For thousands of years, philosophers, mathematicians, and musicians have theorised about the connection between music and mathematics.
Pythagoras, the ancient Greek philosopher, was the first we know of to make the connection when he noticed that halving the length of a musical string produced the musical interval of an octave.
Two notes an octave apart sound the same to the ear but have a different pitch. The octave is in the string ratio of 2:1, if the string ratio is 3:2 you get a fifth higher note and so on. The sounds relate to the vibrations carried through the air to the body and ear with higher vibrations or frequencies bringing higher pitched notes.
While the Greek musical scale was based on perfect fifths like many mathematical theorems, it didn’t quite work throughout the entire scale and eventually in the 1500s in its place came the method of equal temperament.
As the name suggests, with equal temperament an octave is divided into equal intervals with the smallest interval, the semitone, being the twelfth root of two (2^1/12) with larger intervals representing greater powers of twelve and so on.
This new system of adapting to the “creator’s mathematics” also has its flaws, but it does manage to spread the tuning issues evenly over the spectrum, thereby minimising their impact. However, the drawback is if you want your fifths perfectly in tune, the third’s will be ever so slightly out of tune — imperceivable to the human ear but ever so slightly flat or sharp never-the-less.
Rather than accept the limitations and imperfections of equal temperament in the late 17th century, tuners came up with the concept of well-temperament where keys were allowed their own individual pitch and character. Proponents of well-temperament such as J.S. Bach wrote the powerful preludes and fugues of The Well-Tempered Clavier.
The anomalies of equal temperament and well-temperament musical scales are similar to the uncertainty principle known in quantum mechanics as Heisenberg’s uncertainty principle. Heisenberg’s principle helps to explain one of natures jokes on mathematicians that there is a fundamental limit on what we are able to predict about the behaviour of quantum physics.
On the quantum scale, Heisenberg postulates that we can calculate the probability of where things are and how they will behave. However, the uncertainty principle postulates we cannot measure both the position and the momentum of a particle with precision. The more accurately we know one of their values, the less accurately we know the other and vice-versa. Just as under equal temperament if you want your fifths in tune, the thirds will be ever so slightly off.
But what if both music and quantum mechanics are drawn from the same mathematics and the deficiencies in the Pythagoras and equal temperament scale can be explained away by Heisenberg’s uncertainty principle?
Music might illuminate a secret window allowing us to feel closer to and connect with the physical universe through the “harmonies of the quantum.” Also, since the carbon, nitrogen and oxygen atoms in our bodies along with the heavy elements were created in the stars over 4 billion years ago, one can argue that we are literally made of the stars and in a parallel universe maybe even made of music.
After all, in1952 Erwin Schrödinger the Nobel prize-winning Austrian physicist and father of modern quantum mechanics gave a lecture where he warned his audience that what he was about to say might “seem lunatic.” While his equations of the quantum seem to be describing several different histories, they are not discrete alternatives but happen simultaneously, in effect they are multiverses occurring simultaneously.
Music, therefore, could represent an alternative universe of that which takes place in the physical universe. Atoms, particles, the stars, and humanity itself are irrevocably connected through the harmonies of the quantum, perhaps explaining why music hypnotises, connects and soothes the soul.
Maybe it also helps to explain why we are naturally drawn towards sounds and harmonies; not just music but birds singing in the morning or waves resonating with a natural kinetic timbre as they break onshore, or else rain falling on a tin roof on a summers day.
Perhaps Einstein, himself a violinist saw this when he said “life without music is inconceivable for me, I live my daydreams in music, I see my life in terms of music…I get most joy in life out of music.”