A Performer’s Investigation, Part 1

Knowledge

In order to acquire knowledge about John Bull’s work, it is important to know a little bit about what knowledge actually meant at the time the work was created. Here we are dealing with the late Renaissance–early Baroque, the exact date of the composition itself, as far as I have been able to determine, being unknown. Michel Foucault in his book, The Order of Things: An Archaeology of the Human Sciences, states:

Up to the end of the sixteenth century, resemblance played a constructive role in the knowledge of Western culture. It was resemblance that largely guided exegesis and the interpretation of texts; it was resemblance that organized the play of symbols, made possible knowledge of things visible and invisible, and controlled the art of representing them. The universe was folded in upon itself: the earth echoing the sky, faces seeing themselves reflected in the stars, and plants holding within their stems the secrets that were of use to man (p. 17) . . . To search for a meaning is to bring to light a resemblance (p. 29) . . . There is no difference between the visible marks that God has stamped upon the surface of the earth, so that we may know its inner secrets, and the legible words that the Scriptures, or the sages of Antiquity, have set down in the books preserved for us by tradition. The relation to these texts is of the same nature as the relation to things: in both cases these are signs that must be discovered (p. 33) . . . Knowledge therefore consisted in relating one form of language to another form of language; in restoring the great, unbroken plain of words and things; in making everything speak. That is, in bringing into being, at a level above that of all marks, the secondary discourse of commentary. The function proper to knowledge is not seeing or demonstrating; it is interpreting (p. 40).

If knowledge in the Renaissance and Baroque is interpretation and uncovering order, then knowledge about a work of art created in this transition time at the end of the Renaissance and the beginning of the Baroque can only be about discovering an order and an interpretation. I do not believe that the impossibility of total certainty of the results of such inquiry should deter one from the attempt to understand a work in the sense the maker might have understood that concept of “understanding.” One thing is certainly true. Understanding, in this sense, for a musician cannot simply mean hearing and/or playing a work and responding with “like” or “dislike.” Our response must go deeper. “It is not enough to feel the effects of a science or an art. One must conceptualize these effects in order to render them intelligible” (Rameau, p. xxxv). We must dig in order to uncover what might be hidden from cursory view. We must, as Frescobaldi demands, “endeavour in the first place to discover the character of the passages, the tonal effect intended by the composer  . . . ”(Notes).

John Bull

John Bull (1562–1628) had his feet in the Renaissance and his head in the Baroque. In other words, he was a child of the Renaissance and experienced the beginnings of the new era as a grown man. He was the student of John  Blitheman. John is known as William in the Fitzwilliam Virginal Book, which contains an In nomine of his immediately preceding the Ut, re, mi, fa, sol, la of Bull’s which is the subject of the present essay. Blitheman was known for his cantus firmus compositions, which occasionally demanded great virtuosity of the player. Bull’s education, grounded in Renaissance teaching as it must have been, certainly did not end with his formal studies. He was elected first Public Reader in Music at Gresham College, London in March of 1597 where he remained, except for a year’s leave of absence, until 1607, the year which saw his necessary marriage to one Elizabeth Walter, who was pregnant with his child. During his period at Gresham, the College was a hotbed of discussion of new ideas, inventions and discoveries from all over Europe.

For example, during the last quarter of the sixteenth century the ideas of Copernicus became more widely disseminated among the general public, the world view which stood the previous view of the universe on its head. What was formerly immovable, the earth, now was realized to be hurtling through space at unheard-of speeds. Bull must have been well-informed as to the revolutions in scientific thought in which learned men all across Europe were engaged. He was part of the established intellectual community; the universities did not ignore these new, ground-breaking ideas. He must have known about the fierce debates between the followers of Copernicus and those of Aristotle at Cambridge during the 1580s. For “we find Gresham College was, throughout the first half of the seventeenth century, a general clearinghouse for information concerning the latest scientific discoveries. Its professors of astronomy and geometry were among the ablest scientists of their day, and the college’s central location in London made their rooms a convenient rendezvous for all those who were actually contributing to the advancement of science in England” (Johnson, p. 263).

There is no need to go into the relevance of science to music in either the Renaissance or Baroque eras. That relationship has been amply discussed in a plethora of publications. What is important to note here is that the age in which Bull lived and worked was one of adventurous discovery, one in which science was revolutionizing the view of the world, as well as one in which, first in Italy and then in the rest of Europe, music, too, was undergoing revolutionary change. It is important to note that revolution, new ways of thinking, were part and parcel of Elizabethan life. Bull was no stranger to the new.

The hexachord

The hexachord was first described, but not named, in Guido of Arezzo’s treatise Micrologus of 1025–28. There are three hexachords, all of which have the same intervallic structure: the hexachordum naturale (C - D - E - F - G - A); the hexachordum molle, so-called because it included b molle, i.e., b-flat (F - G - A - B-flat - C - D); and the hexachordum durum, so-called because it included b durum, i.e. b-natural (G - A - B - C - D - E). Since medieval theory did not consider pitches of higher or lower octaves to be identical, seven hexachords were differentiated in the scale from G to e2, all of them beginning on C, F, or G. There was no concept of modulation. A melody exceeding the compass of a single hexachord was considered to be in transition from one hexachord to another. This movement was referred to as mutation. Tonal centers were not established by such movement, but rather the compass of a particular melody simply shifted from one area to another by making use of a pivot tone, a tone which belonged to both hexachords. Thus, for example, the tone sol in one hexachord could at the same time function as the tone ut in another. Yet, because the hexachord has the same construction whether based on C, F, or G, it has one interesting similarity to the major-minor tonal system: it has the potential to form the basis of a relative pitch system.

Guido’s treatise was referred to throughout the ensuing centuries, though the term “hexachord” itself apparently does not appear until about the 16th century. Although Masses based on the hexachord were composed, keyboard composers of the late Renaissance and the early Baroque seem to have been particularly fascinated by the musical possibilities offered by this theme. Pieces based on the hexachord were written by such important composers as Girolamo Frescobaldi (2) and Gregorio Strozzi in Italy, Johann Jakob Froberger in Austria, Pieter Cornet (the piece survives only as a fragment) and Jan Pieterszoon Sweelinck in the Low Countries, Samuel Scheidt in North Germany, Pablo Bruna in Spain, and William Byrd (2), Thomas Tomkins (7!), John Lugge, and John Bull (3) in England.

John Bull and the hexachord

Thomas Morley, as Master Gnorimus in A Plaine and Easie Introdvction to Practicall Mvsick (1597) which is organized in dialogue form, spends at the beginning of that treatise a considerable amount of time explaining musical notation to Philomathes, a student in the dialogue. He does this by using the hexachord and the syllables ut, re, mi, fa, sol, la. Morley’s art of teaching music was not unique in England and musicians must have been familiar with this system.

 The adventurous John Bull composed three very different pieces on the hexachord. One, Ut, re, mi, fa, sol, la [II], is an extended composition (292 measures in the Musica Brittanica edition, 237 irregularly-barred measures in the Fitzwilliam Virginal Book) in which, after the second statement, the hexachord theme is treated principally as a cantus firmus in the soprano in long notes accompanied by figurations which become in the course of the piece quite virtuosic. Beginning with a long section in two voices, Bull introduces a third voice for a similarly long section, and then a fourth voice, the piece remaining four-voiced to the end. The subdivision of the beat changes a number of times in the course of this work and in addition to the metric two-against-three which occurs in the juxtaposition of duple and triple times, rhythmic two-against-three is also found in this composition, a favorite Bull device.

Another is the more contrapuntal, 188-measure Ut, re, mi, fa, sol, la [III] (not found in the Fitzwilliam Virginal Book) composition. The more sustained polyphonic nature of the five-part texture and the avoidance of metric and rhythmic variety (the piece moves principally in halves, quarters and eighths with some dotting of values) starkly differentiate this piece from the preceding one. In addition, the hexachord theme itself is found in several rhythmic forms, principally varying combinations of halves and quarters with some tied notes, dotted values and an occasional eighth-note.

The piece which is the subject of this essay is the shortest of the three hexachord compositions by Bull.

Ut, re, mi, fa, sol, la [I]

Editions

I made the decision to use the version of the piece found in the Fitzwilliam Virginal Book since it is clearly closer to the actual score of the piece as Bull himself might have written it. The version found in the Musica Brittanica edition, with its regularly-barred measures and its conformity to 20th-century notational practices, leads one to think that the piece may be in common time. Whereas I would like, as much as is possible for a musician living very much with both feet planted in the 21st century, to get into the musical mind of Bull as it manifests itself in this composition. One must assume that whoever copied the music in the 17th century had an understanding of the music he was copying and, especially, was closer to the manner in which it was notated than editors in the mid-20th century could have been. And it is the notation which provides the only clues we have directly from the composer, clues we need in order to reach some understanding of the work, without which appropriate interpretive decisions cannot be made. The importance of the manuscript and the collection in general speaks for going to the Fitzwilliam Virginal Book as primary source.

The theme

The theme (see Example 1) has two parts, which mirror each other, consisting of the ascending and descending hexachord. The highest note (at the first appearance of the theme an e1) is always repeated.

As do the other two compositions on this theme, the present work begins not only with the hexachordum durum, but also with the very same note: g0, although it is the soprano voice (not bass or tenor as in the other pieces) which here begins the work in this low register.

Meter

Since the irregular measures of 1/1, 2/1, 3/1, 4/1, 5/1, 9/2, and 12/2 do not seem to indicate any regular occurrence of accent, my attention was brought to the consideration of meter in terms of the theme as a whole. The whole note is the value at which the regular occurrence of the tactus takes place. The piece floats in an unaccentuated flow of regular beats of that tactus. The entrance of the hexachord theme every 13 whole-note units is the important, regularly occurring event in the work. The unit of measure is not the bar line, wherever it is drawn, but rather the whole note itself and we will subsequently refer to whole-note units rather than any measure numbers. The six ascending and six descending notes give us the duration of twelve whole-notes. Except for the first three statements and one curious half note during the 13th statement, the entire theme consists of 12 unvaried note values throughout.  The final pitches of the first two statements consist of two whole notes: two g0’s and two a0’s respectively. The final pitch of the third statement is one b0 whole note tied to another. After that, the final pitch of the theme is always a whole note separated from the following thematic statement by a whole-note rest. This makes the entire theme, the ascending and descending hexachord and the unit of rest, one phrase measuring 13 units (whole notes).

We can think of the hexachord theme as beginning with a downbeat and spanning the duration of 13 whole notes. A secondary accent occurs, perhaps, at the repetition of the highest note of the theme, which results in two units of six whole notes each. The 13th whole note of the first statement repeats the final note, that of the second statement repeats the final note with an ornament, that of the third is tied to the previous whole note. After that, the 13th whole note is a rest. The 13th unit of the hexachord theme functions, especially beginning with the fourth statement, as a breath, a metrical breath if you will, a moment of rest, of gathering energy, before continuing with the next statement. This music breathes in 13-unit phrases with a consistency unbroken until the end.

Transposition

The second statement of the hexachord theme begins a whole-step higher than the first statement; and the third statement begins another whole step higher. This transposition of the theme upwards by whole step is pursued rigorously up to f1, at which point the next statement would appear again on a G (g1, an octave above the first note of the piece). This Bull does not do, but rather jumps down almost two octaves to A-flat and begins the process of transposition by whole step upwards all over again, using the remaining pitches of the twelve-note chromatic scale.

Example 2 gives the initial notes of all 17 statements of the hexachord theme, the last 4 statements of which are all on the same pitch, g1. Thus we see that the cycle of whole-step transposition, beginning on g0, interrupted once at f1 and leaping down to A-flat instead and then continuing the cycle in order to return to g0, involves 13 statements of the hexachord theme.

Modulation

With the transposition of the hexachord theme Bull is forced to modulate to new keys at every single entrance of the theme. The composition manifests remarkable instances of modulatory prowess and enharmonic ambivalence. Consider Example 3.

The E-major chord at the beginning of Example 3 includes b0, the last note of the previous statement of the theme.  D-flat1 is the first note of the fourth entrance of the theme and it appears here immediately as D-flat and not as C-sharp, as might be expected from the previous harmony. The enharmonic modulation must take place somewhere and Bull chooses to do it here. Apparently, in spite of what the Musica Brittanica edition has done here (namely first spell c-sharp1, then tie to d-flat1), Bull is not interested in making a smooth, a plausible, enharmonic modulation (see Example 4).

We can see that Bull has not written a piece concerned with modulating to as many keys as possible, thereby enabling the hexachord theme to appear in those keys. The plan of his work is to transpose, to shift the hexachord theme; he shifts the theme and afterwards draws the harmonic consequences. The transposition of the hexachord theme is the given, leading to necessary modulation—not modulation leading to transposition of the theme. The transposition of the hexachord theme is the postulate which implies the stipulation of key, not vice versa.  In other words: the form is a priori and precipitates the harmony; the harmony does not precipitate the form.

Form

We have noted above that after 12 shifts or transpositions of the hexachord theme, i.e. with the 13th transposition, Bull returns, comes full circle transpositionally, to the g0 with which he started the piece, though here it is the bass voice and not the soprano as at the beginning. Here Ut, re, mi, fa, sol, la could conceivably end. Bull has traversed the entire gamut of pitches available to him in the chromatic scale and returned back to where he had started. This disregards, however, the psychological strain through which he has put his listener. Bull must draw the consequences of going so far afield harmonically. He must first establish conclusively for the listener that one has arrived “home.” And that is not achieved by a single statement on G.

