Fibonacci Scales & Melodies ♫ (Author 1 & Author 2 ) ♫
Introduction Add Ons
For interesting sequences, it’s certainly hard to beat the Fibonacci ► About the Authors
numbers. People rightly marvel at the appearance of these numbers ► Student Homework
in nature (i.e. seed heads, pine cones, and petals on flowers), or the ► Related Sites
connections to art (i.e. the golden ratio), but how many people have
heard the Fibonacci numbers transformed into music?
This article profiles the use of a freely-accessible online program called
musicalgorithms, which was designed to accept an input of any sequence
of integers and to generate an output of musical sounds based on those
integers.
By exploring the two processes by which the musicalgorithms converts
sequences into music, students can expand their ideas of transformations
using division and modulo operations. While the activities described in this
article are quite accessible to both middle or high school students, teachers
should note that the requisite knowledge would include proportional reasoning
and some basic ideas of modular arithmetic.
By having students use musicalgorithms even as they learn the mathematics
by which it operates, they gain a new creative venue for exploring sequences
of all types, a venue that links the musical world to that of numbers in a powerful
and appealing way. So enjoy getting started with Fibonacci Scales & Melodies!
[Author 1
& Author 2,