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Comment by iaisfongio | Hacker News Reader

Walk up to a nearest piano, hold down the pedal, and start playing on the black keys. You will find it completely impossible to play something that sounds bad. Much of what you play will even sound good. Someone ignorant of the piano might think you're a skilled pianist. But make no mistake: it is the tuning that is doing all the work.

I have nothing against this post, so long as people recognize this is an interpretation of the fractal designed to make it sound good. Any random input would also sound harmonious if mapped to the same scale.

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It doesn't just has tone, it has rhythm too. Everything is based on powers of two, it will give you a nice 4:4 time signature at any scale. It is the same idea as for hitting the black keys randomly: you can't get wrong with powers of two.

(edit: note that in this case, it is a property of the fractal itself, not just the way it is interpreted)

This comment is so confidently ignorant of rhythm and melody, lol

Pay attention to the counterpoint (one voice rising, one voice falling) when one big triangle ends and the one above/below it starts.

Music is harmony, melody, rhythm, and dynamics. Dynamics means variations in softness/loudness, but none applied here, and someone else has noted the rhythmic component.

I wonder, with the right choice of mapping/filters, how much variation you can admit on the input side while still ending up with something that sounds basically okay at the end.

Context: I've been thinking about this recently whenever something to do with machine-written music comes up. My best attempt to describe what music is to me is something like "the patterned construction and resolution of rhythmic and tonal dissonance" — i.e. start neutral, create something that feels slightly uncomfortable, but hint through the pattern how it might be resolved to make you comfortable again. Kinda like storytelling, come to think of it.

So what if instead of a series of Sierpinski triangles, you used hailstone sequences, or anything else that contains interesting complexity and eventually returns to the origin. Could you mix and match different filters ("reject anything that doesn't fit this equality") and maps ("natural numbers to pentatonic scale", "natural numbers to commonly used chord progression"), and then apply them recursively? Could you end up with something that people would interpret as "real music", or would it always still sound like obviously computer generated "not-quite-music"?

Check out https://en.wikipedia.org/wiki/Algorave and Sonic Pi https://www.youtube.com/watch?v=YvsoWehBbec :)

I know that. I play the piano. I think I even qualify as a "fairly experienced singer and pianist" [1].

As others have pointed out, there is structure here beyond the fact that the tones are constrained in a way that results in harmonious intervals. This isn't random wind-chimes. Specifically:

* The mind tends to hear lines in the music, associating notes with particular preceding notes to hear melodies embedded in the polyphony. These lines move together in interesting and (to me) pleasant sounding ways, some moving together at fixed intervals and some moving in contrary motion. The avoidance of consecutive fifths and octaves in counterpoint is to prevent lines seeming to blend together into block chords, but here that happens a lot so the lines don't "live" for long. They briefly pop out of the harmony and merge back. There are many ways to hear that depending on what you focus on, so there's an ambiguity/interplay between hearing separate lines and hearing chords that tickles my brain pleasantly.

* The fractal is built step by step (in two different ways if you listen to the whole thing), which creates a rising/falling/growing pattern that builds a pleasing tension and release. It also provides a rhythmic framework and emphasises the self-similarity, as the previous pattern is repeated while further similar copies are added over the top.

Sierpinski's gasket isn't a picture. It's an abstract mathematical object. The image and the sound are both imperfect physical realisations of that platonic ideal and are directly related to each other by a very simple mapping. You could certainly argue that in the sound you are "hearing Sierpinski's gasket" to the same extent that you are "seeing Sierpinski's gasket" when you view the image. You'd be on far stronger ground than people who take physical phenomena such as black holes that in no sense "sound like" anything, arbitrarily map some aspect of them to a waveform and claim the result is the "sound of" the original phenomenon.

But the post doesn't make any such claim. It just points out that you can use the fractal to make something that both looks and sounds cool. I agree.

[1] https://news.ycombinator.com/item?id=34132576

Black keys = pentatonic scale for anyone curious. It basically always sounds good, but is repetitive after a while.

Why does such a scale always sound good? Music theory like this is fascinating to me but i don't understand it in the least.

It’s because all five notes are adjacent to each other on the circle of fifths. Notes that are a fifth apart (adjacent on the circle of fifths) are consonant when played together. Limiting it to 5 notes makes it so that no two notes would sound too dissonant together. The more colors you try to use from the 12 chromatic notes, the greater potential for clashing colors. (The circle of fifths is kind of like a color wheel in that colors on opposite sides of the circle are maximally dissimilar to each other, so limiting yourself to 5 consecutive colors on the wheel means no colors are opposite each other)

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