-Leibniz

I am myself a musician and been stunned by the interconnectedness between music and mathematics (or science of patterns).

I present here some interesting facts of the deep relationship.

Did you know?

-The harmonic scale (thus the name!) explains the different timbre of instruments.

-Each new note, if we start on 1, on the standard 12-note scale exists thanks to a prime or prime power(e.g. 9).

-All music is beats. The lowest we call rhythm and the highest and more intricate harmony. This is precisely the same as arithmetic and natural numbers. It is interesting to note the universal appraise of melody, very likely as the critical connecting point without which music can feel "empty".

-The great Fourier through his discovery found an infinite number of differently tuned tuning forks can play what an orchestra can play. Today we see this with audio speakers. Fast Fourier Transforms are at the heart of electronic music.

-If the Riemann hypothesis is right, the primes form a metamodern orchestra where no instrument (prime) plays any louder than any other.

-In the west, due to equal temperament, we hear "irrational music" because we tune are pianos with equal steps to foster transposition. This yields exact frequencies as logarithms of 2, from the octave. It is an irony of fate the European civilization most renowned for its harmony is in fact more out of tune than others such as the Chinese which tune their instruments using rational fractions instead.

-Music has a darker side. Ad music, slot machines and so called "muzak", or store music, manipulate people to spend more. Although this is also supported by elegant mathematics, for sure Hardy is whirling in his grave.

-It is astounding how the deep relationship between music and mathematics has come full circle from Pythagoras and his music of the spheres to modern String Theory. Sound harmonics have gone from the violin to the possible component of nature, the one-dimensional String.

Even when mathematics becomes the rigorous, austere and difficult companion, a sweet melody can remind those of ous fallen in love with it how good it sounds to the ears of the soul.