The Mathematics, Physics & Biology Of Music — Science At Play & Cultures Colliding

The idea that something as abstract as music is quantifiable into patterns of mathematics & is explained by phenomena of physics & biology…

Oct 09, 2022

The idea that something as abstract as music is quantifiable into patterns of mathematics & is explained by phenomena of physics & biology, explores, in essence, how the areas of study overlap with the art form, and also how music has developed since as far back as you can date its inception.

In an older post, I deliberated about ‘What Is The Point of Music’, but coming back, both music and mathematics blossomed and were pioneered in the courtyards of the ancient world and developed from one form to the next as time progressed.

You have Carnatic music and its complex ragas & time signatures, you have Hindustani classical music with the Sa Re Ga Ma Pa for Do Re Mi etc.(I’m not sure which was invented first), Classical music in Europe, and then Qawwalis (Sufi music), & other forms of ethnic music developed all over the world.

Add this to brass instruments that developed from the 11th-12th century onwards, the the piano, an instrument invented in the West in the late 17th century, the violin in the 16th century that pioneered Western Classical music & spread to India, and then of course the guitar, which came about in the late 19th century which became fixed after several varieties of guitars that were differently shaped (16–17th century Spain) which led to the standard guitar of the 19th century.

When you mix all these musical instruments with ideas, formats, with their own set of rules & nuances you have something unique which would have perhaps been conceived in the melting pot of the meetings of these diverse cultures throughout history.

Fast forward to 2022, and we have Electronic & Digital music which has made significant progress from the 1970s up to the 21st century, and now it’s commonplace for music to be conceived on computers, creating more genres that have exploded on the scene since we’ve begun using computing power to make music, and the future is quite exciting to see the boundaries we can push technology to create the music of the future.

I explored the implications of AIVA — an AI composer in an earlier post. But this post is very basic, a bit abstract yet informative & delves into the confluence of diverse music spanning different cultures and the science & mathematics behind it. You can click on the links I’ve tagged to read & understand further.

The Physics Of Music

When it comes to the physics of music, the major point of understanding is that sound is a wave.

And waves vibrate or rather oscillate at a particular frequency.

So each note is actually a particular different frequency.

As explained on Simplifying Theory.com,

“What is frequency? It is a repetition with time reference. Imagine a bicycle wheel spinning. If this wheel completes one revolution in 1 second, we say that the frequency of that wheel is “one revolution per second”, or “one Hertz”.”

“Hertz is just a name given to represent the unit of frequency, and is often abbreviated to “Hz”. If this wheel in our example completed 10 revolutions in 1 second, its frequency would be 10 Hertz (10 Hz).”

“Great, but what does that have to do with sound? Well, sound is a wave, and that wave oscillates with a certain frequency. If a sound wave completes one oscillation in 1 second, its frequency will be 1 Hz.”

“If a sound wave completes 10 oscillations in 1 second, its frequency will be 10 Hz. For each frequency, we have a different sound (a different note). The A note, for example, corresponds to a frequency of 440 Hz.”

“And where does mathematics come into play here? It has been observed that when a frequency is multiplied by 2, the note remains the same. For example, the A note (440 Hz) multiplied by 2 = 880 Hz is also an A note, just one octave above.”

“If the goal was to lower an octave, it would be enough to divide it by 2. We can then conclude that a note and its respective octave maintain a ratio of ½.”

Mathematics In Music

Music has patterns, and so does mathematics. That’s essentially where music and math overlap. The patterns and repetition in music can be correlated to various mathematical ideas.

As explained by Reema Krishnan on Discmakers.com

“The biggest similarity between math and music is patterns. For example, music has repeating verses and choruses while math uses patterns to explain the unknown.”

“You can use different mathematical phenomena in music. These include geometry, signal processing, differential calculus, and even trigonometry. In fact, research has shown that when music shows some mathematical structure, it tends to be more popular.”

“Numbers can tell us more about music. Sounds weird but it’s true. Music is divided into sections that are called measures, where each measure has equal amounts of beats. This is comparable to mathematical divisions of time.”

