Contents

Introduction
10 commonly misinterpreted Bach works in terms of tempo
Prelude and Fugue in E-flat Major for organ (St. Anne)

Introduction

When I discuss my Bach tempo theory with friends or colleagues, usually one of the first questions brought up is whether or not performers play the tempos I advocate. My answer to this question is “yes” and “no.” We have seen in the majority of examples discussed in previous pages that the tempos I believe to have been Bach’s tempos are not radical or revolutionary by any means.

For example, the most usual or average tempo taken by most performers for the famous C-major Prelude from book 1 of The Well-Tempered Clavier is indeed what I advocate, quarter = 72, or at least something close to this. Moreover, most performers sense that the following Fugue should be a little slower at around quarter = 54, which is also very often close to what we tend to hear in recorded or live performances. I find this to be the case with many other preludes and fugues as well, most likely because of the simple observation that “good performers and good musicians tend to sense good tempos.” One does not need to be a rocket scientist or have a Ph.D. in mathematics to choose sensible tempos for Bach’s works. One only needs to be a good musician and possess common sense.

Comparing the tempos I advocate with real-world performances can also be extended to all Bach’s other major works, including the some two hundred cantatas and other large-scale works. For example, I own a set of the complete Bach sacred cantatas conducted by a fine Dutch conductor accompanied by many outstanding Dutch instrumentalists and singers. I estimate the tempos they choose are about 70% of the time within a 5% range of the tempos I advocate. Likewise, my analysis of the B-minor Mass on this web site produces tempos that are followed by most conductors within a range of about 5%, especially the Allegro-style choruses. In sum, about 70% of the tempos I give are anything but radical or revolutionary, which if anything corroborates a major premise of my theory—that there do exist tempos universally ideal for certain styles, good musicians tend to gravitate toward these tempos, and average listeners tend to desire these tempos. (Please refer to Elaboration 2 for more on the concept of ideal tempos.)

I am also asked a lot about Glenn Gould, since Gould is undoubtedly the most popular topic when discussing tempo in Bach. Well, what can I say? Gould was a genius and a great pianist, and his tempo for the Aria in his first recording of the Goldberg Variations was perfect (quarter = 54, which I advocate), but other than that I am sure most of us sense that his tempo choices were often atrocious. Please understand though that my goal here is not to dictate to performers how slow or fast to play Bach’s music. I am merely presenting the evidence and making conclusions based on this evidence. Whether one wishes to believe my evidence is one’s personal choice. (Please refer to my disclaimer in Elaboration 8.)

It is easy to forgive Gould for his poor tempo choices. After all, he was an extremely eccentric genius who “marched to the beat of a different drummer.” What I find puzzling though is when highly educated performers and performer/scholars—many of them world-class artists—choose tempos that defy all the rules and make no sense theoretically or historically. This does not occur often, and applies only to a small percentage of Bach’s works, but nevertheless occurs. As much as performers dislike being told what tempos to choose, I see it as my duty as a scholar and researcher to point these instances out. In doing so, I only wish to help performers, not castigate them. Here is a list of works that are misinterpreted in terms of tempo by the majority of performers, the majority of the time. This list is not exhaustive. I have chosen just ten examples at random that happen to stick out in my mind.

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10 commonly misinterpreted Bach works in terms of tempo

1. Invention in C Major. Analysis shows Bach conceived this Invention in an Allegro-style tempo at quarter = 84; however, many performers assume more of an Andante-style tempo at about twenty beats per minute slower. Please refer to my study, “Tempo and Architecture in the Inventions and Sinfonias”.

2. Invention in D Minor. Analysis shows Bach conceived this Invention at a slightly slower tempo than the previous Invention in D Major; however, most performers mix up this hierarchy, playing the D-minor Invention extremely fast and faster than the D-major Invention.

3. Invention in B-flat Major. Analysis shows Bach conceived this Invention at an Andante-style tempo and character with a smooth, cantabile style of touch; however, many performers play it at a lively Allegro with detached articulation.

4. O Mensch, bewein deine Sünde gross from the Orgelbüchlein. Bach did indicate “Adagio assai” for this organ chorale; however, analysis indicates the usual tempo taken by most organists is substantially slower than the tempo Bach intended.

5. Variations 5, 8, 17, 26 from the Goldberg Variations. These are, indeed, lively Allegro-style variations; however, analysis shows that the usual extremely fast tempos taken by most performers—Czerny or Liszt “Allegros”—are more the product of nineteenth-century esthetics rather than Bach’s esthetics. Please refer to my study, “Bach's Goldberg Variations Demystified”.

6. Variation 25 from the Goldberg Variations. Bach did indicate “Adagio” for this variation; however, analysis shows that Bach conceived it substantially faster than the usual extremely slow tempo heard by most artists. The popular tradition of a tempo as slow as humanly possible for this variation was probably begun by Glenn Gould.

