Part I: Foreword

This foreword should perhaps be headed ‘Directions for Use.’ Not because I feel that the reader cannot be trusted—he is, of course, free to make what he will of the article he has been kind enough to read. What right have I, then, to suggest that it would be used in one way rather than another? When I was writing it there were many things that were not clear to me: some of these seemed too obvious, others too obscure. So I said to myself: this is how my ideal reader would have approached my article, if my intentions had been clearer and my project more ready to take form…

I should like this work to be approached as a series of windows that all look in upon a single room with a single object inside it—a fugue written by J. S. Bach in 1722. These windows vary in their color, their clarity, and their scope. Some of the windows are prisms. All windows distort the object observed; but all provide it with new dimensions. I have arranged them in a digestible order. In the absence of a better system, the reader should return to previous windows as her fancy arises. Read this article not to enjoy an essay, nor to understand components of musical analysis, but to discover the object in the room. Admittedly, an object which I told you was important. Nonetheless, commit yourself to understanding this thing of beauty!

On a technical note, hyperlinks turn up frequently in the analysis. Some are essential, others are useful, and a few are humorous. They, along with the footnotes, are meant to interrupt the flow, lest the reader be lulled into a false sense of security. But you don’t have to click them all. Consider this article as a resource for examining the fugue, and an open site to be explored.

Part II: Introduction

Listen to Bach’s Prelude and Fugue in C-sharp Minor from the Well-Tempered Clavier, Book I. It is performed on piano by Sviatslav Richter, one of the best-regarded pianists of the twentieth century. Take special care with the fugue, which begins at 3:13. Sketch down your impressions. Convince yourself of your opinion.¹ Here are some preliminary questions to think about while listening:

1. What am I hearing in the fugue? What can I consider its elemental pieces of sound? How do these pieces combine? What structure do I hear?
2. How does it make me feel? Am I reminded of anything? Are there thoughts or emotions which are portrayed but not felt?
3. Does it speak to a specific historical era? Is it telling a story?

Different voices, or musical lines, are being played at the same time. A number of elementary melodies reappear throughout. These themes are recombined in various permutations, sometimes simultaneously in two or three different voices. Yet, the voices are not in conflict—they don’t sound dissonant in concert. So, the two main characteristics of fugue are exhibited: (1) counterpoint, the relationship between multiple voices that move with relative independence, but interact harmonically, and (2) imitation, the repetition of melodies in different voices at different times. These may seem like no brainers to anyone who listens to music these days—songs would be boring if all the instruments were playing the same thing at once, and feel random if no melodies were repeated!

Historically, these assumptions of music were not always made. The Gregorian chants of early medieval church music employed parallel motion; that is to say, the voices sang the same tune at different pitches. Furthermore, they imposed strict harmonic and rhythmic constraints, limiting freedom of composition. In contrast, polyphony, the musical texture of simultaneous melodically distinct voices, arose in the late middle ages. It origins are unclear—it may have evolved naturally from the Gregorian chants and progressed under the Avignon antipopes. Polyphony, along with harmony, was considered impious, in part because it reduced the audibility of words, elevating the music above its content. Pope John XXII banned it in 1322, but music’s progress could not be stop-gapped. Polyphony continued to develop through the Renaissance. It reached its apotheosis in 17th-18th century counterpoint, and in particular in the fugues of J. S. Bach.

Perhaps the best way to visualize polyphony is by considering a physical score. All notes played in a single instant of time form a chord. Notes played simultaneously are vertically aligned; so to think of music as a progression of chords is a vertical perspective. On the other hand, the notes in a melody are horizontally aligned; so to think of music as a sequence of possibly overlapping melodies is a horizontal perspective. Fugues are focused on the horizontal. Chord sequences are still present in the work, but subject to the constraint that the individual notes of a chord come from distinct melodies. This is why they’re hard to compose.

Fugues begin with a main theme that each voice initially states and repeats periodically throughout the work; but the content is not limited to such. Other themes or motifs are introduced to interact with the main theme, and each other. In a school fugue, these raw materials are manipulated and combined according to a set of rules that make explicit the allowable nexuses between voices—for example, the notion of contrary motion, that a high and low voice should move in opposite directions. Furthermore, a theme may be altered via four fundamental transformations. They are (1) inversion, which plays a theme upside down, (2) retrogradation, which plays it backwards in time, and (3) diminution and (4) augmentation, which speed it up and slow it down by a fixed factor, respectively.² The picture below depicts a musical theme, its retrograde, its inversion, and its retrograde-inversion:

From the description of school fugues, they sound like puzzles. A composer must construct themes that contrast melodically, and combine them in various ways, all the while ensuring that the harmony or chord sequence is pleasing. Strict obeisance to the rules, however, is pedagogical and was rarely employed by composers; for example, Bach’s fugues from the Well-Tempered Clavier, Books I and II occasionally “break the rules.” It is best not to think of fugue as a musical form, or set of rules, but rather as a musical texture—layering and unity resulting from counterpoint and imitation.