There follow four more statements of the hexachord theme, all on G, all on the same g1, all in the soprano voice. However, just as Bull begins to anchor the listener in the hexachordum durum, he changes what has up to that point been a duple to a triple division of the beat. Now this is a common device found at the ends of many compositions of this period and others: triple subdivision as ecstatic conclusion. Statement 14 consists of three half notes per whole note. Occasionally the half notes are subdivided into duple quarters which sound against the (now dotted) whole notes. Statement 15 contains both duple and triple subdivisions of the beat; the quarter notes here are ambiguously either triple subdivisions of the duple half notes or duple subdivisions of the triplet half notes. This rhythmic ambiguity occurs exactly at the point where Bull is interested in being unambiguous harmonically, i.e., he can now afford to be ambiguous on the rhythmic level now that the harmonic level has become more stable. Statements 16 and 17 return to duple subdivisions on all levels, as had been the case from statements 1 to 13.

So at the end of the composition there are five statements of the hexachordum durum. The first of these five statements (on g0) occurs at the end of the transposition process begun at the outset of the piece and belongs to that process. It rounds off that section of the piece. The final four statements (on g1) are no longer part of that process, but provide the necessary anchoring in G in order for the piece to come to a satisfactory close.

Counterpoint I: beginning and end

The hexachord appears as a cantus firmus, it does not take part in any imitative counterpoint. Three of the four voices are, then, not predetermined by the form. The opening of Ut, re, mi, fa, sol, la is instructive (see Example 5) and merits a close look. It is not marked by strict imitation carried through the three free voices.

The soprano begins, opening with the hexachordum durum on g0. The bass enters one half note later on the same g0, before the soprano moves to its second note. The two voices sound together for the duration of one half note with the same pitch, thus obscuring the two-voiced texture. The bass continues stepwise downwards through the fourth unit. At unit three the alto enters with a motive different from both the hexachord in the soprano and the descending motive in the bass. It enters on the only available note between soprano and bass: g0. The tenor enters one unit later with the descending motive first heard at the bass entrance. However, the entrance of the tenor is obscured by the fact that at that same moment the alto and the soprano sound the same note together: c1. In other words, at the entrance of the fourth voice one hears only three voices. This obscures not only the texture again, but the imitation between bass and tenor as well. Significant, and genial, about the beginning of the work is that all four voices start from exactly the same point, exactly the same pitch: the final of the hexachordum durum, g0.

The descending fifth motive, found in the bass and tenor voices, does not reappear as such throughout the rest of the work until the very last measures. The motive is given one prefix note and is found here in all three free voices. This reminiscence of the beginning provides a fitting and appropriate close to the work (see Example 6).

Counterpoint II: alto motive

At the beginning of the work (see example 5) the soprano has the hexachord as cantus firmus and the bass and tenor voices imitate each other, in fact the first five pitches are exactly the same. The alto voice is here unique, free. It proves to have a more productive motive than that shared by tenor and bass, and, indeed, we find that it is not imitation which is most significant here or in the work as a whole. There are scattered passages which employ imitation in one form or another, more or less strictly, between two or three voices. There seems to be no overall formal principle which dictates when and where imitation between the voices takes place. It is one of the compositional means at Bull’s disposal and he uses it without ever losing the prevailing sense of freedom which the three voices have in the face of the strict formal construction of the transposition scheme of the hexachord.

The emphasis is not on imitative counterpoint, but rather on a free development of the concept of imitation. One can see this on the freedom with which Bull treats the alto motive, heard at the outset (see Example 7) and referred to henceforth as the alto motive no matter in which voice it is found.

During the course of the second statement of the hexachord theme, we hear this motive in different guises in three of the four voices (see Example 8).

Rhythm and intervals are altered, and inversion is heard in the alto and bass as well as retrograde in the bass voice. Just a few units later, during the third statement of the hexachord theme, the alto motive is found using a passing tone (see Example 9).

The part of the motive which is found at units 33–34, using the quarter-note passing tone, is one that is found in all the three free voices at that point and plays a role through the fourth entrance of the hexachord theme. The alteration of the alto motive thus generates a further motive that is used contrapuntally in these passages.

In Example 10, taken from the fourth statement of the hexachord theme, we find an interesting canon, interesting in the fact that it is not strict. The bass voice leads, followed by the alto voice one whole note later with a rhythmically enlivened version of the bass voice. Also noteworthy is how the same note takes on different harmonic functions. This is due, of course, to the fact that one of the voices is the bass and the other the alto. It also has to do with the fact that, although the entrance of the d-flat1 in the alto is rhythmically analogous to the entrance of the d-flat0 in the bass, namely mid-unit, the d-flat1 enters with the length of a whole note and obscures the fact that the alto voice is, contrary to the bass, placed on the unit (beat). Thus the g-flat0 in the bass becomes dissonant at unit 44, whereas the g-flat1 in the alto at unit 45 is consonant for its entire duration. So, too, the e-flat0 in the bass is consonant for its duration, but, the e-flat1 in the alto at unit 47 becomes dissonant.

This last example demonstrates the developmental possibilities of the alto motive. Given its construction (see Example 7), the small ambitus of a perfect fourth, the prominent interval of the third, and the half step at the end, it is a motive that is related to any other motive using those intervals. It is possible to recognize in example 10 that the alto line is directly derived from the alto motive in the bass voice. In other cases it is more difficult to assert that other motives with similar constructions were consciously fashioned from the alto motive. Nevertheless, many of the passages contain motives constructed with thirds and fourths, or often end with a half step, which fact is not surprising in music that is articulated with cadences.

From units 86–93 (see Example 11), the end of the seventh and the beginning of the eighth statement of the hexachord theme, we find the alto motive used in free imitative fashion between soprano, alto and tenor. Interesting is the alto voice which mirrors itself beginning at unit 89 and then tacks on a cadential e-flat1 - d1 - e-flat1.

Example 12, from the tenth statement of the hexachord theme, demonstrates a still freer treatment of the alto motive or, if you will, those primary intervals of which the alto motive is constructed. The passage does not illustrate imitative counterpoint, but rather a free development of the alto motive. Notice particularly the alto voice which, as in the previous example, mirrors itself and pivots around f-sharp1.

Immediately following this passage, at the end of the tenth and the beginning of the eleventh statement of the hexachord theme, the soprano states two versions of the alto motive successively, the first descending (i.e, inverted), the second ascending (see Example 13).

There are further passages in which the alto motive or fragments thereof play a role in the contrapuntal texture of the work. Often, just as is the case in a number of the above examples, they are worked into phrases which are much longer. The motive shines forth suddenly from within the context of something larger than itself and contributes to the unity of the work.          

Gary Verkade was born in Chicago and grew up in the south suburbs. He studied music at Calvin College and the University of Iowa in the United States, and in 1978 he received a Fulbright grant to study at the Folkwang-Hochschule in Essen, Germany, and lived in Germany for 17 years. He has performed much new music throughout Europe and the United States and is the composer of music for organ, electronics, chamber and improvisational ensembles.Verkade has been a guest professor/lecturer/performer at universities in Europe and the United States; he served on the music faculty of Carthage College, Kenosha, Wisconsin, from 1995–2000. He is presently on the faculty of the Musikhögskolan i Pitea, Sweden, where he continues to teach, perform, compose, record, and write about music.

The Development of Musica Poetica

Since the rediscovery of Quintilian's texts in the early Renaissance, many humanist writers have suggested a link between oratory and musical composition. With his treatise Musica poetica, Joachim Burmeister coined the term musica poetica for study of rhetorical relationships in music. This discipline, musica poetica, rationally explained the creative process of a composer, the structure of compositions, and the mechanism through which music moved the listener. Thereby a composer's craft could prompt a predictable emotional response from the listener--a principal goal of early Baroque composers. Although writers throughout Europe attested to the affective nature of music, German theorists cultivated musica poetica.

Influenced by Lutheran theology, humanists in Germany borrowed rhetorical techniques from the classical authors including Cicero and his successor Quintilian in order to deliver the Holy Word more effectively. (See Diagram 1, left-hand column.) Philipp Melanchthon emphasized this area of the trivium in the Lateinschulen curriculum and applied the traditional pedagogical method: (1)  praeceptum or the study of rules which required exact definitions and well-articulated concepts, (2) exemplus or the study of examples which encouraged analysis of well constructed works, and (3) imitatio or the imitation of examples which emphasized craft, not genius and inspiration typically associated with the Enlightenment or Romantic periods. In this way, the rhetorical concepts became not only a way of thinking about pre-existing works but also became prescriptive.

Martin Luther emphasized the power of music to secure faith: "after theology I accord to music the highest place and the greatest honor."1  (See Diagram 1, middle column.)  As the handmaiden to the Word, music can be understood as a "sermon in sound." Influenced by Boethius's cosmological conception of music, many seventeenth- and eighteenth-century writers justified music's holy power by explaining how ratios representing God's perfection resonated in the listener's soul.

The ancient Doctrine of Ethos convinced Luther of the didactic power of music. (See Diagram 1, right column.)  With the rise of the Doctrine of Affections during the seventeenth century as codified by Descartes, writers in Germany could then explain the mechanism through which music affected  listeners' passions. (See center of Diagram 1.)  Kircher, Bernhard, and Mattheson suggested that music no longer simply reflected the meaning of texts but actually moved listeners to predicable emotional states called affections. Cantors, such as Buxtehude and Bach, drew upon elements of musica poetica which served as a code for various affections in their compositions. With the rise of the Enlightenment, however, philosophers encouraged "natural" expression in music, which reflected a composer's personal sentiment and inspiration. With this emerging viewpoint, both the Doctrine of Affections and the cosmological conception of music became less tenable, and musical rhetoric declined with them. By the end of the eighteenth century, musica poetica had become a historical curiosity cataloged in Forkel's Allgemeine Geschichte der Musik (1788).

An Overview of Musica Poetica

Consider the rhetorical model of the composer's creative process presented in Table 1. Following Cicero's ideas that directly applied to music, Bernhard prescribes three compositional stages while Mattheson retains five stages somewhat analogous to rhetoric. In his first stage, inventio, the composer determines what his/her piece will be about, the loci topici. Mattheson suggests fundamental musical elements such as meter, key, and theme. This stage could also involve the working out of invertible counterpoint and other devices.   In the second stage, dispositio, the composer places this pre-compositional material in a logical succession and in appropriate keys. Later, in the elaboratio stage,  episodes connect the contrapuntal complexes or theme entrances determined in the dispositio. The composer also adds musical-rhetorical figures intended to persuade or move the listener to particular affections. In the decoratio, the composer ornaments themes and may incorporate further figures. Embellishments reinforce the work's style and can further alter the affect. The fifth stage, executio, involves performance of the work, frequently with additional improvised ornaments.

The disposition of any artwork in the rhetorical model can be described in two ways: (1) the Aristotelian model, beginning-middle-end, or (2) the more complicated Cicerone model. (See Table 2.) Burmeister subscribes to the first and Mattheson to the later. Consider the purpose of each section in the Cicerone model. The exordium of a speech arouses the listener's attention.  (Buxtehude praeludia invariably start with an opening toccata for this purpose.) The narratio establishes the composition's subject matter, but in musical discourse, Mattheson states that one may omit the narratio. The propositio presents the actual content of a speech or musical composition, i.e., the theme. In the body of the speech, the orator can alternate between arguments supporting his proposition, the confirmatio, and those refuting possible objections to the orator's proposition, the confutatio.  In music, confutatio sections frequently contain  contrasting themes and characters, heightened by increased dissonance. At the end, compositions conclude with the peroratio. This section often recalls the opening material with a ritornello or closes with pedal points and melodic repetition.

Many scholars question whether a singular Doctrine of Affections exists. Nonetheless, Table 3 presents an overview of the various viewpoints as codified by Descartes. According to this doctrine, people can have four different temperaments or a combination thereof: Sanguine, Choleric, Melancholic, and Phlegmatic. Specific body parts and humors participate in producing a variety of distinct emotional states, called affections. These fundamental affections can blend in various ways to create other affections. This rational system explains why and how listeners of different temperaments react to music. A year following Descartes' treatise, Kircher published an influential compendium of knowledge that connected various affections to specific musical elements. (See Table 4. Amour is especially provoking.)

Composers could choose a variety of musical figures to summon listeners' affections. In classical oratory according to Quintilian, figures are simply deviations from normal speech intended to make one's oration more effective. By the seventeenth century, composers not only employed figures to express the text but also to move listeners to particular passions according to the Doctrine of Affections. To avoid problems of marking every musical event as a figure and trivializing the procedure, let us employ a working definition for our purpose: a figure is any departure from established musical syntax that arouses the affections.5 Not every dissonance is really a figure, but only those that express a particular emotion or inflect the music in a noticeable way. Now we can briefly examine three influential theorists of the musica poetica tradition and identify a few of their figures in three Buxtehude praeludia, BuxWV 142, 146, and 149.

Joachim Burmeister

And if we examine music more closely, we will surely find very little difference between its nature and that of oratory.  For just as the art of oratory derives its power not from a simple collection of simple words, or from a proper yet rather plain construction of periods, or from their meticulous yet bare and uniform connection, but rather from those elements where there is an underlying grace and elegance due to arrangement and to weighty words of wit, and where periods are rounded with emphatic words so, this art of music . . .6

Joachim Burmeister (1564-1529) served as cantor to St. Marien in Rostock and taught at the Gymnasium there. He developed a relatively systematic approach to identifying figures which aided his teaching of composition and reflected the Lutheran tradition of praeceptum, exemplus, et imitatio. He cites numerous late sixteenth-century vocal works and demonstrates how specific musical figures in the Lassus motet In me transierunt contribute to an effect much like that of successful oration. Elias Walther's dissertation of 1664 leans heavily on Burmeister's treatise and even analyzes the same Lassus motet, thereby revealing Burmeister's continuing influence in Lutheran Germany. By this point, Walther does not even define musical figures suggesting that their use had become commonplace.

