Carl Philipp Emanuel Bach (1714 - 1788)

The original cover for the publication "Historisch-kritische Beyträge zur Aufnahme der Musik" (click to enlarge).

Carl Philipp Emanuel Bach (1714 –1788), was the fifth child and second (surviving) son of Johann Sebastian Bach and Maria Barbara Bach. He was an influential composer working at a time of transition between his father's baroque style and the classical and romantic styles that followed it.

In 1757 a book was published, authored by Friedrich Wilhelm Marpurg, and titled: "Historisch-kritische Beyträge zur Aufnahme der Musik". It presented, on four fold-out pages, Carl Philipp Emanuel Bach's musical dice game with the title "Einfall, einen doppelten Contrapunct in der Octave von 6 Tacten zu machen, ohne die Regeln davon zu wissen" (A method for making 6 bars of double counterpoint at the octave without knowing the rules). In the same year, Johann Philipp Kirnbergers "Allezeit fertiger Polonaisen- und Menuettencomponist" was published. As such, Kirnberger was not the only ancestor of the musical dice games.

Looking at the title of Bach's game in a little more detail, it becomes clear that we are not dealing here with a tool for random controlled "composition" of dance music, as is the case with Kirnberger. The task is therefore a completely different one. In Kirnberger's game, und those of others, two or more small sentences are assembled from an abundance of prefabricated components from which a random selection is made. The bass is the carrier of harmonic functions which moves almost similar in all possible combinations. It is also rhythmically and melodically subordinated to the upper voice. In Bach's game, however, bass and treble are in an equal, i.e. contrapuntal relationship to each other (Haupenthal). Also Bach's game at first glance appears to be a seemingly random assortment of single notes and measures. The composer's accompanying instructions outline how, by following a simple, and to all appearances arbitrary, algorithm a perfectly good piece of double counterpoint at the octave can be obtained, and without any knowledge of its workings: pick six random numbers; apply the first number to the first table [there are different tables for the right and left hand], counting forward by nine until the first measure is complete; proceed in the same way until all six measures have been filled with the proper note values. Astoundingly, a perfectly good piece of mechanically correct invertible counterpoint results (Yearsley)

The numbers in the top row represent the encoding of the upper part of the two-part setting, while the numbers of the bottom row of the lower voice match. In other musical dice games (and also in Kirnberger's), it is common that the upper and lower voice are determined together. In this case, however, the upper and lower voice each get their own numbers. When the upper part of a bar is fixed, the associated lower voice has still to be chosen. In other words, to one and the same upper voice several lower voices are equally conceivable. Consequently, the number of possible combinations is increased enormously (Haupenthal). We calculated the total number of unique compositions to be 31,381,059,609.

Marpurg reveals that Bach simply composed nine different invertible counterpoints over a given harmonic pattern, then cut up each one and spread them out at nine measure intervals. But once in place, the algorithm yields unfailingly grammatical and intricate music: the real genius in the game is that no ingenuity is required of the players. (Yearsley).

• Bach, C.P.E. (1755), Einfall. einen doppelten Contrapunct in der Octave von sechs Tacten zu machen, ohne die Regeln davon zu wissen. In: F.W. Marpurg, Historisch-kritische Beytrage zur Aufnahme der Musik, Vol.3.
• Haupenthal, Gerhard (1994), Geschichte der Würfelmusik in Beispiele, 2 Volumes, University of Saarbrücken.
• Yearsley, David (2002), Bach and the Meanings of Counterpoint, Cambridge University Press.