Evolving Pairs: The Sonatas and Partitas for Violin by Johann Sebastian Bach
Notes by Nicholas Kitchen written in connection with his presentation of the cycle for The Cambridge Society for Early Music, January, 2011

How many da capo fugues do you know of in music, where the entire first section of the fugue is repeated as its conclusion? How many Suites or Partitas do you know of that have 8 movements organized as exact doubled pairs: Allemande - Double; Corrente - Double, etc.? How many times do you see Bach opening two sonatas (Sonatas No. 1 and 2) with movements using almost exactly the same type of ornamentation? How many groups of pieces do you see organized as Sonata-Partita-Sonata-Partita-Sonata-Partita with numbers putting them in strict order? How many Ciaconnas or Passacaglias do you know that organize their opening theme in a repeating pair? These are just a few of the remarkable features of Bach's Sonatas and Partitas for Solo Violin, all of them exhibiting "pairing" in their fundamental structure.

Every advanced violinist is compelled to take a journey of discovery with these pieces. I found as I spent more time with the entire set that I continued to discover features that pointed to a beautiful organization of the entire cycle and almost an obsession with organizing music by pairs, all part of an enormous progression of descent into darkness and despair followed an ascent into brightness and joy.

Let's look at some of the features of these works.

In terms of the types of pieces, 3 "church" sonatas with four movements (grand slow movement, animated Fugue, lyrical slow movement and brilliant fast movement) alternate with 3 Partitas that each have a unique architecture in their movement structure. This makes three pairs: Sonata, Partita; Sonata, Partita; Sonata, Partita.

Let's start by looking at the largest feature: the pitch centers. In a set of works for solo violin it would be logical to use the pitch centers (keys) of the open strings of the violin, G-D-A-E. Bach does this, and includes two other keys, C major (a not unusual key for the violin) and B minor (a rather unusual key for the violin). The choice of these particular keys seems purposeful, especially when you look at the pattern they create:

G - B - A - D - C - E (For anyone who doesn't read or play music, the musical scale which repeats a little over 7 times on a piano keyboard goes A-B-C-D-E-F-G and then starts again at A, so the "G" in the pattern at the beginning of this line is just one note lower in pitch than the "A" that is the third entry)

These pitch centers very nicely start at the bottom of the violin (G) and end at the top (E), but let's look at the interval relationships between these pitch centers counting the number of half steps (the closest notes on the piano, like a black key and the white key next to it).

G to B = up 4 half-steps; B to A = down 2 half-steps; A to D = up 5 half-steps; D to C = down 2 half-steps; C to E = up 4 half-steps

This makes 4 - 2 - 5 - 2 - 4, a palindrome of interval distances.

Looked at another way, the pitches form a spiral zig-zag as two trios: low high middle (G,B,A) - larger leap - middle low high (D,C,E).

A spiral – radially symmetrical around the large leap in the middle. So, in the largest architectural view of the pitch centers of the cycle we see a spiral pattern of symmetry. Let's remember "spiral zig-zag" as we look at more details.

The journey through the cycle begins with the Sonata No. 1 in G minor. The G minor Adagio and Fugue I would characterize as based on harmonic circles. There is a clear harmonic center which moves to agonizing dissonances which are soon resolved, creating a sequence of emotionally rich circles of tension and release. The stately chord progression of the Adagio follows this pattern but also outlines a large arc which is a "spiral zig-zag". In the Adagio there are clear cadences where our ear is drawn to pitch centers. The pattern created by these pitch centers and the progression which connects them is radially symmetrical. The movements starts with the center on the home pitch (G). It progresses to a center 5 notes higher than home pitch (D); then there is a middle section with a notable stop with a fermata on the most symmetrical chord in music - the diminished seventh chord where every interval is three half steps apart. Resuming motion from this fermata, the last section starts on a center 5 notes lower than home pitch (C) and progresses back to center on the home pitch (G). This would already represent a remarkably symmetrical pattern but it is more organized still. The two outer sections not only cover the same distance but follow strictly the same chord progression, the first going out from home pitch, the second concluding at the home pitch center. A spiral zig-zag. It is important to note that though the chord progression and pacing is strictly parallel, Bach ornaments this structure with elaborate variety. The strictness of the symmetry is only the form in the background.

