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RECORDED MUSIC | 6.30-9p Fractal Music in Honor of Benoît Mandelbrot (1924–2010) PERFORMANCE | 8p Music for Pieces of Wood, by Steve Reich | Performed by the Yale Percussion Group Welcome Reception | Music Program Peabody Museum of Natural History Yale University November 6, 2010 Fractal Music in Honor of Benoît Mandelbrot (1924–2010) In the visual domain, the eye can quickly guide us in identifying fractal structure. Looking at the Mandelbrot set, we instantly examine its boundary rather than
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  RECORDED MUSIC | 6.30-9pFractal Music in Honor of Benoît Mandelbrot(1924–2010) PERFORMANCE | 8p Music for Pieces of Wood  ,by Steve Reich | Performed bythe Yale Percussion Group Welcome Reception | Music ProgramPeabody Museum of Natural HistoryYale UniversityNovember 6, 2010Fractal Musicin Honor of Benoît Mandelbrot (1924–2010) In the visual domain, the eye can quickly guide us in identifying fractalstructure. Looking at the Mandelbrot set, we instantly examine its bound-ary rather than the interior. On the other hand, a glimpse of the Sierpin-ski triangle draws us not to its outer boundary, but directly to its gasket-like interior. Sometimes we discern multiple possibilities for measurement,as in the case of a tree: we can investigate the structure of its branches,root system, canopy, or perhaps its mass distribution; the view from a dis-tance might suggest assessing its relation to the forest as a whole. As with graphics, to find fractal structure in music we must first decide what characteristic we wish to examine. However, given music’s ephemeralnature, it is more difficult for the ear to guide us in identifying potentially fractal structure. Musical compositions can indeed manifest a wide variety of the power-law relationships that form the foundation of fractal geometry.Echoing the self-similarity of cloud-like structures, these relationships of-ten arise in a statistical sense that requires careful measurement. The follow-ing types of fractal scaling are represented in this evening’s recorded music:Pitch scaling: The distribution of pitches is statistically self-similar.ãDuration scaling: The distribution of durations is statistically self-similar.ãMelodic interval scaling: The distribution of melodic in-ãtervals (changes in pitch) is statistically self-similar.Melodic moment scaling: The distribution of the chang-ães in melodic intervals is statistically self-similar.Motivic scaling: A melodic or rhythmic motif is re-ãpeated simultaneously at different time scales.Event density scaling: The distribution of note activity as mea-ãsured by onset and release times is statistically self-similar.Structural scaling: An aspect of the composi-ãtional structure follows a recursive form.To be clear, music can also exhibit other types of scaling, some based onthe properties of audio signals. However, the selection of music you will hearthis evening was chosen because it shows strong evidence of fractal struc-ture with respect to some aspect of the written score. Here, we are interestedthe intentional, or more often, unintentional design of the composer.>> Over for compositions being played tonight >> For further information, visit:  Music for Pieces of Wood  , by Steve ReichPerformed by the Yale Percussion Group About the Yale Percussion Group Founded in 1997 by Robert van Sice, the Yale Percussion Group has been called “something truly ex-traordinary” by composer Steve Reich. It is composed of talented and dedicated young artists whohave come from around the world for graduate study at the Yale School of Music. Members of the YPG have gone on to form the acclaimed quartet So Percussion and to perform with Lincoln Cen-ter’s Chamber Music Two, the Carnegie Hall Academy Ensemble, the Oslo Philharmonic, and the Or-pheus Chamber Orchestra. Yale percussion students and graduates have recently won the Linz (Aus-tria) International Marimba Competition and the Concert Artist Guild Competition. Recent alumniteach at institutions such as Cornell University, Dartmouth College, Michigan State University, SUNY Stony Brook, UMass Amherst, Baylor University, and the Conservatoire de Genève (Switzerland). About the music “  Music for Pieces of Wood  grows out of the same roots as Clapping Music  : a desire to make music withthe simplest possible instruments. The claves—cylindrical pieces of hard wood—used in the piece wereselected for their particular pitches (A, B, C-sharp, D-sharp, and D-sharp an octave above), and fortheir resonant timbre. This piece is one of the loudest I have ever composed, but uses no amplifica-tion whatsoever. The rhythmic structure is based entirely on the process of rhythmic “build-ups” orthe substitution of beats for rests, and is in three sections of decreasing pattern length: 6/4, 4/4, 3/4.”(Adapted from Steve Reich’s notes for “Steve Reich @ 70” at Carnegie Hall [] ) About the composer Steve Reich has recently been called “our greatest living composer” ( The New York Times  ), “America’sgreatest living composer” ( The Village Voice  ), “. . . the most srcinal musical thinker of our time” ( The New Yorker  ), and “. . . among the great composers of the century” ( The New York Times  ). From his early tapedspeech pieces It’s Gonna Rain (1965) and Come Out  (1966) to his collaboration with video artist Beryl Koroton the digital video opera Three Tales  (2002), Reich’s path has embraced not only aspects of Western Clas-sical music, but the structures, harmonies, and rhythms of non-Western and American vernacular music,particularly jazz. “There’s just a handful of living composers who can legitimately claim to have altered thedirection of musical history and Steve Reich is one of them,” says The Guardian . In April 2009 Reich wasawarded the Pulitzer Prize in music for his composition Double Sextet  . (Adapted from Recordings played tonight  Agnus Dei II  from Missa L’homme ArméSuper Voces Musicales , by Josquin desPrez (1440–1521), Motivic scaling  Allemande from Cello Suite No. 1, BWV 1007  , by Johann Sebastian Bach (1685–1750), Interval & moment scaling Go for Baroque , by Harlan Brothers(Contemporary), Duration scaling Sarabande from Partita for Solo Flute ,BWV 1013, by Johann SebastianBach, Interval & moment scaling Country Dance , by Harlan Broth-ers, Pitch & duration scaling Bourrée I  from Cello Suite No. 3, BWV 1009 , by Johann Sebastian Bach,Structural scaling (form: AAB) Polonaises, Op. 40: No. 1 , by Frédéric Chopin(1810–1849), Event density scaling  Art of Fugue, Contrapunctus IX, BWV 1080 , byJohann Sebastian Bach, Interval scaling Reel One , by Harlan Brothers, Struc-tural scaling (form: AABA) Stretch , by Harlan Brothers, Motivic scaling  Anemonae , by Dmitry Kormann(Contemporary), Structural scal-ing (based on Golden Ratio) Le Tombeau de Couperin (Forlane) , by MauriceRavel (1875–1937), Event density scaling Study No. 31—Canon 21/24/25 , by ConlonNancarrow (1912–1997), Motivic scaling Funky Cantor  , by Harlan Brothers,Structural scaling (form: AABA) Monkey Run , by Harlan Brothers, Mo-tivic scaling (percussion part) Brecker 8 , by Harlan Brothers, Interval scaling Giant Steps , by John Coltrane (1926–1967),Interval & moment scaling (saxophone solo) Benoît Mandelbrotendlesslyextolled the virtue and power of the eye in discerning mathemati-cal truth. It guided him relentlesslythrough an eclectic array of natural,cultural, and scientific phenomenawhere issues of scaling, texture,and roughness arise. He alwayshad a strong sense that music,too, shared something of thesequalities in a measurable sense.During a discussion at Yalein 2003, Benoît suggested I ex-plore exactly what it means tosay that a given piece music isfractal. The simple sincerity of his request profoundly influ-enced the course of my life.This evening’s music is dedicatedto Benoît and his boundless legacy.— Harlan J. Brothers ©2010
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