Sample
Activity Demos
Functional
Composer
Functional
Composer is set in the context of a musical composer struggling with
writer's block. Students solve the composer's problem by creating
various mathematical transformations of a simple melody. The original
melody is defined as f(x). Students create various transformations
of f(x) to generate musical material for a composition. The audio
CD demonstrates a musical compostion that can be made from the transformations.
Students can then use this mathematical tool to create original compositions
in subsequent projects. Teacher notes in the book suggest how the transformations
can be used as a pure mathematical tool applicable to functions of
all sorts; algebraic, trigonometric and logarithmic.
Shown
below is the assortment of transformations studied in the activity
and their graphs. Click here to hear a sample
musical segment that utilizes the functions. (Note: You will need
RealPlayer to hear the music. A free version of RealPlayer can be
downloaded at http://www.real.com.)
With the exception of a few small embellishments, each melody in the audio track is derived precisely from the agebraic functions (graphs presneted below).
The harmonic accomaniment (background chords) suggests one way a composer might support
the mathematically generated melodies.
It
is important to note that the graph below is not an exact representation
of what is heard on the audio. This representation is something of
an interpretation, designed to highlight the shape of the function
more clearly in the interest of teaching translation, stretching and
reflection. This can be a good discussion to have with students, to
point out that an exact mathematical graph of the sound would be a
step function. The interpretation below might more accurately be described
as vector resultants of the musical movements from note to note.
Copyright 2000 Key Curriculum Press
Inside
Out
In
this activity students use a polar coordinate system as an interface
between the visual and sonic worlds. A graphic image is traced onto
a polar coordinate grid and intersection points of the image with
rays generate musical notes, a tone series that embodies the shape
of the image, sonically.
Shown
below is a sample from the book. Click here
to hear a musical segment generated from it. The bass line is the
fish contour while the high string line was created from the function,
y=-f(x)+11 using the techniques of Functional Composer.
Copyright 2000 Key Curriculum Press
