In this week's episode, Daniel Ketter presents an essential voice analysis arrangement of J. S. Bach’s fugue for solo cello. It traces the composer’s solution to weaving a four-part fugal texture with nearly no chords or double stops through inventive combinations of a subject and countersubject.

This episode was produced by Jason Jedlicka along with Team Lead Leah Frederick. Special thanks to peer reviewers Gilad Rabinovich, Ed Klorman, and Joe Straus. Additional thanks to Jason Orr, Jessie Black, and Royce Diamond at Phosphor Studios.

SMT-Pod’s theme music was written by Maria Tartaglia, with closing music by Yike Zhang. For supplementary materials on this episode and more information on our authors and composers, check out our website: https://smt-pod.org/episodes/

[Intro Theme by Maria Tartaglia.]

Welcome to SMT-Pod, the premier audio publication of the Society for Music Theory! In this week's episode, Daniel Ketter presents an essential voice analysis arrangement of J. S. Bach’s fugue for solo cello. It traces the composer’s solution to weaving a four-part fugal texture with nearly no chords or double stops through inventive combinations of a subject and countersubject.

Johann Sebastian Bach’s fugues are challenging enough to perform and understand when the fugal parts are specified, such as in Art of Fugue or Well-Tempered Clavier, but Bach also wrote fugues for solo violin sonatas and partitas, and even a fugue for solo cello in the Suite No. 5 in C minor.

How can a single line played by the cello project multiple lines of counterpoint at the same time to create a fugue? How do we distinguish between fugal parts? This is important for performance reasons as well: with the unified timbre of a single instrument, and the unique circumstance of this fugue being written almost entirely without chords or double stops, performers need this information to create meaningful distinctions in articulation and voicing between contrapuntal lines.

The following discussion is aimed towards music performance students, or music connoisseurs who may already have basic knowledge of fugal technique but would like a better picture of how Bach’s fugue for cello may fit into their expectations for fugue technique overall.

Music theorists and other experts may find Bach’s strategies for maximizing the capabilities of the instrument to engage with a fugal texture to be interesting. While some experts may view this as an imitation of fugal texture, I argue that through inventive usage of a combined subject and countersubject, this movement for cello may be considered a strict fugue.

A Baroque fugue traditionally is written across a number of “parts” characterized by register (like an Alto part, Soprano part, or Tenor and Bass parts in a 4-part fugue). For this discussion, we will follow Eric Wen in making a distinction between a contrapuntal essential “voice,” which is a continuous, melodically fluent string of counterpoint, and a fugal “part,” which might be performed by a single instrument or designated by stem direction in a piano or organ score. In a fugue’s exposition, each part introduces the subject or answer in its register and for the fugue’s remainder, the material is varied and transformed through non-subject episodes and other subject statements.

So, fugues usually begin with the subject stated alone: let’s hear the first subject statement of Bach’s C minor fugue for solo cello. Here’s the subject:

[Bach’s C minor fugue for solo cello: subject]

Like most fugue subjects, the first eight measures of this one is a compound melody, which means it can be broken clearly into two essential voice lines of counterpoint: an upper voice decorated by sixteenth notes, moving down generally at one tone per measure----and a lower part generally moving upward in contrary motion eighth-notes.

[Bach’s C minor fugue for solo cello: subject with layered upper and lower parts]

The subject is usually followed by a second statement in another part, called an answer, in the dominant key. The leading part continues to accompany the subject in counterpoint, resulting in a thicker texture of two parts. Here’s the answer:

[Bach’s C minor fugue for solo cello: answer]

Wait a second…. Was there any new counterpoint of the first alto part against the soprano answer? Let’s listen again with the descending voice highlighted by a second cello

[Bach’s C minor fugue for solo cello: answer with layered upper and lower parts]

The answer appears to be the opening eight bars transposed up a fifth into the soprano register in the key of the minor dominant without any extra counterpoint added. Hmm, let’s see what happens next…

After a brief link, we should hear a third statement of the original subject in a lower part back in C minor, with the alto and soprano adding counterpoint as the fugue exposition continues, filling out the texture.

[Bach’s C minor fugue for solo cello: link next to subject]

Wait a second, was that even the subject still? The rising eighth note voice was now in the tenor register, above the slower descending voice in the bass register.

[Bach’s C minor fugue for solo cello: subject with layered upper and lower parts]

What we would expect to be the final following answer has the same problem, with the slower descending line in the tenor register, and the rising eighth-note line in the alto register, leading to a cadence that concludes the exposition. Here it is:

[Bach’s C minor fugue for solo cello: answer]

And here it is the descending part highlighted again by a second cello

[Bach’s C minor fugue for solo cello: answer with layered upper and lower parts].