Part III: Listening

The C-sharp minor fugue from Das Wohltemperierte Klavier, Book I, is in five voices—shocking, given that humans only have two hands. Luckily the voices usually don’t appear all at once. Regardless, the real difficulties in playing this piece lie not in its physical demands, but mental ones. The ear is incapable of separating out five voices and understanding all of them simultaneously. One only hears the deafening incomprehensibility, which hints at extreme complexity and divine machination.

So listen to one of the voices while blocking out the others. It’s like talking to a friend at a loud party, for which we luckily do have the capacity.³ The highest voice is easiest to make out, as it is most piercing. The instructional video has a great audio-visual aid—it represents the five voices in five different colors. But it is an ear-crutch (as is a score to a lesser degree). So switch back to Richter's recording, and listen to the bass. The first five notes constitute the main theme, denoted T.

One of the most difficult aspects of isolating the theme is that it consists of very long notes. When T appears in one voice, the other voices usually play many intermediate notes. Thus, I hum the theme to emphasize it in my ear. Isolate the theme T at the following locations in the Richter:

1. At 3:13, 3:22, 3:33, 3:48, and 3:54, the entries of the five voices.
2. At 5:11 in the middle voice.
3. At 6:13 in the soprano.

The mental processes which separate voices and recognize repeated themes are normally unconscious. The goal of these exercises is to make that process conscious—to explicate the unity of the fugue by finding commonalities in its tapestry. There are two essential melodies other than T that have been woven through the fugue. One is the eighth-note “brook” motif M, introduced at 5:03 in the soprano. It slowly descends as it winds, hence the term “brook.” In the middle section of the fugue, from 5:03-8:03, M is nearly omnipresent. Just click around randomly within this time frame, and it’ll very likely be playing. M is an incessant forward-moving force. Here are few instances:

1. At 6:16 in the middle voice.
2. At 7:00, 7:10, and 7:16 in the middle, low, and middle voices.
3. At 5:19; it is the lowest voice playing at the time, but it’s the inversion of M. So instead of slowly descending, it’s slowly rising!

The other essential melody is the “tolling” subject S which first appears at 5:43. This subject may remind you of the tolling of church bells, though it also has an insistent character. To test your new ears, listen for S:

1. At 6:45 in a middle voice, and at 6:51 an octave higher.
2. From 7:57 and until around 8:30. How many times did you hear it?

As you gain familiarity with the themes, they’ll develop characteristics of their own, independent of where they land inside the score. Write down some impressions of T, M, and S. What is their character? Are they saying different things? Greater familiarity with the themes will ease in isolating and characterizing them. They begin to sound more like individual units. The Nokia fugue provides a perfect example: everyone can hear each instance of the theme very clearly.

Unfortunately, many listeners, including myself, are incapable of isolating two distinct voices simultaneously. The jump to two melodies is insurmountable; it is like hearing two conversations at once and trying to understand both. For the lowly like me, we must partially rely on gut feeling and partially rely on the score. Especially with a five-voice fugue! The listening exercises are unending…

If you had trouble with Part III, don’t hesitate to come back later, free of charge.

Part IV: Analysis

For this technical section, consider using Glenn Gould’s performance. Gould is a genius and known almost exclusively for his Bach interpretation. He plays slightly faster than Richter, but presents the themes with extreme clarity and independence. If you can read music, either download a score of the fugue with each voice written separately, or in condensed form. If you cannot read music, try using my simplified score (enlarged here) below for the following discussion (musical material may still be present in empty spaces). The numbers are measure markings:

The voices enter from lowest to highest, introducing the theme T

in measures 1, 4, 7, 12, and 14. Let’s name the voices the first, second, third, fourth, and fifth, going from lowest to highest. In general, the entries are on rather dissonant chords. The theme varies slightly each time it appears. For example, the third, fourth, and fifth voices enter with only a half note, not a whole note, and the fourth voice enters with first note higher than normal. Such alterations are to be expected in fugues, and are especially common with the first and last notes of a theme. In particular, the fifth note of the theme is least relevant and often excluded.

Examine the passage below, which is the continuation of the first voice in m. 4-7 after its statement of the theme:

Bach has hidden something in the above excerpt: Excluding the last note, it is an almost perfect palindrome! The pitches of the retrograde differ slightly from the original, but the lengths of the notes exactly match up.

