8 ms·

Interpreting a Sierpinski Triangle Fractal as musical notes sounds good

167 points by _Microft 4y ago

gaudat 4y ago
Spoiler: Putting all the notes in a melodic scale than every note on 12-TET makes things sound good.
- deleted 4y ago
  [deleted]
- squeaky-clean 4y ago
  It makes things sound inoffensive, but not necessarily good. This actually sounds good. It'd be a lovely generic arpeggio pattern in addition to the standard up/down/alternating patterns.
gumboza 4y ago
Fairly experienced guitarist and pianist here. No that does not sound good. It sounds less than bad but not good.
- freetime2 4y ago
  Would it be possible to share one of your own compositions/performances for comparison?
  - FpUser 4y ago
    >"Would it be possible to share one of your own compositions" One does not have to be composer to judge music. Also it is very subjective. In my opinion the piece is a short phrase that does not cause immediate allergic reaction. But it is not a composition. Some math translated to notes and producing reasonable harmony is not really that exciting imo.
    - dbalatero 4y ago
      It's not a piece, nor does the link at any point claim to be anything at all beyond a cool sound.
- cmbell715 4y ago
  Great technical review. I appreciate the insight and thoroughness from someone who obviously knows their craft extremely well. The nuance in which you broke down how "[i]t sounds less than bad" left me incredulous, and then you completely rendered any type of retort useless by affirming that it was "... not good". There's just no countering that. Spot on. I will never trust a musical review on fractal musical composition by anyone other than fairly experienced guitarists and/or pianists ever again.
  - gumboza 4y ago
    My review was spot on. It’s subjectively not terrible but you wouldn’t use it as the basis of a composition. Perhaps a school bell. But it would get annoying as fuck very quickly. Actually perhaps sticking it on repeat in a torture cell would be a good place for it. It’s not bad enough or good enough to be likeable.
Tokkemon 4y ago
Sounds like fourth-rate Philip Glass.
- gumboza 4y ago
  With a head injury.
wardedVibe 4y ago
Reminds me of the infinite polyrhythm from the last summer of math exposition[0], though this has the more frequent notes in the base rather than in the treble. How pleasant the "Musification" is depends quite a lot on your choice of map. [0] https://www.youtube.com/watch?v=8x374slJGuo https://www.youtube.com/watch?v=8x374slJGuo
- bambax 4y ago
  Great video, thanks!
omnicognate 4y ago
All 4 comments so far are middlebrow dismissals. Disapponting, HN. It sounds pretty cool to me. It's not a fully formed musical piece in its own right, but did you expect drawing a fractal with note positions on a sequencer to sound like Beethoven's Fifth? It's an curious little idea that produced an interesting sound, and unlike all the "this is what a black hole sounds like" nonsense it isn't presented as anything more than that. I expect with a little imagination the general idea could be developed into some interesting music, but the post doesn't even claim that.
- survirtual 4y ago
  I accidentally generated the Sierpinski Triangle when I was debugging a k-tree’s XOR space (I think I was using XOR with the distance function but I’d have to review the test case to be more exact). I wanted to visualize what was happening to the values and generated a bitmap of the coordinates translated to XOR space — it created this fractal. I might have some specifics wrong (it was a while ago) but the fractal popped out and I found it very interesting. Seeing it used to generate music is also interesting. I enjoyed it as a curiosity and it reminded me of my own encounter with the fractal. Not sure where the hate comes from, it is really a fascinating sound. If it was expanded into something musical, I would no doubt enjoy where that music takes me.
- iaisfongio 4y ago
  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.
  - xdfgh1112 4y ago
    Black keys = pentatonic scale for anyone curious. It basically always sounds good, but is repetitive after a while.
LunarAurora 4y ago
Not Bad. Reminds me of GeoMusica [1] .The patterns are geometric rather than fractal. Complex Example : https://www.youtube.com/watch?v=ZdDT3hj7L2M https://www.youtube.com/watch?v=ZdDT3hj7L2M Simpler : https://www.youtube.com/watch?v=EfZ6E06FNF4 https://www.youtube.com/watch?v=EfZ6E06FNF4 [1] https://github.com/ruigato/geoMusica https://github.com/ruigato/geoMusica
medo-bear 4y ago
cool! now do mandelbrot set
stelliosk 4y ago
Can someone explain is this a breakthrough or a coincidence?
- jablongo 4y ago
  Neither, it sounds good mostly because of the major scale that it was mapped to.
nine_k 4y ago
Sounds like a canon, as expected, just a bit fast. But why just one scale? Put on the natural major scale, minor pentatonic scale, something like mixolydian, the blues scale, etc. They all have a chance to sound reasonably good, but with different flavors.
