Mozart’s Dice Game and other beautiful connections between probability, music, art, drama, film




Дата канвертавання24.04.2016
Памер46.29 Kb.





Mozart’s Dice Game and other beautiful connections between probability,

music, art, drama, film,

literature and poetry




Ron Lancaster

35 Oak Knoll Drive

Hamilton, ON

L8S 4C2
ron2718@nas.net

Lecturer, Mathematics Education

University of Toronto
rlancaster@oise.utoronto.ca




Mozart's Numbers, Section 37.6.9 of the book Mazes for the Mind by Clifford Pickover (St. Martin's Press, ISBN 0-312-10353-0)
In order to compute any Mozart symphony number S from its Kochel number K you can use

The Kochel catalogue is a chronological list of all of Mozart's works, and work of Mozart's may be referred uniquely by its Kochel number. For example, the "Symphony number 40 in G minor" is K.550. The formula will give an answer not more than two off, 85% of the time.
Information about cataloging music is available at

Music Cataloging

http://library.gmu.edu/resources/fa/musiccat.html
What's In a Name - Indexing Systems

http://www.5mbs.com/insys.htm




Mozart's Dice Game (Musikalisches Würfelspiel) and aleatoric music
Mozart's Melody Machine

www.sciencenews.org/articles/20010901/mathtrek.asp


Mozart's Dice Waltz

http://tamw.atari-users.net/mozart.htm


Schott Musik International: Links

www.schott-music.com/dicegames/links.htm


Mozart - Musical Game in C K. 516f

www.asahi-net.or.jp/~rb5h-ngc/e/k516f.htm


Mozart's dice game

http://maven.smith.edu/~mcharley/multimedia/mozartdice/dice_game.html


Mozart Dice Game

http://jmusic.ci.qut.edu.au/jmtutorial/MozartDiceGame.html


Robert Xavier Rodríguez : Musical Dice Game

www.schirmer.com/default.aspx?TabId=2420&State_2874=2&workId_2874=25473


aleatoric music: Information from Answers.com

http://www.answers.com/topic/aleatoric-music


Carousel Publications

1304 Route 42, Sparrowbush, NY 12780

Telephone: (212) 758-9399

Website: www.carousel-music.com/index2.html


Carousel Publications sells kits for teachers that contain the sheet music for playing Mozart's Dice Game along with background information. They also sell kits for Mozart's Dice game played on a guitar and for composing jazz and ragtime music on any instrument.

Chance in Art

Ellsworth Kelly

Ellsworth Kelly: Spectrum Colors Arranged by Chance

www.moma.org/collection/browse_results.php?criteria=O%3AAD%3AE%3A3048&page_number=7&template_id=1&sort_order=1
ART VIEW; Ellsworth Kelly's Coming of Age in Paris

http://query.nytimes.com/gst/fullpage.html?res=9E0CEFDF1230F932A35752C1A964958260&pagewanted=all


Grids

http://iaaa.nl/cursusAA&AI/grid.html


A Throw of the Dice Never Will Abolish Chance

http://www.artextbooks.com/images/a17122.html


Chaos and Fractals

http://classes.yale.edu/fractals/MacSoftware/DSCInstr.html


George Korsmit

1st Color Room

www.edbprojects.nl/exhibitions/george_korsmit.htm
Chance in Drama

The Aleatory Project

Thought for Food Productions: The Aleatory Project

http://webdesign.senecac.on.ca/cmcdowell/tff/aleatory.html
Thing 1 and Thing 2

Mobius Fall 2003

http://world.std.com/~mobius/fall03/thing.html
Chance in Film

You Bet Your Life ( Spiele Leben)

Toronto International Film Festival Talk

http://tifftalk.blogspot.com/2005/09/spiele-leben-you-bet-your-life.html
Bangkok International Film Festival 2006

www.bangkokfilm.org/2006/en/films/film_detail.aspx?searchby=title&id=F0254


Six Reels Of Film To Be Shown In Any Order (Permutations)

http://ftvdb.bfi.org.uk/sift/title/50946#


SN by Fred Camper

http://www.fredcamper.com/F/SN.html



Chance in Literature

Composition No. 1 by Marc Saporta

http://nickm.com/if/composition_no_1.html


Ergodic literature

http://www.mathdaily.com/lessons/Ergodic_literature


Dice Man and The Book of the Die by George Cockcroft

http://www.answers.com/topic/the-dice-man

http://www.answers.com/topic/the-book-of-the-die
Chance in Poetry
One Hundred Thousand Billion Sonnets (Cent Mille Milliards de poèmes) by Raymond Queneau
Cent mille milliards de poemes

http://mathforum.org/library/drmath/view/56211.html


100,000,000,000,000 Sonnets by Raymond Queneau

http://www.growndodo.com/wordplay/oulipo/10%5E14sonnets.html


Queneau Sonnets

http://www.bevrowe.info/Poems/QueneauRandom.htm


Chance in your life: Need help making a decision?
decision dice by bombay duck

www.bombayduck.co.uk/bbd/store/product_list.jsp?id=126&oby=&brc=125


Books on probability; mathematics and music
Struck by Lightning: The Curious World of Probabilities, Jeffrey Rosenthal

