** 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, ^{th}, 2006

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