Math and Music

Fibonacci Numbers

Fibonacci numbers is a mathematical pattern. This Pattern shows how to find the next number in the sequence you add the two before it. This sequence like pi (π) doesn’t end, but will keep reoccurring.

An example of this is:

1,1,2,3,5,8,13,21, 34…..

To get to 2 you must add 1+1.

To get to the next number, you add 2 and the number that came before it (1).

2+1=3

This applies to all Fibonacci Numbers.

Fibonacci Numbers can be found in many places, such as nature. You can demonstrate this by making a sequence of rectangles that spiral outward as they become larger. This is called the golden rectangle.

The golden rectangle looks like:

This pattern is naturally occurring in nature. One of the Best examples of this is in shells. Shells spiral outwards like these rectangles.

If you put this image over a picture of a shell it will look like this:

Fibonacci and Music

Fibonacci numbers are found in music. Some say that the works of Mozart follow this sequence with the different movements of his songs. This has never been proved, but many still claim that you can find a sequence like the Fibonacci numbers in Mozart’s songs. You can find Fibonacci Numbers in a musical scale.

There are 13 notes in each octave. Each scale uses 8 of those notes, which means that 5 notes are left out.

1,1,2,3,5,8,13,21, 34…..

To get to 13(number of notes in each octave) you must add the number of notes used in a scale (8) and the number of notes not played (5).

5+8=13

This rule applies to all scales.

An example of this is:

The C scale:

There are 5 notes in the octave that weren’t played. The notes not played are C♯, D♯, F♯, G♯, and A♯.

Fibonacci numbers also apply to the piano. There are 13 notes in an octave, so there must be groups of 13 keys on the piano. On the Piano there are 8 keys that play natural notes. The other 5 keys play sharp (♯) and flat (ƅ) notes.

Sound Waves and Harmonics

Sound waves are produced when an object vibrates at its own natural frequency. The objects particles vibrate in a repeating back and forth motion to create this frequency. A frequency is the amount of complete vibrations in a set time. When an object is vibrating at its own natural frequency, it is called harmonics. A common unit used to measure a sound frequency is a hertz. Sound waves are one of the forms of a pressure wave. Each time the sound wave changes between high and low pressure it is a complete wave. To read these waves you some sort of detector. With musical instruments this detector is called a tuner. A tuner tells a person if their instrument is in tune (on their natural frequency) or if adjustments to slides (brass) and mouthpieces (woodwinds) need to be made.

The human ear can detect almost any sound frequency. Humans can’t hear sounds above or below a certain frequencies. Frequencies above this frequency are called ultra sound, and frequencies below a certain frequency are called infrasound. When your ears detect different frequencies, the frequencies are known as pitches. When two pitches that harmonize or sound good together are played, you are hearing a chord. The intervals of chards can be seconds, thirds, and fourths.

The musical notes on the staff below make up the C major chord.

The three notes harmonize with one another. The notes are the 1st, 3rd, and 5th, notes on a C major scale.

The musical notes on the staff below make up a D major chord.

The notes on the staff are the 1st, 3rd, and 5th notes on a d major scale.

On any musical instrument, you need harmonics, and sound waves to make music.

To play music you always need to know your math.