Debussy Mathematics

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Transcript of Debussy Mathematics

  • Paula A. Wilhite, Ed. D. Professor of Mathematics Division Director Math, Physics, & Engineering AMATYC 2013 Grand Salon E S063

  • 1862 - Birth

    1870 - Music Lessons

    1872 - Paris Conservatory

    1879 - First Compositions

    1890s - Clair de lune

    1905 - Reflet de leau

    1910 - Girl with the Flaxen Hair 1918 - Death

  • Mona Lisa

    Leonardo da Vinci

    Early 1500s

  • Nicknamed for Leonardo da Pisa (1170-1250)

    Fn+1 = Fn-1 + Fn , if n>1

    F0 = 0 F1 = 1

    0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,

  • 2 3 1.5

    3 5 1.66667

    5 8 1.6

    8 13 1.625

    13 21 1.6153846

    21 34 1.6190476

    34 55 1.6176471

    55 89 1.6181818

    89 144 1.6179775

  • French Mathematician Edouard Lucas (1842-1891)

    Ln = Ln-1 + Ln-2 for n>1 L0 = 2 L1 = 1

    2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199,

  • 55 bars of introduction to the last

    movement of La mer;

    21 bars of introduction to Rondes de Printemps from the orchestral Images;

    34 bars comprising the first 3/8 section of Jeux;

    34 bars in first reprise of Reflets dans leau 55 bars to the beginning of its climax.

  • Three primary GS divisions

    40 bars: 25 bars 16 bars: 10 bars

    24 bars: 15 bars

    All above equivalent to 8:5

    8 and 5 are both Fibonacci numbers.

  • Most lucid exposition of the structural and proportional

    principles

    Dramatic & Dynamic Shape

  • Total: 94 bars Dynamic Focus: 58 bars Overall GS -- 94:58

    Cancels to 47:29 -- Lucas Numbers

    Primary GS -- 34:21

    Secondary GS -- 15:24 Cancels to 13:8 Fibonacci Numbers

  • Overall GS 39: 23 bars One bar removed from 13:8

    GS of GS 26: 10 bars Cancels to 13:5 Fibonacci Numbers

    Central GS 5: 3 bars or 15:9 beats

    Cancels to 5:3 Fibonacci Numbers

  • Dr. Ron Clinton Executive Vice President for Instruction Mary Galloway Wade Technical Designer Mary Lou Goodson Videographer

  • Crilly, David. Perception of Mathematical Structure and Architectural Design: Form and Forming in Music. Department of Music, Anglia Polytechnic University, Cambridge, England. Griffiths, Paul. 1985. Modern Music, A Concise History from Debussy to Boulez. New York: Thames and Hudson Inc. Howat, Roy. 1983. Debussy in Proportion; A Musical Analysis. Great Britain: Cambridge University Press.

  • McHard, James L. 2008. The Future of Modern Music. Michigan: Iconic Press. Pages 45 53. Rosen, Kenneth H. 2000. Elementary Number Theory and Its Applications. 4th Edition. New York: Addison Wesley Longman, Inc. www.debussy.fr/encd/bio/bio1_62-82.php www.goldennumber.net/architecture/fineart www.maa.org/2008foundmath/2009foundmath www.maths.surrey.ac.uk/hostedsites

  • Paula A. Wilhite, Ed.D.

    Northeast Texas Community College

    [email protected]

  • A mathematician, like a painter or poet, is a maker of patterns. If his (her) patterns are more prominent than theirs, it is because they are made with ideas.