What I find is that the Sonata No. 1 in G minor and the Sonata No. 2 in A minor form an "evolving pair," where compelling symmetries and similarities are perceived alongside meaningful differences. The first striking similarity is the use of similar florid ornamentation for the the first movements of each of these Sonatas. A further parallel is that the Grave, which starts Sonata No. 2 in A minor, is not quite as strict but basically follows a pattern similar to the harmonic zig-zag we saw in the G minor Adagio (A progressing to E; middle section; D progressing back to A). What is also striking is the "pairing" of the rhythmic profiles of their fugue themes. The fugue themes of Sonata no. 1 and Sonata No. 2 both fill the rhythmic mold of four quarter notes in the following way:

(silent downbeat) - and - 2 - and - 3 - and - 4 - and - 1, with "1" being an arrival and all of the other numbers leading towards it.

Bach g and a fugue theme

In the Sonata No. 1, the quick notes are in the second half of the first measure (the "and" before beat 4). In the A minor, they are in the first half of the measure (the "and " before beat 2). So the rhythmic order is switched. The G minor features a scale which descends in it's second half (D, C, Bb); the A minor ascends in it's second half (A, B, C). As you see, these pitches are inversions of each other in direction. So, we are seeing a checkerboard symmetry: two fugue themes with the same rhythmic span (4 quarter notes) with switched rhythmic orders, with inverted overall direction. Now, let's look at what is NOT symmetrical between the G minor and A minor Sonata. The G minor Sonata, as mentioned, seems to work in circles of dissonance and resolution. The A minor Sonata, on the other hand, seems to set itself up around long scales. "Scales" in music are like "steps" in a set of stairs - the word in fact comes from "stairs" in Italian "le scale." So, in the A minor Sonata we move through long scales, as if walking with our fingers up and down the keyboard of a piano. This gives a very different emotional framework to the piece, making it more "wandering." Indeed, many students find this the most difficult fugue to memorize, and I can understand why! The A minor Grave and Fuga construct themselves around these scales, employing everything from running ornamental scales to powerful mountain-climbing sequences of consecutive chords, each stepping to the next note. And we are about to see how this "pair" of fugues "evolves" into the Fugue of Sonata No. 3 in C.

On the way to looking at the relationship of the three fugues, let's consider the Adagio of the C major, the Sonata No. 3. This Adagio does not in any way resemble either member of the pair of the Adagio of the G minor or the Grave of the A minor. Where in the first two there is constant motion through elaborate ornamentation of practically every progression from one chord to another, in the C major Adagio the texture has an eloquent simplicity, with ornaments used at only a few choice junctures. Like so much of the music of the Sonatas and Partitas, the C major Adagio is profoundly moving, and it makes a suitably grand introduction to its fugue. Now, let's look at this fugue. Here we can see the fantastic connection between the G minor, A minor and C major fugues. Now written in half notes the C major Fugue has the rhythmic profile (silent downbeat) - 2 - 3 - and - 4 - and - 1, 2 - and - 3 - and - 4 - and 1, with a significant half-stop in the exact middle of the theme.

