Seeing Double.

Double is a French term for a technique of variation where a movement—typically from a dance suite (called the simple)—is followed by a single variation (called the double). The two movements share the same harmonic progression, and the rhythmic values of the double are often halved. This Double, from Bach’s Violin Partita in B Minor (BWV 1002), is paired with the Sarabande that precedes it.

For the most part Bach generally avoided variation forms, though the times he did employ them resulted in some of his most celebrated compositions, such as the Goldberg VariationsPassacaglia in C Minor, and Chaconne in D Minor, etc. There are others, to be sure, but sectional and continuous variations account for only a small percentage of Bach’s output. The doubles from the first Partita, apart from being transcendent and sublime pieces in their own right, are especially valuable because they illustrate a second interpretation of the same harmonic material. An analogy might be made to a classical poet composing two poems, both of the same length and about the same subject or theme, but in two contrasting metres. Musically, being able to compare a simple with its double can illuminate both pieces, and reveal ways in which Bach went about solving particular musical problems (i.e. not just contrapuntal and voice-leading issues, but the restrictions inherent in writing for solo instruments, etc.).

Consider the restrictions involved with this piece: it’s for a solo instrument, it needs to be essentially melodic, and it must also express a sense of harmonic progression (i.e. provide forward “motion”), but there aren’t any harmonic intervals (i.e. no multi-stops). Too many triadic outlines and there’s little sense of melody. Too many scalar passages and there’s little sense of harmony. Making things even more challenging is the fact that rhythmically, Bach chose a continuous stream of eighth notes; with no variety of rhythm it means that contrasts can only be achieved through the dimension of pitch. Combine all of that with the harmonic and voice-leading conventions of Bach’s time, and it makes for a very small compositional nutshell. But despite all of this (and like Hamlet), Bach could still “count himself king of infinite space.”

Partita I in B Minor for Solo Violin by J.S. Bach, mm. 1-8.

The large leaps are the first clue about the texture: The D on b. 2 of m. 2 seems to be picked up again on b. 3, then continues stepwise through C-sharp to B on the downbeat of m. 3. Similarly, the higher E on b. 2 of m. 3 continues through D, then C-sharp through B on b. 3, leading to A-sharp on the downbeat of m. 4. There is a clear stepwise descent from D in m. 5 b. 1 to A in m. 6 b. 1.

There are triadic figures that very clearly express the harmony, such as m. 1 b. 1, m. 2 b. 2, and m. 4 b. 1, etc. But figures such as those on b. 2 and 3 of m. 5 are less clear. It turns out that the B on b. 2 of m. 5 is a re-articulated suspension from the previous beat, and the same goes for the A on the following beat. It’s worth noting that when you only have three notes per beat and no harmonic intervals at your disposal, expressing suspensions in that manner is a risky business—but it makes for one of the many contrasts Bach was able to achieve through pitch and interval alone.

Seeing Voices

I should state at the beginning that there are several, equally valid ways to interpret the individual voices. The version below is rendered in two voices, but an argument can be made for three in places. For example, in m. 1, the first pitch (B) could be considered the lowest voice, followed by D as a middle voice, then F-sharp as the highest voice; both the B and D are prolonged through the next beat (as iv4/3), etc. The same with m. 5, b. 1—the F-sharp could be considered an inner voice, but for the scope of this post I’ve rendered similar figures as belonging to the same voice:

An interesting situation arises in mm. 3-4. In m. 3 the lower voice progresses from E to E-sharp; an applied chord that tonicizes the arrival to F-sharp (the dominant). However in the score, the downbeat of m. 4 is an A-sharp. The E-sharp does resolve to F-sharp, but as Bach was wont to do, he reaches over the upper voice and displaces it an octave higher; in the expanded version I placed parentheses around the lower F-sharp to indicate it is an implied tone. This lower F-sharp also helps to explain the A-sharp to G in the following beat. Usually, melodic augmented 2nds are avoided, though they sometimes appear in a texture such as this where there might not be enough space to both avoid them and still arrive at the next desired pitch. But with the F-sharp resolved in its obligatory register, the G that follows is just an upper-neighbor, while the A-sharp above it is prolonged through beats 2 and 3.