Bach often hid musical symbols, messages, or puzzles within works. The primary examples are The Musical Offering and The Art of Fugue. The former is a series of canons and riddles with perfect palindromes, upside down clefs, secret voices, and other mysteries. The latter includes “mirror” fugues in which the score can be turned upside-down and retain musicality, and a fugue on Bach’s own name in musical tones (B-A-C-H).⁴ As proof of Bach’s stunning capacity to construct puzzles and see structure, examine the unbelievably concise notation he used to encode canons. And so when, despite all probability, the first thirteen notes after the theme form a palindrome, it is not a coincidence. But is it significant? We’ll see.

Onward! The continuation of the second voice after its statement of the theme is the same as the above, except that it truncates the first two notes, while the continuation of the third voice further truncates to the last four notes. Bach pares down the response to the theme T as new voices enter. The last four notes of the above excerpt form structure B—a long note followed by descending quarter-notes. It occurs frequently in the exposition, as seen on the simplified score. A similar structure C appears in the first voice in m. 17-18:

As with B, there are quarter-notes on the second, third, and fourth beats of C, but they rise instead of descend. In other words, C is an inversion of B, followed by an alteration of its first note. Finally, there is structure D, which is the last three descending quarter-notes of structure B. Differentiating between B, C, and D is unnecessary, as they all have D as their primary component, but I’ve distinguished them for the sticklers.

Many small structures in the fugue are imitated, but there is a reason I call attention to B, C, and D in particular. This fugue’s exposition is an exploration—the musical character of the fugue is not yet determined—many chords are unstable and dissonant and the pace is slow. Small structures arise only to fade away, as if in mist. Only the theme is constant. As B replicates itself and mutates into C and D, these strains undergo transformations, attempting to discover the Brook motif. The transition from m. 35 to m. 36 marks this discovery in the fifth voice:

Structure C appears in m. 35 as it did in its arrival at m. 17. But instead of continuing as in m. 18, it undergoes a diminution by a factor of 2. Only once this diminution has occurred is the beginning of the brook motif revealed.

Thus, the original continuation of the first voice in m. 4 morphs into the brook motif in m. 36 by truncation, then inversion, then diminution. Amazingly this initial counterpoint to the theme would not have been connected to M if Bach had not left the evolutionary traces⁵ behind in structures B, C, and D. Finally, to prove to us that we didn’t make it all up, he lets us see the diminution in our own eyes between m. 35 and m. 36! The fugue may begin in the murky and dissonant unknown, but from the primordial goo emerges clarity and structure.

With the entry of M,

the fugue enters a new section, one with a plenty of momentum and greater clarity of purpose. Eighth-notes are the smallest rhythmic unit appearing in the piece, and so provide a ceaseless impulse as they wind slowly downward. It’s Newton’s first Law of Physics—that objects in motion tend to stay in motion. In fact, M is practically always present until its last appearance in m. 93. With M introduced, no force can hold back the development of the fugue.

As mentioned previously, the brook motif consists uniformly of eighth notes; it does not capture the ear via melody or rhythm, but texture. Furthermore, M is diatonic, viz., it plays within the scale of the ambient key. As a result, M is not dissonant and reinforces the ambient harmony.⁶ Finally, M does not receive an exposition in the standard style of a fugue theme—it is not introduced in sequence by each of the voices. For these reasons, I call M a textural motif rather than a full-on subject. Yet it still plays a significant role.

Keep in mind that the theme T has been appearing frequently; any developments take place under its ever watchful eye. By comparison to other motifs, the long note values and pronounced quality of the theme are domineering. And in contrast to the diatonic M, the theme is chromatic; it contains notes adjacent to each other by a half-step and is much more dissonant. The contrast is particularly evident in m. 38-40, when M and T occupy the fourth and fifth voices.

The tolling subject S first arises in the third voice in m. 49:

The entries of S are in m. 49, m.52, m. 55, m. 57, and m. 60 in the third, fifth, first, fourth, and second voices, respectively. Try hearing all five entries in a single play; they’re at 1:19, 1:24, 1:28, 1:31, and 1:35. With the third and final piece of the puzzle introduced, T, M, and S join as perfect clockwork, interlocking in astoundingly satisfying and beautiful ways. As Cecil Gray writes in “The Forty-Eight Preludes and Fugues of J. S. Bach,”

This miracle once accomplished, the fugue simply makes itself. With three such themes even a second-rate composer could hardly fail to create a masterpiece if he took sufficient trouble; to describe what Bach makes of it would demand the invention of a superlative to the word 'masterpiece.’ One could write a whole book about this fugue alone without exhausting one part of its splendors; to do justice to the inspired ingenuity of its contrapuntal combinations here one would have to quote it in its entirety. One bar leads into another with such inevitability and such absolute continuity that it is difficult to cut out any single episode and present it in isolation; it is probably the most organically constructed piece of music in existence.

