Contents

Introduction
Relationship between polonaise and minuet tempos
Formulating a general tempo hierarchy of styles
Duration ratios in French Suite 6
Renouncing 19th-century biases
Bach’s compositional process
Establishment of six axioms and conclusion

Introduction

In his well-known musical treatise Die Kunst des reinen Satzes in der Musik (Berlin, 1774-79), translated as The Art of Strict Musical Composition (Beach and Thym, New Haven: Yale University Press, 1982), Bach’s most famous student and disciple, Johann Philip Kirnberger (1721-83), tried to the best of his abilities to describe Bach’s art of composition. (This is what Kirnberger says in his preface.) Kirnberger was one of the few eighteenth-century writers on music to describe tempo and tempo practices in detail and is probably the best source to rely on regarding all aspects of Bach’s compositional art and techniques, and especially, tempo.

It is difficult to find a whole lot of information on eighteenth-century tempo practices and even more difficult to find information relevant to Bach’s tempo practices, since Bach left us virtually no theoretical documents. Bach was a quiet, private person and apparently did not reveal much about his art and techniques even to his closest associates and relatives. It is a good thing we have Kirnberger’s writings, because even though Bach may not have revealed much to others about his “musical science” (as Christoph Wolff calls Bach’s art), Kirnberger at least experienced Bach’s practices first hand and tried to the best of his abilities to describe Bach’s practices in The Art of Strict Musical Composition.

Kirnberger is extremely explicit when he describes what was presumably Bach’s system of tempo. Basically, Kirnberger emphasizes that each musical style has a “definite” tempo, which is the most natural or normal tempo, which he calls tempo giusto. Kirnberger says that one can find the most natural tempo by studying all types of dance pieces, which I interpret more broadly as meaning not just all dance styles, but all styles in general:

Furthermore, he [the composer] must have acquired a correct feeling for the natural tempo of every meter, or for what is called tempo giusto. This is attained by diligent study of all kinds of dance pieces. Every dance has its definite tempo, determined by the meter and note values that are employed in it. Regarding meter, those having larger values, like alla breve, 3/2, and 6/4 meter, have a heavier and slower tempo than those of smaller values, like 2/4, 3/4, and 6/8 meter, and these in turn are less lively than 3/8 or 6/16 meter. Thus, for example, a loure in 3/2 (6/4) has a slower tempo than a menuet in 3/4 meter, and the latter is in turn slower than a passepied in 3/8 meter. Regarding note values, dance pieces involving sixteenth and thirty-second notes have a slower tempo than those that tolerate only eighth and at most sixteenth notes as the fastest note values in the same meter. Thus, for example, a sarabande in 3/4 meter has a slower tempo than a menuet, even though both are written in the same meter.

Thus, the tempo giusto is determined by the meter and the longer and shorter note values of a composition. Once the young composer has a feeling for this, he will soon understand to what degree the adjectives largo, adagio, andante, allegro, presto, and their modifications larghetto, andantino, allegretto, and prestissimo add or take away from the fast or slow motion of the natural tempo. He will soon be able to write in every type of tempo, but also in such a way that this tempo is captured quickly and correctly by the performers (376-377).

Kirnberger and Bach lived in a different time and era from that in which we live today, known as the Enlightenment, or Age of Reason. Philosophers and writers in the Enlightenment (known as philosophes) became particularly fond of emulating the practices of the ancient Greeks, whose ideals were characterized by such esthetics as balance, order, symmetry, rationality, and restraint. The Enlightenment was also the first time in which scholars attempted to put the sum of human knowledge down on paper, which culminated in Diderot’s and D’Alembert’s Encyclopédie (1751-72).

Moreover, the Enlightenment was the first time in history that science and scientific discoveries were made accessible to the general public, which was due to the work of Francis Bacon (1561-1626), who believed that the fruits of the Scientific Revolution (1500-1600’s) should be of practical use to the common person. In essence, the Scientific Revolution was a time of making discoveries about natural laws, while the Enlightenment was a time of applying and explaining these natural laws as they applied to inventions, architecture, art, and even music. In my essay, Bach, the “musical scientist” and in the following analysis of the B-minor Mass (see Elaboration 6), I explain and show that Bach approached his music in the same fashion as a scientist like Isaac Newton approached his science. For now though, let us return to Bach and Kirnberger.