For the most part, Burmeister's treatise Musica poetica (1606) transmits Zarlino's theories, and thus, Burmeister's ideas are strongly linked to late sixteenth-century styles. Burmeister's explicit development of a rhetorical theory, however, distinguishes him from his sixteenth-century predecessors.  Burmeister's figures focus on imitation and repetition. (See Diagram 2.)  Burmeister derived most figurative names from rhetorical sources. Thus, many terms maintain a strong association with the original rhetorical meanings, though some are uniquely musical. To reflect the traditional rhetorical division of figures into those applied to words and those applied to sentences, Burmeister placed musical figures in three categories: (1) Figurae harmoniae, figures involving more than one voice; (2) Figurae melodiae, figures involving one voice, and (3) Figurae tam harmoniae quam melodiae. (See Diagram 2.) Let us consider a couple examples:

Noëma--This figure strikes the listener when the texture changes to a homophonic passage. Most later writers imply that these passages are composed of consonant sonorities. Burmeister describes its effect: "When introduced at the right time, it sweetly affects and wondrously soothes the ears, or indeed the heart."7 For the performer, this suggests not only a sensitive touch but also a sweet registration and calm tempo. In the Praeludium in f#, mm. 14-27, Buxtehude places such a passage between the foreboding exordium and the brooding fugue. (See Example 1.) In this case, suspensions and chromaticism further modify the figure's effect within this dark piece.

Pathopoeia--Throughout the final fugue of the Praeludium in g, chromatic pitches contribute a heightened emotional affect; the pathopoeia is "suited to arousing the affections."8 Consider m. 126, where Buxtehude temporarily introduces Bb minor with half-steps outside the reigning mode.  (See Example 2.)

Aposiopesis--Returning to the Praeludium in f#, mm. 20-27, we find that the musical texture breaks off with a notated silence in m. 24. (See Example 3.) This figure, the aposiopesis, foreshadows motives that seem to lead only to silence throughout the praeludium. Burmeister suggests the topic of pieces employing this figure: "The aposiopesis is frequently encountered in compositions whose texts deal with death or eternity."9 Burmeister borrowed this term from rhetoric: "What is aposiopesis? It is when, because of an affection, some part of a sentence is cut off."10 Performers should consider exaggerating the stop for this effect.

Christoph Bernhard

Stylus Luxurians is the type consisting in part of rather quick notes and strange leaps--so that it is well suited for stirring the affects--and of more kinds of dissonance treatment . . . than the foregoing. Its melodies agree with the text as much as possible, unlike those of the preceding type . . . It [Stylus Theatralis] was devised to represent speech in music . . .  And since language is the absolute master of music in this genre . . . one should represent speech in the most natural way possible.11

Christoph Bernhard (1627-1692) was cantor for Johanneum in Hamburg from 1664-74 and co-director of the famous Collegium Musicum there with Matthias Weckmann. Later, Bernhard returned to Dresden where he had studied and worked with Schütz for many years. In the Tractatus (c. 1660), Bernhard describes three main seventeenth-century compositional styles: Stylus Gravis, Stylus Luxurians Communis, and Stylus Theatralis. Bernard not only distinguishes these styles by their venue, but more importantly, by their use of specific figures. These figures primarily depend upon dissonance treatment and modern styles which employ more sophisticated, implicit voice leading. While Bernhard emphasizes smaller details of dissonance treatment, the earlier Burmeister basically describes texture and a larger scope. Bernhard does emphasize proper reflection of the text in music, but he does not associate specific figures with affects nor does he explicitly show how to do this. Rather, Bernhard instructs his students to study works of respected composers in each of the styles. One may assume that composers use particular figures for different affects depending on context. In any case, Bernhard's brevity and prose suggest that the application of these figures is relatively obvious to the reader.

Please consider the following figures from Diagram 3 in Buxtehude's praeludia:

Passus duriusculus--This Latin term literarily means a "harsh passage" or "difficult passage." The subject of the second fugue in the Praeludium in e, mm. 47-49, contains a descending chromatic passage. (See Example 4.) The difficulty of this short span in the subject is heightened by on-beat chromaticism, and suggests a "difficult" touch and a slower tempo.

Saltus duriusculus--In this same passage, we also find a "harsh leap" or "difficult leap" called the saltus duriusculus between C and G-sharp, and between G and D-sharp. A more striking example can be found in the first fugue of the Praeludium in f# entitled "Grave," mm. 29-31. (See the leap down from D to E-sharp in Example 5.) Here we find a striking example of compound melody which Bernhard calls Heterolepsis, an element of the theatrical style. Buxtehude's fugues normally do not venture into this highly dissonant style, and these figures contribute to a morose affect.

Inchoatio imperfecta--Although Bernhard defines this term in strictly musical language, the figure carries not only structural value but also affective meaning to a German Baroque listener. (Remember that dissonances utilize ratios far from perfection, and thus, elicit darker affects in the listener.) The opening of the Praeludium in g begins with an inchoatio imperfecta: the first note, F#5, forms a dissonance with the  implied g minor chord of the first measure. (See Example 6.) The opening toccata also surprises the listener when he/she discovers that it is not a toccata, but instead a ground bass variation where variations precede the bass ostinato. Strangely, the ground bass continues alone at the end of the section in abbreviated form.

Abruptio--Bernhard discusses how this figure ruptures a melodic line by the unexpected insertion of a rest. Once again, returning to the homophonic noëma of the Praeludium in f#, mm. 14-23, the passage resumes after the aposiopesis (the breaking off), but quickly disperses into a brief stylus fantasticus section where the melodic lines are interrupted with rests (mm. 27-28), reflecting the distress that Buxtehude mollifies with the Noëma. (See Example 3.)

In his discussion of melodic composition within Der vollkommene Capellmeister (1739), Johann Mattheson (1681-1764) divides figures into embellishments added by the performer, Figurae cantionis, and rhetorical figures incorporated by the composer, Figurae cantus. Mattheson deemphasizes the mathematical derivations and instead encourages a natural expression concentrated on melody, not counterpoint. The rise of the Empfindsamerstil led to the decline of the musica poetica tradition because expressivity of the performer and ornamentation surpassed the concern for a rationally trained composer to evoke categorized affections.

In summary, these writers seem to address different aspects of musica poetica. Burmeister initiated serious inquiry of the rhetorical model in musical analysis and composition. He described a method of formally dividing compositions by use of figures. Most of his figures deal with musical textures. Bernhard provided a vocabulary of figures based on dissonance treatment. He also demonstrated how these small-scope figures define various seventeenth-century styles. Mattheson was concerned with the structural relationships between composition and oratory, i.e., how composers distribute musical ideas to impart the best rhetorical effect.

Dietrich Buxtehude and Musica Poetica

Now we ask: was Dietrich Buxtehude (1637-1707) aware of these theories? As I have shown, musical figures and basic knowledge of rhetoric were taken for granted. Furthermore, many cantors taught rhetoric and Latin while fulfilling their musical duties. Buxtehude served as organist at Marienkirche in Lübeck. Because only sixty kilometers separate Hamburg and Lübeck, Buxtehude traveled to Hamburg where Bernhard worked. Kerala Snyder has even demonstrated that Buxtehude modeled a piece after an obscure work by Bernhard. Furthermore, Snyder states "Buxtehude would certainly have been familiar with the system that Christoph Bernhard expounded in his treatise 'Tractatus compositionis augmentatus.'"12 Other treatises were also readily available. For instance, George Buelow states that Kircher's "Musurgia universalis, one of the really influential works of music theory, was drawn upon by almost every later German music theorist until well into the 18th century. Its popularity was greatly aided by a German translation of a major part of it in 1662."13 Early in Buxtehude's career, this compendium certainly would have been available in Hamburg and probably in Lübeck as well.

So far, we have studied a few figures that contribute to the affect of three Buxtehude praeludia in minor keys.  But how closely do his preludes follow the organizational precepts of oratory? Let us briefly examine the typical disposition of Buxtehude's praeludia.

After an opening flourish comparable to an exordium in a speech, Buxtehude's preludes generally alternate between free sections and imitative sections, analogous to confutatio and confirmatio sections. A variable number of confutatio/confirmatio sections probably would lead Burmeister to simply lump these together into the "body." The final free section, or  peroratio, provides a successful conclusion through repetition (to recapitulate an argument) and the strictly musical devices of pedal points and tonal closure.

Snyder compares the opposition of free sections and fugues to that of prelude and aria. This apt analogy captures fugal entries as an amplification technique of confirmatio sections that conveys a single affection in agreement with the pieces' mode and overall affect.14 Free sections often use stylus theatralis while fugues tend to employ less dissonant styles. Although Buxtehude's works follow a definition of stylus phantasicus somewhere between that of Mattheson and his predecessor Kircher, Mattheson's directions guide performers particularly well on the performance of the free sections: these pieces follow "all kinds of otherwise unusual progressions, hidden ornaments, ingenious turns and embellishments . . . without actual observation of the measure and the key, regardless of what is placed on the page . . . now swift, now hesitating, now in one voice, now in many voices, . . . but not without the intent to please, to overtake and to astonish."15 In other words, these free sections display an improvisatory and unpredictable character, often with the purpose to astonish the listener. Certainly opening sections fulfill Mattheson's description while interior free sections tend toward more melancholy moods, especially in the three minor key pieces this article examines.

The Disposition of the Praeludia in g, e, and f#

The fully worked-out fugues and other hallmarks of Buxtehude's mature style lead Snyder to date the Praeludium in g before 1675. (See Table 5.)  Lawrence Archbold uses these same characteristics to support a later dating.16 Despite differences among scholars here, all agree this praeludium displays Buxtehude's best work.17 The canonic voices in the manuals opening the exordium make the delayed ground bass entrance surprising. Transformations of this theme pervade the entire work, perhaps a legacy of the composer's inventio stage. This flashy start precedes a ricercar fugue that takes its theme from the previous ostinato to create a sort of textural modulation into the first confirmatio. (See Example 7.) As usual in Buxtehude's praeludia, the first fugue disintegrates after significant development. The following free section contains the only example of strict continuo style in Buxtehude's organ works.  This confutatio leads back to the tonic while subtly reintroducing the main theme, like an orator who skillfully employs opposing points-of-view to his advantage during a rebuttal. Marked Largo and with dotted rhythms, the last fugue then boldly announces yet another version of the piece's theme with a variety of stylus theatricus figures to emphasize its dark character. Even Archbold cannot resist calling the last fugue "the most stately, even elegaic of Buxtehude's fugues." The peroratio concludes with figurative repetition via a free ciacona and appropriate pedal points.

Like many other scholars, Philipp Spitta described the Praeludium in e as "one of his [Buxtehude's] greatest organ compositions. . . ."18 (See Table 6.) This work was probably composed in 1684 because of tuning considerations. According to Snyder, the heavy emphasis on counterpoint links it with early works of the 1670s when Buxtehude assimilated the writings of Bernhard, Theile, and Reinken. The Praeludium in e opens with a free, figural exordium, but three fugues dominate the work. The well-developed first fugue displays a canzona-like subject with three distinct motives, and it concludes with a brief noëma derived from the subject's eighth notes. The second fugue is "the most contrapuntally elegant, and at the same time one of the most expressive fugues in all the praeludia. Brossard . . . would undoubtedly have called it a fuga pathetica [with its leaps, chromaticism, meter, and strict contrapuntal procedures]."19 The following free section is imaginative and quite rhapsodic with highly ornamented passage-work often juxtaposed against slow, unadorned notes. Characteristic of Kircher's affection amour, the harmonies here seem to wander (between the dominant and subdominant areas). The contrapuntally "lax" but vigorous fugue that constitutes the fifth section is a gigue that quickly dissolves into a concertato texture and ends with a short flourish. The capricious character of the Lombard rhythms at the very end may harken back to the canzona-like first fugue.

Probably written in the 1690s, the Preludium in f#  emphasizes free sections. (See Table 7.) After a brief flourish, the exordium presents an unadorned passus duriusculus in quarter notes accompanied by right hand arpeggios. This figure and the dissonant key of f# minor in unequal temperaments present a particularly gloomy and somewhat inward character.20 The following noëma provides brief but limited relief because of dissonances and an aposiopesis. The first fugue, marked Grave, continues the dissonant discourse with its figures and dotted rhythms. When the fugal texture dissolves, a second fugue marked vivace interjects into the final cadence with a variant of the subject from the first fugue. Although of a livelier nature, the saltus duriusculus in the second fugue subject still reminds the listener of the principal affect. This faster fugue quickly dissolves into motivic interplay, temporarily escaping to the parallel major. The following free section is the most adventuresome harmonically of Buxtehude's praeludia: it explores g-sharp minor--an especially remote and dissonant key; the melodic material seems to trail off, rhapsodically speeding up and then slowing unpredictably; and melodies suggest thoughts that lead nowhere. But Buxtehude fuses this final confutatio to the succeeding peroratio with a pedal note. The peroratio repeats an extremely loose ostinato, presenting motives from previous sections, in a virtuosic display of stylus phantasticus.

Summary

 We must conclude that Buxtehude must have been familiar with Bernhard's ideas. He may have also known Burmeister's groundbreaking treatise Musica poetica. Especially in Buxtehude's praeludia, the rhetorical figures of Burmeister suggest various touches and large-scale effects while the small rhetorical figures identified by Bernhard accumulate, fashioning affects with various types of dissonances. Buxtehude cast the three praeludia above into minor keys to project darker affects than his rhetorical figures suggest. The contrast of thematic material and figures seems to divide internal sections into alternations similar to supporting arguments and rebuttals found in rhetoric. Outer sections introduce and conclude pieces magnificently. The strong correlation between so-called Toccata Form and rhetorical organization may even explain why this form flourished in the Lutheran stronghold of northern Germany during the seventeenth century.  n

Markus Rathey, Ph.D. is Associate Professor of Music History at the Yale Institute of Sacred Music and the Yale School of Music. His research focuses on Johann Sebastian Bach and the relationship of music, religion and society in the 17th and 18th centuries.

