A Musikalisches Würfelspiel (German for "musical dice game") was a system for using dice to randomly generate music from precomposed options. These games were quite popular throughout Western Europe in the 18th century. Several different games were devised, some that did not require dice, but merely choosing a random number.
The earliest example is Johann Kirnberger's Der allezeit fertige Menuetten- und Polonaisencomponist (German for "The Ever-Ready Minuet and Polonaise Composer") (1757 [1st edition; revised 2nd 1783]). Examples by well known composers include C. P. E. Bach's Einfall, einen doppelten Contrapunct in der Octave von sechs Tacten zu machen, ohne die Regeln davon zu wissen (German for "A method for making six bars of double counterpoint at the octave without knowing the rules") (1758) and Maximilian Stadler's Table pour composer des minuets et des Trios à la infinie; avec deux dez à jouer (French for "A table for composing minuets and trios to infinity, by playing with two dice") (1780).
According to Lawrence Zbikowski, "In truth, chance played little part in the success of the music produced by such games. Instead, what was required of the compilers...[was] a little knowledge about how to put the game together and an understanding of the formal design of waltzes, etc."
According to Stephen Hedges, "The 'galant' middle class in Europe was playing with mathematics. In this atmosphere of investigation and cataloguing, a systematic device that would seem to make it possible for anyone to write music was practically guaranteed popularity.
According to Leonard Meyer, "Eighteenth-century composers constructed musical dice games while nineteenth century composers did not. ... [W]hat constrained the choice of figures [in seventeenth- and eighteenth-century music] were the claims of taste, coherent expression and propriety, given the genre of work being composed, rather than the inner necessity of a gradually unfolding, underlying process [as in nineteenth century music]". See: musical development.
The way these games work may be understood in analogy to sentence construction.
1 The cow ran past the field. 2 The pig walked through the yard. 3 The sheep ran into the marsh.
One rolls one die for each word and selects the word from the appropriate column according to the number. Thus if one rolls 1 2 3 1 2 3 one is given, "The pig ran past the marsh." Each progression is essentially the same, there may be more or less choices for different slots, and the choices offered for each slot are slight variations rather than being entirely different.
The most well-known was published in 1792, by Mozart's publisher Nikolaus Simrock in Berlin (K. 294dK3 or K. 516fK6). The game was attributed to Mozart, but this attribution has not been authenticated. The dice rolls randomly selected small sections of music, which would be patched together to create a musical piece. This game is capable of producing 1116 = 45,949,729,863,572,161 different yet similar waltzes. Some measures have only one possibility no matter what the roll of the dice (measure 8/16) while other measures have a different possibility for each roll (measure 1/16).
Mozart's manuscript, written in 1787, consisting of 176 one-bar fragments of music, appears to be some kind of game or system for constructing music out of two-bar fragments, but contains no instructions and there is no evidence that dice were involved.
The titles of the supposed Mozart compositions are:
- Anleitung zum Componieren von Walzern so viele man will vermittelst zweier Würfel, ohne etwas von der Musik oder Composition zu verstehen (German for "Instructions for the composition of as many waltzes as one desires with two dice, without understanding anything about music or composition")
- Anleitung zum Componieren von Polonaisen... (German for "Instructions for the composition of polonaises...")
The attribution of Joseph Haydn's Gioco filarmonico o sia maniera facile per comporre un infinito numero de minuetti e trio anche senza sapere il contrappunto (Italian for "The game of harmony, or an easy method for composing an infinite number of minuet-trios, without any knowledge of counterpoint") has also not been authenticated.
- Algorithmic composition
- Aleatoric music
- The Glass Bead Game, 1943 novel by Hermann Hesse
- Nierhaus, Gerhard (2009). Algorithmic Composition: Paradigms of Automated Music Generation, pp. 36 & 38n7. ISBN 9783211755396.
- Nierhaus (2009), p. 262.
- Zbikowski, Lawrence M. (2002). Conceptualizing Music: Cognitive Structure, Theory, and Analysis, pp. 142–143. ISBN 9780195187977. Quoted in Berkowitz, Aaron (2010). The Improvising Mind: Cognition and Creativity in the Musical Moment, p. 65. ISBN 9780199590957.
- Hedges, Stephen A. (1978). "Dice Music in the Eighteenth Century", pp. 184–185, Music & Letters, vol. 59, pp. 180–187. Quoted in Berkowitz (2010), p. 65n60.
- Meyer, Leonard (1989). Style and Music: Theory, History, and Ideology, p. 193. ISBN 9780226521527.
- Cope, David (1996). Experiments in Musical Intelligence, p. 7. Madison, Wisconsin: A–R Editions, Inc. ISBN 978-0895793379.
- Zbikowski (2002), p. 148.
- Berkowitz (2010), p. 66.
- Musikalisches Würfelspiel, K. 516f: Scores at the International Music Score Library Project
- "Robert Xavier Rodríguez: Musical Dice Game", Schirmer.com.
- Klotz, Sebastian (1999). "Ars combinatoria oder 'Musik ohne Kopfzerbrechen': Kalküle des Musikalischen von Kircher bis Kirnberger", Musiktheorie 14: 231–245. (in German) Cited in Zbikowski (2005), p. 140n8.
- Levy, David (2006). Robots Unlimited, p. 51. Wellesly, Massachusetts: A. K. Peters. ISBN 9781568812397.
- Ratner, Leondard G. (1979). "Ars combinatoria: Chance and Choice in Eighteenth-Century Music", Studies in Eighteenth-Century Music: 343–363. Cited in Zbikowski (2005), p. 140n8.
- Noguchi, Hideo. "Mozart – Musical Game in C K. 516f*", Mozart Studies Online.
- dice.humdrum.org (Online implementation of K 516f)
- Mozart Dice Game (iOS App with score and MIDI generator)
- Mozart (Browser-based implementation with score and MIDI generator)
- Musical Dice (Sibelius notation software plugin)