(back to contents)

Relationship between polonaise and minuet tempos

Judging from the way Kirnberger describes Bach’s tempo practices, it becomes apparent that Bach did not “decide upon” tempos for personal, subjective reasons, but rather, the style and time signatures Bach employed usually “dictated” its tempo giusto. In fact, Kirnberger’s descriptions of Bach’s tempo practices imply that the hierarchy of musical tempos followed some sort of “natural law,” no different from natural laws or axioms in mathematics. Perhaps the one quote by Kirnberger that suggests this more than any other is his description of the relationship between polonaise and minuet tempos. It is quite possible that these words came directly from Bach himself, implying indeed that the dance tempos followed a natural and logical hierarchy according to natural laws over which Bach would have had no control.

The polonaise is faster than the sarabande and one-third slower than the minuet so that eight measures of a polonaise equal twelve measures of a minuet (216).

This is the most explicit information about tempos that Kirnberger gives, which if interpreted correctly serves as a “missing link” in the determination of the complete dance tempo hierarchy. To use an analogy, imagine a jigsaw puzzle in which no pieces have been put together. This is the most difficult step in putting together a puzzle, since no piece can be used as a point of reference. However, once one finds two important pieces and discovers they fit together, assembling the complete puzzle becomes much easier.

(back to contents)

Formulating a general tempo hierarchy of styles

Let us now determine the main dance tempos used by Bach. To begin, we must first find the polonaise and minuet tempos, which have a 2:3 tempo ratio. In order to do this, let us use the only work in which Bach used a polonaise and minuet in their normal, unmodified forms, French Suite 6.

The most likely tempos for these pieces can be found simply by using good judgment and a process of elimination using the ideal tempo matrix determined in Elaboration 2. Here are several possibilities for tempo pairs that relate 2:3 or very close to 2:3, all taken from the “quadruplet” column (for the polonaise) and “duplet” column (for the minuet), which all apply to the speed of the quarter note:

Polonaise	48	54	63	72	84	96
Minuet	72	84	96	108	126	144

Trying out these pairs for the Polonaise and Menuet in French Suite 6 suggests the tempos best suited for these pieces are quarter = 84 and 126. This is concluded because the next slowest pair, quarter = 72 and 108, seems a little too slow while the next fastest pair, quarter = 96 and 144, seems a little too fast, not so much for the Polonaise but more so for the Menuet.

Let us assume quarter = 84 and 126 as the polonaise and minuet tempos to which Kirnberger (and presumably Bach) refers. It now becomes possible to formulate a logical hierarchy of dance tempos using the polonaise and minuet tempos as a point of reference and missing link. I rely here on my experience as a musical collaborator in Renaissance and Baroque dance, in that I have very good knowledge regarding which tempos are faster or slower than others. For example, referring to some of the main simple-meter styles, sarabandes and French courantes are “slow,” gavottes are something closer to “moderate,” bourrées are closer to “fast.” Similarly, referring to some of the compound-meter styles, minuets in 3/4 are “moderate,” the 3/8 for correntes implies a faster tempo than otherwise similar 3/4 minuets, and passepieds and gigues in 3/8 (and other related meters) are the fastest dances of all. Now, the problem simply becomes arranging all the tempos into a logical hierarchy. Most of the tempos I assign for Bach’s works can be summarized in this table:

Ideal tempo matrix applied to logical tempo hierarchy for the major dance styles

Duplets	Triplets	Quadruplets
72	48	36 molto Adagio; highly ornate 3/4 sarabandes and 4/4 allemandes
84	56	42 Adagio; highly ornate 3/4 sarabandes and 4/4 allemandes
96	64	48 Largo, Adagio; moderately ornate 3/4 sarabandes and 4/4 allemandes
108 3/8, 6/8, 12/8 sicilianos; normal 6/4 courantes, some slower 3/4 minuets	72	54 Andante, Largo; normal 3/4 sarabandes and 4/4 allemandes; normal 3/2 courantes
126 normal 3/4 minuets	84 12/8 gigues	63 Andante; perhaps the fastest sarabandes; overtures
144 3/8 correntes	96 3/4 or 9/8 triplet correntes; 6/16, 9/16, and 12/16 gigues	72 moderato; 2/2 gavottes
168 3/8 passepieds and gigues	112 3/4 or 9/8 triplet correntes; 6/16, 9/16, 12/16 gigues	84 Allegro, Vivace; normal 3/4 polonaises
192 3/8, 6/8 gigues	128	96 Allegro, Vivace; bourrées
216 3/8, 6/8 gigues	144	108 Presto