jablongo 4y ago
This is more complex than pentatonic noodling, but I agree with other posts that this sounds the way it does mostly because of the choices made by the interpreter. The crucial choice was that every pixel of sierpinski’s triangle is a note in a major scale. All sierpinskis triangle encodes is the ordinal rank of the notes, everything else is added by the choice of how to translate it into the musical space. If the mapping were to a 12-tone chromatic scale and the result were somehow tonal with interesting harmonies that would be really remarkable. Even then though the 12 tone scale is an interpretation of tonality from western music. That said even if it’s not a sign of the hand of god it’s still pretty cool…
- vinaypai 4y ago
  I think it's more then that, there is a sort of base rhythm that has variations built on it.
- wyager 4y ago
  > Even then though the 12 tone scale is an interpretation of tonality from western music I hear this a lot, but this is a pretty uncharitable description of the 12-tone scale. The 12-tone scale is pretty easy to derive from first principles - the only non-mathematically-"obvious" part is the weird behavior of the multiplicative group generated by 2^(1/12) approximating lots of low-entropy rational numbers. The rest of it (identifying integer powers of 2, group properties of C12, etc) are relatively "obvious" to justify mathematically/physically. It's not just "what western people are used to" or something like that.
  - jablongo 4y ago
    Thanks for this comment. I mostly agree with you. A music theory professor used to lazily say that "nature says so" when asked why a major 3rd sounds better than an augmented 4th (i.e. tritone). Lacking a better explanation I assumed this had to do with consonant chords having notes whose wavelength had a lesser common multiple, but am not entirely sure. Can you provide some citations or resources describing the mathematical justification for a 12-tone basis for tonal music in more detail? I know there was a group theory element to some of Schoenberg's compositions but aside from that I have not been exposed much to this idea.
jasonjayr 4y ago
https://www.oocities.org/vienna/9349/ https://www.oocities.org/vienna/9349/ This reminded me of this way back page on the internet, from the time where phone ring tones could only be Midi files. (Sony Ericsson T610). I used "rabbit.mid" on that page as my ring tone, which gave my phone a very unique sound. That page is but one of many different ways of mapping functions/fractals to sounds + music, while trying to build something artistic + aesthetically pleasing to the ear.
- iamtedd 4y ago
  For anyone wondering, it's the link next to The Golden String.
motohagiography 4y ago
This is pretty cool, even if by good it just means consonant. I happen to use fractals a fair bit in my own musical experiments, and I do it with a specific synth module called a fractal sequencer from Bloom. It takes a scale, a sequence length, a root sequence, and then various depths of mutations and iterates them. There is something about the way our minds select and sort information from noise that it's just complex enough to entrain the listeners attention where it seems predictable but it isn't, and it has just enough texture to create satisfying tension and release. My use of it has been pretty coarse and I just record live sessions without any composition, but as I get more competent with it, I could see some formal fractal techniques emerging. Technically it's noise, but 1/f or recursive noise, and consonant instead of the dissonant noise we think of when we hear random music.
raydiatian 4y ago
Do it chromatically.
raydiatian 4y ago
Do it microtonally.
bitwize 4y ago
It sounds like it could be part of a leitmotif from Zelda, which is interesting because the Triforce is the first iteration of Sierpinski.
blululu 4y ago
Nice. Shameless plug, but I once did something like this with a Sierpinski triangle back in the day: https://www.youtube.com/watch?v=72FmQAfQv1E https://www.youtube.com/watch?v=72FmQAfQv1E When you start to think about it, there are really a lot of different ways you could turn the Sierpinski triangle into sound. They generally have something interesting about them since the fractal pattern has a nice balance of same but different. I would personally recommend trying to make sound from a fractal as a good exercise to do if you have a Jupiter (or Colab) notebook handy.
2-718-281-828 4y ago
i'm not a music expert by any means but this strikes up strong association with "indian" music. maybe played on the sitar?
- robinsonb5 4y ago
  What it brought to mind for me was John Adams' "China Gates".
ilyt 4y ago
It's because author added extra spacing so the notes happen to land in musical intervals ?

