The first episode of the season features a discussion of what it means to be first by Scott Murphy (University of Kansas).

This episode was produced by David Thurmaier and Jennifer Beavers.

SMT-Pod Theme music by Zhangcheng Lu; Closing music "hnna" by David Voss. Other original compositions by Anthony Esland, Jamie Allen, and Liam Hynes-Tawa. For supplementary materials on this episode and more information on our authors and composers, check out our website: https://smt-pod.org/episodes/season01/.

SMT-Pod Theme Music Playing

Welcome to SMT-Pod, a publication of the Society for Music Theory. SMT Pod's first episode challenges what it is to be first, in Scott Murphy's "Buxtehude Beats Bach? Qualifying a Canonic Claim"

Who’s on first? In the famous mid-20th-century comedy sketch, it doesn’t take a scholar of humor to understand what makes the titular line so funny: Costello hears it as a question—who’s on first? Abbott declares this as a statement—who’s on first.

When we make statements about history, we often invoke firsts, don’t we? The Great War of 1914 was the first world war. The Wright Brothers performed the first heavier-than-air flight. Sgt. Pepper was the first pop/rock concept album. To claim that something was the first of its kind in history involves power, but also risk.

The power is in delineating the writing of history with a single stroke, putting events into more easily comprehended categories, or dividing time into more easily comprehended ages, eras, and periods. The risk is in oversimplifying or even distorting history. To be sure, some of this risk is calculated: since we’re not all-knowing, there’s a decent chance that some information that comes to light later, either to an individual or a society, tempers the initial statement’s potency.

At one point in his writing, Sigmund Freud discussed who was the first to recognize the significance of neurotic symptoms, and he said that [quote] “On the whole it may be of small importance to us who is responsible for this discovery, for you know that every discovery is made more than once, [and] that none is made all at once.” [unquote]

But there’s another perspective on this risk that one could take here that reverses the Abbott and Costello play on words: what we think is just a statement about a first is perhaps also a question. Was the Great War of 1914 the first world war? Did the Wright Brothers perform the first heavier-than-air flight? Was Sgt. Pepper the first rock/pop concept album?

Turning a first-based claim into a question invites us to study the premises of the claim more closely, and, if we can, to accompany the claim with qualifying details that mitigate its risk by making the claim more precise. In this episode, I take one such claim from a musicologist, turn it into a question, and subject it to some music theory that I believe makes the claim a bit more accurate and, I hope, more interesting.

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In 1974, almost fifty years ago, the French organist Olivier Alain discovered Johann Sebastian Bach’s own handwritten copy of his Goldberg Variations, composed in 1741\. Accompanying this copy were fourteen canons that Bach composed, likely years after the variations, on the first eight notes of Goldberg’s bass line, which sound like this: [sing G-F#-E-D-B-C-D-G].

As twelve of these fourteen canons had never been seen before, this set of canons was given a new catalog number: BWV 1087\. Peter Williams has documented how multiple composers before 1741 used this eight-note theme as a bass line for variation sets. However, Bach, in keeping with a deeper investment in canonic writing and monothematicism in the last decade of his life, explored in BWV 1087 how the bass line could be combined with versions of itself. These canonic combinations take three basic forms among the fourteen canons: prolation, retrograde, and inversion.

I’ll sing an example of each form. First, here’s an example of prolation: the theme sounds in counterpoint with a version of a theme one fourth of the first duration later, and four times as fast: [sing]. Second, here’s an example of retrograde: the theme lines up with a carbon copy version of itself, but backwards. [sing]

Third, here’s an example of inversion: the theme combines with a flipped-over version of itself starting a fourth lower and four of its notes later: [sing]. Not only does the second half of the theme well coincide with the first half of its inversion, but the first half of the theme well coincides with the second half of its inversion. Therefore, this also works as a perpetual canon where both theme and its inversion are immediately repeated, creating continual overlap: [sing]

In 1976, two years after Alain’s discovery, the German musicologist Christoph Wolff published a study of these new findings. As part of this study, he made this claim regarding the fourteen canons in BWV 1087: [quote] “Although the theme, as such, was not designed by Bach, no one before him seems to have recognized its inherent canonic potential.” [unquote] Turning this claim into a question—“Was Bach the first to recognize this theme’s inherent canonic potential?”— encourages us to unpack what is meant both by “theme” and “canonic potential.”

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Let us start with “theme”: what kinds of alteration of this theme can this claim accommodate? Surely if someone realized this potential in a different key, or tempo, or so forth, this discovery would stand shoulder-to-shoulder with Bach’s, as long as both parts moved in tandem into the new conditions. It also seems right that a recognition of inherent canonic potential in the inversion of this theme likewise is on a par with Bach’s realization, especially since these two versions are intertwined in both the retrograde and inverted forms of the canon I most sung.

As an analogy: If I recognize the English word “Scott” as special because its phonetic retrograde happens to also sound like an English word, then it makes sense that the English word “talks” should be recognized as special for the same reason: Scott talks. What makes one distinctive makes both distinctive, reciprocally.