(back to contents)

Duration ratios in French Suite 6

Let us now apply some of these tempos to a series of movements in French Suite 6. The four successive movements from the Gavotte to the Menuet show a gradual tempo increase from 72 to 126 beats per minute. The Gavotte is “moderate” at half = 72. The Polonaise is a little faster at quarter = 84. The Bourrée is yet a little faster at half = 96. And finally, the Menuet is the fastest of all in terms of beats per minute at quarter = 126 (although the perceived tempo is slower due to the absence of sixteenth notes).

It is significant that all four measure counts are different except those of the Polonaise and Menuet, which both have 24 measures. Assuming a 2:3 tempo ratio as Kirnberger (and presumably Bach) says, the same number of measures at a 2:3 tempo ratio automatically results in a 2:3 duration ratio.

Further analysis shows that there is something very “peculiar” going on here in addition to the Polonaise and Menuet having equal measures, a 2:3 tempo ratio, and a 2:3 duration ratio. Namely, the gradually accelerating tempos of 72-84-96-126 result in a virtually precise symmetrical 2:3:3:2 duration ratio, in that the outer movements, the Gavotte and Menuet, have equal durations while the inner movements, the Polonaise and Bourrée, have equal durations one-half longer than the outer durations. The average discrepancy here is just 1.2%, which translates to merely less than one-second discrepancy for every minute of music. In other words, had Bach given the Gavotte just one more measure, 21, and the Bourrée just one less measure, 41, the symmetrical 2:3:3:2 duration ratio here would be precise.

Symmetrical 2:3:3:2 duration ratio in French Suite 6

4. Gavotte	2/2	20	H = 72	0:33.33	0:34.28	2	2.8%
5. Polonaise	3/4	24	Q = 84	0:51.42	0:51.42	3	0.0%
6. Bourrée	2/2	42	H = 96	0:52.5	0:51.42	3	2.1%
7. Menuet	3/4	24	Q = 126	0:34.28	0:34.28	2	0.0%

Please keep this analysis in mind throughout the discussions in the following elaborations. These intriguing observations in French Suite 6 are too important to simply cast off as coincidence. This suggests Bach’s and Kirnberger’s dance styles may have indeed conformed to some sort of natural laws beyond human control. If so, the tempos given for these movements cannot be considered “Bach’s tempos” at all, but rather something closer to “God’s tempos.” But one thing is for certain; they are certainly not “my tempos” since they had always been in existence before I had discovered them. (Please refer to this topic in Elaboration 2.)

(back to contents)

Renouncing 19th-century biases

The idea of “definite,” “ideal,” or “perfect,” tempos is a difficult concept for us to fathom today because our esthetics have been influenced so heavily by the radical, free-spirited, individualistic, emotional, and subjective ideals of nineteenth-century romanticism. Probably the first composer to “break all the rules” with tempo tradition was Beethoven, who claimed: “We can scarcely have tempi ordinari [i.e., standard tempos] any longer, since one must fall into line with the ideas of unfettered genius” (Emily Anderson, translator and editor, The Letters of Beethoven, London: Macmillan, 1961, 727).

I believe that in order to get to the heart of the matter and truly determine Bach’s tempos, it is essential that one understand the difference between objective, idealistic eighteenth-century conventions and subjective, free-spirited nineteenth-century conventions. A composer like Bach, for example, wrote his music for the glory of God and considered his compositions to be works of “musical science.” A composer like Liszt, on the other hand, wrote his music mainly to stir up emotions and mesmerize audiences.