If you have time now, listen to the Samuil Feinberg’s recording. It’s didactic, but in the good way—his emphasis of the theme is unparalleled, and the tolling subject is well-treated too. Follow along, either with the real or simplified score, attempting to hear each instance of T and/or M and/or S. Though, usually at least two of T, M, and S are present, and very often all three. So don’t bite off more than you can chew! As Gray notes, they are perfectly suited to “contrapuntal combination.” Bach even showcases his virtuosity by placing all three voices in the right hand simultaneously, in m. 85-87. Clearly, Bach could continue indefinitely on T, M, and S, but he has given us enough and retires M in m. 94.

The transition to a new section is accomplished by the fact when m. 94 arrives, Bach has already begun a stretto—a musical sequence characterized by multiple voices stating the same subject in close succession. The key aspect of stretto is that the statements of the subject overlap. In other words, an imitating voice begins the subject before the previous voice has finished it. This can be chained multiply. Amazingly, Bach composes a stretto of the tolling subject with ten successively chained statements of the tolling subject S! From m. 92-101 they appear chronologically in voices 5, 4, 2, 3, 2, 3, 4, 2, 5, and 1.

Alone, such a feat is difficult to perform. Constructing a subject that works well when overlaid upon itself is tricky, but possible. After all, plenty of tunes are well-suited to round- or canon-style singing. But, in what can hardly be called anything less than an act of pure daredevilry, Bach inserts a second stretto on the theme T contained within the stretto on S! It occurs in m. 94-101 in voices 5, 4, 5, 1, and 2. Unfortunately, we are human; the chance of hearing and comprehending such complexity is remote.

With the main stretto complete, mini-stretti of S spin off as the structure the begins to decay. The music becomes languid; by m. 109, the tempo has slowed and the notes are long-valued. The ritardando and belabored motion seem to depict exhaustion. The pain-laden, highly dissonant chord in m. 112 is a mix of anguish and acceptance. It resolves into a final major chord in m. 115, which provides harmonic resolution, but the remembrance of dissonance lingers.

A switch to major at the end may be surprising to modern day listeners, but was common, perhaps even expected, in Bach’s time. Minor thirds were considered imperfect and pessimistic, thus inappropriate for the final chord. Hence the picardy third—instead of ending the work on the expected minor tonic chord, the minor third would be altered to a major third. Bach was particularly enamored with Picardy thirds at the time of his writing WTC, Book I; only one of the minor key movements ends in minor.⁷ Peter Kivy, a philosopher of music at Rutgers, states,

The picardy third is absolute music's happy ending. Furthermore, I hypothesize that in gaining this expressive property of happiness or contentment, the picardy third augmented its power as the perfect, most stable cadential chord, being both the most emotionally consonant chord, so to speak, as well as the most musically consonant.

Yet, hidden in this seemingly complete, perfect ending is a statement of both T and S. Exceptional is the presence of T in the fourth voice. The first four notes of T form an unresolved melody; they pose a harmonic question. The “question mark” of this question is the fourth note of the theme. Sometimes the fifth note of the theme resolves this question. Other times, only the first four notes of the theme appear, leading to modulation. What is surprising is that the fourth note of the theme is one of the five notes in the final chord of the piece (one note for each voice). Simply put, the theme is stated in an unresolved form at the very end of the fugue. Admittedly, it is almost inaudible to the ear. Perhaps this is an intellectual point on Bach’s part: Even a satisfying conclusion has some unresolved question contained therein.

This Bach fugue is structurally and harmonically atypical. There are no episodes, modulating passages in which the full statement of the theme is avoided in order that it may return triumphantly. Furthermore, Bach avoids the “stepping” sequential modulation that characterizes episodes, as satirized by Victor Borge. In “Analysis of J. S. Bach’s Forty-Eight Fugues,” Ebenezer Prout, 19th century music theorist, comments, “In spite of the comparatively small amount of modulation, this fugue is remarkable for its great variety combined with perfect unity.” Prout astutely notes the limited harmonic variation of the work: The theme’s appearances number 31, of which 14 are in the tonic of C-sharp minor. Bach doesn’t wander around, or fill time; he just recombines the raw materials in novel ways. Looking at the simplified score, one finds that five of the six possible vertical permutations of T, M, and S occur!

The “unity” of which Prout speaks comes in a couple forms. First, there is horizontal unity arising from the repetition of the themes T, M, and S. This unity of content makes it hard to distinguish two moments within the same section. Two distinct presentations of a theme are mentally overlaid onto a single event, like a wrinkle in time. Second, there is vertical unity—the very distinct themes meld into a cohesive, harmonic block of music. What were fragmented ideas become inseparable in the ear and the desire to isolate voices is overthrown by harmonic “satisfaction.”

