not simply a statement of grandeur as the above quote would suggest; as already stated, the piece displays not only passion, but penitence and hushed reverence through the use of a relatively small orchestra to accompany the expanded choir. The use of the key of B minor would appear to be integral to the humble nature of the music. In 1784, C.F.D. Schubart described the key as
The key of patience, of calm awaiting one’s fate and of submission to divine dispensation. For that reason its lament is so mild, without ever breaking out into offensive murmuring or whimpering.4
The key was also described in the Eighteenth Century as “morose and melancholy” as well as “sweet and tender.”5 Although D major is the key of the whole (several sections including the Gloria and Sanctus are set in this key), which would suggest that the use of B minor is a matter of utilizing the primary key’s relative minor, the above descriptions of the characteristics of the key suggest that affect may have been another reason why Bach chose it to begin the Mass.
The piece opens with the full orchestra and choir doubling each other, homophonic in the first measure and becoming more contrapuntal in the following measures. The choir articulates the text “Kyrie eleison”; the use of the full ensemble for the introduction (typically performed at the dynamic of forte) creates the sense of a passionate plea for mercy. This introduction also serves to introduce the thematic material for the movement. In the example below, the first soprano in the opening four measures is compared with the forthcoming fugue subject:
The opening measures show a rising scale on the strong beats, starting on the D in the first soprano and continuing to the G in m. 3. This rising scale mirrors the rising motive, beginning on the B and continuing to the D of the fugue subject. The passage starting on the G, to the F# at the end of m. 4 in the first soprano is similar to a portion of the subject. This portion follows the diminished seventh leap from the A# to the G, beginning in the first flutes and oboes at m. 7.6
Following this introduction is a 24 measure orchestral passage that states the thematic and motivic material for the entire piece. The first flutes and oboes state the fugue subject, beginning on the downbeat of m. 5, while the first violin states the cadential semi-tone motive that may or may not end the subject on the second beat. The varying interpretations of where the subject ends will be discussed with the entry of the choral parts. The subject statement continues to the semi-tone motive on F# at m. 8, implying that this is the end of the subject, but this does not resolve the matter, as we shall see. The second flutes and oboes imitate the subject at the dominant level, while the B minor harmony acts as a pivot towards F# minor tonality. Although the subject is imitated at the fifth, this section is less fugal than the choral passages that follow, since the subject does not appear again for nearly fifteen measures. Also, there is no departure from the tonic and dominant keys following this final entry. Instead, the first choral fugue begins almost immediately afterwards. Therefore, I do not consider this orchestral section a fugue. Following the subject statements in both voices is a sequential idea consisting of an upwards leap of a fourth, followed by a stepwise descent. During the choral passages, this motif also appears following subject statements. At measure fifteen, Bach provides the first instance of binary form; a PAC in the dominant is followed by a motivic change, in this case the introduction of a rhythmic motive consisting of two sixteenth notes followed by a long note. In this miniature binary AB form, the subject statements occupy the A section (mm. 5-15), while the B section (mm. 15-30) contains passages without the subject (except for a single bass entry at m. 22) in the dominant key. At m. 19, a variation of a portion of the subject is introduced, harmonized in thirds by the flutes and oboes.
This variation makes use of the chromatic climb and the neighbour note motive from the subject. Here, the climb is changed to a descent after one measure, creating what I will call an inverted subject fragment. This variation is used extensively during development passages. The sequential nature of the variation brings the music back to the tonic and the subject in the bass at m. 22. This brings to mind rounded binary, although rounded binary generally only repeats a brief passage of the A section at the close. Nevertheless, the subject in the bass in this piece often represents the end of a section.
One may ask why Bach has such a lengthy instrumental passage in a choral movement. Again, the scale of the entire work must be taken into account: this section seems to serve not only as an introduction to this movement’s subject, but as an “overture” to the entire Another question is what structural function does this section serve? Tovey refers to this introduction as a ritornello7, but I disagree as this piece does not rely on alternating fragmented statements of the ritornello with passages of contrasting material. Rather, the introduction serves a different structural function, as this section is repeated twice more (once in the dominant, once in the tonic). This section serves to end sections as I will discuss further on.
Following a PAC in the tonic at m. 29, the first of two five-voiced choral fugues begins in the tenor.
The plan of entries for this section is as follows:
The fugue does not contain a countersubject. The reason may have to do with the meaning of the text: the fugue subject is the plea for mercy, so all voices singing one subject may represent a unified plea. This may also be why the instrumental accompaniment generally resembles the choral parts: all forces are unified for a single purpose.
