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Home , Embraceable You, Girl Crazy, I Got Rhythm, Porgy and Bess, Rhapsody in Blue

“Best of Gershwin” https://www.youtube.c om/watch?v=5cLZBeQE qq8 8:00 – 12:08 14:58 – 16:10 23:49 – 24:52 32:28 – 34:24 51:36 – 54:37

The Beauty of Mathematics in Gershwin’s Classical

AMATYC 2015 New Orleans “City of Jazz” S074 - Rhythm II Paula Wilhite (Jacob Gershvin) Born: September 26, 1898 Brooklyn, Died: July 11, 1937 Hollywood, California

George Gershwin “” https://www.youtube.com/watch?v=eFHdRkeEn pM 0:00 – 2:30

Musical Preparation

 Gershwin first - 1910  Charles Hambitzer – Classical piano teacher  Edward Kilenyi – Musical theory teacher  – Mathematical System of Composition Instructor Famous Musical Compositions “Swanee” 1918 “Rhapsody in Blue” 1924 “ in F” 1925 “” 1928 “I’ve Got Rhythm” 1930

Famous Shows Oh, Kay! 1927 Strike Up the Band 1930 1930 1931 and Bess 1935

Time July 20, 1925 The first American composer to reach this notoriety. Impact of Gershwin’s Life  Popularized musical jazz compositions  Wrote over 12 Broadway shows  Congressional Gold Medal – 1985  Pulitzer Prize Awarded Posthumously – 1998  The George and Lifetime Musical Achievement Award

Gershwin & Rolling Stone

“Someone to Watch Over Me” Sting “Summertime” “S Wonderful” Diana Krall “” “They Can’t Take That Away Rob Stewart & From Me” Michael Buble Nat King Cole “Embraceable You”

https://www.youtube.co m/watch?v=Eo5X54WXvN M&list=RDCbTcBGPeIrE&i ndex=4 0:00 – 0:40

Ella Fitzgerald “Summertime”

https://www.youtube.co m/watch?v=XivELBdxVR M 0:00 – 0:45

Sting “Someone To Watch Over Me”

https://www.youtube.c om/watch?v=v19QY6n atR4 1:10 – 1:34

Diana Krall “S Wonderful” https://www.youtub e.com/watch?v=P1s 6Fc0E9oc 0:38 – 1:21 Short version

Rod Stewart & Michael Buble “They Can’t Take That Away From Me”

https://www.youtube.com/watch ?v=EPdnWa4PNTs 0:08 – 0:48

George Gershwin “I’ve Got Rhythm” https://www.youtube.co m/watch?v=1bKstQNsQKc

0:00 – 1:52

George Gershwin “Variations on I’ve Got Rhythm” Schillinger System of Musical Composition I. Rhythmic and Melodic Design Permutation; Coordination Time Structures; Geometrical Projections II. Pitch-Organization III. Elaboration of a Melodic Line

George Gershwin “Variations on I’ve Got Rhythm”

https://www.youtube.com/watch? v=mR5Uy8hU1iE 0:20 – 0:29

Gershwin’s Variations on “” Expansion of Initial Motive mm. # coefficient 1st int. 2nd int. 3rd int. 1-2 1 2 3 2 3-4 2 Whole-tone color 4 6 4 5-6 3 Octatonic color 6 9 6 7-8 5 Chromatic Element 10 15 10

Allusions to Scales by Geometric Expansion , Act II, Scene 3 Systematic Geometric Expansion Porgy and Bess “Act III Scene 3 Introduction” https://www.youtube.com/watch?v =1YGavxuQlOY 0:00 – 1:20

Geometrical Inversion of a Melody A

Retrograde Inversion Retrograde Inversion Melody Line Constructed From Geometric Projections of Melody A Motives Porgy & Bess

< P, I(P) >

Motives a, b, c, d, e Motives Porgy & Bess Act III Scene 3

R 125 3 – 5 < a, b, c > R 126 1 – 2 < I(a), I(b), c > R 126 3 – 5 < a, b > R 126 6 - R 127 1 < I(b), I(a) > R 127 2-3 < a, b >

Schillinger’s Techniques Porgy and Bess Act III Scene 3

Schillinger’s Techniques Porgy and Bess Act III Scene 3

The Beauty of Mathematics in Gershwin’s Classical Jazz

Jazz It Up at AMATYC 2015!

Paula A. Wilhite, Ed.D. Professor of Mathematics Division Chair Math, Physics, Eng Northeast Texas Community College [email protected]

Works Cited Feinstein, Michael, Jackman, Ian. The Gershwins and me: a personal history in twelve songs. Simon & Schuster. NY 2012. Levinson, Ilya. What the Triangles Have Told Me: Manifestations of The Schillinger System of Musical Composition in George Gershwin’s Porgy and Bess. University of . 1997. Works Cited Muth, Lisa K. “The Schillinger System: Mathematics, or ?” www.conn8diva.net/lkm/ schillinger.pd Nauert, Paul. “Theory and Practice in Porgy and Bess: The Gershwin-Schillinger Connection”. The Musical Quarterly. Vol 78. No 1. pp. 9 – 33. Pollack, Howard. George Gershwin. University of California Press. 2006. Rimler, Walter. George Gershwin: an intimate portrait. University of Illinois, 2009.

Works Cited

Schneider, Wayne, J. The Gershwin Style: new looks at the Music of George Gershwin. University Press. 1999. Schwartz, Charles. Gershwin: His Life and His Music. Da Capo Inc. 1979. Wyatt, Robert, Andrew, John. The George Gershwin Reader. Oxford Press University. 2004.

Works Cited http://gershwin.com/gershwin-timeline/ http://nationalhumanitiescenter.org/tserve/freedom/1917beyo nd/essays/jazz.htm https://songbook1.wordpress.com/fx/si/sw/composers-and- lyricists/george-gershwin/george-gershwin-biography/

Music Downloaded Best of Gershwin https://www.youtube.com/watch?v=5cLZBeQEqq8 “Embraceable You” https://www.youtube.com/watch?v=Eo5X54WXvNM&list=RDCbTcB GPeIrE&index=4 “I’ve Got Rhythm” https://www.youtube.com/watch?v=1bKstQNsQKc “Rhapsody in Blue” https://www.youtube.com/watch?v=eFHdRkeEnpM

Music Downloaded “S Wonderful” https://www.youtube.com/watch?v=P1s6Fc0E9oc “Someone to Watch Over Me” https://www.youtube.com/watch?v=v19QY6natR4 “Summertime” https://www.youtube.com/watch?v=XivELBdxVRM “They Can’t Take That Away From Me” https://www.youtube.com/watch?v=EPdnWa4PNTs

Music Downloaded Porgy & Bess “Act III Scene 3 Introduction” https://www.youtube.com/watch?v=1YGavxuQlOY “Variations on I’ve Got Rhythm” https://www.youtube.com/watch?v=mR5Uy8hU1iE