Buxtehude’s chorale variations
The number of chorale variations in Dietrich Buxtehude’s organ works is considerably smaller than in the oeuvre of other northern and central German composers like Samuel Scheidt, Georg Böhm, and Jan Pieterszoon Sweelinck. Among Buxtehude’s organ works the chorale variations form a rather small group of six sets:1

BuxWV 177, Ach Gott und Herr, 2 variations
BuxWV 179, Auf meinen lieben Gott, 5 variations
BuxWV 181, Danket dem Herren, 3 variations
BuxWV 205, Meine Seele erhebt den Herren, 2 variations
BuxWV 207, Nimm von uns Herr, du treuer Gott, 4 variations
BuxWV 213, Nun lob, mein Seel, den Herren, 3 variations

An overview of Buxtehude’s chorale variations would, however, be incomplete without considering the use of chorale-based variation in other genres. Among his organ works, we find traditional techniques of the chorale variation in his chorale fantasies. Here, each phrase of the melody is treated “separately and in different voices,”2 whereas in the chorale partita (or chorale variation) the technique of variation changes with each stanza of the hymn.3 Yet another type of “chorale variation” in Buxtehude’s oeuvre is the variation of chorale melodies in his numerous chorale cantatas. The chorale cantatas are based on the texts and melodies of Protestant hymns, in which each movement (or larger section) treats a single stanza employing a different technique.4 Buxtehude’s chorale cantatas range from rather simple settings like In dulci jubilo, BuxWV 52, to complex compositions that transform the traditional melody into an expressive vocal concerto, like Jesu, meine Freude, BuxWV 60.5
While there is no doubt that Buxtehude’s chorale cantatas and chorale fantasies are significant contributions to their respective genres, his chorale variations stand, as far as their reception goes, in the shadow of these more elaborate compositions. Kerala Snyder, in her seminal biography of Buxtehude, gives a rather negative assessment:

Chorale variations play the least important role in Buxtehude’s keyboard music. Not only are they few in number, but the style in which most of them are composed is not distinctive. [...] With one significant exception [BuxWV 179] these variation sets do not form convincing cycles, and they appear to have been composed either for alternatim performance or for teaching purposes.6

Similarly, Kathryn Welter states that Buxtehude’s chorale variations have a “non-distinctive style.”7
Arnfried Edler, on the other hand, in his recent history of keyboard music, finds more positive words for Buxtehude’s chorale variations:

The principle of a unifying climax in sound and tension can be seen [in Buxtehude’s chorale variations] to different degrees; it is most obvious in Nun lob mein Seel den Herren (BuxWV 213), where the variations begin with a bicinium; then follows a tricinium with cantus firmus in the upper voice until the set is closed by a tricinium with bass cantus firmus.8

For other chorale variations, however, the unifying elements are less obvious and often nonexistent.
While the chorale partitas seem to lack the compelling structural coherence and the depth in text interpretation exhibited by the fantasies and the cantatas, they are more than simple Gebrauchsmusik, compositions that fulfill a merely utilitarian purpose. The following essay will focus on Buxtehude’s chorale variations on the hymn Nimm von uns Herr, du treuer Gott, BuxWV 207, examining its musical structure, its function, and its contexts in contemporary piety.

Nimm von uns Herr, BuxWV 207
The variations are based on a Protestant chorale from the second half of the 16th century. The text has seven stanzas and was published in 1584 by the 16th-century poet and theologian Martin Moller (1547–1606); the words were traditionally combined with Martin Luther’s melody for the hymn Vater unser, im Himmelreich. (See Example 1: Melody, “Nimm von uns Herr.”)

First movement
Buxtehude’s set of variations consists of four verses. The first verse is a three-part setting, with the cantus firmus in mostly unembellished fashion in the upper voice. The occasional embellishments of the melody (mm. 8, 11, and 27) occur only at the beginning or the middle of a phrase, never at the end. This movement is basically a figuratively embellished chorale harmonization. The harmonic backdrop is dissolved into a continuous sixteenth-note motion. The lower voices serve primarily as accompaniment. Only occasionally (in the interludes between the lines of the chorale or later in mm. 21–24) does the alto voice develop a certain degree of independence and engage into a motivic dialogue with the bass.
The texture of the movement resembles the type we find in the chorale variations of Buxtehude’s contemporary Johann Pachelbel, and even in the works of Johann Gottfried Walther, who was of a later generation. Buxtehude himself used this type only rarely. The single chorale setting Jesus Christus, unser Heiland, BuxWV 198, is very similar to the first verse of BuxWV 207. In both pieces Buxtehude employs an analogous “running” sixteenth figuration in the lower voices, while the chorale melody is played in the upper voice. Like BuxWV 207/1, the piece is not a strict trio but rather a figuratively embellished chorale harmonization. The same is true for the first verse of the chorale variations on Danket dem Herren, BuxWV 181, and the second verse of the chorale partita Nun lob, mein Seel, den Herren, BuxWV 213. Even though he used it only rarely, Buxtehude seems to have preferred this type of chorale setting mostly in his chorale variations rather than in independent chorale preludes. Only one such individual setting (BuxWV 198) has come down to us; however, it cannot be ruled out that other, similar compositions by Buxtehude have been lost.

Second (and fourth) movement(s)
The second movement of Nimm von uns Herr is a traditional bicinium, standing in the tradition of similar pieces by Jan Pieterszoon Sweelinck and Samuel Scheidt. The melody in the upper voice, even less embellished than in the first movement, is accompanied by a lower voice of extraordinarily wide tessitura, spanning the range from alto (mm. 7–9) to a low bass voice (m. 28). (See Example 2.) A comparison with similar settings by Sweelinck (Example 3) and Scheidt (Example 4) exhibits Buxtehude’s roots in these traditions. All three examples begin with the first note of the cantus firmus; the accompanying voice enters later (here a quarter note) in unison, before it reaches the third of the chorale melody through passing notes.
The few embellishments of the melody (mainly simple passing notes) in Buxtehude’s bicinium are encountered at the same places as they were in the first movement: in the middle of the second and the beginning of the third phrase. Only the short melismatic embellishment of the last phrase in the first movement finds no correspondence in the second movement.
We pass over the third movement for a moment and come to the last section of Buxtehude’s chorale partita. It is another bicinium with the cantus firmus in the upper voice and a vivid, motivically independent lower voice of wide tessitura. The embellishments of the melodic line (again mainly passing notes) are at the same places as in the first bicinium—a feature that ensures a certain degree of motivic consistency between the two bicinia.
Monody and expression: the third movement of BuxWV 207
The third movement is exceptional. It conforms to the type of chorale setting that is traditionally labeled as “organ chorale” (Orgelchoral) or “monodic organ chorale” (monodischer Orgelchoral).9 The melody in the upper voice is highly embellished, while the lower three voices serve as an accompaniment and bridge the gaps between the chorale lines with short, imitative interludes. It is the type of chorale setting Buxtehude uses in most of his single-movement chorale preludes.10 The structure is the same as in the chorale preludes: the upper voice begins (here with a vivid embellishment of the first note of the hymn) before the three lower voices enter with a mostly homophonic accompaniment.11 (See Examples 5 and 6.)
While the majority of Buxtehude’s settings of this type begin with a simple long note in the upper voice,12 this one is opened by an extensive, octave-encompassing embellishment of the first note of the cantus firmus, establishing the d-minor tonality, which is later confirmed by the entrance of the lower voices. Example 6, Buxtehude’s setting of the hymn Komm, Heiliger Geist, shows that the composer occasionally employs a similar opening in other monodic chorale settings as well.
While the movement stays within the margins of Buxtehude’s style, it is unusual to find a setting of this type in the context of an otherwise rather simple chorale partita, breaking up the frame established by the other movements. It is also the only movement in the partita that requires pedal. The unusual structure of the set of variations requires explanation.
One explanation could be that the chorale partita, in its current form, is not the partita Buxtehude composed. A reduction of the work to verses 1, 2 and 4 would turn the composition into a more coherent set of three variations for manual only, with a three-part setting at the beginning and two bicinia following. In that way, the composition would somewhat resemble the chorale variations on Nun lob, mein Seel, den Herren, BuxWV 213 (Bicinium–Trio–Trio). However, the sources for the partita do not justify the exclusion of the third movement. Not a single source (even those with that are incomplete) preserves the chorale partita without the third movement.13 One manuscript (the now lost Königsberg manuscript, Sammlung Gotthold Ms 15.839, copied by Johann Gottfried Walther) contains only the third movement, but it is more likely that Walther (or the source he used) took the piece out of its original context than that the movement was inserted into the already existing set of the variations 1, 2, and 4.
The combination of unembellished and highly embellished verses in a chorale variation was not entirely unusual in the 17th century. We find similar combinations in the chorale variations by Heinrich Scheidemann (~1596–1663), who, as Kerala Snyder suggests, could have been Buxtehude’s teacher in Hamburg.14 But even if Buxtehude did not directly study with Scheidemann, the latter’s pieces were widely disseminated in manuscripts, and Buxtehude surely had access to compositions by the Hamburg organ master. In other words, Buxtehude’s chorale variations on Nimm von uns Herr—even though they seem to be incoherent—stay within the margins of both the composer’s style and the style of northern German organ music in the second half of the 17th century in general.

Form and function
How was Buxtehude’s chorale partita used? We know from Lübeck sources from the 17th and early 18th centuries that chorales were sung “alternatim,” which means that the congregation and the organ alternated in the performance of the hymns.15 One verse was sung by the congregation, which in Lübeck at this time still normally sang without the accompaniment of the organ. The next verse was then played by the organist while the congregation “sang” the text of the stanza, which they knew by heart, in their minds. Then another verse was sung by the congregation, and so forth. Furthermore, the hymns were preceded by an organ prelude.
We can assume that the chorale variations on Nimm von uns Herr were also used in alternation with the singing of the congregation. They were probably performed in the following way:

BuxWV 207/1 Organ prelude
Congregation Verse 1
BuxWV 207/2 Verse 2
Congregation Verse 3
BuxWV 207/3 Verse 4
Congregation Verse 5
BuxWV 207/4 Verse 6
Congregation Verse 7
The four movements fit perfectly into the seven-verse structure of the hymn. The first movement served as a prelude; the remaining movements replaced the even numbered verses, while the congregation sang the odd numbered.
A comparison between the hymn stanzas the organ replaced and Buxtehude’s compositional realization suggests a correspondence between musical form and lyrical content. The first bicinium in the set of variations (movement 2) replaced the following stanza:

Erbarm dich deiner bösen Knecht.
Wir bitten Gnad und nicht das Recht;
Denn so du, Herr, den rechten Lohn
Uns geben wolltst nach unserm Thun,
So müßt die ganze Welt vergehn
Und könnt kein Mensch vor dir bestehn.

Have mercy upon your evil servants.
We ask for mercy and not for justice;
For if you, Lord, wanted to give
The earned reward to us for our deeds,
The whole world would have to perish
And no man could stand before thee.

It would be too much to expect a set of chorale variations of this time to give a musical exegesis of the text; however, the movement clearly transfers the affect of the stanza into music. The restrained sonority of the two-part texture, the chromaticism and hushed thirty-second notes accompanying the third phrase of the melody (“for if you, Lord, wanted to give the earned reward,” mm. 12–14), and the restless sixteenth-note motion towards the end of the setting (“and no man could stand before thee”) capture the mood of the text, a feeling of trepidation and hope.
The second bicinium, replacing the sixth stanza, reflects the general affect of the words in a similar fashion:

Gedenk an deins Sohns bittern Tod,
Sieh an sein heilig Wunden rot,
Die sind ja für die ganze Welt
Die Zahlung und das Lösegeld,
Des trösten wir uns allezeit
Und hoffen auf Barmherzigkeit.

Remember your son’s bitter death,
Look upon His holy red wounds,
That are indeed for the entire world
The settlement and ransom,
From this we gain consolation always
And hope in your compassion.
The restrained sonority of the two-part texture underlines the meditative character of the text. An interesting melismatic embellishment appears in the second phrase, emphasizing the words “look upon His holy red wounds.” Furthermore, the textural similarity between the two settings (both are bicinia with the melody in the upper voice) underlines the theological correspondence of stanzas 2 and 6. Both focus on the juxtaposition of grace and justice, using monetary images (“reward” in verse 2 and “ransom” in verse 6). In other words, the musical structure reflects the theological structure of the hymn text.
Stanza four of the chorale was replaced with the extraordinarily embellished third verse of the partita.

Warum willt du doch zornig sein
Über uns arme Würmelein?
Weißt du doch wohl, du großer Gott,
Daß wir nichts sind als Erd und Kot;
Es ist ja vor deim Angesicht
Unser Schwachheit verborgen nicht.

Why would you be so angry
Against us poor little worms?
For you know well, great God,
That we are nothing but dirt and dung;
Indeed before your face
our weakness is not hidden.

Between wrath and melancholy
Even though is it possible to find correspondences between single words of the text and Buxtehude’s way of embellishing the chorale melody (the wrathful God, mentioned in the initial line, could be the reason for the rhythmically agitated embellishment of the first note of the melody), it is more important to see how the movement captures the mood of the entire stanza. The most agitated and graphic verse of the text finds its equivalent in the most agitated and expressive verse of the partita. That this correspondence between text and instrumental realization is more than a coincidence is revealed through a comparison with a vocal setting of the same hymn by Johann Sebastian Bach. While Buxtehude himself in his chorale cantata Nimm von uns Herr, BuxWV 78, leaves out verses 4–6 of the hymn and only sets 1–3 and 7, Bach in his chorale cantata BWV 101 (composed in 1724) employs all seven verses (even though some appear in free paraphrase). Bach writes a similarly agitated aria when he sets the fourth verse of the hymn.16 He even features an agitated broken minor chord at the very beginning, just as Buxtehude does. The paraphrase of the fourth stanza in Bach’s cantata can be read as a theological commentary on the chorale text, enforcing the dramatic affect of the hymn text:

Warum willst du so zornig sein?
Es schlagen deines Eifers Flammen
Schon über unserm Haupt zusammen.
Ach, stelle doch die Strafen ein
Und trag aus väterlicher Huld
Mit unserm schwachen Fleisch Geduld.

