Music is math

Coming from a science background, yet having learnt the Electone (that’s an electric organ, if you have never heard of it before), I saw music as a form of mathematics.

It is a series of rules and algorithms that when put together, creates a very pleasant series of simultaneous equations for majority of humanity.

First something easy. What is sound? Well, it is the vibration of air particles. That is what music instruments seek to do. Vibrate air particles! But of course, in a very structured, and regular manner. The air particles vibrate and create what we call, sound waves. These sound waves can be described using 2 distinct measurements: Frequency and Amplitude.

Frequency, or how many times the same pattern repeats, can be heard in our ears as the ‘tune’ of the music. For example, the middle note of a piano, A (“la”), has the frequency 440Hz.

Amplitude, or how big/much the air particles vibrate, is heard as the ‘volume’ of the music. The larger the amplitude, the louder the music.

So how did we get out “do, re, mi, fa, so, la, ti, do” (what is commonly called solfege)? It began when people noticed that by doubling the frequency of sound, you get a tune that sounds the same, yet feels higher. Try singing the “do, re, mi, fa, so, la, ti, do”. Notice that at the start, and the end, both tunes are called “do”, but they sound different? In music theory, this is what we call an “OCTAVE”. Think of it as the same tune, but in a higher plane. Mathematically, when we double the frequency but keep everything else constant, the results look like this:

double.jpg

Interestingly in visual form, the 2 more ‘squeezed’ together waves fit in the same length of time as the original wave. But… what about everything else in between? Actually, depending on the culture and part of history you belong to, many musicians have used different frequencies. There is the Pentatonic scale, Monotonic scale, etc. But the most commonly standardized on we use in modern today is the Equal tempered scale.

There is a very special number that musicians depend on when they use the Equal tempered scale – twelfth root of 2, or roughly 1.06. What is so special about this number? (twelfth root of 2) ^ 12 = 2. Recall earlier on, we discussed that an octave is the doubling of the frequency? Let us use the note A again for example. The note A begins at 440Hz. If we multiply it by the special number, the sound of this frequency will be roughly 466.4Hz. Visually on a piano, it is the next button on the right side of the A button.

piano.jpg

By multiplying the frequency by 1.06, it is equivalent to playing the next button on the piano (see the orange arrow in the picture above)! What happens if we were to do this 12 times? We would end up moving up by 12 buttons, to the higher A, to the frequency 440Hz*2 = 880Hz!

 

Image result for music math cartoon

 

References

  1. Retrieved from https://s-media-cache-ak0.pinimg.com/originals/5d/d5/5f/5dd55f5716dad5c4246ddd11c3523f79.gif
  2. Retrieved from http://www.viewzone.com/pp/432.scale.jpg
  3. Sound and Music : The Chromatic Scale : How Music Works. (n.d.). Retrieved from http://www.howmusicworks.org/109/Sound-and-Music/The-Chromatic-Scale
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