To begin the transition towards more abstract analysis, let’s return to Cecil Gray’s grossly devotional praise:

It may be observed, in conclusion, that although it is written for five parts, the greater portion of the texture is in four and three: Not, it need hardly be said, because Bach found any difficulty in handling five parts (he could have handled twenty without so much as noticing it) as because he chooses to husband the full weight of his resources for crucial moments.

Part V: Interlude

What are those crucial moments? And from what source do they derive their power? Name the passage in the middle section that you find most striking. People often choose the lead-up and follow-through of measure 73. Why? To understand the climactic nature of m. 73, listen to the fugue, charting your emotional intensity with a pen or pencil on a lengthwise piece of blank paper. Don’t think about it too much; it should intensify, not clinicalize, your feelings. It’s almost impossible not to speed up as you go, so just wrap the graph around when you get to the edge. Here’s mine (measure markings were added later and are approximate):

For me, the beginning of m. 73 is moment when that which was predestined is revealed. It is the revelation that death is coming and that fate is inescapable. And at the same time it is the response to this revelation—a defiant looking-at and determined acceptance. It is an epic moment; from the theme in the bass emanates raw power.⁸ The first six eighth notes of m. 73 enhance this effect; they presage the theme by using the same four notes B#, C#, D#, E—as though a harbinger of its coming. If the brook motif provided momentum, it was exactly enough to get to m. 73. Once this turning point is reached, the fugue can fall to conclusion from its own weight.

Part VI: What about Jesus?

When one hear this fugue, it’s hard not to think of Christianity. The melodies are sanctified and solemn, the tone is tragic, the chords are pain-laden; even in a tiny practice room, the sound could hardly but take up the resonance of a grand cathedral. Combined with the suffering, the fateful climax, and the exhausted, pain-laden conclusion, it is reasonable to conjecture that this work is a depiction of the Passion of Christ. And depending on your faith in Christian symbolism, that may be the only reasonable conjecture. Bach was highly devout; he composed huge quantities of church music, including so-called “passions.” He is also known to have referenced the crucifixion using secret signs in musical works. Following Timothy A. Smith’s interactive Shockwave analysis of the fugue, partially reproduced below, Bach intentionally references the crucifixion, the wounds of Christ, and our lament of Christ’s death through musical symbols.

Upon closer examination of the first four notes of the theme, one finds a symmetry: T is its own retrograde inversion, or equivalently, has 180 degree rotational symmetry. Such symmetry could be a coincidence, on its own, but there are other examples of surprising symmetry in various melodies—for example, the palindromic qualities of the melody in m. 4-7 directly following the first statement of the theme. I asked whether this palindrome was significant. It is. Another particularly good example appears in the third voice in m. 102-104:

Chiasmus literally means to shape like the letter χ. It is used to describe the literary or rhetorical technique of reverse parallelism or palindrome. For example, Shakespeare’s Richard II employs ABBA chiasmus in “I wasted time, and now doth time waste me.” As χ is the first letter of Christ’s name and shaped like a cross, some Christian poets and musicians used chiasmus to reference the crucifixion. Smith claims that Bach employed the theme T for the same purpose. The evidence for Bach’s intentional inclusion of palindromes is incontrovertible. Whether or not Bach specifically thought of the mentioned melodies as chiasmus or a reference to the cross is less clear.

Bach was surely conscious of his evocation of anguish. The passages marked in yellow on the simplified score (m. 71-73 and m. 101-105 in the soprano) are examples of passus duriusculus. Literally translating to “harsh passage,” passus duriusculus, or chromatic fourth, consists of a chromatically descending scale whose first and last notes are separated by a perfect fourth. When appearing in the bass, such passages were called a lament, and German baroque composers used the chromatic fourth generally for lamentation. By placing these chromatic fourths in the soprano, Bach ensured they would be comprehended.

Let L denote the chromatic fourth. The first obvious example of L directly precedes the climax, but it actually makes a hidden appearance earlier. In the second voice in m. 41-44, the first notes of the inverted brook motif M are altered such that they form a chromatically rising fourth. There is no other reason for Bach to include L here, as the normal inversion of M would have been harmonically viable. Thus, L appears three times in the fugue; it’s third appearance coincides with the above palindrome. The convolution of these two symbols of crucifixion lends credence to the chiasmus hypothesis.