Why would You be so angry?
The flames of Your zeal already
Strike together over our heads.
Ah, leave off Your punishments
And out of paternal favor deal
Patiently with our weak flesh.17

The similarities between Bach and Buxtehude are rooted in a similar type of religiosity. In the fourth verse, the hymn talks about the remembrance of mortality, an aspect of central importance to the piety of the 17th and early 18th centuries. The recognition of one’s own fallibility and transience was a precondition for salvation. Only one who recognized one’s sinfulness was also able to embrace God’s grace. The Lübeck Superintendent August Pfeiffer, at this time serving at the same church as Buxtehude, in his Anti-melancholicus, oder Melancholey-Vertreiber (1691), gives a very graphic description of the final hours:

I take fright as well whenever I think that my limbs, which I so carefully nourished and clothed and so tenderly cared for in my lifetime and which did me such steadfast service, should moulder and rot in the earth, and become a stinking carcass, dung, and filth, and perhaps be carried off by a thousand worms or maggots.18

Pfeiffer’s text uses metaphors similar to the fourth stanza of the hymn. The memento mori, the remembrance (and awareness) of death, was a cornerstone of contemporary piety. Again, if one verse deserved an embellished treatment in the course of the chorale partita, it was the fourth one. Even if we mistrust a literal identification of single embellishments with individual words of the chorale text, we must concede that the emotional quality of the fourth stanza, a quality that found its equivalent in the contemporary religiosity, lends itself to a more emotional treatment in the set of chorale variations.

Conclusions
The initial question remains: What is a convincing cycle? The structure of the set of variations was obviously determined by the text of the chorale. It also reacts to the necessities of its intended performance practice (alternatim). The partita was not intended for performance in a recital, but was planned as a composition that needed the integration of congregational singing. In this context, the set of variations appeared as a prelude and an embellished organ chorale that was framed by two bicinia, with the congregation adding another layer of structure to the performance. One could label the resulting form a ritornello-structure—only that the “ritornello” was not provided by the composer because it was sung by the congregation.
In this way, BuxWV 207 is different from Buxtehude’s partita Auf meinen lieben Gott, BuxWV 179, where the five stanzas of the hymn are transfigured into five dances, forming the movements of a conventional dance suite. That piece was composed for use at home, specifically for individual religious edification in the realm of domestic piety. Each of the five instrumental movements replaces the singing of the five stanzas of the chorale, and Buxtehude chose the form of a suite as the external idea to connect the movements.19 In our example, the circumstances of the performance already provided a “convincing” cyclic concept, in which the composer only had to insert the movements of the chorale partita. This granted him the liberty to react to the individual texts of the chorale melody. The chorale variation is characterized not so much by a lack of structure, but by the freedom given the composer through the existent structure in the alternatim practice.
When we perform Buxtehude’s chorale variations today, we mostly do so in a concert setting and not in the context of the liturgy. However, a modern performance that simply strings together the four movements of BuxWV 207 neglects an important aspect of historical performance practice. Even if we do not ask our concert audience to sing the verses of the hymn (but why should we not?), we could insert hymn settings of the chorale between the single movements. This would also enable the listeners, most of whom are probably unaware of the actual melody, to recognize the hymn tune in the variations. This could be especially helpful for the highly embellished third movement of the chorale partita.

Part 1 was published in the October issue of The Diapason, pp. 22–25.

Wir glauben all’ an einen Gott
[We all believe in one God]
(BWV 680–681)
The arrangement of the chorale Wir glauben all’ an einen Gott, the Protestant version of the Credo, opens a series of dramatic chorale preludes in the Clavierübung III. Their themes are built on the minor keys and gravitate around the interval of the fifth.
In this piece the fugal upper voices are contrasted against a melodic line in the bass that occurs seven times. (Example 9) This melody is based on a leap of a fourth followed by a downward move within the octave and displays a structural similarity to the theme of the so-called Dorian Fugue (BWV 538).55 The ostinato motif appears altogether six times in the pedal; once (the sixth appearance) in modified form on the manuals: there only the beginning of the motif appears, repeated three times.
Not just the relationship (6 + 1) in the use of this striking melody is important, but also the fact that its form is changed in the one time it is used on the manuals. Naturally, this begs the question as to the purpose of this change. We have here possibly an allusion to the Old Testament injunction: Six days you shall labor and do all your work, but one day must be reserved for prayer and spiritual needs. From here stem the characteristics of one of the developments: an elevation of the tessitura, the use of only upward leaps, the softening of the harshness of the harmonic minor, and finally the heterolepsis figure used in the upper voices.
The manual voices are developed out of the beginning of the melody of the chorale Wir glauben all’ an einen Gott. The first four notes of this motif in a tonal answer form a musical rhetorical figure, often encountered in the works of Bach, which Boleslav Javorsky called the predestination motif.56 The origin of this motif lies in the chorale melody Was mein Gott will, das g’scheh’ allzeit [What my God wills may always happen] and is usually used by the composer as a culminant, dramatic or recapitulating figure (Fugue in G Minor, BWV 542, Fugue in A Minor, BWV 543, etc.). The whole musical fabric of this chorale prelude is shot through with this predestination motif.
Towards the end of the composition, Bach quotes in the tenor, first in its entirety, the first line of the cantus firmus (bars 89–98). Typically, the subsequent figure in the pedal that accompanies the chorale melody is enlarged, not only in its range (two octaves), but also in the number of notes (to 43—CREDO). One can also hardly describe it as a coincidence that the work has 100 bars: Bach could not have found a better numerological symbol to underscore the idea of “We all believe in one God.”
If we had the task of finding within Bach’s output a work for organ where the dramatic element was more pronounced, we could, paradoxically, hardly do better than choose the small 15-bar manualiter fughetta on the chorale melody Wir glauben all’ an einen Gott in the Clavierübung III. Written in Handelian style,57 it is very chromatic. The traditional double dotting, the richly ornamented musical fabric, the use of characteristic rhetorical figures—tiratas—all combine to sharpen up the harmonic impact of this three-voice fughetta to the highest degree.
The high point of the piece comes in the 12th bar, which results in the interesting proportions of 4:5.58 The density of chords in this bar is a rare example in Bach’s organ works. (Example 10) The diminished seventh on the strong beat contains seven notes. The following diminished seventh from D sharp–C contains six notes, which together makes 13 notes—most certainly another numerological symbol and one that needs no explanation. The impact of the intensive harmonies is strengthened by “talking pauses” and the declamatory answers on the “weak” beats of the bars. The intonations from the introduction (viola da gamba solo) of the aria Es ist vollbracht from the St. John Passion (BWV 245) can be heard in the music. (Example 11)
The descending seconds in Lombardic rhythm, with articulation marks written out in full by the composer (bar 11), the key role of the striking diminished seventh from D sharp–C at the high point of the work, and the key chosen—this is by no means a complete list of the methods the composer has used to create a smooth transition to the subsequent part of the composition.

Vater unser im Himmelreich
[Our Father in Heaven]
(BWV 682–683)
In the extensive arrangement of the chorale melody Vater unser im Himmelreich we encounter an example of a trio that is from time to time expanded to five voices by means of the cantus firmus in canon. This is one of the rare works of Bach full of articulation marks. Thoroughness of articulation shows how important this aspect of organ playing was for the Leipzig cantor.
Already, the choice of key says a great deal about the associative structure of this music. E minor is the key of the opening chorus of the St. Matthew Passion (BWV 244), the Crucifixus from the Mass in B Minor (BWV 232), the Prelude and Fugue for organ (BWV 548), the chorale prelude Da Jesus an dem Kreuze stund (BWV 621) from the Orgelbüchlein, and many other works in which Bach created an atmosphere of grief, sorrow, and misfortune.
The narrative flow of the music in the greater chorale Vater unser im Himmelreich creates an atmosphere of stillness and calm, and invites the hearer to intense prayer. The movement in seconds in Lombardic rhythm59 is akin to the sighs of a humble soul turned towards God. Time moves gently, so as not to disturb the state of intimate prayer.
This composition is literally suffused with thematic symbolism. Allow me to name just a few (following B. Javorsky): the descending third – a symbol of grief; a smooth chromatic movement of 5 to 7 notes – pain; a progression in triplets – fatigue, weariness; a movement along the notes of a first inversion – a symbol of inevitable realization; and so on.
The musical fabric of the composition resembles the tenor aria Wo wird in diesem Jammertale für meinen Geist die Zuflucht sein? [Where will my spirit find its refuge in this vale of tears?] from the cantata Ach, lieben Christen, seid getrost [Ah dear Christians, be comforted] (BWV 114), which Bach completed in Leipzig in 1724. Without a doubt there is an inner connection between the two works. The text of the aria, especially the treatment of the key word “Jammertal” [“vale of tears“ in German] can give the performer the right feeling for the interpretation of the greater chorale prelude Vater unser im Himmelreich.
Another interesting detail of the work is the movement in seconds in Lombardic rhythm in the pedal. This occurs only once in the whole work, at bar 41
(JSBACH), an allusion to the composer’s unseen participation in the prayer to God the Father. (Example 12)
The intricately crafted rhythms of the greater chorale prelude Vater unser im Himmelreich give way in the manual version to flowing linear movement in sextuplets. This sharp contrast has not gone unnoticed by scholars. “As complicated as the rhythms in the large Our-Father prelude may be, so simple is the calm flow of the 16th notes in the manuals version . . .” wrote Christoph Albrecht.60 An interesting explanation for this contrast has been put forward by Albert Clement, who connects the greater chorale prelude with the text of the fourth verse of Luther’s chorale Vater unser im Himmelreich,61 and the smaller prelude with the following verses (5–8). The fourth verse appeals to God’s patience in a time of sorrow, while verses 5–8 speak of trust in His compassion and assistance.62
The placid wave motion of the accompanying voices in the manuals version of the chorale prelude Vater unser im Himmelreich gently prepares us for the stormy motion of the 16th notes in the greater chorale prelude Christ, unser Herr, zum Jordan kam [Christ, our Lord, to Jordan came] as the following section of the Clavierübung III.

Christ, unser Herr, zum Jordan kam [Christ, our Lord, to Jordan came] (BWV 684–685)
The greater chorale prelude Christ, unser Herr, zum Jordan kam presents us once again with something quite out of the ordinary. This is the first occurrence in the whole work of the cantus firmus being transferred to the pedal in a high register. The composer indulges here in musical picture painting: the 16th-note runs produce a sort of perpetuum mobile and create the impression of waves on the Jordan. The music is dominated by an atmosphere of waiting for the miracle of God’s appearance and with it, the forgiveness of sins through the ritual of baptism. (Example 13)
Attempts have been made by various authors to see in the upper voices a dialogue between the Savior and St. John the Baptist,63 a view that I personally do not find very convincing. Built on the symbolic motifs of the Cross and Willingness to Sacrifice,64 the dialogue in the upper voices is often syncopated or transformed into a typical Bachian motion. It does not seem in the least to be associated with the dialogue between God’s Incarnation and His forerunner, but rather serves, as does the stormy motion of the bass, to create a state of what I would call “joyful excitement”—an atmosphere that is typical of many iconographic depictions of the Feast of the Baptism of the Lord.
The appearance of the Holy Trinity—as the Spirit in the form of a dove descending from heaven and as the supernatural light surrounding Christ at His baptism in the waters of the Jordan—is present in this prelude at the deeper level of mystical numerological symbolism. The cantus firmus appears nine times against the three-voiced accompaniment (9×3 = 27), while the total number of bars in the prelude is 81 (27×3).
Each appearance of the cantus firmus is built on a particular number of notes: in four cases it is nine notes, in the other five cases it is eight. And they occur in a strict sequence: 9 + 8 + 9 + 8; 8 + 9 + 8 + 9 + 8. The symbolism of the numbers 3, 9, 27, 81 focuses our attention on the picture of the Holy Trinity, while the number 8 is associated with the heavenly chronos or with the Coming of the Messiah.65
The legitimacy of the numerical proportions in the greater chorale prelude is borne out by the numerological symbolism of the manual fugato in three voices on Christ, unser Herr, zum Jordan kam. The fugato is written in simple triple time and has 27 bars (27×3 = 81). The main theme—the first line of the chorale—occurs three times in the original and three times in the inversion, and each time it is accompanied by a counter-melody based on thematic material in diminution, which forms a kind of canon. (Example 14)
In the opinion of Christoph Albrecht, this is a musical representation of the Gospel words of St. John the Baptist: “He [Jesus] must increase, but I must decrease” (John 3:30).66 It is worth mentioning that the bridges in the fugato (bars 8–10 and 18–20) have an evident three-part structure containing the countersubject (= the diminished theme).
All in all, the composer introduces the theme a total of 14 times (three times the original theme, three times inverted, and eight times diminished).67 The concluding development of the theme in its original form (bass in bar 20) has been slightly altered through the introduction of the Willingness to Sacrifice motif as an anacrusis. This results in interesting proportions for the presentation of the thematic material: 2 + 1 + 3 + 8. It is not difficult to see that these numbers represent a numerical version of the name of the composer (BACH).