Clearly, something unusual is going on in this four-part fugue exposition. While the opening subject answer pair is unusual because there appears to be no extra counterpoint added to the answer, the following subject answer pair is unusual because the two lines of essential voice counterpoint are inverted, with the rising eighth note voice stated above the slower voice decorated by sixteenth notes.

To resolve this puzzle, we can identify the slower descending essential voice as the fugue’s subject, while the faster voice in eighth notes is a countersubject. When a fugue has a countersubject, it will always accompany the subject above or below once it is introduced. In this special fugue, the countersubject appears with the subject even in the very first statement, so that the subject itself is never stated alone.

Recognizing the four statements of the slower descending subject in the fugue exposition in m. 28 (A), m. 36 (S), m. 47 (B), and m. 56 (T) for those of you keeping score, suggests that in Baroque practice, this is a four-part fugue with each part occupying an essential register, roughly corresponding to the four strings of the cello. While these four parts are not always literally sounding, a full essential voice analysis completes the texture to fill out each harmonic moment to uncover details about the contrapuntal design of the piece.

With this in mind, let’s listen to our full fugue exposition with all four parts realized in an essential voice analysis. Listen for the subject stated once in each register: Alto, Soprano, Bass, and Tenor, counterpointed by the countersubject, first below the subject, then above.

[Bach’s C minor fugue for solo cello: full fugue exposition]

Given these two keys of the slow descending subject and quicker rising countersubject, we can follow the rest of the fugue through subject statements and episodes, even when they are highly ornamented or transformed. As performers, to differentiate between the subject and countersubject it is helpful to use characteristic articulations or bowings for each so that they can be recognized throughout the movement as distinct parts, so identifying them is critical, especially in ornamental contexts. I personally try to emphasize the linear aspects of the subject with a connected detache bowing, contrasting the countersubject parts with a heavy spiccato stroke or sharper articulation.

After the fugue’s exposition, the next subject statement is in E-flat major, in mm. 72-79. Here it is.

[Bach’s C minor fugue for solo cello: next subject statement in E-flat major, mm. 72-79]

The next partial subject statement is in C minor, but heavily ornamented, in mm. 88-94. We can hear this partial subject statement descending slowly overlayed with the original cello ornamentation.

[Bach’s C minor fugue for solo cello: partial subject statement in C minor, mm. 88-94]

The next subject statement is in G minor in mm. 102-109, very similar to the original fugal answer in the exposition, but with the subject and countersubject separated by an extra octave. Let’s listen now.

[Bach’s C minor fugue for solo cello: subject statement in G minor, mm. 102-109]

The next subject statement is in F minor from mm. 130-137.

[Bach’s C minor fugue for solo cello: subject statement in F minor, mm. 130-137]

The next subject statement is in C minor from m. 150-157, a return to the home key, inverted with the subject in the bass, very similar to the second subject statement in the exposition, but with subject and countersubject dramatically separated again by an extra octave. Let’s listen now.

[Bach’s C minor fugue for solo cello: subject statement in C minor, mm. 150-157]

The next subject statement is in C minor, the home key again, after a long dominant pedal, returning to the original register and figuration of the first subject/countersubject pair. The cadential portion of the statement is transposed up an octave, and the dominant is resolved deceptively in m. 183 to dramatically extend the end of this fugue.

[Bach’s C minor fugue for solo cello: subject statement in C minor, m. 183]

The final, most dramatic subject statement from m. 197-209 includes significant register leaps between the subject and countersubject, and is also extended to span an entire octave from C4 to C3 instead of only a sixth like all of the other subject statements. This final dramatic statement brings the fugue to a close and introduces the coda.

[Bach’s C minor fugue for solo cello: final subject statement in C minor, mm. 197-209]

Now that we have listened to all of the subject statements throughout the fugue, let's listen to the entire fugue with the subjects interspersed by their episodes. Listen out for statements of the subject and ways that materials from the subject and countersubject are recombined in the episodes between subject statements.

[Bach’s C minor fugue for solo cello: entire fugue]

Special thanks to peer reviewers Gilad Rabinovich, Ed Klorman, and Joe Strauss, as well as Jason Orr, Jessie Black, and Royce Diamond at Phosphor Studios for making this episode a possibility.

[Outro Theme by Yike Zhang.]

Visit our website, smt-pod.org, for supplemental materials related to this episode and to learn how to submit an episode proposal. You can join in the conversation by tweeting us your questions and comments to @SMT_Pod. SMT-Pod’s theme music was written by Maria Tartaglia, with closing music by Yike Zhang. Thanks for listening!