In order to enter Bach's world, it is necessary to break down the “Beethoven barrier.” I realize this is difficult to do, but really the only way you can even approach getting close to determining Bach’s true tempo conventions is to pretend that you have never heard any music composed after 1750. I also ask that you not put much stock in modern recordings, since as good as many of them may be, they have most likely “tainted” your judgment and influenced you with some “biases” you may not even realize you have.

One of my favorite examples of this is Variations 25 and 26 from Glenn Gould’s famous debut recording of the Goldberg Variations, quite possibly the most influential recording of Bach in history. I know through experience that the more you listen to such recordings, the more it will shape your biases. (It certainly biased me many years ago.) I can’t count the number of times I have heard recordings by other artists who play Variation 25 as slowly as humanly possible and Variation 26 as fast as humanly possible. But honestly now, is this really the way Bach intended these variations?

(back to contents)

Bach’s compositional process

Bach was arguably the most methodical and systematic composer in the history of music. We would naturally expect such a composer to put great thought into his musical creations and not to just write things out in a hurried and careless fashion without thinking. Let us try to retrace the process Bach would follow in the composition of a work.

First, Bach would have to choose a style. For example, will the work resemble a sacred form (such as the C-sharp minor Fugue from WTC I, which emulates a sacred chorus), or perhaps a dance style of some type (such as the Aria from the Goldberg Variations, which resembles a sarabande)? Next, Bach would have to choose a time signature, which is usually linked to the particular style chosen. For example, a cut-time meter would naturally be associated with a sacred chorus, a gavotte, or bourrée, while 3/4 would naturally be associated with a sarabande, polonaise, or minuet. Finally, after putting his pen to paper Bach would have to make a conscious decision about when to end the composition, that is, how many measures it should contain.

Kirnberger makes it very clear that tempo is directly linked with style. This does not necessarily imply, for example, that all sarabandes should have the same tempo, but rather, one needs to study all types of sarabandes and all the various sub-styles within the sarabande category in order to make informed decisions about tempo. It is a reasonable assumption that Bach knew all the musical styles and would have been able to choose the most appropriate tempo for each style. So then, before putting a composition down on paper Bach would have had to choose a style, a meter, and associated with this style and meter, a particular tempo. We can see clearly that this was apparently the case in French Suite 6, discussed above.

(back to contents)

Establishment of six axioms and conclusion

Kirnberger does not say that each of Bach’s musical styles has a liberal range of tempos that may vary greatly from performance venue to performance venue, instrument to instrument, and depending on a variety of external factors. Kirnberger also does not say that polonaises and minuets only relate 2:3 if played on responsive instruments in ideal acoustical settings and danced by competent dancers. Regardless of the skill of the dancers, the acoustical environment, the instrument used, or the whim of the performer, the ideal dance tempo hierarchy that Kirnberger so diligently tries to explain was apparently just that—“ideal.” I do not wish to sound dictatorial here, but there is simply no getting around the overwhelming evidence that, as Kirnberger explicitly says, each style has its most natural or “definite” tempo. If true, then no performer and not even the “Master” himself (i.e., Bach) would have had the power to change this. (For more on the topic of ideal or perfect tempos, please refer to my study, “Determining Ideal Tempos: A Unified Theory of Tempo Relativity”.)

Let us now formulate six reasonable assumptions or axioms, which can be considered true unless proven otherwise:

Six axioms that can be considered true unless proven otherwise

1. The ideal dance tempos and ideal tempos for all styles in general conform to a hierarchy governed by special and unexplainable natural laws that are beyond human control. (This assumption is based on the unique properties of the ideal tempo matrix discussed in Elaboration 2 as well as Kirnberger’s descriptions here.)

2. Bach associated each style or composition with a particular tempo.

3. Bach chose one tempo for any one composition, its “definite” tempo as Kirnberger calls it, meaning that he usually did not operate with ranges.

4. Before putting a composition down on paper, Bach chose a style as well as a tempo and meter associated with that style.

5. Bach was fully aware of how many measures he achieved in his works.

6. Bach knew his usual or standard tempos in beats per minute, the tempi giusti to which Kirnberger refers, which he could have easily figured out using a clock or watch.

Continue to next Elaboration -->

Top of page

Disclaimer