Also, in m. 6, the low A is prolonged across beats 1 and 2, then is displaced by the A-sharp on b. 3 (though it is in a different register). The voice-leading there is an echo of the lower voice in m. 3—the E, to E-sharp, then to F-sharp—but with octave displacement.

Taking things further, this rhythmic reduction verticalizes the chord tones:

Now, compare that reduction to the first eight measures of the score to the Sarabande that precedes it, and notice how similar they are:

I’ve listened to many performances of the Suites, Partitas, and Sonatas on as many different instruments. While a great deal of attention goes into the more physically challenging pieces (and rightly so), I’m often struck by some of the opportunities that are missed with pieces such as this Double. It’s understandable to think that there is less here than there is in the Chaconne, but exploring what lies beneath a line like this only informs the Chaconne, and all the others as well.

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8 Responses to Seeing Double.

  1. Very interesting and well-done. I once wrote about the possibility of combining these dances and their doubles into duets, and showed that it works quite well with the Courante from this partita:

    Someone somwhere (can’t remember where) commented that she used to do this with her teacher with some of these doubles.

    I also would prefer (at least sometimes) to hear these Doubles used as the repeats for the simples in performance instead of the usual AABB A’A’B’B’.

    My only minor comment would be with your saying “with no variety of rhythm it means that contrasts can only be achieved through the dimension of pitch.” There is much variety of rhythm, of course, that is achieved through the metrical implications of the dance, as your analysis shows. So metrical placement has a lot to do with helping Bach articulate the voice-leading, although the ambiguities are part of the fun as well.


    • Sean says:

      Thanks for your comments, Michael. Doubles-as-repeats is an interesting notion, and it seems to me that it comports to the Baroque ideal of embellished repeats. In fact, it may even elevate the double to being a kind of “meta-repeat”: If I were to describe it in Schenkerian terms, a standard embellished repeat would be a foreground repeat, but your double-as-repeat would be a middleground repeat. 🙂

      Doubles-as-duets sound a bit more like proof of concept or demonstration to me, rather than as viable performances.

      Re: rhythm, yes I was speaking of the dearth of different note values only. Certainly his choice of metrical placement avails variety to him (the re-articulated suspensions are but one example), but those devices are also tied to pitch.


  2. A reader from Paris says:

    ¶ A double as a “meta-repeat”: I think the distinction between the standard embellished repeat and the more elaborate double was clear to Bach himself; at least this idea may be supported by the English Suites for harpsichord. In the second Suite (BWV 807), Bach wrote after the Sarabande “Les Agrémens de la même Sarabande”, i.e. embellishments for the same Sarabande; no doubt it is a set of written-out ornamented reprises, to be played AA’BB’. Same thing with the Sarabande of the third Suite. Now if we look at the sixth Suite (BWV 811), we find the Sarabande, then a “Double” of it. The use of this term contrasts with the mere “Agrémens” of the second and third Suites; meaningfully, I think, since the rewriting of the previous Sarabande is much more elaborate in the Double than in the “Agrémens”. So it is to be played separately, after a complete performance of the Sarabande with its own reprises (embellished extempore by the performer, if possible): AA’BB’ A”B”.
    I don’t know if Bach indicates optional reprises in the Double itself (AA’BB’ A”A”‘B”B”‘…); to me, this would seem quite redundant. The structure: dance with reprises + double without, is hinted in the indication of an optional reprise of the whole dance movement (AA’BB’A”B”) in the end of the Gigue of the first English Suite (if I remember well). Bach may have found it in the harpsichord pieces of Jean-Henry d’Anglebert (same indication in some of his Gigues): he knew well this book published in Paris in 1689, since he made a copy of its incredibly sophisticated table of ornaments:

    ¶ In 17th century French music for lute or harpsichord, one finds sometimes optional “contreparties”: a second upper part to be performed in duet, both performers playing the same bass… So the idea to use the double to create a duet seems quite relevant with regard to performance practices of the baroque era.