Bach g, a and C fugue themes

As you can see, this is quite literally putting together the rhythmic profile of the G minor fugue and the A minor fugue and combining them into a pair. You can also see that the significant three-note scales of the two component themes are still the main building blocks, but in the C major fugue theme they are allowed to take on a much more complex pattern. And if symmetry and pairing does not seem to be at the heart of the ideas of this fugue, think again! This fugue has the VERY unusual feature of being a "da capo" (this instruction means return "to the head") fugue, meaning that the long first section of the fugue is repeated in its entirety as the last section of the fugue – almost like two symmetrical wings of a grand building. Also, there is pairing and symmetry in the structure of the sections in between the first statement and its "da capo". Right after the opening section, there is a fantasy section with running notes. This leads to a highly elaborate fugal section based on closely spaced "paired" canons of the fugue theme (canons are what we create when we sing "Row, row, row your boat"). This section has a wide range of emotions and exploits the half-stop (see above) in the main theme for stunning register and texture changes. Then comes another fantasy section of running notes finishing with a massive pedal point elaboration, which prepares a truly rare and electrifying "il riverso" section where the fugue theme is turned precisely upside-down. This section allows the theme to be musically "dismembered" in a chaotic sequence of partial themes before it comes together into a massive complete theme, rising in reverse from the bottom of the instrument. After this comes another fantasy section with a nearly exact repeat of the massive pedal point elaboration (another pair!), and this propels us to the large (da capo) repetition of the main first section.

We have skipped ahead to look at the relationships existing among the three Sonatas. During this concert we will be observing the very famous and beautiful primary manuscript of the Sonatas and Partitas. When doing this we will follow Bach's order and will, after the Sonata No.1, go to the Partita No. 1

So, let's look at the Partita No. 1, the B minor Partita. Personally, I find it quite conceivable that this Partita was created with its features systematically planned prior to composition, so that they would conform to a larger idea, namely the idea of pairs - in this case "Doubles". Again, I ask, where else in music do you have four (I know instances of one, but not four) pairs of movements which are all twins of each other? Each pair has exactly the same structure of meter and harmony for both the main movement and its "Double". The main movement has a simple texture and its "Double" is floridly ornamented. Consider, also, all this being put in a key which is not particularly attractive on the violin, but which satisfies the symmetrical key pattern mentioned above (G-B-A-D-C-E). Further, consider that the 8 movements have a symmetry of their meters. The first and fourth pair, movements 1,2,7,8, are in even meters (four beats in one bar). The second and third pair, movements 3,4,5,6, are in triple meters (three beats in one bar). Further, there is an element of radial symmetry concerning tempo. The Sarabande (movement 5) is undoubtedly the slowest of the 8 movements, and the Double of the Corrente (movement 4) is actually marked Presto, so it is definitely the fastest. Violinists often feel that there needs to be a connection between the tempo of each main movement and its double, but in the first and second movements, it is difficult to feel the double exactly as slow as the Allemande – it is natural for it to be a little faster. So if we let this happen subtly, then we get a stately Allemande, a slightly faster double, a faster Corrente and very fast Presto Double. Then we have the slowest motion in the Sarabande, again a natural increase in flow in its Double, a robust Tempo di Borea with again an attractively faster Double. Here, once again, is our "zig-zag spiral" symmetry: medium, faster, faster, fastest; slowest, faster, faster, faster. What a remarkable rhyme with the harmonic structural pattern of the first movements of Sonatas No. 1 and No. 2 and the radial symmetry of the keys of the set of six!

Partita No. 1 and Partita No. 2 also are symmetrical with each other in some other interesting ways, another "evolving pair." Both have four dance movements, Allemande, Corrente, Sarabande and Tempo di Borea (Partita 1) or Giga (Partita 2). In the Partita No. 1 , the four movements are balanced by their Doubles. In the Partita No. 2, the counterbalance is the massive Ciaconna, the center of gravity for the whole cycle of Sonatas and Partitas.