This logic can be taken further. The overlapping and perpetual structure of the inverted canon in particular can, at least for a time, convey a sense of limitlessness: a canon without beginning or ending. Therefore, not only does the Goldberg theme and its inversion possess this canonic potential, but also does any succession of eight notes lifted from this looped arrangement. Discovering the potential for one uncovers the potential for all. I’ll demonstrate this with more singing.

This time, I’ll add words that loop with the notes, in which the word “there” matches the note understood at the time as the “first note.” I’ll start initially with the first note as defined by the Goldberg theme, but, in the voice added second, I’ll switch the word “there” to another note, shifting the beginning to another position. You will notice that this switch will toggle any duple meter you are experiencing, so that might be a little unsettling, but at least the new first note, the “there,” will remain on the first scale degree.

Then I will drop out the first voice, making the follower the leader, then re-enter the second voice with its words similarly shifted, producing a canon that is both new and not new. [sing: “There do I start, end I do here”]

Let’s return to Wolff’s claim. When he says that “no one before him [that is, no one before Bach] seems to have recognized its inherent canonic potential,” does he mean all of the canonic potential we see evidenced in BWV 1087? Some of it? What if someone before him recognized only some of the potential on display in BWV 1087, but also some potential not found among Bach’s 14 canons? That is the case I want to make here, but it requires the broader definition of the “theme” for which I argued earlier.

I should give this someone a name! This someone is Dietrich Buxtehude, a seventeenth-century organist and composer who died no less than 34 years before Bach wrote his Goldberg Variations and the canons derived from them. A famous long walk in 1705 makes vivid the chronological relationship between these two composers: as a young man of twenty, Bach trekked on foot over 250 miles north through Germany from Arnstadt to Lübeck to hear Buxtehude, an older man of around 68 years who would live only two more, play the organ.

In her biography of Buxtehude, Kerala Snyder speculates that, during his visit, Bach made many copies of the elder composer’s organ music, both studying these compositions himself and circulating thirty of them among his relatives, friends, and students. Among these thirty works is the Canzonetta BuxWV 168, which is a succession of three fugues.

This canzonetta must have been well known enough for Friedrich Marpurg to cite this piece in his Abhandlung von der Fuge of 1753\. Two hundred years later, in his anthology The Study of Fugue from 1958, Alfred Mann excerpted Marpurg’s treatise among three others, including Marpurg’s reference to Buxtehude’s canzonetta.

But perhaps less well known is how Buxtehude’s piece relates to the Goldberg theme. Once again, here is the Goldberg theme. [sing] And here again is the Goldberg theme, inverted and shifted in the particular manner demonstrated earlier. [sing] Let’s make three more small adjustments: transpose it down a fourth [sing], put it in the parallel minor mode [sing], and add a single passing tone. [sing]

This is the subject of the third and final fugue in Buxtehude’s Canzonetta BuxWV 168\. [play] The exposition of this fugue alternates entrances of the subject with those of its inversion, which motivates Marpurg to call this a counterfugue. [play] Immediately after the exposition, the subject and its inverted form appear using the same overlap found in BWV 1087\. [play]

Although this overlap lacks a looped repeat of the first voice found in Bach’s perpetual canon, Buxtehude includes the beginning of a looped repeat in the fugue five measures later; he even omits the passing tone, bringing the music in two ways into a closer resemblance to the inverted canon from 1087\. [play]

Immediately after this briefly looped presentation, Buxtehude then again combines the subject with an inverted form of itself delayed by half the length of the subject. But, this time, their combination taps into a canonic potential inherent in this theme that Bach does not propose anywhere in his fourteen canons: invertible counterpoint at the twelfth.

One can well hear the difference, because the harmonic octaves in Bach’s version [sing] become harmonic fifths in Buxtehude’s [sing]. Here is what is sounds like in Buxtehude’s fugue. Here then is Buxtehude’s final fugue in BuxWV 168 up to its first cadence, showcasing the unlooped, then looped, then at-the-twelfth options. [play]

At the least, these observations refine Wolff’s claim to some degree. Allowing for a modified version of the subject, coequal with the original in its canonic potential, Buxtehude realizes some of this potential before Bach does. But not all of it: nowhere in this fugue are demonstrations of its canonic potential regarding retrograde and prolation, as far as I can tell. As Freud said, every discovery is not made all at once.

But, moreover, I hope these observations prompt further questions, such as: did anyone before Bach realize the retrograde and prolation canonic potential of this subject? or, did anyone before Buxtehude realize the inversion canonic potential of this subject? or, moving beyond who’s first, to what degree if any did Bach’s familiarity with Buxtehude’s canzonetta influence his composition of the fourteen canons, or, to use Freud’s words as a question, was this discovery made more than once?

While we may yet not know, and may never know, the answers to these and other questions, that’s OK: even Abbott and Costello gave “I don’t know” a position on the field.

Thanks to Peter Franck for his careful review and helpful suggestions. To James Higdon for his Francophonic advice, and to my wife for suggesting our walk-in closet as a recording studio. I performed and recorded the excerpt f Buxtehude's canzona at Murphy Hall on the campus of the Universityof Kansas. No the hall is not named after me.