Did you know that fractions can help create different musical tones? First, let's think about sound. Sound travels through air in waves with unique frequencies, which are measured in **Hertz** (Hz). Human ears generally can hear sounds in a frequency range from 20 Hz to 20,000 Hz. Each musical note has a unique **pitch**, which is determined by the frequency of its sound wave. Tones can be made up of one frequency or a combination of frequencies.

#### Why It Matters

Each note in a musical **scale** can be determined by multiplying fractions. When each pitch is multiplied by a fraction, the next tone in the scale is created. To create a major scale, start at any note. Then, multiply the frequency of that note by \begin{align*}\frac{9}{8}\end{align*} to get the frequency of the second note. Multiply the frequency of the second note by \begin{align*}\frac{10}{9}\end{align*} to get the frequency of the third note. Multiply the frequency of the third note by \begin{align*}\frac{16}{15}\end{align*} to get the frequency of the fourth note. Then repeat this pattern. So, to get the frequency of the fifth note, you would again multiply by \begin{align*}\frac{9}{8}\end{align*}.

The C major scale is pictured above. "Middle C" on the left has a frequency of 264 Hz. How can we use fractions to build the C major scale?

Given that \begin{align*}264 \ \mathrm{Hz}=\mathrm{C}\end{align*}, the next note, D, is created by multiplying 264 by \begin{align*}\frac{9}{8}\end{align*}:

\begin{align*}264 \ \mathrm{Hz} \times \frac{9}{8}=297 \ \mathrm{Hz}=\mathrm{D}\end{align*}

Multiplying 297 by \begin{align*}\frac{10}{9}\end{align*} gives the frequency of the next note, E:

\begin{align*}297 \ \mathrm{Hz} \times \frac{10}{9}=330 \ \mathrm{Hz}=\mathrm{E}\end{align*}

And so on—we could keep multiplying and multiplying until all of the notes of the scale have been created!

Hear the C major scale for yourself: http://en.wikipedia.org/wiki/C_major

#### Explore More

Follow the instructions at the following link to create your very own "shoebox guitar" to help you learn more about sound and music.

http://scienceforkids.kidipede.com/physics/sound/doing/sound.htm