Music as Science: The C Minor Series, No. 1--Bach's "Musical Offering"

DAILY DOSE OF BEETHOVEN (June 29, 2020)

We've discussed the musical dialogue between Beethoven and other great composers in several of our past posts. In this C-minor series, we intend to delve deeper into the discoveries of Beethoven's predecessors and successors, and extraordinary dialogue through time, that took place among them. We hope that our readers will enjoy this journey through time.

The romantic notion of "art for art's sake" locates the source of a great work of art in the passion of the artist, which he or she must 'externalize'. Each work is thus seen as an autonomous expression of the artist's deep feelings. Yet, while great passion lies within a great work, scientific problem-solving also lies within it. Like a scientist, the great artist sees what they are doing not as mere entertainment, but as also advancing civilization. Such individuals are always making new discoveries that expand our collective knowledge of the world around us. Thus, just as scientists are happy to pass problems and questions, such as "What is the nature of light?" down to subsequent generations, the same is true of great composers.

Johann Sebastian Bach's name is synonymous with what is called "Classical music" throughout the Western world. His perfection of the well-tempered system of musical composition laid the groundwork for future great composers such as Mozart and Beethoven. His advanced innovations in musical composition were realized in well over a thousand surviving masterworks. Several of these, such as the "St. Matthew Passion", "The Art of Fugue", "Mass in B Minor", "The Well-Tempered Clavier" and "A Musical Offering" are acknowledged as fundamental contributions to human thought. They make him the bedrock of any serious attempt to study, write, or perform Classical music.

Bach's discoveries did not come out of nowhere. He build them upon the work of his contemporaries and predecessors, such as Andreas Werckmeister, Dieterich Buxtehude, and Italian composers such as Corelli. Many of Bach's predecessors were engaged in the effort to establish a Well-Tempered system. They followed the work of even earlier composers, as well as that of the great astronomer Johannes Kepler, whose discoveries (reported in his 1618 Harmonice Mundi--Harmonies of the World) proved that the orbits of the planets correspond to the musical intervals. This discovery overthrew Aristotle's insistence that the Music of the World and the Music of the Spheres were two different things, and that the latter was inaudible and unknowable to man. Kepler proved that the musical system was ordered according to the laws of the universe. It was not something invented by mankind, but something discovered by us, and earthly music was not vulgar, but divine!

Werckmeister wrote several works on the need for a Well-Tempered System, and insisted that he found its basis in Kepler's astronomy. Many of Bach's earlier predecessors also saw the need for such a system. This is not just a matter of how to tune the keyboard. Some of their works were scientific experiments that were not only investigations of problems within the Well-Tempered System, but also investigations into the VERY NATURE of the musical system, in order to help establish the new Well-Tempered System. The Modal system that came before, which had governed music for centuries, produced some beautiful works. But it was limited. It was difficult to change modalities within it. The Well-Tempered System advanced and changed this.

In his 1722 Well-Tempered Clavier (Bach wrote two books of Well-Tempered Clavier "WTC", 20 years apart), Bach composed for all 24 major and minor keys. For the first time, they all could be played in tune, on the same instrument. Within a piece, he could modulate lawfully to any other key. Some of these keys had never been effectively used before. A tremendous degree of freedom was opened up!

THE MUSICAL OFFERING

In 1747, as an old man, Bach visited the court of Frederick the Great in Potsdam. His son, Carl Philipp Emmanuel Bach (CPE Bach), was the King's music master. The King, an avid music lover and amateur musician, was eager to test out "Old Bach" 's legendary abilities. He played a theme of his own invention on the flute, and reportedly asked Bach to compose a 6 part Ricercare (basically a fugue) on it. Bach replied, "let me start with something in 3-part" and improvised a rather amazing work right on the spot!

here is a scored version: https://youtu.be/NG7H8TQfGmQ

Performance by Tatyana Nikolayeva: https://youtu.be/WTVXQE9GCWA

Upon returning home, Bach composed the "Thema Regium" ("King's Theme"). The theme, in the key of C minor, was not only difficult, took some of the questions that had been posed for over a century to a new level. For example, the second half of the theme is a descending chromatic scale. The necessity for twelve different tones was known 2,000 years earlier by the Greeks. Investigating the chromatic scale by composing with it was crucial for the attempt to break out of the modal system. Several composers wrote chromatic experimental works in the early 1600's, such as J P Sweelinck, John Bull, and Girolamo Frescabaldi. Here's an example of "The Fantasia Chromatica" by Sweelinck (https://youtu.be/9zHWp9nEL0s).

The other idea addressed in the "Thema Regium" lies in the first 5 notes: C Eb G Ab B. The first three tones comprise a C-Minor triad. The tones C and G, a Fifth, is in the strong tonic-dominant relationship. Ab is a half-step up from G, and B is a half-step down from C. Thus we have a half-step motion in inversion, a mirror image. G-Ab, and C-B. Bach had experimented with this configuration 25 years earlier in the "G Minor Fugue" of his WTC Book 1, which begins D-Eb G-F# G. However, the "Thema Regium" explores something new: the large, dissonant leap from Ab to B, which is a diminished 7th. We will see the importance of that interval for investigating the scientific nature of the musical system in future postings.

Bach explored both of these ideas in the same piece, but not at the same time. The "A Minor Prelude and Fugue" from his WTC Book 2 (composed around 1742, some 20 years after he composed Book 1), explore the chromatic scale in its long prelude, and the diminished-7th leap in the fugue, starting at 6:10 in this recording. ( Friedrich Gulda plays on the Clavichord, an instrument which Bach loved, but played only in private settings, as it was too quiet for a public concert. Unlike the harpsichord, it can play louder and softer, and even with vibrato, which you will hear at the opening of the fugue.)

https://youtu.be/Em9tZaphIPM

The "Thema Regium", to our knowledge, was the first time that the two ideas were addressed together. We suspect that CPE Bach may have had a hand in coaching the King on posting a true challenge to his father. How fortunate for us that this came to pass!

Two months after returning home, Bach sent the King a package called the "Musical Offering", which employed the "Thema Regium" in many ways, including a spectacular 6-part Ricercare, that represented a great breakthrough in composition.

https://youtu.be/OSm9LEYixvA