Prelude
“Don’t confuse hypothesis and theory. The former is a possible explanation; the latter, the correct one. The establishment of theory is the very purpose of science.” – Martin H. Fischer
Introduction
Tempo is the speed at which music is performed, which may range from very slow to very fast. Imagine if a song were not popular, and hence, the song had not developed a standardized tempo tradition. In this case, which singer’s or performer’s tempo would be the most correct in terms of tempo? Now, imagine if a song were popular, and hence, the song had over time developed a standard tempo. In this case, if a well-educated and experienced singer were to perform the song significantly faster or slower than the standard, would his/her tempo be “incorrect”? This is a difficult question that cannot be answered definitively.
Claiming such a tempo to be “incorrect” implies that the critic knows the definitively “correct” tempo. And what does “correct” imply anyway? Putting all conditioning aside and judging the performer’s overall performance with no preconceptions, is it possible that this “incorrect” tempo could in fact be “correct”? The answer is “certainly”! Most performers and listeners use “correct” synonymously with “most popular.” That is, a “correct” tempo simply means the tempo most musicians play for the song/piece/work. In other words, majority rules. The glaring problem with this philosophy is that musical interpretation does not operate under democratic principles, and this includes tempo. If a performer decides on a certain tempo, then who is to say if it is correct or not? Isn’t this no different than the philosophy of Jesus’ famous words, “He who is without sin be the first to cast a stone”?
Now enter the great Johann Sebastian Bach. We today are 300 years away from ever having heard Baroque musicians perform. Is there such a thing as “correct” tempo in Bach’s music? Let us reword this question to: Could Bach have intended a specific type of tempo for each style he used in his music? The answer to the first question is an unequivocal “no” while the answer to the second question is an unequivocal “yes.” Going a step further, if Bach intended a specific tempo for each style, what would be the best and most logical way to determine these tempos expressed in beats per minute according to the modern metronome? (The metronome was not invented until around 70 years after Bach’s death.) If these tempos are determinable, do they relate proportionally or do they relate at all?
This author seeks to answer these questions and much more. Discovering Bach’s Secret Tempo Code introduces the hypothesis or theory that Bach planned duration ratios between movements analogous to how an architect plans specific dimensions for the rooms of a house. For example, an architect may specify one room to be 20 square feet and another room to be perhaps two times larger at 40 square feet. The dimensions of a rooms of a house are analogous to the lengths of movements in which lengths can further be defined by number of measures or actual performance duration in minutes and seconds. In the same fashion, like the way an architect plans a 1:2 dimension ratio between rooms, could Bach have planned one movement to be half or two times the duration of the next or previous movement? Indeed, Bach not only “could have” but this study will show that Bach “definitely did” this in virtually all his works.
The Hypothesis
Let us as an introduction consider an example, the comparison of Inventions 8 and 9. Not only does this pair represent a major-minor pair, in the same key of F, but both have the same meter, 3/4, and the same number of measures, 34. The only other inventions to have the same meter and number of measures are nos. 1 and 15. (These first and last inventions are discussed further in later chapters.) Considering that invention 8 is “fast” (in the corrente style, which was a fast dance) while invention 9 is “slow” (in the sarabande style, which was a slow dance), and both have the same number of measures, is it reasonable to assume Bach intended invention 9 to be half the speed of invention 8 to create a 1:2 duration ratio like an architect’s 1:2 dimension ratio? This is not only a reasonable assumption, but these two inventions work very well musically with a 2:1 tempo relationship like Q = 96 and 48. Most performers tend to play tempos like these because they seem to be the natural tempos for these markedly contrasting styles. Invention 8 is “fast” and mostly staccato while invention 9 is “slow” and mostly legato. “Slow” is, more specifically, half “fast.” This automatically makes invention 9 twice the duration of invention 8 due to the same number of measures, 34. (See Diagram1.)