Smith believes that the five notes of T, the last five notes of L, and even the five voices all represent the five wounds of Christ. The decision to consider only the last five notes of L seems arbitrary, but he claims that lamenti did not need to be exactly six notes. Furthermore, in both cases, the first note of the L has unusual length compared to its last five notes. The coincidences do seem to build suspiciously—after all, this fugue’s theme is exceptional for being the shortest in all of the Well-Tempered Clavier. Furthermore, the exhausted and painful final passages, including the passus duriusculus, fit very well into an interpretation as the Passion of Christ. The highly dissonant chord in m. 112 is a mix of anguish and acceptance, and the resolution to a picardy third provides peace, salvation, and absolution.

But there’s no smoking gun… no Bach manuscript with the theme written in blood and a little Jesus doodle next to it.

In a fit of speculation, at least one scholar has already constructed an isomorphism between the fugue and specific events of the Passion. Vera Nosina claims a parallel to the Agony in the Garden, where Christ prayed in the Gethsemane garden that his “cup” of suffering pass, so long as it did not contradict God’s will. Like Smith, Nosina states that the theme symbolizes the cross, but she goes further, claiming the brook motif symbolizes the cup, and the tolling subject predetermination. The disappearance of the cup in the third section, followed the double stretto of the cross and predetermination, represents Christ’s acceptance of his suffering, i.e. “the cup.”

Such detailed interpretations may have solid ground in the symbolism of baroque German music, but to me, the most surprising fact is that from seemingly simple building blocks, Bach conveyed a Christian atmosphere; he managed to speak to the collective unconscious, to the residues of European culture and heritage; he communed with those murky under-forces, the tectonic plates of culture, with facility. Three hundred years later, the work still communicates an intelligible message. None of the themes in isolation bear Christ, so to speak; only in combination do they gain that association. By combining elements well, Bach has convinced us that these elements didn’t exist in the first place—a false gestalt effect!

Part VII: Emotional Analysis

The Passion perspective is well-formulated and well-evidenced. But it is a selfish interpretation—once caught in the Christian mode of analysis, escaping feels impossible. It is too engrossing, too convincing, too much about interpreting, too little about uncovering. What do the themes actually express? On this point, disagreement is inevitable. The “raw materials” are too quixotic—it is impossible to accurately derive an emotional or spiritual language of analysis for music. But one can try anyways. So let’s attempt the naïve: To decompose the themes into their rhythmic, melodic, and harmonic “components,” then patch together the emotional data:

The theme T consists of whole and half-notes. It is chromatic, occupies a small range of pitches, and is almost always based in a minor key. These qualities evoke sobriety (slow), pain (chromatic), and sadness (minor-key). To be heard over the other themes, the long note values of T necessitate an increase in its volume. In addition, T is the only theme to appear throughout. Thus, when juxtaposed against other themes, T exhibits dominance or power. Bach usually places T in the highest or lowest (most audible) voice to highlight it. Considering the above qualities, one may associate to the theme a weighty and sorrowful event.

The brook motif M consists of all eighth notes. It is diatonic and can be continued indefinitely. It has lots of little motion, and an overall downward motion. It is well-based in the ambient key, usually minor. It is textural, rarely layered, and plays an inferior aural role to the strong melodies S and T. These qualities evoke progress (faster-paced and directed), sadness (minor-key), and atmosphere (textural, diatonic, forgotten). And so perhaps M represents time, or some vehicle towards suffering.

The tolling subject S consists of mostly of quarter notes. It is the only melody to include repeated notes. It is harmonically neutral, appearing frequently in both major and minor. It is easily layered and put in stretto. These qualities show insistence (repeated notes and stretto) and objectivity (harmonic neutrality), which are perhaps best encapsulated by the notion of fate.

When themes interact, their distinct rhythmic profiles are as the second, minute, and hour hand—synchronized but ticking at different rates—hence the impression of clockwork. At the same time, their distinct melodic profiles are as different people speaking at once—hence the impression of incomprehensibility.

The words “weight,” “sorrow,” “time,” “fate,” “clockwork,” and “incomprehensibility” give an overall tone to the work; but what about our emotional seismographs? Why is m. 73 so climactic? First, there is a certain “satisfaction” derived from returning to the home key of C-sharp minor, especially after the long, chromatic passus duriusculus. Second, the physical placing of the themes highlights their qualities, with the slowest and most powerful at the bottom, and the fastest and most delicate at the top. Third, all three voices are relatively low, adding significance to the moment. Fourth, the key words above come into sharp focus as the various qualities of the themes are highlighted. That still doesn’t really explain the climax—why a chill runs through the spine. But nothing will! Perhaps emotional responses to music are inherently inexplicable.

Part VIII: Performances

With so much highfalutin language, it is easy to ignore the conflict between theoretical “perfection” and the physical limitations or conditions of playing a piece. Each pianist must choose which aspects of the work should be emphasized.

