No, music is not math

Stop saying "music is math".

How much mathematics was needed to develop musical instruments? Too much math, for sure! However, the same thing happened to cooking utensils, but no one says that "cooking is mathematics", or that "driving a vehicle is mathematics"...

Mathematics is the basis of all sciences. There isn't a single subject that doesn't have anything to do with math. Everything needs numbers.

When people think of the information in music, they basically think:

1. That the music runs through time, and time is measured, and most music uses fractions to specify durations -- a musical score is primarily a function of notes over time, and the duration of all notes is planned.
2. That at the same time, the melodic lines or musical events (tones) have another dimension: pitch, which is specified by the musical scale (do re mi fa sol la ti) or measured in Herz; for example, the most usual pitch of La is 440 Hz.
3. That tones simultaneously have intensity, which means that sounds can be accentuated or hidden, and they can be loud or soft. Intensity is also dynamic, meaning that a single sustained note from a brass instrument can, for example, start with an accent, drop quickly to a low volume, and then grow louder again.
4. That tones at the same time express timbre (sound color), which mainly depends on the musical instrument and the way it is played. Timbre is the most mysterious and difficult parameter to measure, but science does measure it... using mathematics.

In short, musical notes have 4 parameters: duration, pitch, intensity and timbre. As a result, music also has more or less the same 4 parameters. During a piece of music, these parameters change independently and constantly, and great composers establish relationships between all these parts.

But, so far, we have only concluded that the technique of music depends on numbers. Yes, the basic parameters can be expressed in numbers -- you count the beats while you play: 1, 2, 3, 4, repeat. However, the message is always human and often takes place in another dimension.

Hmm, a very mathematical composer... Have you ever heard the music of Iannis Xenakis? He developed a compositional technique called stochastic music, which uses statistics during composition. He was an architect and he wrote computer programs to help him compose. In this case, I agree that music has a deep connection to mathematics. But the computer didn't compose -- Xenakis did.

By the way, you've probably never heard his music; you probably even dislike such musical modernism; so why do you keep saying that music is math?

Most composers aren't mathematicians, they do little more than counting.

Let's take another example: Frédéric Chopin. The first thing about Chopin is that his music contains a sentimentality that is undeniable. Some Chopin music conveys the sadness of sadness, the misery of misery. To achieve his unique nostalgic effect, he developed a combination of existing techniques (such as pedal tones, chromatic harmonic changes etc.). But even in the happy pieces there is a tenderness that is not found in other composers.

Of the four parameters, the fourth is straightforward in Chopin: he always uses the piano. Timbre is only a consideration in piano solo music inasmuch as the piano is a symphonic instrument, capable of expression comparable to an entire orchestra, under just two hands.

Chopin liked 4 things: the piano, Bach, opera, and Polish music.

1. Chopin developed the piano technique, but he did not do it alone. He knew pianists and composers of the time, who also demanded more than Beethoven in their scores.
2. From Bach he learned that grace in the art of music lies in simultaneity -- simultaneous melodies and the relationships between them. The polyphony of the most brilliant composers is often more complex. This is the case in Chopin. But some listeners don't realize that -- they are not aware of the complex polyphony hidden in Chopin's "accompaniment", which is much more than accompaniment. A good pianist will make this polyphony clear and a good listener will know how to hear it.
3. From opera he loved bel canto melodies. He especially appreciated Vincenzo Bellini. Opera is the most popular genre of classical music. If polyphony is a complex aspect, the melody of the opera is what every music lover does understand. It is what the people take away with their whistles. Melodies on the piano must be played giving the impression of a singer singing. And the listener can help with his imagination...
4. Chopin was a nationalist and in exile he expressed his love for his country in his polonaises and mazurkas, which actually contain an influence of the Polish music he heard as a child.

The rhythm in Chopin is completely new. If you think that time in music is exact like in mathematics, you are squarely mistaken. The pianist must play romantic music like a human, not like a robot. This means that time is not as written, it is divined by the interpreter, who speeds up the beginnings of phrases and lengthens the ends of phrases, creating a kind of breathing between sentences, about which mathematics has no idea. A rhythmically straightforward rendering would strike anyone as false and quite unbearable.

And that is how playing Chopin can become a national sport. But they play Chopin from memory. Above I said one can count the beats when playing music. Well, maybe pianists counted a bit while learning certain pieces... but not when they finally play it live from memory. In that moment, they make sure they are free. So the notated durations are an instance of Wittgenstein's ladder. You use the ladder to climb the wall, but when you get up there, you throw the ladder away and become free.

In the mazurkas, time is very important. The rhythm of the mazurkas is strange because the second beat often lasts a little longer, creating a feeling of limping. In fact, changes in the rhythm are much more complex than the generalization I just made. And this is not written in the scores. Even Chopin's waltzes need this freedom in the rhythm, which is greater than in other waltzes. If you gave the sheet music to an alien, he wouldn't understand it. Music is part of cultural and human tradition.

How many times did I need numbers to talk about the most basic traits of Chopin's art? Zero. He counted triolets and polyrhythms like any composer, but that's not important. In both Xenakis and Chopin, what we perceive are two very different worldviews. Technique is very important in art and it always depends on mathematics, but worldview is just as important. They had sincere, new, important things to say.

The content of music is certainly not mathematics. The languages of music are many, so they cannot be mathematical either. They are systems developed by entire peoples, each in a different culture.

The art of music is the most profound and powerful art that man has devised. It can tell abstract stories and will move you to tears if you pay attention to it. Chopin and Xenakis are two of the most innovative composers. Chopin's entire second sonata talks about death, without a single word, of course. The fifth Polonaise is a nightmare of war with an idyll in the middle to give you a sense of what the war destroyed. But being an abstract story, maybe it's something analogous to war. The Berceuse is hypnotically tender, with flourishes like fireworks made of petals… I could go on. If an alien asked me what it is like to be human, I would give him Adam Harasiewicz's recordings of Chopin.

When you say that "music is mathematics", I wonder if you have had any contact with its true power. You should listen to composers who create whole worlds, like Mahler...

Music is the most striking testimony to the creative freedom of man; in that city, math is only one of the bricks.