Aus tiefer Not schrei’ ich zu dir
[Out of the depths have I cried unto Thee] (BWV 686–687)
The only organ work of Bach written in true six parts with double pedal is the chorale prelude on Psalm 130 (129) Aus tiefer Not schrei’ ich zu dir—a further example of the stile antico in his work. Each verse of this monumental penitential chorale,68 welling up out of the depths of the heart, is introduced in the fugal-like exposition that concludes each time with the cantus firmus in the upper pedal voice. This gives the work, written in the best tradition of J. Pachelbel, the form of an unbroken chain of seven fugues, corresponding to the number of verses of the chorale.
Albert Schweitzer’s attention had already been drawn to the “motif (rhythm) of joy” that first greets one in the initial phrases of the countersubject. As the music develops, this symbolic motif is further elaborated and at the end totally dominates the musical fabric. (Example 15) Schweitzer proposed a dogmatic interpretation for its presence: “Bach . . . is trying to represent the Lutheran doctrine of repentance, according to which all true repentance leads of itself to the joyful certainty of salvation.”69
Schweitzer’s observation is, of course, interesting and not without subtlety, but in my opinion one is dealing here less with joy, but rather with the cleansing power of repentance and the resulting confidence of the penitent in his own future. The motif under consideration conveys just this feeling of confidence.
What motives led Bach to introduce the chorale prelude Aus tiefer Not schrei’ ich zu dir into the Clavierübung III at all? Penance was not a component of the Ordinary of the old Mass, although it had been included in the liturgy in Saxony since 1601. Neither was penance dealt with by Luther in his Great Catechism, although he sometimes mentioned it along with Baptism and the Eucharist as one of the Sacraments. This was apparently the decisive argument for Bach to place two fantasies on Aus tiefer Not schrei’ ich zu dir between the parts relating to Baptism and the Eucharist.
Numerological symbolism plays an important role in both works. As has already been said, the seven fugues that make up this work correspond to each of the seven verses of the chorale. The cantus firmus that crowns each fugue always consists of nine notes, whereas it is interesting to note that it first occurs in the ninth bar. In addition, the length of the cantus firmus from its first to last note always has the same length of eight half-bars.
This changelessness of the cantus firmus, with its connection to the numbers nine, eight, and seven is obviously meant to signify the objective, almost unearthly quality of the beneficial cleansing power that flows over the penitent sinner. An additional indication can be found in the fact that at each occurrence the cantus firmus is first woven into the musical structure only after the completion of the exposition with its five voices. (We recall that the number five symbolizes “sensual Mankind.”)
Our attention is also drawn to the relationship between the number seven (seven verses of the chorale and the seven fugues) and the number five (the five-part musical structure70). These two numbers have an interesting internal proportion: 7:5 = 1.4 (BACH). One could probably regard this as pure chance, were it not that these two numbers occur again within this work. The chorale prelude has 75 bars, where the number 75 is the numerological expression of the word ELEISON (5 + 11 + 5 + 9 + 18 + 14 + 13). The relevance of this cry for mercy in a work dealing with remorse can hardly be doubted.
It is characteristic that the manualiter version of the chorale Aus tiefer Not schrei’ ich zu dir displays the same numerological symbolism as the greater version. A slight change in the rhythmical structure makes the initial motif of the theme correspond to the eighth fugue of the Ariadne Musica Neo-Organoedum Per Viginti by Johann Caspar Ferdinand Fischer (ca. 1660–1746).
Bach’s work impresses us by its architecture. Just as in the first chorale prelude, we encounter an unbroken chain of fugues that treat the seven verses of the chorale one after the other, both in its tonic form and its inversion, where each is brought to a close by the statement of the cantus firmus in the soprano. This results in seven fugues. Six of them are of the same length. The cantus firmus occurs after the fifth bar and lasts for eight bars. But here we encounter an interesting new development: after the cantus firmus has run its course, Bach does not immediately begin with the following fugato, but each time inserts an extra bar as a sort of résumé. Thus the six units have the following structure: 5 + 8 + 1. It is not difficult to see that the résumé thus occurs in the 14th (BACH) bar of the appropriate unit.71
The last and seventh unit differs in its structure from the preceding six, and introduces a proportion that we have already encountered in the greater choral prelude on Credo (6+1). After it has started as all the preceding units (five bars of fugato without the cantus firmus, followed by eight bars with the cantus firmus), this seventh unit has instead of the “Bach résumé” an extension of the second cantus part for a further five bars, resulting in the new proportion of 5 + (8 + 5). It is not difficult to see that this new proportion brings us close to the Golden Rule: 8:5 = 1.6 whereas 13:8 = 1.625. This is not altogether surprising. Thus when the composer understood the combination 6 + 1 as the biblical command to labor for six days, but to keep the seventh as a Sabbath for your God, then it was appropriate that this “special” seventh day be not simply adorned with ordinary music, but be bejewelled with golden tones!

Jesus Christus unser Heiland
[Jesus Christ our Savior]
(BWV 688–689)
The last two chorale preludes in the Clavierübung III deal with the events surrounding the Last Supper. Viewed from a cultural perspective, the iconography of this subject centers around two key moments. The first is the Transubstantiation of the bread and wine into the Body and Blood of Christ. The second moment concerns the circumstances of Judas’s betrayal.
The greater chorale prelude Jesus Christus unser Heiland is woven out of three voices. The cantus firmus, based on an intonation of fifth, is written out in long notes and appears in the pedal. The lively duet in the upper voices simultaneously spins out the three-note stepwise motif (according to Javorsky, a motif of reconciliation), both in its tonic form and its inversion. (Example 16)
We have already encountered this characteristic method in the Clavierübung III: in the greater chorale prelude on Kyrie, Gott heiliger Geist. Its use with quickened tempi produces a mood of agitation and worried concern. A special feature of the musical language is the frequent use of unprepared dissonances that heighten the sense of drama. Speaking personally, this music always conjures up for me Leonardo da Vinci’s famous Milanese fresco of the Last Supper, where the disciples of Christ, unsettled by his prophecy of betrayal, turn to the Savior with just one question “Surely not I, Lord?” (St. Matthew 26:22).
The cantus firmus appears altogether four times in the pedal as the embodiment of Christ’s serenity and his willingness to drink the Cup of his Passion. Its 44 notes are arranged as a pattern of 10 + 12 + 10 + 12. It would appear that the composer has applied this numerical pattern to emphasize the union of the Old Testament (the Law) and the New Testament (the Testament of Christ). Obviously, it is appropriate to remember at this point that St. Augustine considered the number twelve to be a symbol of the Church of Christ. The universal, catholic character of the Church is portrayed by the numerical symbol 144 (= 12×12). Note that the three-note motif of reconciliation in the manuals occurs exactly this many times in the musical texture of this composition.72
Another mysterious symbol is embedded in the score. When one connects the first and the sixth notes of the first bar, and the second and fifth notes, and the third and fourth notes (d1-d2, f2-f1, e1-e2) with a straight line, one produces a graphic figure which resembles the Greek letters X (Chi) and I (Iota) superimposed on each other. (Example 17)
This figure is the emblem of God made Man (Ιησυ Χριστ – Iesus Christos), and one must assume that the composer intentionally built this motif into the structure of the chorale prelude, a chorale that begins with the words “Jesus Christus unser Heiland” [Jesus Christ our Savior]. Typically this emblem occurs 72 times within the work, something that can hardly be attributed to chance. In accordance with tradition, this symbolic number corresponds to the 72 biblical names of the Lord, 72 biblical angels, the 72 nations of the ancient world, and the 72 disciples that Jesus sent out to preach his gospel. The Old Testament book of Numbers tells of 72 elders who received the gift of prophecy from God (Numbers 11:24, 26).73
The manualiter version of Jesus Christus unser Heiland (an extensive fugal composition in four voices) displays a very interesting feature—the placement of the theme does not match the metrical structure. The use of such a technique in the final chorale work of the Clavierübung III undoubtedly has good reasons. Perhaps Bach wanted to underline that the teachings of Christ have an eternal relevance that is not bound by the confines of physical time.
The theme of this fugue displays a striking structure. It consists of 13 notes74 and is based on two elements, which have a significant structural function in the whole cycle: a leap over a fifth and a stepwise motif over a third. The first notes of the tonal answer replicate exactly the final cadence of the chorale Was mein Gott will, das g’scheh’ allzeit, which (following Javorsky) we have interpreted as a predestination motif. (Example 18)
The countersubject is worked out with a circulatio figure that represents the Cup of Sorrows. The theme occurs 17 times altogether, with the final statement in augmentation. Bach undoubtedly considers the number 17 to be the union of ten and seven, especially as the eleventh statement is introduced by a longer bridge passage. The number ten is associated with the Law of the Old Testament (The Decalogue), while according to Werckmeister, the number seven is the symbol for purity and peace.
Thus one can summarize the conjunction of all these symbols as follows: The predestination from above (predestination motif) and the reconciliation prophesied in the Old Testament (reconciliation motif) through the suffering of Christ on the Cross (the Cup of Sorrows motif) purifies the fallen world (13) and gives it eternal peace and bliss (7).

Four Duets: E minor, F major,
G major, A minor
Scholars agree that the four duets of the Clavierübung III are very difficult indeed to interpret. As Hermann Keller remarked, the duets are “so unique and in part so difficult to understand that one must almost be led to believe that Bach wished to express something very special, but no one has yet found the key to them.”75 And in fact the opinions of the experts concerning both the content and the meaning of these works are indeed very contradictory. Some of them are of the opinion that they should be played during the Eucharist, while others see them as symbolic representation of the four Gospels.76 Albert Schweitzer is most probably the furthest removed from the truth with his opinion that they have only found their way into the Clavierübung III by mistake. He thus underestimates the significance of numerical symbolism within this work. Above all he did not “notice” that with the addition of the four duets the total number of works in the Clavierübung III reached the “cosmic” number of 27.
How does this music present itself?
All four pieces are highly individual and represent the highest achievement within the development of the genre of keyboard music for two voices known as inventions. They display no direct connection to the church chorales, but one is aware that while they have an element of tone painting it would not be illogical to interpret them as representations of the four material elements of this world: fire, air, water, and earth. Indeed, just this sort of interpretation was first suggested by Rudolf Steglich.77
Let us now look at the musical design of the duets.
The duet in E minor (BWV 802) is pure energy. Whole rivers of fire flow in the rapid succession of 32nd notes and the broken line of the syncopated motif recalls tongues of fire. The jagged melisma, the semitone movement within the range of diminished thirds: all reinforce a pervading feeling of tension. An almost pagan cult of fire dominates this music. (Example 19)
The F major duet (BWV 803) is built on the idea of contrast. The sphere of air is represented as a contrast of light and dark elements. The main theme, the embodiment of light, occurs in a major key in both the exposition and the recapitulation. The central part gives the impression of sudden twilight, which shrouds all life and transforms everything into a ghostly world of shadows. The contrast of major and minor suggests conflict—the elements of light struggle to free themselves from the chains of the mythological shadow world. (Example 20)
The G major duet (BWV 804) paints a picture of a body of water sparkling in the rays of the morning sun. Murmuring and iridescent flowing passages stirred by a light breeze create the impression of an unending stream of flowing water, magically calling to us by its freshness and purity. (Example 21) The musical texture of this work shows a high degree of similarity to the aria Von der Welt verlang ich nichts [From the world I nought desire] as the seventh part of the cantata Sehet, welch eine Liebe hat uns der Vater erzeiget [See what love the Father has bestowed on us], 1 John 3:1 (BWV 64). (Example 22)

The duet in A minor (BWV 805) has a different character. Behind the slow unfolding of its ideas, behind the gravity of its utterances one can discern an unbending internal force that holds everything in its thrall and directs all things. The extended, epically expanding theme strives to embrace all earthly things. The rocklike solidity of this musical picture calls to mind the immovable foundation of the earth. (Example 23)
Unlike Rudolf Steglich, Albert Clement suggested another approach. He sees in the duets a connection to the tradition of home prayer.78 In the opinion of this expert, the four duets serve as a musical illustration of the 194th chapter of the book Geistliche Erquick-Stunden Oder Dreyhundert Haus- und Tisch-Andachten79 [Hours of Spiritual Refreshments, or 300 Prayers for Home and Table] by the renowned theologian Heinrich Müller (1631–1675). Entitled “Von vier süßen Dingen” [On Four Sweet Things], this part of Müller’s monograph is devoted to the interpretation of the religious essentials: the Word of God, the Cross, Death and heavenly Bliss.
Let us now look at the structure of the duets in detail (Figure 1). One’s attention is immediately drawn to the emphasized strictness in the handling of the meter and the thematic material in all four duets. This is especially apparent in the first and second duets.
In the third duet, the length of the bridge-passages creates an interesting relationship (Figure 2).
The theme of the fourth duet is exceptionally long (48 notes) and consists of two parts: the first part has 11 notes, while the second contains 37 notes. All three numbers have clear sacred connotations: 11 is the symbol for sin, 37 for the monogram of Christ, and 48 is the numerical equivalent of the abbreviation INRI (Iesus Nazarenus Rex Iudaeorum).80
The first duets contain not only the numbers 11 and 37 but also other numbers that are relevant to the theme of Golgotha: 13 (death), 17 (symbol of spirituality), 31 (the numerical equivalent of PNC as the abbreviation of Pro Nobis Crucifixus). It is remarkable that these are simply different combinations of just three numbers—one, three, and seven—and that 137 is itself the numerical equivalent of DOMINUS DEUS.
It is also noteworthy that the sum of 22 + 15 (first duet) and 18 + 13 (second duet) lead us again to the symbols 37 and 31. Moreover, the combination of the pairs 17 (first duet) and 31 (second duet), as well as the pairs 11 (first duet) and 37 (second duet) both lead to the above-mentioned key number 48. The same number results from the addition of 11, 31 (third duet), and 6 (fourth duet).
It is clear that Bach wove the numerical symbolism into the duets to illustrate the content of these works. The numerology leaves no doubt as to the subject of these works: the music of the duets revolves around the theme of the Passion.
The idea that the four duets in the Clavierübung III symbolize the Cross was first suggested by Gerhard Friedemann.81 His work contained a number of highly original ideas about numerical significance within these pieces, but also many valuable observations concerning the biblical symbolism present in the other sections of the Clavierübung III.
Unfortunately it would be beyond the scope of this article to discuss further in depth the many other interesting details that are to be found in the four duets. So I would like to confine myself to bringing just a few salient points to the attention of the reader. The total number of bars in all four pieces is 369, which is in itself an indication of the association of these works with the Passion.82 The number 16 (4×4), which forms the basis of the A minor duet, is a numerical representation of the Cross. 112 (the sum of the numbers of bars in the E minor and G major duets) is the equivalent of CHRISTUS (3 + 8 + 17 + 9 + 18 + 19 + 20 + 18), and 149 (the number of bars in the F major duet) represents RESURREXIT (17 + 5 + 18 + 20 + 17 + 17 + 5 + 22 + 9 + 19).83
It is difficult to deny the validity of Gerhard Friedmann’s conclusions, based as they are on the analysis of the numerical structure of the duets. But this raises a further question: Is there a connection between, on the one hand, the hidden numerological references to the Cross in the four duets of the Clavierübung III and on the other hand the obvious descriptive character of the music?
Yes, one can indeed find such a connection! It is well known that in earlier times the cross was used as a symbolic representation of the four elements. But with the coming of Christendom, it became an object of adoration and so lost the association with the pagan worship of fire, air, water, and earth.
So now we wish to put ourselves in the shoes of the composer and try to answer the following question: How is it possible to portray musically a Cross, the product of human hands, soaked with the divine Blood of the Savior and transformed by the divine Will into an object of salvation? The answer is obvious. The best way to accomplish this is that chosen by Bach in the four duets of the Clavierübung III.