Tatiana Nikolayeva embraces dissonances more than the other performances we’ve heard; she doesn’t hide a voice when it plays an unusual note. She includes lots of rubato, small-scale slowing down and speeding up. For example, she consistently slows slightly at the beginning of the tolling subject. Her phrases build pressure then explode outward in a tumble of eighth notes. Her fingertips carry weight, and the dynamics, or loudness of notes, change quickly. The style is romantic, which reflects her relationship to the music—total absorption. Her performance highlights the fugue’s emotional narrative.

Gould’s genius is particularly suited to Bach; his polyphony is excellent. Amongst other eccentricities, he hums as he plays. One gets the impression that he actually comprehends all the voices at once! Later in life, he sequestered himself in a cabin in Canada, hermit-style, and played piano for himself. He interacts with Bach’s music through expression and conversation, rather than submission. In the case of BWV 849, Gould’s performance is rare—one that few would dare conceive. The tempo is brisk, and the tone is comparatively light. This does not mean Gould is frivolous, though his performance is particularly ill-suited to “religious” interpretation. At the same time, there are traditional aspects to the performance; the dynamics and tempo vary little. His precision highlights Bach’s contrapuntal craftsmanship.

Richter, on the other hand, plays very heavily. A passionate, powerhouse Russian pianist, he ironically viewed himself as totally subservient to the score and the intentions of the composer. In his own words,

The interpreter is really an executant, carrying out the composer's intentions to the letter. He doesn't add anything that isn't already in the work. If he is talented, he allows us to glimpse the truth of the work that is in itself a thing of genius and that is reflected in him. He shouldn't dominate the music, but should dissolve into it.

Richter plays the fugue slowly and clearly, particularly emphasizing the theme. Richter’s style has some romantic aspects, such as rubato and wide dynamic variation, but remains dignified, ethereal, and spiritual. His performance is extremely serious, highlighting the sobriety, sanctity, and suffering.

Part IX: Language and History

Because of his special seat in the narrative of classical music, a lot of speculation goes into the analysis of Bach works. He has gained semi-occult following. Some musicologists, including Smith, overextend—they venture into Bach numerology. Reminiscent of Kabalistic gematria, these scholars claim that Bach has a signature in the number

14 = 2 (B) + 1 (A) + 3 (C) + 8 (H).

Some of the connections are far-fetched, others less so. For example, the fugue with the theme B-A-C-H in The Art of Fugue is called Contrapunctus XIV—perhaps the best evidence. But Smith also “finds” the B-A-C-H motif and appearances of the numbers 14 and 41 in the C-sharp minor fugue! Bach’s fondness for puzzles encourages those who tend toward conspiracy. Though religious symbolism and alphabet numerology were common in Bach’s time, there is no evidence to support the claim that he was communicating in a hidden, unspoken language. Yet, in some sense, he was. Like medieval religious painting or alchemy, Bach was surely representing concepts through a system of signs to which we no longer have access. The flaw of the numerologists is that they think they can uncover this language through some art. But the language is too nebulous, too close to “musical experience in the context of a culture,” to ever be recovered.

The Bach numerologists are not alone in their desire to “speak the language.” There are also the Bach traditionalists, who prefer not to play on instruments invented after Bach’s time—in particular, the piano. The Well-Tempered Clavier was written for harpsichord (or clavichord or organ).

Traditionalists occasionally improvise, adding various trills and frills, as was common in Baroque times. They may apply Bach scholarship to their performances, e.g. by playing in a specifically Passion style, or by examining Bach’s biography, including his personal sorrow. One point about which they argue interminably is how to tune the keyboard…

The argument has arisen because “well-tempered” or wohltemperierte is a poorly understood term. Many believe it means the tuning used on modern pianos, called equal temperament, in which the ratio of the frequencies of two adjacent notes is constant. In other words, the frequencies form a geometric series. Various others have proposed different tuning systems that Bach possibly intended. Of course the mystics get their word in, too, claiming that the squiggles and loop-de-loops on the front cover of the Well-Tempered Clavier secretly indicate which type of tuning was meant. In any case, as essentially the first collection of keyboard pieces written in all 24 keys, the WTC established that there was a tuning system in which all keys sounded in tune.

Regarding tuning, we’re once more faced with a question of language—can one possibly play what Bach intended, and does it matter? As we reinterpret Bach, we create our own truths about his music and illuminate the unconscious forces behind it, but we also lose our window into the past. Long-standing pedagogical traditions, such as music, allow us the occasional anachronistic experience. In complete ignorance of the history of music, Bach’s works would, of course, cease to be great. Luckily, the torch was carried through the generations.