As is common in fugue, there is ambiguity as to where the subject ends; the example above continues to the cadential motive. This would make sense, as the subject modulates to the new key and states the complete text. However, this is not repeated during the answers. The semi-tone motive is delayed by episodic material. One could interpret the subject as only being complete and uninterrupted in the tonic key; the interruption in the dominant creates tension by delaying the resolution. However, the subject could also be seen as ending on the A# in m. 32 as it ends the text and is repeated in all statements. The major problem with this is that ending on the leading tone does not provide a satisfactory sense of resolution to the subject. A third interpretation is derived by observing the polyphonic nature of the subject.
As the example shows, the voice leading of the polyphonic line shows an F# sustained in the lower voice which is then transferred to the upper voice. While the upper voice moves down to D in m. 32, the lower voice A-sharp resolves to an implied B, while the G moves to F#. Since the D is where the polyphony is resolved with a cadence8, one could interpret the subject as ending here. However, this occurs in the middle of the text. Perhaps this ambiguity is part of the rhetoric of the piece; a subject without a clear ending conveys the notion that penitence and pleading for mercy is a never-ending process.
The exposition proceeds in the expected fashion, with episodic material delaying the entries of the first soprano and the bass. As noted, the fugue contains no countersubject. It would be a mistake to conclude that free counterpoint is employed; while the first soprano enters with the subject at m. 37, the alto contains a leap from F# to B. This is a fragment of the sequential idea that followed the subject statements in the opening instrumental section, which overlaps with the cadential motive that completes the answer, if one interprets the answer that way. Against the second soprano entry at m. 39, the alto has the same fourth-leap, which is followed by a stepwise descent to a G# on the downbeat of m. 40. Although this is not free counterpoint, as it utilizes previously established music, it is not employed in a systematic manner throughout this exposition.
Before the bass entry, the second soprano has another entry in m. 44 in the key of D major. What is the reason for this seemingly unnecessary entry? The entry serves to move the music back to the tonic key, but why use the subject? Perhaps this is Bach’s gesture to a convention of fugue that the movement otherwise does not follow, which is to have a middle section with entries in the relative major as a relief from the prevailing minor tonality. By beginning this entry on an F#, the entry harmonizes with the D major chord and also suggests answer form, which helps move the piece back to B minor so the exposition may be completed.9 Finally, placing two entries in close proximity creates a stretto-like effect, another fugal convention that is little used in this piece. The bass enters on the third beat of m. 45 and continues to the cadential motive. At m. 48, the second soprano enters with the answer. While at first glance this appears to be a redundant entry, a common element of fugal exposition, it turns out to have greater structural importance. A comparison of the bass line from mm. 48-72 to the bass from the orchestral introduction starting at m. 5 shows that, with a few deviations, the bass precisely transposes the opening section to the dominant key. The entries of the subject use the same voices as well, but in a different order. In the opening section, the first flutes and oboes could be thought of as the first soprano, while the second flutes and oboes would be the second soprano. As before, a soprano entry is imitated at the dominant (this time, the dominant is C# minor) and the bass enters fifteen measures later. The return of this passage moves the tonality away from tonic and dominant to the distant key of ii, which is common after expositions as it creates tension, facilitating the development passages which follow. Structurally, this twenty-four measure passage moves the piece into a new section; this particular passage ends the A section of the overall structure, with a PAC on the dominant at m. 72, leading to the second instrumental segment, which begins the B section.
Before this happens, there is a PAC in C# minor at m. 58. Following is a change in texture as all voices but the tenor drop out and re-enter in succession. Also noticeable is the motivic change: the sixteenth note motive introduced in m. 15 dominates the texture, especially in the orchestra, where it is passed amongst the various instruments. This is not the first time it has been used in this section, but it has not been in an exposed position until this point. The cadence along with the texture and motive change provides the binary division of this choral section. Beginning at m. 61 in the first soprano, the inverted subject fragment appears, mirroring its use at m. 19. This leads the music back to F# minor and the bass entry of the subject. The A section of the movement is brought to a close with a PAC on beat three of m. 72.
The B section of the piece, beginning with a second orchestral passage, overlaps with the cadence and begins with a second oboe entry. Bach moves into D major at m. 75 (minor mode binary pieces often begin the B section in the relative major) and breaks up the subject entries with statements of the inverted subject fragment. The binary division in this section is created on the downbeat of m. 76 (the middle measure of this nine measure section) with an imperfect cadence in the tonic. The music quickly moves to A major and a subject entry in the second violin. This is again followed by the inverted subject fragment, leading back to B minor. The return of purely orchestral music is designed to be reminiscent of the beginning of the piece, separating the piece into two distinct sections (each consisting of an instrumental section followed by a choral section). This is typical of binary form, where the B section complements the A section by using similar material At the same time, by altering the plan of entries in this passage as well as the instrumentation, Bach is able to disguise the rewriting of his previous section with remarkable economy.