Now, we have looked at the home pitch center pattern of the cycle of six works and seen its symmetry. What about the mode of the key centers: major and minor (happy and sad, to put it very simply)? The keys of the cycle of six are organized in a striking pattern: minor, minor, minor, minor, major, major. And this pattern has as its turning point the Ciaconna, one of the centers of gravity of not only the Sonatas and Partitas, but of the entire repertoire of the violin. On a personal note, I remember my first encounter with the Ciaconna on a set of records with Henryk Szering's playing of the entire cycle. I fell so in love with the Ciaconna that I wore out that track of the LP. You can see the damaged ring of the LP even at a distance! What Bach seems to set up for the cycle of six is a descent through four works in minor keys that reaches its extreme in the Ciaconna. From this point it turns around and ascends in mood through the two works in the major mode. This ascent ends with the third Partita, which is as joyous a music as one could imagine.

So, what is going on in this magnificent Ciaconna? What are some of the features that make it so impressive? I recall a wonderful quote of Johannes Brahms saying roughly "if I could have composed the Ciaconna, I would have lost my mind." A unique situation in this concert series is that we will spend a little time with a quite puzzling manuscript of the Sonatas and Partitas, the manuscript of organist Johann Peter Kellner. Kellner had direct contact with Bach, and Kellner and his students copied many works of Bach, including keyboard works as well as the Cello Suites and the Sonatas and Partitas for Violin. Kellner's 1726 version of the Sonatas and Partitas is quite different from the 1720 manuscript that we know, and in particular presents us with a totally different version of the Ciaconna. I plan to perform the Kellner version of the Ciaconna alongside the one we know, and we will have the privilege of considering an alternate version of a great masterwork.

The Bach Ciaconna is built on a basic theme or bass line used to great emotional effect by many composers in Passacaglias and Ciaconnas. The bass starts on the home note, descends one tone, descends one more tone which is chromatically altered to the very evocative flattened sixth note of the scale, then descends one more to establish a dominant chord which propels us back to the home tone. The Bach Ciaconna modifies and augments this bass pattern in such a variety of ways that at first it is hard to see the basic pattern, but in many variations it is quite easily recognized. This pattern takes four measures to cover the four tones, and in the case of the Bach Ciaconna there is the notable choice to combine two 4-bar cycles into a single "paired" 8-bar theme. The Ciaconna we know goes through its four-note, four-bar cycle 64 times. 64 is a very evocative number. Now, we have seen pairs show up in nearly every place we look in the Sonatas and Partitas. So, how does the number 2 relate to 64? Might the relationship even involve the number 6? Well, 64 = 2 x 2 x 2 x 2 x 2 x 2 = 2 to the 6th power. Hm! The very noticeable Minor, Major and Minor sections of the Ciaconna (Minore, Maggiore and Minore) correspond very closely in size to the last three stages of these multiplications: 8, 16 and 32. The order in which they are encountered in the music is 32,16 and 8 (to be exact 31,17 and 8). But these numbers only add up to 56(!). The Final 8 cycles are created by four double-cycle (paired!) themes which act as pillars organizing the whole large structure. The four pillars are (1) the opening of the piece, (2) the opening of the Maggiore section, (3) the opening of the return of Minore, and (4) the concluding statement of the piece. These four pillar statements echo the choice of four as the number of main movements for the rest of this partita and 4 movements for the basis of the Partita No. 1. Well, what about the Kellner? In this version there are only two pillar pairs, at the beginning and end of the Ciaconna, and the whole work has 40 cycles instead of 64. And, instead of the relationships 32, 16 and 8, the relationships are 20, 9 and 7 with a pillar pair at the opening and a pillar pair at the end. Interestingly, the Kellner version seems to organize itself around subdivisions of four: two sections minor, one major, and one minor. In the Kellner, not only are the internal pillar phrases not there, but the main arpeggiando section which has always been such a charismatic part of the work, is not there at all. In addition, the sustained rising section at the end of the Maggiore that concludes with a second arpeggiando section is not there. It is very difficult to determine the origin of the Kellner version. Was it a draft version by Bach himself which would mean the date 1720 on the title page of the finished product has a different meaning? Or did Kellner take liberties in his copying? Kellner was deeply devoted to J. S. Bach and his music and had first-hand knowledge of Bach's music-making. If he took liberties in copying, was it based on an understood alternative logic? I don't think we can have a real answer to these questions. So let us just consider what Kellner left behind and let it help us understand better the final form that Bach created. The one element of Kellner's musicianship that I find disturbing is frequent careless mistakes. It makes us doubt Kellner, but also makes us appreciate even more the painstaking accuracy of what Bach himself left behind. I think numbers were very important to Bach and do give the architecture of the Ciaconna much of its impact, but what is breathtaking is the way Bach navigated with such control of proportion in a texture which is basically a stream-of-consciousness improvisation, all the while delving without artifice into a huge range of emotions.

