Programs for Students  >  Grades 7-12  >
MATH, SCIENCE & NATURE

PATTERNS AND FORM IN MUSIC,
NATURE & MATHEMATICS

Grades 10-12
2 performing/teaching artists - Three presentations/day
$475 + $350 + $225= $1050

The shape of a nautilus shell, the symmetry of mathematical expressions, the shape of a musical composition... Human beings and Nature express themselves in patterns which give structure and meaning to the things we create. When the Italian merchant Leonardo of Pisa, better known by his nickname "Fibonacci", discovered the fascinating series of numbers which bears his name, it was surely a memorable day. But it was doubly memorable when future botanists realized that Fibonacci's series described perfectly the illusive branching pattern in trees! Hungarian composer Bela Bartok, also fascinated by Fibonacci's series, composed an ingenious sonata whose phrases and forms are themselves governed by Fibonacci's ratios. Yes, it was possible to hear as well as see mathematical proportions! From the geometry of the ancient Greeks to current-day fractal patterns, mathematical creations have often offered insight into Nature's beauty and informed the imaginations of musical composers. In this workshop, students working with a team of mathematical musicians, explore these fundamental patterns, study how repetition and variation interweave to give structure, and discover similarities between the patterns in Nature and those within the human mind.

SOUND THINKING: MUSIC & SCIENCE

Grades 7-10
2 performing/teaching artists - Three presentations/day
$475 + $350 + $225= $1050

In this program, music becomes a curious and fascinating tool through which students enlarge their understanding of scientific thinking. As students explore the physical properties of sound, they are encouraged to make thoughtful observations, form hypotheses and then test their theories before drawing conclusions. Elements of performance are mixed with numerous acoustical demonstrations and experiments designed to spark critical thinking. The presenters - both trained scientists and musicians - work with a variety of musical instruments and common objects to bring several basic acoustical concepts to life: vibration, frequency, pitch, resonance and overtones. The beauty and pleasure of music are linked to the wonder and satisfaction found in exploring the world through science.

THE PHYSICS OF MUSIC

Grades 11-12
2 performing/teaching artists - Three presentations/day
$475 + $350 + $225= $1050

This interdisciplinary workshop explores both the musical and scientific properties of sound. The approach is one of discovery, critical thinking and experimentation. The presenters - veteran scientists as well as musicians - begin with a "live" musical performance and then lead students through dozens of acoustical demonstrations and scientific puzzles designed to make students think and make thinking fun. The cleverly disguised formal topics include waveforms, overtones, frequency, pitch, timbre, resonance, formants, beats, vibrato, the physics of various musical instruments and the human voice. "What special qualities make some sounds musical?" "What gives an instrument or voice its characteristic sound color?" "What can a squeaky violin player learn from a swarm of bees?" Hands-on participation, creative problem-solving, and basic intuition are nurtured every step of the way. The presentation level is flexible, but recommended for advanced students ready to be challenged.

MUSIC OF THE SPHERES:
MUSICAL IDEAS IN THE HISTORY OF SCIENCE

Grades 11 & 12
2 performing/teaching artists - Three presentations/day
$475 + $350 + $225= $1050

In the history of science, one deeply held belief has guided the pursuit of knowledge more than any other, namely that there exists in Nature a "harmony of orderly principles" which human beings can potentially understand, if only we persist in the search. It is no accident that this most fundamental idea, expressed in the writings of Pythagoras, Galileo, Kepler and Einstein, was often envisioned in musical language: "The Harmony of the Worlds", "The Music of the Spheres", "The Vibrational Character of Space, Time and Matter". Our most basic grasp of harmonious order, whether in Nature or the world of ideas, grows out of our experience of music - the physical and intellectual sensation of musical harmony. What's more, that harmony is built upon a logic we can discover through intuition and relatively simple, if not ingenious, experiments. In this workshop, students will put their intuitive skills to work on some of the great problems of science guided, as were discovers before them, by the logic of a harmonious universe. Topics may include orbital motion, Archemedes's and Euler's principles, a measurement of ?, Aristotle's vs. Galileo's view of falling bodies, Xeno's paradox, and the origins of integral calculus. Hands-on creative problem solving, lively conversation, and "live" musical performance.

MATHMUSE: MUSIC & MATHEMATICS

Grades 7-12
2 performing/teaching artists - Three presentations/day
$475 + $350 + $225= $1050

What is a number? Add, subtract, multiply or divide these little symbols with pencil and paper (or on a calculator) and you have mathematics! Do the same with body-movement and sound, and you have rhythm! - the foundation of all music. Math and music are inextricably linked together through rhythm and meter, through musical notation, through pitch relations, through the basic principles of acoustics. What do 2 and 3 really feel like? How do we physically relate to the fact that 8 can be written as 4 + 4 and also as 3 + 3 + 2 ? In this program, students explore, together with our mathematical musicians, the many connections between music and its sister field of mathematics. Via experiments, demonstrations and musical performances, students will discover how the math and science of a whirling tube can lead to a musical scale, how binary math became the basis for musical notation, and how complex polyrhythms can be reproduced by the simple addition of basic numbers. MATHMUSE helps students to cross the perceptual bridge between feeling and counting, between beauty and numerical proportions.

COMING SOON! – EXPLORING PHYSICS THROUGH MOVEMENT