Iara Lima

I am driven by music.

That is a fact. I was analyzing my Spotify metrics and noticed that, for several consecutive months, my monthly average has been around 11,700 minutes of listening to music. That represents approximately 195 hours per month.
Considering that a 31-day month has 744 hours, this means I spend about 26% of that time listening to music. That’s more than six hours a day.
And these data are only from Spotify, which is my main source, but not the only one.

Anyway… did you notice that music is important to me?

Music is, fundamentally, an organized construction of sounds. It has relationships, proportions, repetitions, intervals, rhythms, and patterns that can be studied, described, and even represented mathematically.

In the Western tonal system, for example, we work with twelve pitch classes. The relationship between these notes is not arbitrary. Since Antiquity, different musical traditions have sought to mathematically understand the relationships between sounds. Pythagoras became known precisely for his studies on proportions related to musical intervals, such as the octave, associated with the ratio 2:1, and the fifth, associated with the ratio 3:2.

Time can also be organized.

A 4/4 time signature, for example, establishes a certain metric division. A 3/4 establishes another. Music thus creates a kind of temporal architecture, in which sounds appear, disappear, return, transform, and establish relationships with one another.

Perhaps that is why I find so much familiarity between music, mathematics, and programming.

A repetition can function as a pattern. A variation modifies that pattern without necessarily destroying it. A musical structure can return after an interval, undergo a transformation, and reappear different.

When we listen to music digitally, what seems to be just sound reaching our ears has previously gone through a chain of transformations. The sound is sampled at regular intervals, converted into numerical values, and stored according to digital representation systems.

What we perceive as a continuous experience can, therefore, be described by a succession of values.

It’s a strange thing when we think about it.

A piece of music can make you cry, study, work, remember someone, create something, or simply get through an entire afternoon while you pay no conscious attention to any of these structures.
And yet, there is mathematics in there.

Music notation itself tells an interesting story about the human attempt to record sound. The letters used to represent notes have an ancient history, while staff notation was systematized throughout the Middle Ages. Guido d’Arezzo played an important role in this process, contributing to the organization of musical writing that would become fundamental to the Western tradition.
And that treble clef that appears practically everywhere is not alone. There are also the C clef and the F clef, for which I have a special affection.

The letter system also remained alive in another form. Chord symbols transformed letters into a practical language for representing chords, especially in popular music and among string instruments.

We have created different ways of recording what we hear, but listening remains something else because sound does not exist only as information. It is vibration.

When a sound source produces a wave, this disturbance propagates through the medium and reaches our auditory system. The frequency of this wave is measured in Hertz and corresponds to the number of cycles per second.
This is where music begins to meet the body.

The frequency of 440 Hz, corresponding to the A above middle C, has become a widely used reference for tuning instruments. The standardization of this reference facilitated compatibility between instruments and musical ensembles.

But 440 Hz is not a kind of universal frequency of nature capable, by itself, of producing certain states of consciousness because there is a contemporary tendency to attribute almost magical properties to certain frequencies, as if each number possessed a specific therapeutic capacity. The scientific reality is much more interesting and also much more complex.

Music can indeed produce measurable physiological effects.
Research in music therapy and neuroscience investigates its relationship with stress, anxiety, pain perception, attention, memory, rehabilitation, and cardiovascular responses. Tempo, intensity, predictability, complexity, and even familiarity of a piece can participate in this experience.

A slow piece can favor relaxation in certain circumstances. An intense piece can increase the sensation of energy and excitement. A familiar song can awaken a memory that seemed forgotten. A chord progression can provoke anticipation because our brain recognizes patterns and also because it expects them to continue.

I believe it is precisely because of music’s ability to cross so many different systems that I can never hear it merely as sound.

Author’s note: If you have never seen a musical score and are curious to see one, I am providing access so you can visualize how a song is composed—including the use of the bass clef (F). Below is the audio for the same piece so you can follow along.