Prelude and Fugue in E-flat Major
The Prelude and Fugue in E-flat Major forms an overreaching arch that encloses the whole cycle. It is a work on a truly symphonic scale and is in this respect without parallel in the world’s organ literature. Its epic stature is complemented by the vividness and the passion of the musical language.
In both the prelude and the fugue the composer introduces three different musical spheres nevertheless bound together by such characteristics as common key and thematic material. The work is most commonly thought of as being an expression of the Holy Trinity. But no one to date has been able to produce a truly convincing proof for this view. As a result a number of unresolved controversies exist: which part of the fugue, the second or the third part, represents the Holy Spirit, and which Jesus Christ?
The very existence of these controversies should suggest to us that the work has not yet been sufficiently examined. To say nothing of the “echoes” episodes of the prelude, which most experts have associated with the Son of Man. How should we understand this embellished fluttering “in the spirit of the Rococo” to be a picture of the Savior?
In my opinion one should not view this music as one would a picture on a wall.
It is indeed Bach’s purpose to sing the praises of the Triune God, but it is not his intention to paint a musical picture of God. Three parts that are characterized through changes in the musical texture—in both the prelude and the fugue—are always the same God, the One, the Indivisible, the Holy and Consubstantial Trinity.
With what means does the composer accomplish this task? Let us first examine the prelude.

This article will be continued.

A Performer's Investigation, Part 2

Anomalies I: voice leading

An anomaly here means something unusual, a musical passage that does not conform to contemporary rules of counterpoint or otherwise deviates from the norm. It also entails any incongruities or inconsistencies in melody, harmony, counterpoint, or texture. The concept thus entails interpretation and assumes some knowledge of historical musical practice. In a piece with the rigorous formal construction of the one under consideration, we might expect the voice leading, the treatment of harmony, the handling of texture, etc. to be just as rigorous. Yet there are a number of ambiguities that are noteworthy and curious.

The hexachord theme wanders from voice to voice. This is unusual for the simple reason that the theme is treated as a cantus firmus; cantus firmi, as a rule, do not wander. It is especially peculiar that the wandering takes place in the middle of thematic statements. Only once does it happen at the beginning of the theme (at unit 79) and that is remarkable for another reason. The hexachord theme first begins as the soprano voice. It wanders to the alto voice at unit 10 (see Example 14).

The theme only remains in the alto voice for the duration of nine units before returning to the soprano (see Example 15). Only four units later it wanders again to the alto (see Example 15). The switch in voices takes place on paper at unit 22 where the upper two voices use the same pitch, however it is not audible until unit 23.

The cantus firmus theme returns to the soprano beginning at unit 31, where the ambiguity of which notes represent which of the two upper voices is extended until unit 33 (see Example 16).

Another switch to the alto voice occurs during the space of units 37-38 (see Example 17).

During the first four statements the hexachord theme wanders between the soprano and the alto six times; one hears the theme moving through the fabric of the composition. The return to the soprano, the last until the final section of the piece, is effected at unit 43 (see Example 18).

The shift, at unit 79, of the hexachord theme from the soprano voice to the bass voice, the leap from f1 to A-flat, is one of the more dramatic shifts of the piece, moving very audibly from one outer voice to the other. As we have noted above, the leap occurs as a result of the transposition scheme. After that, the theme continues to wander somewhat. It moves to the tenor at unit 133 (see Example 19). It also moves to the alto voice at unit 163, but that voice crossing is as good as inaudible and is accentuated by Bull in another manner discussed below.

Anomalies II: texture/harmony

Example 20 shows how the hexachord theme, for the space of two and one half whole notes, audibly becomes the highest voice without actually leaving the alto voice on the page. Bull draws attention to this fact by leaving the leading tone, b-natural0 of the cadence on C, hanging without resolution; the soprano voice does not end, but is suddenly abandoned in mid-cadence. This is an abruptio, the sudden cessation of a musical thought. Right at that point, unit 13 of the piece, the effect of being left hanging at the cadence is further emphasized by the open sonority of the fifth, C-G, an anachronism, sounding for an instant in two-voiced texture due to the voice leading of the bass and tenor voices. The effect is one of a hole in the music, and it is one that allows, for a few moments, the theme to sound as if it were the soprano voice.

Example 21 shows another curious passage. One can see that the half-note e-flat1 in the alto at unit 100 is followed by a rest and that the alto proper doesn't reenter until the second half of unit 102. There is, however, right at unit 101, the entrance of an extra voice in the left hand, f0, which sounds for the duration of a whole note only and then disappears. It can only be the alto voice which suddenly plunges down into the tenor area, crossing below the actual tenor at unit 101. The open space between the tenor c1 (which, at unit 101, sounds like the alto voice) and soprano f2 disobeys the rules of counterpoint which stipulate that there be no more than an octave between upper neighboring voices. Not only does the space call attention to itself, but the apparent extra voice, f0, does so as well. The musical-rhetorical figure signified by the space, called longinqua distancia, continues into unit 102 and is found between tenor and soprano (b-flat0 to e-flat2) and then between alto and soprano (c1 to e-flat2).

Example 22 shows, at unit 144, the 12th entrance of the hexachord theme, beginning on f-sharp0. The sonority is unusual, to say the least, and eminently avoidable. First, the natural movement of the soprano voice would be to a1 at unit 144, completing the cadential figure begun around unit 141. The bass voice is expected to drop to A at unit 144 for the same reason, but it does the unexpected also. The alto voice withdraws itself from the affair with a rest, leaving the other voices to form the unusual harmony: octave f-sharps over an e0 in the bass. I have no doubt that Bull knew that the 12th entrance of the theme, using the 12th pitch of the scale, was taking place at the 144th (12 x 12) unit of the piece.

Example 23 illustrates a passage set audibly apart at unit 151 by the manipulation of texture. The four-voiced texture found at the first unit of the example, the alto having first a half-note rest, is thinned out as the soprano drops out at unit 150, while the bass drops out right at unit 151 leaving just a two-voiced texture. This is a unique moment for two reasons. The two-voiced texture is the thinnest used by Bull in this work, and rarely used at that. But that fact alone is not enough. What makes this striking is the open sound of the fifth occurring right at the point where the texture is thinnest. The listener cannot miss the anachronistic sonority; Bull literally diverts our attention away from everything else directly to it as he also did at unit 13 (see Example 20).

Example 24 shows another voice crossing, but one that does not belong to the more audible events of the work.  However, beginning at unit 163, we have an occurrence which acts as an accent and thus draws the ear to it. The alto voice here carries the hexachord theme. One can observe how Bull accentuates this particular event. First, the thematic note, e1, is only a half-note long; this is the only passage in the work which has a thematic note which is not a whole note. Second, the chord played at this point has an added voice in the right hand making it five-voiced; at no other point, excepting the final chord of the work, do more than four voices sound simultaneously. Third, the three inner voices have the same length, a half note, and all are followed by a half-note rest; i.e. the thickest texture is immediately followed by the thinnest texture used by Bull in this piece. Fourth, the five-voiced texture is further emphasized rhythmically by the quarter-note A found in both of the outer voices; the outer voices are the most audible and the A found here presages the cadence on A found across the next bar line. Fifth, the five-voiced texture is restored for the brief period of a half note one unit later. It is an e1 in the right hand, the only tone found both in the A (tonic) and E (dominant) triads which are here forming a cadence--the d1 of the hexachord theme is the seventh of the dominant-seventh chord--though E is conspicuously missing from the a-minor sonority of unit 165.

Order

Hexachord

John Bull uses the hexachord as a cantus firmus. It is not a theme that is developed as the theme of a fugue might be and does not itself undergo transformation. It is a building block with which Bull constructs the framework of his piece. It goes through a number of statements, but each statement is clearly identifiable as a hexachord. The hexachord system reckons with hexachords on G, C, and F although it is clearly a system based on flexible pitch, i.e. it is the relation between each of the hexachord members which remains inviolate; a particular ut may have any G, C, or F pitch. Bull, however, seemingly drawing the consequences of a movable ut, places the hexachord on all 12 chromatic tones, establishing a comprehensive system of relative pitch. Mutation from one hexachord to the next, by way of a pivot tone, a tone which has a function in two successive hexachords and facilitates the transition of one hexachord to the next, does not occur here. Rather, each hexachord stands on its own and demands its unique right to existence independent of the previous hexachord. By setting up his piece in this manner, Bull does away with the entire hexachord theory. The hexachord is used as a tool to dismantle the theory based upon it.

Modulation

Having done away with mutation, Bull employs transposition. Each of the first 12 entrances of the hexachord theme thus demands a harmonic response, a modulation. Bull forces himself to write a music which touches on 12 keys. If we regard major and minor as modes, the entire gamut of keys in the tonal system of the common practice period is utilized--all in one piece of music. And his use of the whole-tone scale in transposing the hexachord theme is truly astounding and sets this piece apart from anything else in the keyboard literature of the time. So, too, did Debussy use the whole-tone scale when, at the turn of the 20th century, traditional tonality was increasingly becoming problematic as a system and composers were experimenting with new systems of harmonic organization.

13

The hexachord theme, used as a cantus firmus in this composition, i.e. unchanged, though transposed, is organized into a 13-unit phrase. The transposition scheme of the piece requires 13 statements of the theme in order to include all of the 12 tones and return to the starting point. The correspondence of the length of the theme and the number of repetitions it undergoes in the transposition scheme represents order on the highest level. This produces a first section of 169 whole-note units (13 x 13).

17

After the transposition scheme has run its course, there are four more statements of the hexachord theme in the soprano voice, bringing the total number of thematic statements to 17. However, the total number of whole-note units which comprise this second section of the work is not 52 (4 x 13). The 13th unit of the last thematic statement is omitted. That leaves us with one unit fewer than anticipated. But 51 = 3 x 17.

11

The two main sections of the work, comprising all of the statements of the hexachord theme, make up the body of the piece. It contains 220 whole-note units of music, instead of the 221 (17 x 13) units it would have had, had the last statement of the hexachord theme contained its 13th unit. 220 (20 x 11 or 2 x 2 x 5 x 11 or 5 x 44) contains no factor of 13 or 17. However, we know that at this period, as part of a very long history, gematria, the theory of numbers and their meanings, was a branch of knowledge in which artists not only dabbled, but used with impunity. One of the common uses of numbers was the representation of names: A = 1, B = 2, C = 3, etc. ("I" and "J" were considered one letter, as were "U" and "V"). Both "John" and "Bull" are represented by the number 44 (4 x 11). By leaving out the final rest of the final statement of the hexachord theme, Bull changes 52 to 51, thus relating the second section of the work to the number 17, but also changing 221 to 220, bringing the body of the piece into relationship with his own name through the common factor of 11.

Almost as an aside I would also like to mention that the number of anomalies, both of voice-leading and of texture-harmony, is 11. In other words, the entire work is regularly constructed employing the accepted rules of counterpoint/composition except those passages which Bull has given his personal stamp by deviating from the norm. His personal stamp also extends to the number of those stamps.

7

The peroration (or coda) comes last. It is extra, the icing on the cake, the statement that ends the oration. It is fitting that it has its own identity. The number seven has great significance in many cultures of the world. It is traditionally related to the length of the week and thus also to creation and the concept of completeness. It has even been maintained that the number seven is responsible for bringing everything into existence, a thought not necessarily misplaced in this context since Bull is calling a new system of musical order into existence. The seven units of peroration bring the total length of the composition to 227 whole-note units.

Primes

The structural numbers of the composition, 7, 11, 13, 17, 227, are all prime numbers. In addition, most of the anomalies take place at or are centered on whole-note units which are prime (10, 13, 23, 31, 37, 43, 101, 133, 144, 151, 163). The only exceptions are units 10 (example 14) and 144 (example 22). Unit 144 has been related to the fact that the 12th statement of the hexachord theme is taking place using the 12th member of the chromatic scale. The passage at unit 10 is the first one in the series of those that appear unusual. It is in fact the case that the numbers 10, 100 and 1000 have an intimate relationship to the number 1. As beginnings of new orders of numbers (the tens, the hundreds, the thousands) they have the same function as the number 1 itself, the beginning of all numbers. Music theorists/philosophers from all over Europe, from Italy to north-Germany, from Zarlino to Kircher to Descartes, recognize in 1 not a number, but rather the concept of unity from which all numbers, indeed all existence has its origin. Even as late as 1722, Rameau makes the statement that the number 2 is the first number, not the second. Observed from this point of view it is not inappropriate that the first of the anomalies should occur at unit 10. Given the nature of music, both the fact that it occurs in time and that it is context-bound--i.e. a context needs to be established before events can be perceived--unit 10 is the first point at which a unique event could occur "at the beginning" without simply being perceived as the beginning of the music. Though the numbers 10 and 144 are not prime, I don't think that one can deny Bull's interest in prime numbers (see Table 1.)

