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



            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, March 24th,  2006]