A (German for "musical dice game") was a system for using

dice Dice (singular die or dice) are small, throwable objects with marked sides that can rest in multiple positions. They are used for generating random values, commonly as part of tabletop games, including dice games, board games, role-playing ...

to randomly generate

music Music is generally defined as the art of arranging sound to create some combination of form, harmony, melody, rhythm or otherwise expressive content. Exact definitions of music vary considerably around the world, though it is an aspe ...

from precomposed options. These games were quite popular throughout Western Europe in the 18th century. Several different

game A game is a structured form of play, usually undertaken for entertainment or fun, and sometimes used as an educational tool. Many games are also considered to be work (such as professional players of spectator sports or games) or art (suc ...

s were devised, some that did not require dice, but merely choosing a

random In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual ran ...

number A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual number ...

. The earliest example is

Johann Kirnberger Johann Philipp Kirnberger (also ''Kernberg''; 24 April 1721, Saalfeld – 27 July 1783, Berlin) was a musician, composer (primarily of fugues), and music theorist. He was a student of Johann Sebastian Bach. According to Ingeborg Allihn, Kirnber ...

's ' (German for "The Ever-Ready Minuet and Polonaise Composer") (1757 st edition; revised 2nd 1783.Nierhaus, Gerhard (2009). ''Algorithmic Composition: Paradigms of Automated Music Generation'', pp. 36 & 38n7. . Examples by well known composers include

C. P. E. Bach Carl Philipp Emanuel Bach (8 March 1714 – 14 December 1788), also formerly spelled Karl Philipp Emmanuel Bach, and commonly abbreviated C. P. E. Bach, was a German Classical period musician and composer, the fifth child and sec ...

's ' (German for "A method for making six bars of double counterpoint at the octave without knowing the rules") (1758) and

Maximilian Stadler Maximilian Johann Karl Dominik Stadler, Abbé Stadler (4 August 1748, in Melk – 8 November 1833, in Vienna), was an Austrian composer, musicologist and pianist. In 1766 he entered the Benedictine Monastery in Melk Abbey where he served as Be ...

's ' (French for "A table for composing minuets and trios to infinity, by playing with two dice") (1780). In the early 20th century the Kaleidacousticon System, using arbitrarily combinable

playing card A playing card is a piece of specially prepared card stock, heavy paper, thin cardboard, plastic-coated paper, cotton-paper blend, or thin plastic that is marked with distinguishing motifs. Often the front (face) and back of each card has a f ...

s, was unsuccessfully marketed in the Boston area as a

parlour game A parlour or parlor game is a group game played indoors using speech (from French Parler). They were often played in a parlour. These games were extremely popular among the upper and middle classes in the United Kingdom and in the United States d ...

Aesthetics

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... asa 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. ... at constrained the choice of figures n seventeenth- and eighteenth-century musicwere 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 s in nineteenth century music. See:

musical development In music, development is a process by which a musical idea is communicated in the course of a composition. It refers to the transformation and restatement of initial material. Development is often contrasted with musical variation, which is a ...

. 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 Variation or Variations may refer to: Science and mathematics * Variation (astronomy), any perturbation of the mean motion or orbit of a planet or satellite, particularly of the moon * Genetic variation, the difference in DNA among individua ...

rather than being entirely different.

Mozart

The best-known was published in 1792, by

Mozart Wolfgang Amadeus Mozart (27 January 17565 December 1791), baptised as Joannes Chrysostomus Wolfgangus Theophilus Mozart, was a prolific and influential composer of the Classical period. Despite his short life, his rapid pace of composition r ...

's publisher

Nikolaus Simrock Nikolaus Simrock (23 August 1751 in Mainz – 12 June 1832 in Bonn) was a German horn player at the court of the Elector of Cologne in Bonn and a music publisher. He was a friend of Ludwig van Beethoven and founder of the N. Simrock music publi ...

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.Zbikowski (2002), p. 149. 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 Bar or BAR may refer to: Food and drink * Bar (establishment), selling alcoholic beverages * Candy bar * Chocolate bar Science and technology * Bar (river morphology), a deposit of sediment * Bar (tropical cyclone), a layer of cloud * 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 Robert Xavier Rodríguez (born June 28, 1946) is an American classical composer, best known for his eight operas and his works for children. Life and career Rodríguez received his early musical education in his native San Antonio and in Au ...

composed his ''Musical Dice Game'' for string orchestra based on K. 516f.Robert Xavier Rodríguez: Musical Dice Game
, Wise Music Classical

Other examples

The attribution to

Joseph Haydn Franz Joseph Haydn ( , ; 31 March 173231 May 1809) was an Austrian composer of the Classical period. He was instrumental in the development of chamber music such as the string quartet and piano trio. His contributions to musical form have le ...

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.

Aesthetics

Mozart

Other examples

See also

References

Further reading

External links