The whole-tone scale

One additional aspect of the piece remains to be mentioned, one that is for me a particularly savory morsel. The whole-tone scale is made up of just that: whole tones. How does the use of this scale tie in with the order found in the rest of the composition? The whole tone is mathematically represented by the proportion 9:8. We can now answer the question why there are four concluding statements of the hexachordum durum, instead of three or five, bringing the total number of statements of the hexachord theme to 17 (13 + 4). The connection between the overall form of the work, which consists of 17 statements of the hexachord theme, and the transposition scheme is given by the whole-tone scale itself: 9 + 8  = 17.

This composition is not to be disposed of as a mere curiosity. It is a clear statement by a serious composer. Ut, re, mi, fa, sol, la: a treatise on a system of music which it methodically, through the organization of its discourse, declares obsolete and actively replaces, utilizing admirable intellectual rigor, with a new order.          n

A Performer's Investigation, Part 2

An anomaly here means something unusual, a musical passage
that does not conform to contemporary rules of counterpoint or otherwise
deviates from the norm. It also entails any incongruities or inconsistencies in
melody, harmony, counterpoint, or texture. The concept thus entails
interpretation and assumes some knowledge of historical musical practice. In a
piece with the rigorous formal construction of the one under consideration, we
might expect the voice leading, the treatment of harmony, the handling of
texture, etc. to be just as rigorous. Yet there are a number of ambiguities
that are noteworthy and curious.

The hexachord theme wanders from voice to voice. This is
unusual for the simple reason that the theme is treated as a cantus firmus;
cantus firmi, as a rule, do not wander. It is especially peculiar that the
wandering takes place in the middle of thematic statements. Only once does it
happen at the beginning of the theme (at unit 79) and that is remarkable for
another reason. The hexachord theme first begins as the soprano voice. It
wanders to the alto voice at unit 10 (see Example 14).

The theme only remains in the alto voice for the duration of
nine units before returning to the soprano (see Example 15). Only four units
later it wanders again to the alto (see Example 15). The switch in voices takes
place on paper at unit 22 where the upper two voices use the same pitch,
however it is not audible until unit 23.

The cantus firmus theme returns to the soprano beginning at
unit 31, where the ambiguity of which notes represent which of the two upper
voices is extended until unit 33 (see Example 16).

Another switch to the alto voice occurs during the space of
units 37-38 (see Example 17).

During the first four statements the hexachord theme wanders
between the soprano and the alto six times; one hears the theme moving through
the fabric of the composition. The return to the soprano, the last until the
final section of the piece, is effected at unit 43 (see Example 18).

The shift, at unit 79, of the hexachord theme from the
soprano voice to the bass voice, the leap from f1 to A-flat, is one of the more
dramatic shifts of the piece, moving very audibly from one outer voice to the
other. As we have noted above, the leap occurs as a result of the transposition
scheme. After that, the theme continues to wander somewhat. It moves to the
tenor at unit 133 (see Example 19). It also moves to the alto voice at unit
163, but that voice crossing is as good as inaudible and is accentuated by Bull
in another manner discussed below.

Anomalies II: texture/harmony

Example 20 shows how the hexachord theme, for the space of
two and one half whole notes, audibly becomes the highest voice without
actually leaving the alto voice on the page. Bull draws attention to this fact
by leaving the leading tone, b-natural0 of the cadence on C, hanging without
resolution; the soprano voice does not end, but is suddenly abandoned in
mid-cadence. This is an abruptio, the sudden cessation of a musical thought.
Right at that point, unit 13 of the piece, the effect of being left hanging at
the cadence is further emphasized by the open sonority of the fifth, C-G, an
anachronism, sounding for an instant in two-voiced texture due to the voice
leading of the bass and tenor voices. The effect is one of a hole in the music,
and it is one that allows, for a few moments, the theme to sound as if it were
the soprano voice.

Example 21 shows another curious passage. One can see that
the half-note e-flat1 in the alto at unit 100 is followed by a rest and that
the alto proper doesn't reenter until the second half of unit 102. There is,
however, right at unit 101, the entrance of an extra voice in the left hand,
f0, which sounds for the duration of a whole note only and then disappears. It
can only be the alto voice which suddenly plunges down into the tenor area,
crossing below the actual tenor at unit 101. The open space between the tenor
c1 (which, at unit 101, sounds like the alto voice) and soprano f2 disobeys the
rules of counterpoint which stipulate that there be no more than an octave
between upper neighboring voices. Not only does the space call attention to
itself, but the apparent extra voice, f0, does so as well. The
musical-rhetorical figure signified by the space, called longinqua distancia,
continues into unit 102 and is found between tenor and soprano (b-flat0 to
e-flat2) and then between alto and soprano (c1 to e-flat2).

Example 22 shows, at unit 144, the 12th entrance of the
hexachord theme, beginning on f-sharp0. The sonority is unusual, to say the
least, and eminently avoidable. First, the natural movement of the soprano
voice would be to a1 at unit 144, completing the cadential figure begun around
unit 141. The bass voice is expected to drop to A at unit 144 for the same
reason, but it does the unexpected also. The alto voice withdraws itself from
the affair with a rest, leaving the other voices to form the unusual harmony:
octave f-sharps over an e0 in the bass. I have no doubt that Bull knew that the
12th entrance of the theme, using the 12th pitch of the scale, was taking place
at the 144th (12 x 12) unit of the piece.

Example 23 illustrates a passage set audibly apart at unit
151 by the manipulation of texture. The four-voiced texture found at the first unit
of the example, the alto having first a half-note rest, is thinned out as the
soprano drops out at unit 150, while the bass drops out right at unit 151
leaving just a two-voiced texture. This is a unique moment for two reasons. The
two-voiced texture is the thinnest used by Bull in this work, and rarely used
at that. But that fact alone is not enough. What makes this striking is the
open sound of the fifth occurring right at the point where the texture is
thinnest. The listener cannot miss the anachronistic sonority; Bull literally
diverts our attention away from everything else directly to it as he also did
at unit 13 (see Example 20).

Example 24 shows another voice crossing, but one that does
not belong to the more audible events of the work.  However, beginning at unit 163, we have an occurrence which
acts as an accent and thus draws the ear to it. The alto voice here carries the
hexachord theme. One can observe how Bull accentuates this particular event.
First, the thematic note, e1, is only a half-note long; this is the only
passage in the work which has a thematic note which is not a whole note.
Second, the chord played at this point has an added voice in the right hand
making it five-voiced; at no other point, excepting the final chord of the work,
do more than four voices sound simultaneously. Third, the three inner voices
have the same length, a half note, and all are followed by a half-note rest;
i.e. the thickest texture is immediately followed by the thinnest texture used
by Bull in this piece. Fourth, the five-voiced texture is further emphasized
rhythmically by the quarter-note A found in both of the outer voices; the outer
voices are the most audible and the A found here presages the cadence on A
found across the next bar line. Fifth, the five-voiced texture is restored for
the brief period of a half note one unit later. It is an e1 in the right hand,
the only tone found both in the A (tonic) and E (dominant) triads which are
here forming a cadence--the d1 of the hexachord theme is the seventh of the
dominant-seventh chord--though E is conspicuously missing from the a-minor
sonority of unit 165.

Order

Hexachord

John Bull uses the hexachord as a cantus firmus. It is not a
theme that is developed as the theme of a fugue might be and does not itself
undergo transformation. It is a building block with which Bull constructs the
framework of his piece. It goes through a number of statements, but each
statement is clearly identifiable as a hexachord. The hexachord system reckons
with hexachords on G, C, and F although it is clearly a system based on
flexible pitch, i.e. it is the relation between each of the hexachord members
which remains inviolate; a particular ut may have any G, C, or F pitch. Bull,
however, seemingly drawing the consequences of a movable ut, places the
hexachord on all 12 chromatic tones, establishing a comprehensive system of
relative pitch. Mutation from one hexachord to the next, by way of a pivot
tone, a tone which has a function in two successive hexachords and facilitates
the transition of one hexachord to the next, does not occur here. Rather, each
hexachord stands on its own and demands its unique right to existence
independent of the previous hexachord. By setting up his piece in this manner,
Bull does away with the entire hexachord theory. The hexachord is used as a
tool to dismantle the theory based upon it.

Modulation

Having done away with mutation, Bull employs transposition.
Each of the first 12 entrances of the hexachord theme thus demands a harmonic
response, a modulation. Bull forces himself to write a music which touches on
12 keys. If we regard major and minor as modes, the entire gamut of keys in the
tonal system of the common practice period is utilized--all in one piece of
music. And his use of the whole-tone scale in transposing the hexachord theme
is truly astounding and sets this piece apart from anything else in the
keyboard literature of the time. So, too, did Debussy use the whole-tone scale
when, at the turn of the 20th century, traditional tonality was increasingly
becoming problematic as a system and composers were experimenting with new
systems of harmonic organization.

13

The hexachord theme, used as a cantus firmus in this
composition, i.e. unchanged, though transposed, is organized into a 13-unit phrase.
The transposition scheme of the piece requires 13 statements of the theme in
order to include all of the 12 tones and return to the starting point. The
correspondence of the length of the theme and the number of repetitions it
undergoes in the transposition scheme represents order on the highest level.
This produces a first section of 169 whole-note units (13 x 13).

17

After the transposition scheme has run its course, there are
four more statements of the hexachord theme in the soprano voice, bringing the
total number of thematic statements to 17. However, the total number of
whole-note units which comprise this second section of the work is not 52 (4 x
13). The 13th unit of the last thematic statement is omitted. That leaves us
with one unit fewer than anticipated. But 51 = 3 x 17.

11

The two main sections of the work, comprising all of the
statements of the hexachord theme, make up the body of the piece. It contains
220 whole-note units of music, instead of the 221 (17 x 13) units it would have
had, had the last statement of the hexachord theme contained its 13th unit. 220
(20 x 11 or 2 x 2 x 5 x 11 or 5 x 44) contains no factor of 13 or 17. However,
we know that at this period, as part of a very long history, gematria, the
theory of numbers and their meanings, was a branch of knowledge in which
artists not only dabbled, but used with impunity. One of the common uses of
numbers was the representation of names: A = 1, B = 2, C = 3, etc.
("I" and "J" were considered one letter, as were
"U" and "V"). Both "John" and "Bull"
are represented by the number 44 (4 x 11). By leaving out the final rest of the
final statement of the hexachord theme, Bull changes 52 to 51, thus relating
the second section of the work to the number 17, but also changing 221 to 220,
bringing the body of the piece into relationship with his own name through the
common factor of 11.

Almost as an aside I would also like to mention that the
number of anomalies, both of voice-leading and of texture-harmony, is 11. In
other words, the entire work is regularly constructed employing the accepted
rules of counterpoint/composition except those passages which Bull has given
his personal stamp by deviating from the norm. His personal stamp also extends
to the number of those stamps.

7

The peroration (or coda) comes last. It is extra, the icing
on the cake, the statement that ends the oration. It is fitting that it has its
own identity. The number seven has great significance in many cultures of the
world. It is traditionally related to the length of the week and thus also to
creation and the concept of completeness. It has even been maintained that the
number seven is responsible for bringing everything into existence, a thought
not necessarily misplaced in this context since Bull is calling a new system of
musical order into existence. The seven units of peroration bring the total
length of the composition to 227 whole-note units.

Primes

The structural numbers of the composition, 7, 11, 13, 17,
227, are all prime numbers. In addition, most of the anomalies take place at or
are centered on whole-note units which are prime (10, 13, 23, 31, 37, 43, 101,
133, 144, 151, 163). The only exceptions are units 10 (example 14) and 144
(example 22). Unit 144 has been related to the fact that the 12th statement of
the hexachord theme is taking place using the 12th member of the chromatic
scale. The passage at unit 10 is the first one in the series of those that
appear unusual. It is in fact the case that the numbers 10, 100 and 1000 have
an intimate relationship to the number 1. As beginnings of new orders of
numbers (the tens, the hundreds, the thousands) they have the same function as
the number 1 itself, the beginning of all numbers. Music theorists/philosophers
from all over Europe, from Italy to north-Germany, from Zarlino to Kircher to
Descartes, recognize in 1 not a number, but rather the concept of unity from
which all numbers, indeed all existence has its origin. Even as late as 1722,
Rameau makes the statement that the number 2 is the first number, not the
second. Observed from this point of view it is not inappropriate that the first
of the anomalies should occur at unit 10. Given the nature of music, both the
fact that it occurs in time and that it is context-bound--i.e. a context needs
to be established before events can be perceived--unit 10 is the first point at
which a unique event could occur "at the beginning" without simply
being perceived as the beginning of the music. Though the numbers 10 and 144
are not prime, I don't think that one can deny Bull's interest in prime numbers
(see Table 1.)

The whole-tone scale

One additional aspect of the piece remains to be mentioned,
one that is for me a particularly savory morsel. The whole-tone scale is made up
of just that: whole tones. How does the use of this scale tie in with the order
found in the rest of the composition? The whole tone is mathematically
represented by the proportion 9:8. We can now answer the question why there are
four concluding statements of the hexachordum durum, instead of three or five,
bringing the total number of statements of the hexachord theme to 17 (13 + 4).
The connection between the overall form of the work, which consists of 17
statements of the hexachord theme, and the transposition scheme is given by the
whole-tone scale itself: 9 + 8  =
17.

This composition is not to be disposed of as a mere
curiosity. It is a clear statement by a serious composer. Ut, re, mi, fa, sol,
la: a treatise on a system of music which it methodically, through the
organization of its discourse, declares obsolete and actively replaces,
utilizing admirable intellectual rigor, with a new order.
style='mso-tab-count:1'>          n