After listening to blacksmith hammers pounding out different pitches, Pythagoras discovered that by plucking a string, one sound was produced. Then by dividing the string in half and plucking it again, the sound produced is exactly one octave higher than the first note.

Trigonometry is also related to music. The vibration of a plucked string can be expressed in a mathematical function. The function is p(t) = A sin (Bt+C). T is point in time where pressure varies. A is the volume of the note and, B is the frequency of the note. Another formula uses the frequency of a tuning fork. This formula is f(t) = A (sin (Bt+C) + sin (B2*t+C)). .

The rhythm or beat of music is also mathematical. The time signature tells the reader how many beats there are pre measure and how long each note is to be played. The time signature is written in the form of a fraction written vertically. The most common time signature is 4/4. The top number tells how many beats are in a measure. 4/4 means that there are four beats in the measure. The bottom number tells what note will have one beat. In 4/4 time, the quarter note has the one beat. Another common time signature is 6/8. There are six beats per measure and the eighth note is a beat long.

In relating music notes to math, the music note on a piece of sheet music divides up the measure. In scene the note is like the musical fraction. In 4/4 time there are four beats to use in the measure. A whole note is four beats, a half note is two beats, a quarter note is one beat, and an eighth note is half of the quarter, and so on. The notes are a visual cue to the reader of how to play the musical piece. Just looking at a piece of music or listening to music, no one would really associate math with music.

Fractions are also involved in harmonies and with what notes sound good together. The Fibonacci sequence is involved aside the Golden Section.

Decibels are also involved in music.