So, you are Johann Sebastian Bach and you have created the Ciaconna and the Sonata No. 3 fugue, two stunning monuments to what can be done in music in general and two gigantic leaps of faith in what can be done with a solo violin. What is the structure that should hold these creations?

The Kellner manuscript shows one idea for a large structure. The Sonatas are in order, no. 1, 2, and 3. The Partitas match each other in that they each have three movements. The E major (Partita No. 3) is first and has Preludio, Gavotte en rondeaux and the first Menuet. The D minor (Partita No. 2) finishes the whole set with the Sarabande, Giga and Ciaconna. And the B minor Partita (Partita No. 1) is not there at all! The Kellner order puts the Adagio and Fugue of the Sonata No. 3 at the center of the cycle with 8 movements before it, and 8 movements after it. This makes the Ciaconna the conclusion of the entire set, and makes the Kellner cycle an arc of moods. This arc starts with the dark Sonata No. 1, ascends to the midpoint of the C major fugue and the exuberant music of the last movement of the Sonata No. 3 immediately followed by the Preludio of the E major Partita. The arc then descends to finish in the darkness of the Ciaconna. How fascinating this alternative logic of the Kellner manuscript is! And what a fresh perspective it gives us on the powerful solution Bach creates when he makes the structure we are familiar with. What Bach has done in the cycle we know is to create an enormous bridge event that straddles the turn around from the minor mode to the major mode. In the finished manuscript, there is one page where the last few lines of the Ciaconna finish in their stately three quarter time, and on the same page, almost like a continuation, begins the Adagio of the Sonata No. 3, also in a stately 3/4. This Adagio of the Sonata No. 3 becomes a fulcrum with the Ciaconna on one side and the Sonata No. 3 fugue on the other. And there is one more connection that I find truly stunning in the joining of pairs. The symmetry of the pitch directions of the Sonata No. 1 and Sonata No. 2 fugues we have already pointed out: (D-C-Bb) paired with (A-B-C). But now look at the fundamental bass line of the Ciaconna (D-C-Bb-A) and look at it compared to the downbeat pitches of the theme of the Sonata No. 3 fugue (A-G-F-E). The intervals are identical! The Sonata No. 3 fugue even refers to the inversion of the two previous fugues by explicitly creating "il riverso" (B-C-D-E). I think you can see how there seems to be endless layers to the beautiful balances and symmetries in the Sonatas and Partitas.

So, after the C major fugue, the ascent continues. The touching Largo of Sonata No. 3 passes into the joyous Allegro assai in 3/4 time, which in turn flows into another joyous 3/4 time movement, the Preludio of the Partita No. 3. This last work in the set of six now lets go of the groups of four movements and creates a Partita more like other Partitas – six movements (counting the pair of Menuets as one movement): Preludio, Loure, Gavotte en rondeaux (where, I might add, there are 6 repetitions of the Gavotte theme), the paired Minuets, a Bouree and finally a small Gigue. This Gigue provides us with a peaceful and smiling conclusion to the epic journey of the Sonatas and Partitas of Johann Sebastian Bach. What a grand creation! What a privilege to learn it, and what a privilege to enjoy it. Bon voyage!

Nicholas Kitchen, Boston, Mass. 2011-01-16