Diagram 1. Inventions 8 and 9 (BWV 779, 780)
Let us consider another example from the 15 Inventions, this time nos. 3 and 4. Once again, this is a major-minor pair, in D, with the same meter, 3/8, and a slightly different number of measures, 59 and 52, respectively. Was Bach trying to indicate something here? If he intended proportionally related durations, it could not possibly be 1:2 or 2:1 like inventions 8 and 9, but instead, the most likely possibility is equal durations or 1:1 duration ratio. If so, then Bach must have intended invention 4 to be a little slower than invention 3. This goes against standard convention since most performers usually play invention 4 faster than invention 3. The tempo of invention 4 has a speed limit inherent within the trills, in that it should only be played as fast as one can play thirty-second-note trills clearly and evenly for multiple measures. Once one chooses a tempo at which the trills can be played properly, this tempo slightly speeds up for the passepied style invention 3. The passepied was often described as a “fast minuet” and was a lively and sprightly dance. Playing invention 3 a little faster than invention 4 now makes much sense, considering the lively passepied style, the major key, and that its extended trills are about half the length of the extended trills in invention 4, thus justifying a slightly faster tempo. Such a tempo relationship automatically creates a 1:1 duration ratio, which is analogous to an architect planning two rooms of the same size. (See Diagram 2.)
Diagram 2. Inventions 2 and 3 (BWV 773, 774)
If our assumptions are correct and Bach intended inventions 3 and 4 to have a 1:1 duration ratio, inventions 8 and 9 to have a 1:2 duration ratio, and other movement pairs to have similar proportional relationships, then it can be concluded that Bach must have known his tempos in beats per minute. After all, it is impossible to plan the relationships between tempos without first having concrete speeds in beats per minute with which to work. This does not imply that Bach timed his works with a stopwatch or that he had his own secret metronome before Johann Maelzel patented his Metronome in 1826, but rather, it implies that Bach was aware and fully cognizant of what his standard tempos were in beats per minute, and he knew how they all relate proportionally in an interrelated system.
All Bach would have needed to accomplish this is the ability to clock a precise minute of time with a clock, thereby making it possible to conduct a certain tempo for one minute to track the number of beats that occur. Then, all Bach would have needed is some basic arithmetic calculations and intimate knowledge of time signatures and their connotations to construct a logical and proportional system of tempo expressed in a matrix of whole numbers. And Bach certainly possessed all these abilities plus more.
Organization of this Book
Discovering Bach’s Secret Tempo Code is organized in two parts. Part 1 represents the historical and analytical half while Part 2 represents the statistical and analytical half. Chapter 1 introduces the reader to this author’s unique story and personal experience. It is not a scholarly chapter, but rather, an extremely important personal story that cannot be discounted. Chapter 2 discusses tempo traditions in Bach’s time versus our modern time. Chapter 3 sets the foundation for understanding Bach as a “musical scientist” with help from Professor Christoph Wolff. Chapter 4 introduces perhaps the most important symbolic element Bach employed both theologically and mathematically to symbolize the Divine and the Imitation of Nature, which is that of The Alpha & The Omega. Chapter 5 explains the present analytical system using some typical musical examples. Chapter 6 shows how Bach further sought the Divine and Imitation of Nature with his use of the numbers 1-2-3 to permeate his works through duration ratios, namely, 1:1, 1:2 (2:1), 2:3 (3:2). Chapter 7 serves as a conclusion to Part 1.
Part 2 is more objective than Part 1, which consists of spreadsheets and analyses of selected works. The works selected are important works that most clearly demonstrate the main hypothesis that Bach planned specific numbers of measures when combined with specific tempos to create specific duration ratios. This mathematically oriented compositional process, which Bach revealed to no one and which this author discovered in the summer of 1992, represented the essence of Bach’s modus operandus. This was Bach’s “secret tempo code,” which remains to be discovered with patience and understanding throughout the pages of this book.
