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Category Archives: Math

Why do musical notes sound different on different instruments?

A musical pitch is a blend of many different frequencies beside the fundamental. Here’s a visualization of the different vibrational modes of an ideal string. The string’s movements are the sum of all these different modes simultaneously.

Is music the most abstract art form?

The Quora question that prompted this post asks: Why has music been historically the most abstract art form? We can see highly developed musical forms in renaissance polyphony and baroque counterpoint. The secular forms of this music is often non-programmatic or “absolute music.” In contrast to this, the paintings and sculpture of those times are [...]

What are the main ideas and highlights of Gödel, Escher, Bach?

Gödel, Escher, Bach by Douglas Hofstadter describes and defines the concept of recursion, and discusses its applications in computer science, consciousness, art, music, biology and various other fields. Recursion is crucial to writing computer programs in a compact, elegant way, but it also opens the door to infinite loops and irreconcilable logical contradictions.

Visualizing music

When you do a lot of computer-based music production and composition, you’re working as much with your eyes as you are with your ears. It’s only natural to start wondering about other music visualization systems. The representations in audio editors like Pro Tools and Ableton Live are purely informational, waveforms and grids and linear graphs. [...]

Music theory and quantum mechanics

In high school science class, you probably saw a picture of an atom that looked like this: The picture shows a stylized nucleus with red protons and blue neutrons, surrounded by three grey electrons. It’s an attractive and iconic image. It makes a nice logo. Unfortunately, it’s also totally wrong. There’s an extent to which [...]

Biggie Biggie Smalls Is The Illest

I always enjoy when hip-hop artists sample themselves. It makes the music recursive, and for me, “recursive” is synonymous with “good.” You can hear self-sampling in “Nas Is Like” by Nas, “The Score” by the Fugees and many songs by Eric B and Rakim. The most recent self-sampling track to cross my radar is “Unbelievable” [...]

What is the relationship between music and math?

Here are the areas of math that can most easily be understood in musical terms. Wave mechanics The concept of orbitals in quantum mechanics made zero sense to me until I finally found out that they’re just harmonics of the electron field’s vibrations. I wasn’t at all surprised to learn that Einstein conceptualized wave mechanics [...]

The Amen Break

If you had to name the most influential drummers in contemporary music, who would you pick? If you’re a rock fan, you might go with Ringo Starr, John Bonham, or Keith Moon. A jazz fan might talk about Max Roach, Elvin Jones or Tony Williams. You probably wouldn’t think to name Gregory Cylvester Coleman. He [...]

Probability

Probability is a deeply weird and disturbing topic. The harder I look at it, the weirder and more disturbing it becomes. I find the many-worlds interpretation of quantum mechanics to be the least weird and disturbing way to think about it.

How does a computer work?

Computers can only do a few very simple operations consisting of flipping electrical switches on and off. You can represent numbers in patterns of the on-off states of sequences of switches. By flipping switches on and off in particular patterns, you can perform simple mathematical operations on the numbers. You can do more complex mathematical [...]