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Mathematica, for solo flute(s) and quadriphonic tape is the first from a set of four pieces entitled Quadrivium.   The four pieces in Quadrivium are designed to be played either individually or together as a complete uninterrupted cycle.  All the pieces are committed in one way or another to exploring the spatialization of sound.

In Mathematica, evolving probability tables define the harmonic, dynamic and rhythmic unfolding of the piece.   What might this mean?  Imagine a walk from the city toward the outlying natural spaces.  At a certain point we can be sure we are no longer in the city, that we have arrived to the natural spaces and no city left in sight.  The dividing line is fuzzy and not abrupt.

Mathematica divides itself into three roughly equal sections. The first ascends and displays the material used in the work. The second is a virtuoso plateau which becomes more and more dense until it eventually gives way to the last section;   a descent, which in purely structural terms (i.e. not immediately perceptible) is a palindrome of the first section. 

Quadrivium was composed in 1994/95 while I was holder of the Fredric A. Julliard/Walter Damrosch 1995 Rome Prize in Music Composition.  The full Quadrivium received its first performance in April of 1998 in Rome. 

The use of the latin term Quadrivium is not without irony.   The Quadrivium, meaning the four ways, (Astronomia, Mathematica (Arithmetica), Geometria, Musica) were the subjects of the medieval liberal arts education.  While composing this collection of pieces, I was a Fellow at the American Academy in Rome. The Academy is a place intended for artists and scholars to find inspiration from the great arts of antiquity; I find this humorous.  No indication in my early life pointed toward an eventual stay in Rome for the purpose of greater artistic enlightenment.  I was really amused the day that the former First Lady, Hillary Rodham Clinton presented me with the Rome Prize in the White House!  Today the irony only deepens; I am a Full Professor in a major University with all rights and privileges due!

In the American Academy there hangs a series of portraits of the educated men who were former fellows, most from well-to-do established American families.  Somewhere the process really became a democratic selection with women, people like me from the other side of the tracks, and other non-insiders invited to participate.  It is a fine tradition, but in honesty no longer functions with its original intent.   The original Rome Academy, at the Villa Medici, was invented by Louis XIV to provide home for artists who were copying the imperial design of Rome for translation to imperial France and in particular Versailles.

Instructions for the performer:

When the piece begins there is no performer present on stage.  The tape is put into play.  After the tape is audible (about 5-8 seconds), the performer enters from the normal stage entrance in a relaxed manner and prepares for his/her performance.  He/she can move freely, place the instruments, the music, warm the instruments, put the headphones on, signal to the mixer that the pre-click has arrived and he/she is in place to play.  This really should not be "theatre", but simply a natural entrance and preparation.  From the beginning of the tape part to the first live flute note is 1'08".

When played with Quadrivium, the piccolo, at the end of the piece, slowly pulls away from the microphone or detaches the contact mic and  descends the stage while the clarinetist is entering and beginning to play.   If possible he/she should exit along the center isle of the auditorium and out the public entrance way at rear.  All of this occurs while the tape is slowly fading out.  The flutist should try and match and respond to the sound and rhythms coming from the tape as he/she makes an exit.

When playing Mathematica as a solo piece, the piccolo should not exit the stage.  At the end of the piece, the piccolo should stay facing the audience and the microphone for approximately 10-15 seconds while ad libing continuous breath and key click sounds (on the pitch indicated).  The performer should slowly move the piccolo close towards the microphone and then pull away repeatedly to create a mixing effect in the hall.  Breath and key clicks are played simultaneously.  The performer imitates and responds to the sounds coming from the tape.  The flutist fades out with the tape.


Since each concert hall has unique acoustics, the mixing must be created separately for each performance.  The four tracks of tape part are "dry" (without reverb).  Reverb should be added to both the tape and the live amplification.  When possible, the amplification of the flute should be louder in the front speakers and softer in the rear to help localize the sound with the stage and the instrumentalist.  Avoid using too much reverb, but not at the expense of creating the very undesirable situation where the sound of the flute and the sound of the tape are segregated in space.

When possible, the flutist should be equipped with headphones that allow him/her to control in real time the level on the click track.  The best situation includes a headphone monitor for the flutist (i.e. clicktrack left, tape part right).  If a stage monitor is used, be sure that it does not impede or cancel the sound spatilization.   Be sure that the click track is not heard at anytime during the performance.