Composers after Bach had high praise for him, though their quotes do not couch Bach as a revolutionary or source of change, per se. Rather, Bach was a pinnacle, a genius to be emulated. His music was most literate and perfect in its own form (counterpoint) and most comprehensive. Despite the ever-present small group of great composers who revered Bach, he was mostly forgotten by the 19th century. Only with the arrival of the romantic era was Bach’s monumental figure unearthed for public display.

Part X: Comments on Comments

Below is Bach’s seal, a favorite plaything for the numerologists, followed by a number of YouTube comments. If you have something to say about BWV 849, please comment! Can you outdo the competition?

On Richter:

When I hear Richter playing Bach I feel that the world stops and that there is no time, unecessary sound. Richter playing Bach feels to me like the whole universe is involved and that there is a strong sense of completeness and grandness and majestical yet not 'grandiosso' .

An often up-voted comment, with sixteen “likes.”

Sviatoslav Richter is my favourite interpreter. The freedom that he puts in his hands, takes my soul away when I hear him playing the piano. His playing is human, sweet, instinctive, not academic and cold like others interpreters (Glen Gould). Personally, I hate him, as pianist and person.

The “and person” got a few people’s feathers ruffed up.

Even though he's playing on an inferior piano it is totally sublime, beautiful, dignified, noble, other-wordly, holy, ecstatic, serene, heart-melting... words fail me.

This person must love wasting everybody’s time with long lists of adjectives followed by claims of wordlessness. Given the implications of the term “inferior piano,” this commenter comes off as pretty repulsive.

the greatest pianist it has been my honor to see--and he did not sell out for "freedom" (i.e. lts of money--considering his history that is remarkable

Weirdly political comment = attention-baiting.

my name is svitoslav to

Awww!

zzzzzzzzz....the prelude ok, but honestly, I was lulled into sleep literally by the fugue.

very ignorant ;D u want fast up beats? go watch 50 cents nigger! xD

YouTube hid both of these comments because they received too many negative votes. The first comment got viciously attacked by pretty much everyone including the video poster. The resulting defense was that Richter’s playing is too slow while Gould’s is more lively. The response was that Richter viewed himself as the executant of the composer’s intentions, so if the poster didn’t like it he should “take it up with Bach’s ghost.” A long series of comments followed, comparing how much Gould or Richter subordinated their egos to the will of the composer.

The most passionate performance of this fugue ever! One gets the impession that he really suffers when the nails literaly enter the body of Christ in the upper voice.
Sublime!

Too much coffee?

On Gould:

this is soooo goooooou(l)d.. :D

Hopefully a nine-year-old wrote this. That would be really cute.

the first couple of times i heard this fugue i was, quite honestly, hoping for it to be pretty. the subjects are not bitter or ugly, and they converge at points quite nicely with each other. of course, it never turned out the way i was hoping it would. but then i realized something. i realized that this song isn't a lullaby or a gentle minuet. its a tremendously logical, perfect formation of everlasting notes symbolizing the great rationality of our universe and all of its glory.

That is a really specific “thing to realize.” But these comments have got me thinking… this piece does remind me of the universe.

This composition is racially superior to those of Vivaldi.

Composing a fugue is a delicate procedure... much like pissing.

Standard YouTube fare.

I love him! He plays so well! Every time he touches the piano, it is simply "Fantastic"

Nice use of quotation marks.

I don't like Gould's interpretation of this piece. I don't think it does justice to Bach's music and I think that Gould is generally overestimated.

This is a common sentiment. Most YouTube users prefer Richter’s more emotional performance to Gould’s carefully measured one.

I would say that Debussy marks the beginning of modern music, and Bach defined music. Before the Baroque period, it was mostly a capella church songs harmonized in 4ths.

I'm guessing you're trying to impress with second hand, or made-up knowledge.

The response, while likely accurate, was down-voted so much it doesn’t appear and you have to click the “Show” button.

MATHEMATICs!

:)

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¹ May it weather the analysis.

² Mathematically, one could imagine the melody as a function f(t). Then the inversion is -f(t), the retrogradation is f(-t), the diminution is f(2t), and the augmentation is f(t/2).

³ If you are very motivated, go here to download the BWV 849 fugue midi file. Start GarageBand, drag the file in, and turn up the volume completely on a single track.

⁴ Germans used B for B-flat and H for B-natural.

⁵ Fossil record?

⁶ The easy way to see whether something is diatonic is if it is written with few sharps or naturals.

⁷ Twenty years later, when he wrote Book II, fourteen of the twenty-four minor movements end without a picardy third.

⁸ The modern piano has a much wider range than old harpsichords and keyboards. In fact, the first two notes of the theme here were the two lowest notes on Bach’s keyboard.

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