7. Prelude in C-sharp Minor and Fugue in C-sharp Minor from book 1 of The Well-Tempered Clavier. Bach’s choice of 6/4 for these pieces, indeed, indicates a slower rather than faster tempo; however, analysis shows the usual tempos heard in most recordings for these pieces are substantially slower than the Andante-style 6/4 courante tempos Bach intended. Please refer to my study, “Of Bach and Courante Tempos”.

8. Credo from the B-minor Mass. The Credo is nowadays often performed at a lively Allegro-style tempo; however, analysis shows Bach conceived this chorus to have a slow, emphatic, and deliberate tempo closer to Andante or even Adagio. Please refer to the analysis of the B-minor Mass in Elaboration 6.

9. Agnus dei from the B-minor Mass. This alto aria is usually taken at an extremely slow tempo, something in the realm of “Adagio” or even slower; however, analysis shows Bach intended a much faster tempo at something closer to “Allegro moderato.”

10. Prelude and Fugue in E-flat major from Clavierübung III. Analysis shows the usual tempos by virtually all organists are much different from those Bach intended. First, the cut-time indication in the Prelude is usually ignored. Second, the 6/4 indication in the Fugue is taken much too fast. Third, the 6/4 and 12/8 sections of the Fugue are usually taken at virtually the same tempo, which Kirnberger makes very clear is incorrect. Please refer to my two studies, both of which analyze this prelude and fugue: “Tempo and Architecture in the Inventions and Sinfonias” as well as “Discovering Bach’s Secret Technique of Outer-Parameter Symmetry”.

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Prelude and Fugue in E-flat Major for organ (St. Anne)

Let us now discuss the last work on this list, the immensely popular Prelude and Fugue in E-flat Major from Clavierübung III, which is the longest and most monumental of all the preludes and fugues Bach ever composed. We can see in the analysis of the complete B-minor Mass and in the conclusions reached what kind of a composer Bach was. My other analyses on this web site, as well as those not on this web site, show the same thing as well—that Bach planned his tempos and duration ratios before putting his pen to paper. This idea may seem crazy at first, but I think the B-minor Mass analysis says it all. Bach simply approached his works like the way a mathematically-minded architect would approach designing a house or building, that is, as organic structures with subdivisions or components that relate proportionally.

The B-minor Mass analysis, as well as many other analyses, also indicates that Bach was preoccupied with symmetry. In my study “Discovering Bach’s Secret Technique of Outer-Parameter Symmetry” I give a list of 110 works that display symmetry in terms of duration. Probably the most obvious of these examples is the Goldberg Variations. Bach was not obligated at all to repeat the Aria at the end, but did so for one simple reason—to achieve outer-parameter symmetry in terms of performance durations. The fact that Bach gave the first and last of the 15 Inventions the same meter and number of measures (4/4 with 22 measures), which implies the same tempo, provides another example of this fascinating and cryptic technique. Apparently, Bach was not just “preoccupied” with symmetry, but perhaps even “obsessed” with the idea. This can be concluded because outer-parameter symmetry simply occurs so many times in so many works.

About three or four years before composing the Goldberg Variations, which was Bach’s fourth and final installment of the Clavierübung series, Bach composed the third part (1738). This large-scale opus for organ consists of 27 movements, 25 inner movements contained within the outer parameters of a prelude and a fugue. Bach could have easily put this prelude and fugue together, but he decided to put them at the beginning and end of his opus for a very good reason. Analysis clearly shows that in his idealized plan Bach intended this prelude and fugue to have equal durations just as he did in the Inventions, would do later in the Goldberg Variations, and did as well in at least one hundred other works.

The tempos that make this symmetry happen are easily arrived at simply by observing Bach’s notation. Bach marked cut-time for the Prelude. Except for some of the middle section, sixteenths are rare and function more as embellishing rather than structural notes. Thus, this is not an unambiguous 4/4 movement that for various reasons happens to have a cut-time indication (like the Allemande from Partita 2 for keyboard), but is a true alla breve movement that requires two beats per measure. I assign the tempo of half = 54, since this seems fast enough to perceive in two beats per measure, but at the same time is not too fast as to make the sixteenths unplayable in the middle section. Even though this is a relatively slow half-note beat, this tempo results in a very lively and energetic movement at quarter = 108, which could be best described as “Presto” like in the third movement of the Italian Concerto.

Most organists simply ignore Bach’s cut-time indication and turn this exceptionally vigorous alla breve movement—one of the most lively of all Bach’s organ compositions—into a normal common-time Allegro at about quarter = 80-90. Bach wrote 205 measures of 2/2, in which a tempo of half = 54 results in a duration of 7:35. This is a full two minutes faster than the average duration heard in most recordings!

