choices for different slots, and the choices offered for each slot are slight variations rather than being entirely different. Mozart The best-known was published in 1792, by Mozart's publisher Nikolaus Simrock in Berlin (K. 294d or K. 516f). 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. All measures except 8 and 16 have different possibilities for each roll (i.e. 11 different versions), with measure 8 only having one possibility and measure 16 having two. This gives a total of 2×1114 = 759,499,667,166,482 different yet similar waltzes. If the game is played with dice (as intended), then these different pieces are not equally likely due to the different probabilities for different dice sums. 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: (German for "Instructions for the composition of as many waltzes as one desires with two dice, without understanding anything about music or composition") (German for "Instructions for the composition of polonaises...") Robert Xavier Rodríguez composed his Musical Dice Game for string orchestra based on K. 516f. Other examples The attribution to Joseph Haydn of (Italian for "The game of harmony, or an easy method for composing an infinite number of minuet-trios, without any knowledge of counterpoint") has not been authenticated either. See also Algorithmic composition Aleatoric music PermutationThe Glass Bead Game, 1943 novel by Hermann Hesse References Further reading Klotz, Sebastian (1999). "Ars combinatoria oder 'Musik ohne Kopfzerbrechen': Kalküle des Musikalischen von Kircher bis Kirnberger", Musiktheorie 14: 231–245. Cited in Zbikowski (2005), p. 140n8. Levy, David (2006). Robots Unlimited, p. 51. Wellesly, Massachusetts: A. K. Peters. . 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. External links Noguchi, Hideo. "Mozart – Musical Game in C K. 516f*", Mozart Studies Online''. Musikalisches Würfelspiel (Online implementation of K 516f) Mozart Dice Game (iOS App with score and MIDI generator) Musical Dice (Sibelius notation software plugin) Compositions by Wolfgang Amadeus Mozart Combinatorics Games of chance Music education