Harper-Collins, ISBN 0-002-00791-6


Music: A Mathematical Offering, Dave Benson

Cambridge University Press, ISBN 0-521-85387-7


The Math Behind the Music, Leon Harkleroad

Cambridge University Press, ISBN 0-521-00935-9


Music and Mathematics: From Pythagoras to Fractals

Edited by J. Flauvel, R. Flood, and R. Wilson



Oxford University Press, ISBN 0-19-929893-9



Mazes for the Mind: Computers and the Unexpected

Clifford Pickover, St. Martin's Press, ISBN 0-312-10353-0


37.6.5 Chess Music
A one-time chess player, artist Ronald R. Brown from Pennsylvania composes music using the chess Knight's Tour. The Knight's tour problem is one of the oldest known problems in the history of chess. In chess, the Knight can only move in a prescribed L-shaped pattern. The problem is to move a Knight on a chessboard so that all 64 squares of the board are traversed only once. The number of distinct solutions to the Knight's tour problem is immense - estimates range from 31 million to To create chess music, Brown first writes a solution to the Knight's problem, such as the one below:


50

11

24

63

14

37

26

35

Up 4

23

62

51

12

25

34

15

38

Up 3

10

49

64

21

40

13

36

27

Up 2

61

22

9

52

33

28

39

16

Up 1

48

7

60

1

20

41

54

29

Middle C

59

4

45

8

53

32

17

42

Down 1

6

47

2

57

44

19

30

55

Down 2

3

58

5

46

31

56

43

18

Down 3

To understand the table of numbers, the knight starts at the position marked "1" and then proceeds to the position marked "2" and so on, traversing all the squares on the chessboard. This can be mapped to interesting music by considering each knight's position as a note, the pitch of which is determined by the row it is in. Starting at middle C, the next note is two white notes lower, the third note three white notes lower (from middle C), etc.


Summary of mapping:
0, -2, -1, +2, -2, +1, +2, -1, +2, +1, +2, -1, -1, +2, -1, -2, -2, -2, +1, +2, +2, -1, +2, +1, -1, +1, -2, -1, -1, -2, -1, +2, +2, +2, +1, -2, +2, -1, -2, +1, -2, -1, -2, +1, +1, -2, +1, +2, +2, +2, -1, -2, -2, +1, -2, -1, +1, -1, +2, +1, +1, +2, +1, -2
Information about how a Knight's Tour can be used to create art can be found at

Knight's Tour Art



http://www.borderschess.org/KTart.htm



CODEBOOK by Rudresh Mahanthappa, Pi Recordings


Jazztimes, December 2006 (CD Reviews)
Rudresh Mahanthappa composed the nine pieces on Codebook by taking inspiration from ideas and concepts found in cryptography; rhythms and melodies were encoded or convoluted in order to approach the music from newer, more challenging angles. Daunting as this may seem, the alto saxophonist wound up with results that justify the means without being overshadowed by them. Codebook might not win listeners immediately, but it keeps pulling you back to decipher its contours.
The rapid, complex alto melody of “The Decider” that launches the album presents a good jump-off point, with pianist Vijay Iyer, bassist Francois Moutin and drummer Dan Weiss keeping the music grounded, but lying in wait for a moment to push it in a different direction. This happens in “Enhanced Performance,” where an uneven time signature keeps increasing in tempo, stoking the saxophonist’s fire only to come to an abrupt end. “D (Dee-Dee)” begins with a more conventional theme, only to move in and out of tempo, landing in bass and piano solos marked by strange accents and torrents on clusters, respectively.
With a tone that could be described as pungent, Mahanthappa’s performance comes across much like a compelling narrator whose presence immediately puts you under his spell. But Iyer, Moutin and Weiss also perform at such a level that their accompaniment proves as intriguing as their solo sections.
Science, September 15, 2006
COUNT THOSE BEATS. Modern jazz can be as complex as an exotic mathematical problem. But saxophonist Rudresh Mahanthappa's music is inspired by math itself.
The New York-based jazz composer's latest album, Codebook, conveys elements of number theory and cryptography in musical form. In some pieces, concepts such as the Fibonacci sequence--an infinite set of integers created by adding the last two numbers in the series--serve as the basis of the rhythm and melodies. In others, mathematical ideas dictate the evolution of the score. Encoded throughout the music are the names of the band members and famous jazz melodies.
"Math has always been at the core of what I do," says Mahanthappa, 35, who has been fascinated by math from an early age. He has made a name for himself by blending jazz with the complex rhythms of Indian classical music. Adding a mathematical component was an even bigger challenge. "Translating an idea from number theory or cryptography to music doesn't automatically yield anything that's playable or that sounds good," says Mahanthappa.
"He proves, by using musical notes, what mathematicians have always believed: that math is beautiful," says Princeton University mathematician Manjul Barghava, himself an acclaimed player of the tabla, an Indian percussion instrument. Codebook will be available from Pi Recordings on 26 September.




База данных защищена авторским правом ©shkola.of.by 2016
звярнуцца да адміністрацыі

    Галоўная старонка