The Fugue consists of three sections. The first section, a true alla breve in 4/2, consists mainly of quarter-note motion with few eighths, suggesting a tempo faster than other stile antico movements with more eighths, such as Contrapunctus 1 from The Art of Fugue (which I assign half = 54). I find half = 72 an ideal tempo for this first section, whose 36 measures result in a duration of precisely two minutes. Most organists tend to play this first section closer to half = 60, which sounds too slow.

Bach notated the second section of the Fugue in 6/4. This is a rare meter that has very special qualities. Kirnberger says the large note values in meters such as 6/4 and 3/2 imply a “heavy and emphatic” tempo and character. Indeed, 6/4 is the usual meter for some French courantes and all loures, both of which are slow styles. There is no good reason at all to play this 6/4 section fast, yet virtually all organists—even highly educated “historically informed” organists—play it as if it were an Allegro at around dotted-half = 60. Had Bach intended Allegro for this section, he would have chosen 6/8 rather than 6/4. I assign the same tempo as to most other pieces in 6/4, the usual courante tempo of quarter = 108, whose 45 measures result in a duration of 2:30. In sum, this is a slow and expressive section whose character is not only ruined with an Allegro-style tempo, but also with the mixtures and bright registrations organists often choose.

Bach indicated 12/8 for the third and final section of the Fugue in order to distinguish its faster tempo from the slower 6/4 second section. Most organists make virtually no tempo change between these sections—once again, even highly educated organists—which clearly violates Bach’s notation. Bach chose 6/4 followed by 12/8 for one very important reason—to indicate a slower followed by a faster tempo. I assign a moderately fast dotted-quarter = 48 to the 12/8 section, whose 36 measures result in a duration of precisely three minutes. This is slower than the more usual dotted-quarter = 60 we often hear; however, when the 6/4 section is played slowly and deliberately at its correct tempo, a tempo of dotted-quarter = 48 for the 12/8 section seems faster than it really is.

Let us now summarize all this data in spreadsheet form. The Prelude consists of 205 measures of 2/2 whose tempo of half = 54 results in a duration of 7:35. The first section of the Fugue consists of 36 measures of 2/2 whose tempo of half = 72 results in a duration of 2:00. The second section of the Fugue consists of 45 measures of 6/4 whose tempo of quarter = 108 results in a duration of 2:30. And finally, the third section of the Fugue consists of 36 measures of 12/8 whose tempo of dotted-quarter = 48 (eighth = 144) results in a duration of 3:00.

Worth noting is the measure counts of the three Fugue sections are symmetrical, 36:45:36. Also worth noting is the ratio of the tempos of the three Fugue sections in terms of half, quarter, and eighth-note beats is 2:3:4—that is, 72:108:144 = 2:3:4. Also worth noting is the durations of the three Fugue sections increase by half-minute intervals from two to three minutes, 2:00-2:30-3:00. And the most significant observation of all—which I believe is one of the most fascinating and revealing examples in all of Bach’s works—is that when added together, the total duration of the three Fugue sections equals that of the Prelude with a mere five-second discrepancy!

This shows a fifteen-minute Prelude and Fugue divided equally as 7:30 + 7:30, which as explained in previous Elaborations, Bach could have easily calculated, and when finally committing it to paper, achieved with the precision and tenacity of a scientist.

Equal durations of 7:30 in the E-flat major Prelude and Fugue for organ

1. Prelude	2/2	205	H = 54	7:35.55	7:30	1	1.2%
27. Fugue	4/2	36	H = 72	2:00	2:00	2	0.0%
(second section)	6/4	45	Q = 108	2:30	2:30		0.0%
(third section)	12/8	36	E = 144	3:00	3:00	3	0.0%
(total of Fugue)				7:30	7:30	1	0.0%

Bach was only two measures off from his idealized plan, suggesting that he was aiming for two fewer measures in the Prelude, 203, to achieve the same duration as the Fugue, 7:30. This is how Bach apparently sought to unify the overall, large-scale design of his Clavierübung III, with equal outer parameters of 7:30 and a total duration of precisely fifteen minutes.

Organists would be wise to follow this plan and try to play these tempos and achieve these durations. After all, shouldn’t the goal of all conscientious performers be to get as close as possible to how Bach conceived his works? What is the theoretical or historical justification for ignoring the cut-time in the Prelude, playing the 6/4 as an Allegro, and not changing tempos between the 6/4 and 12/8 sections?

Although as many as 70% of Bach’s works seem to be interpreted with reasonable tempos by the majority of performers, analysis shows the highly popular E-flat Major Prelude and Fugue is one of the most misinterpreted works in Bach’s oeuvre. I have yet to hear an organist play the proper tempos and achieve Bach’s durations even within an acceptable range. But please do not take offense here, as I merely wish to help organists, not castigate them.

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