“Now, each piece of music has a time signature which gives its rhythmic information, like how many beats there are in each measure. All the music notes have numerical connections and a number of beats. As a musician, it is important that you understand the value of fractions and notes to count the music correctly.:”

“Whether it is classical, jazz, rock, hip hop, or any other type of music, you can find math’s influence and impact”

Carnatic Music & Its Use Of Mathematics

Carnatic music in its infancy was firmly based around mathematics at the time. The greats of Carnatic music, like Tyagaraja, Muthuswami Dikshitar and Syama Sastri — referred to by Carnatic music followers as the trinity or three jewels of the genre — also had a firm understanding of how counting relates to music.

Reema Krishnan further writes,

“Carnatic music has a system of ragam, talam, and layam which are fundamentally based on different mathematical rules. For instance, Carnatic music starts with seven swaras, which are nothing but frequency bands.”

“Now, these seven swaras are subdivided into 13 swara sthana’s. By modulating swaras and swara sthanas, ragas are evolved. To further explore the raga structure, we need to apply the mathematical rules of counts, also known as taals. We use taal (or count) to derive the applicable swara sthana within the boundary of the raga bhava.”

“So, a raga is constructed within the mathematical boundaries and constructed based on understanding different components of Carnatic music like swara stana (frequency band), and mathematical rules of counts associated with it.”

How Our Brains Perceive Music

When it comes to how our brains perceive music, the brain translates sounds — vibrations that travel through the air — into the patterns of neural activity, and the process & results are staggering.

As explained on the website Kennedy Centre.org,

“Exploring how our brains work is one of the most exciting areas of modern-day science. Magnetic resonance imaging (MRI) and other high-tech scanners let researchers see which parts of our brains tackle different tasks.”

“With MRIs, a person is slid inside a tube-shaped tank. Then the machine finds where his or her brain “lights up” when undertaking certain activities, such as reading or doing math problems. The scan can also spot what parts of the brain go to work as the person sees pictures, hears sounds, or feels sensations.”

“How the brain processes music is an exciting area of this research. Researchers have discovered that the brain does not have one special place to analyze music.”

“Instead, different parts of the brain handle different aspects of a song, like rhythm (the beat) and tone (pitch and loudness).”

“And one of the most mind-blowing discoveries is that the parts of the brain that deal with emotions also fire up in response to music.”

“In other words, music is wired directly into our feelings.”

A TED Talk About The Intersection Of Science & Music

In his TED Talk, UK based Indian artist Nitin Sawhney explores & talks about the connections between art and science and mathematics.

So music is, also a science, and not just an art form. It’s field of study that’s deeply emotional & on par with all our other human endeavors that and must also be considered as an important area of study in higher education, which it sadly isn’t at the moment.

In an older article, I recounted how important music and the arts were to survivors of the holocaust — Carrying The Light In Humanity’s Darkest Hours: Why We Must Re-Think The Value Of Music & The Arts

In other words, music moves people and touches lives in a way no other art form can.

The Collision Of Different Cultures In Music

Music is transcendental in nature and it transcends boundaries and divides, and unites people across the globe irrespective of nations, notions, or beliefs.

Here are some of my favourite collaborations, you could call it ‘Fusion’ but artists within the genre don’t like to call it that.

Anyway here they are

Jonny Greenwood’s Collaboration With Shye Ben-Tzur & The Rajasthan Express

“Shye Ben-Tzur and guest guitarist Radiohead’s Jonny Greenwood. Together they give traditional sounds a new and experimental edge. Israeli composer, poet and performer Shye Ben-Tzur’s musical roots lie in Indian classical music, and have evolved to become a cross-cultural mix of genres, languages and rhythms. He has collaborated with traditional Sufi Qawwals and folk artists from various communities in Rajasthan, and also composes and writes poetry in Urdru, Hindi and Hebrew. He now spends his time between India and Israel, and tours around the world.”