    ¶ Finally I would like to mention here one of the first experiments of the young JSB with the aria & variations form: the delightful and too neglected Aria variata alla maniera italiana BWV 989. The great harpsichordist Gustav Leonhardt, who died a few months ago aged 83, performed it very often in the concerts he gave the last fifteen years (although he didn’t play anymore the Partitas, the French & English Suites, the Goldberg); and Glenn Gould recorded it for its unfinished Bach “Italian Album”. A lovely and very refined piece indeed. But you’re probably already familiar with it, so I end up this too long comment with a French piece you may not know: Rameau’s Gavotte with six Doubles for harpsichord (1728), here performed on the piano by Marcelle Meyer:

    Thank you so much for this blog.
    I havn’t found a copy of Monsaingeon’s Mademoiselle for you yet, but I’m on it.


    • Sean says:

      Thank you for your detailed thoughts. I have to be honest and say that period performance practice isn’t something that I get too concerned about. But then again, the reasons composers chose certain repeats in certain orders can tell us more about the music than just how it is to be performed. Michael’s notion of double-as-repeat interests me because of what it says about the nature of embellishment (or rather, the nature of the thing being embellished). In other words, if the first pass of the Sarabande is the “stuff”, then the repeat is an embellishment of that “stuff”. But if we accept the Double as the repeat, then we’ve jumped a layer (Schenker would say, schicht) of “stuff”, though it belongs to the same piece. This leads me directly to the only Schenkerian Analysis joke I know: In music, schicht happens. 🙂

      Yes, I’m familiar with BWV 989, especially Gould’s recording of it. It’s a beautiful piece and as you said, all too neglected.


  3. Sean, to your comment: “Doubles-as-duets sound a bit more like proof of concept or demonstration to me, rather than as viable performances.” My main response would be that it sounds very viable as a performance option; thus, it’s viable. (Put even more simply: I’d like to hear it!) I should clarify that I’m not trying to make a musicological argument about what Bach may have had in mind (although the Musical Offering is proof that he enjoyed hiding possibilities in puzzles). The same goes for my idea about using the Doubles as repeats; it’s not that I think Bach necessarily intended it, nor do I even care. I just think it would work well in performance.

    I also think that some of the Schumann accompaniments to the Bach solo violin works are of interest; I’d love to hear them played more. Here’s the Courante:


    • Sean says:

      Thanks for the link to the Bach/Schumann, I enjoyed the performance.

      Like you, my feeling about the duets isn’t grounded on whether Bach made a provision for it (personally, I just prefer to let the dusty-music people argue those sorts of things amongst themselves). But I’m not prepared to elevate their fitting together as being akin to a musical puzzle. My reticence regarding the doubles played as duets is that all manner of voice-leading problems occur, as well as awkward doublings.

      One of the most important aspects of the single-line works for solo instruments is that they are built upon an unheard yet ever-present field of influence against which we perceive the sense of voice-leading (perhaps I’d go so far as to call it the “silent continuo”). The same is true for all of his music of course, but the more voices or additional instruments there are, the less anything needs to be implied; everything is usually accounted for in the texture (e.g. downward-resolving 7ths, leading tone to tonic in outer voices, tritone resolutions, sufficient chord members, etc.). But even without accompaniment, Bach still manages to give you just enough to perceive this framework, and we fill-in the rest based on musical expectations we have developed as musicians or as listeners. Bach is peerless in this skill, I think. Overlaying a piece with its double, for me at least, disrupts and displaces the backdrop he meticulously wrought for each piece individually. Despite the fact that they share the same harmonic middleground, each piece’s sense of voice-leading (and by extension, its musical identity) is dependent on how it, and it alone, interacts with the harmonic tapestry from which it is woven.

      That’s not to say I still wouldn’t be curious to hear it, but, it would only be as a curiosity.

      In a sense, what I’ve shown in this post is akin to an overlay. Though they weren’t played together, the rhythmic reduction of the first eight bars of the Double looks remarkably similar to the score of the Sarabande (as does the rest of the piece). Of course, this is no surprise, but I am hopelessly intrigued by how he fashioned such incredible complexity from the most basic contrapuntal materials.


  4. Kevin says:

    Boy, I sure wish I knew something/anything about music theory to comment…so, I just commented anyway….what the heck.


    • Sean says:

      I should try to come up with some topics that pepper the music posts with crossover pencil appeal (and vice versa). 🙂 Don’t want to alienate any of this blog’s 22 readers!


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