Making Waves in Mathematics

Mathematics and music may seem like strange companions at first, but upon closer examination, it becomes clear that these two subjects have more in common than meets the eye. From the frequencies that determine pitch to the waves that create sound to the Fibonacci sequence found in song structure, the connection between mathematics and music is undeniable. So let's put aside the stereotype that mathematics is all numbers and music is all emotion, and instead embrace the harmonious relationship between these two subjects.

"Music is the pleasure the human mind experiences from counting without being aware that it is counting" - Gottfried Leibniz

Frequencies and Waves

Let’s start with frequencies. In math, a frequency is defined as the number of times a particular event occurs within a specific time frame. In music, frequency refers to the number of vibrations per second of a particular sound wave. This is important because it determines the pitch of a sound. For example, a higher frequency sound wave will have a higher pitch, like a high-pitched violin, while a lower frequency sound wave will have a lower pitch, like a deep bass guitar. In fact, the frequencies of musical notes can be represented using the formula f=1/T, where f is the frequency and T is the time it takes for one complete wave cycle.

But what are waves, you ask? Well, in math, a wave is simply a repeating pattern that moves through space and time. Sine and cosine functions are used in trigonometry to describe and illustrate the oscillation of waves. In music, waves are all about the vibration of sound. When a musician plucks a string on their guitar, for example, they create a wave that travels through the air and eventually hits your eardrum, allowing you to hear the sound. Sound waves are created when a vibrating object causes the particles in the air around it to vibrate as well.

These vibrations then travel through the air and reach our ears, where they are translated into sound.

Understanding the mathematics behind waves is crucial in understanding the properties of sound and how it can be manipulated in music.

Fibonacci

Now, let's talk about one of the most famous mathematicians in history, Leonardo Fibonacci. You may know him from his famous sequence of numbers, but did you know that he also had a big impact on the world of music? Fibonacci's work on the golden ratio (a mathematical ratio that appears in everything from art to architecture) has been applied to the structure of musical compositions. In fact, many famous composers, such as Bach and Mozart, have been known to use the golden ratio in their compositions.

The Fibonacci sequence, named after the Leonardo Fibonacci, is a series of numbers in which each number is the sum of the two preceding numbers. The sequence starts with 0 and 1, and then continues as 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 etc. But what does this have to do with music? The Fibonacci sequence can be found in the structure of many songs, particularly in the arrangement of chords. For example, the song “Stairway to Heaven” by Led Zeppelin follows the Fibonacci sequence in the progression of its chords.

Numbers in Songs

It is not just the Fibonacci sequence that has found its way into music. Other mathematical concepts, such as ratios and intervals, are also used in songwriting and composing. For example, the most commonly used interval in Western music is the octave, which is a ratio of 1:2. This interval is found in many popular songs, such as "Twinkle, Twinkle, Little Star" and "Happy Birthday." The exact mathematics used in songwriting and composing can also play a role. For instance, the concept of time signature in music is a mathematical concept. Time signature refers to the number of beats per measure in a song and is represented by two numbers, such as 4/4 or 3/4. The top number represents the number of beats per measure, while the bottom number represents the type of note that gets one beat.

Another common technique is to use the Circle of Fifths, which is a chart that shows the relationships between different chords. By understanding the relationships between these chords, musicians can come up with chord progressions that sound harmonious and pleasing to the ear.

So, as you can see, math and music are more intertwined than you might have thought. Next time you listen to a piece of music, try to think about the mathematics behind it. Who knows, you might even start to appreciate math a little more.

"Music is the shorthand of emotion" - Leo Tolstoy

And if all else fails, just remember what Leo Tolstoy once said: "Music is the shorthand of emotion." Even if you don't understand the math behind a song, you can still enjoy the emotion it brings and next time you're jamming out to your favourite song, remember that mathematics is making waves behind the scenes!