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,

In June 1992 I had just finished my first year at the University of Kansas working towards a D.M.A. in piano performance and M.M. in historical musicology. One of the courses I really enjoyed that year was a “Performance Practice Seminar” taught by Professor J. Bunker Clark. For this course I wrote a term paper on “Tempo in the Baroque,”

In the eighteenth century, the normal or natural tempo that represents the music most clearly was known as tempo giusto, also sometimes referred to as tempo ordinario. Eighteenth-century performers were generally steeped in tradition and would have rarely chosen a tempo outside the accepted range for any given style. It was not until the time of Beethoven that composers and performers began to do away with the idea of tempo giusto and to challenge established conventions.

In his biography Johann Sebastian Bach: The Learned Musician, Christoph Wolff begins with a ten-page essay, a Proloque titled “Bach and the Notion of Musical Science,” which sets forth the thesis that Bach preferred to refer to himself as “one who produces works of musical science” rather than a “mere practitioner of music”. Wolff writes:

The letters Alpha and Omega, Α and Ω, are the first and last letters of the Classical Greek alphabet, which symbolize the unity and oneness of “God, the Father” and “God, the Son” in Christian theology. Since Christ and God are understood as being equal, incorporating such symbolism into multi-movement musical works requires making the first and last “elements” equal, which may refer to the first and last notes of a melody or fugue subject.

Theorizing about proportional tempos in Bach’s music is nothing new and this book is certainly not the first publication to propose such a thing; however, this author is perhaps the first person to categorize these proportional tempos into a logical and coherent system of rows and columns consisting exclusively of integers.

In Chapter 5, the forty examples of extremely accurate duration ratios (with an average discrepancy of 1.2%) from a wide variety of works and genres indicates that Bach operated with a special kind of system that allowed him to achieve these ratios.

coming soon!

The first and third movements, chorus and bass aria, have a close 3:2 beat ratio, 296:192, and 1:1 tempo ratio, 48:48, resulting in virtually equal durations, 3:02 and 3:03.

The first and second movements, (Allegro) and Adagio, have a close 2:1 measure ratio, 58:28, and equal tempos, 84 bpm, resulting in a close 2:3 duration ratio, 2:45-4:00. Two fewer measures for the first movement, 56, result in a 2:3 duration ratio of 2:40-4:00…