Bach avoids a bass entry in the instrumental section to prevent redundancy, as he begins the second fugue with the bass at m. 81. The plan for this choral section is as follows:
Bach contrasts this choral section with the previous one in several ways; the most obvious is the different order of entries. The full orchestra accompanies the choir throughout this section, whereas the previous section began with only the oboes and continuo, gradually expanding to the full ensemble. In terms of rhetoric, the use of the full ensemble conveys a sense of finality: since the forces cannot expand any more (which would indicate a climax), we are given a sense from the beginning that this section will end the piece.
As in the previous fugue, the instrumental parts closely resemble the choral parts in order to unify the entire ensemble in its pleas and again, there is no countersubject. Bach counterpoints the subject with material similar to the first exposition: the bass states an E on the anacrusis to m. 85 which leads to the sequence D-C#-D in eighth notes. When this motive is compared to the sixteenth note motive in the tenor at m. 34, it becomes apparent that m. 85 is an augmentation of the earlier motive. This is followed by the leap followed by stepwise descent, with the leap being altered from a fourth to a minor seventh. The tenor at m. 88 features the eighth note leap from F# to B, which leads to the cadential motive from the (possible) end of the answer. The exposition continues in a manner similar to the previous section until m. 97, when the second soprano enters with the subject in E minor. To present the subject in the sub-dominant key before the exposition is completed seems highly irregular.10 However, there are two reasons why this happens: the first is to maintain a sense of forward momentum. Had the soprano entered with the answer, the final entry would have been in the tonic, which would have eliminated the tension which would provide a basis for episodic passages and eventually lead to a final resolution. The sub-dominant entry, followed by a tonic entry at m. 102 separates two entries in the dominant (the second soprano enters with the answer at m. 104). The second reason is that it facilitates the return of the orchestral section starting at m. 5, this time in the tonic key. The entries are also restored to the original order of first soprano, second soprano, and bass. Once again, with some minor exceptions, the bass line from mm. 102-126 is a verbatim transcript of the opening section. The aforementioned soprano entry at m. 102 (doubled by the first flutes and oboes) begins this reprise. The second soprano entry at m. 104 is simultaneously the fifth entry of the exposition and the imitation of the subject in the reprise (which is doubled by the second flutes and oboes). Similar to the previous exposition, there is a PAC in the dominant at m. 112, leading to a similar texture and motivic change (all but the alto drop out and then successively re-enter and the sixteenth note/long note motive is taken up). This provides the A/B division for this section of the piece. The inverted subject fragment is taken up by the sopranos and the treble instruments at m. 116 before the final bass entry of the subject in the tonic at m. 119 completes the reprise and concludes with a PAC (with a Picardy third) at m. 126.
Throughout this essay, I have analyzed this piece as being binary form, even though the repetition of mm. 5 through 29 in triplicate suggests a possible ternary form (especially considering that a dominant statement is framed by two tonic statements). I reject this view because I see too many examples of binary division within the individual sections. Also, the division of the piece into two orchestral introductions followed by choral fugues is very reminiscent of binary form’s tendency to consist of two complimentary sections. The fact that the first statement is instrumental, while the others are choral also makes a ternary analysis problematic. I believe that the recurrence of the 24 measure passage serves to provide formal endings to the major sections of the piece while the increasingly complex texture prevents each return from being obvious to the listener. The reworking of material is a common thread throughout this movement; Bach has taken a small amount of melodic material and created an elaborate opening to a work on a massive scale. By adapting binary form to suit his complex plan and combining an expanded choir with a rather small orchestra, Bach created an opening movement that is both epic and intimate.
2[Back]George B. Stauffer, Bach: The Mass in B Minor (The Great Catholic Mass) (New York: Schirmer,1997), 53.
3[Back]Donald Tovey, Essays in Musical Analysis Volume V: Vocal Music (London: Oxford University Press, 1937), 25.
4[Back]Rita Steblin, A History of Key Characteristics in the Eighteenth and Early Nineteenth Centuries (Ann Arbor: UMI Research Press, 1983), 306.
6[Back]Stephen Daw, The Music of Johann Sebastian Bach: The Choral Works (Rutherford: Farleigh Dickinson University Press, 1981) 162-163.
8[Back]Dr. Renwick demonstrated this to me.
9[Back]Dr. Renwick also pointed this out to me.
10[Back]Interestingly, it is always the second soprano that deviates from the fugal paradigms. Perhaps this is an acknowledgement by Bach that he is expanding the traditional four part choir, as if the second soprano is the “extra voice.”
Copyright 2003 by Dan Sheridan