167 points by _Microft 4y ago

gaudat 4y ago

Spoiler: Putting all the notes in a melodic scale than every note on 12-TET makes things sound good.

deleted 4y ago
[deleted]
squeaky-clean 4y ago
It makes things sound inoffensive, but not necessarily good. This actually sounds good. It'd be a lovely generic arpeggio pattern in addition to the standard up/down/alternating patterns.

gumboza 4y ago

Fairly experienced guitarist and pianist here. No that does not sound good. It sounds less than bad but not good.

freetime2 4y ago
Would it be possible to share one of your own compositions/performances for comparison?
- FpUser 4y ago
  >"Would it be possible to share one of your own compositions" One does not have to be composer to judge music. Also it is very subjective. In my opinion the piece is a short phrase that does not cause immediate allergic reaction. But it is not a composition. Some math translated to notes and producing reasonable harmony is not really that exciting imo.
  - dbalatero 4y ago
    It's not a piece, nor does the link at any point claim to be anything at all beyond a cool sound.
cmbell715 4y ago
Great technical review. I appreciate the insight and thoroughness from someone who obviously knows their craft extremely well. The nuance in which you broke down how "[i]t sounds less than bad" left me incredulous, and then you completely rendered any type of retort useless by affirming that it was "... not good". There's just no countering that. Spot on. I will never trust a musical review on fractal musical composition by anyone other than fairly experienced guitarists and/or pianists ever again.
- gumboza 4y ago
  My review was spot on. It’s subjectively not terrible but you wouldn’t use it as the basis of a composition. Perhaps a school bell. But it would get annoying as fuck very quickly. Actually perhaps sticking it on repeat in a torture cell would be a good place for it. It’s not bad enough or good enough to be likeable.

Tokkemon 4y ago

Sounds like fourth-rate Philip Glass.

gumboza 4y ago
With a head injury.

wardedVibe 4y ago

Reminds me of the infinite polyrhythm from the last summer of math exposition[0], though this has the more frequent notes in the base rather than in the treble. How pleasant the "Musification" is depends quite a lot on your choice of map. [0] https://www.youtube.com/watch?v=8x374slJGuo https://www.youtube.com/watch?v=8x374slJGuo

bambax 4y ago
Great video, thanks!

omnicognate 4y ago

All 4 comments so far are middlebrow dismissals. Disapponting, HN. It sounds pretty cool to me. It's not a fully formed musical piece in its own right, but did you expect drawing a fractal with note positions on a sequencer to sound like Beethoven's Fifth? It's an curious little idea that produced an interesting sound, and unlike all the "this is what a black hole sounds like" nonsense it isn't presented as anything more than that. I expect with a little imagination the general idea could be developed into some interesting music, but the post doesn't even claim that.

survirtual 4y ago
I accidentally generated the Sierpinski Triangle when I was debugging a k-tree’s XOR space (I think I was using XOR with the distance function but I’d have to review the test case to be more exact). I wanted to visualize what was happening to the values and generated a bitmap of the coordinates translated to XOR space — it created this fractal. I might have some specifics wrong (it was a while ago) but the fractal popped out and I found it very interesting. Seeing it used to generate music is also interesting. I enjoyed it as a curiosity and it reminded me of my own encounter with the fractal. Not sure where the hate comes from, it is really a fascinating sound. If it was expanded into something musical, I would no doubt enjoy where that music takes me.
iaisfongio 4y ago
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.
- xdfgh1112 4y ago
  Black keys = pentatonic scale for anyone curious. It basically always sounds good, but is repetitive after a while.

LunarAurora 4y ago

Not Bad. Reminds me of GeoMusica [1] .The patterns are geometric rather than fractal. Complex Example : https://www.youtube.com/watch?v=ZdDT3hj7L2M https://www.youtube.com/watch?v=ZdDT3hj7L2M Simpler : https://www.youtube.com/watch?v=EfZ6E06FNF4 https://www.youtube.com/watch?v=EfZ6E06FNF4 [1] https://github.com/ruigato/geoMusica https://github.com/ruigato/geoMusica

medo-bear 4y ago

cool! now do mandelbrot set

stelliosk 4y ago

Can someone explain is this a breakthrough or a coincidence?

jablongo 4y ago
Neither, it sounds good mostly because of the major scale that it was mapped to.

nine_k 4y ago

Sounds like a canon, as expected, just a bit fast. But why just one scale? Put on the natural major scale, minor pentatonic scale, something like mixolydian, the blues scale, etc. They all have a chance to sound reasonably good, but with different flavors.

jablongo 4y ago

This is more complex than pentatonic noodling, but I agree with other posts that this sounds the way it does mostly because of the choices made by the interpreter. The crucial choice was that every pixel of sierpinski’s triangle is a note in a major scale. All sierpinskis triangle encodes is the ordinal rank of the notes, everything else is added by the choice of how to translate it into the musical space. If the mapping were to a 12-tone chromatic scale and the result were somehow tonal with interesting harmonies that would be really remarkable. Even then though the 12 tone scale is an interpretation of tonality from western music. That said even if it’s not a sign of the hand of god it’s still pretty cool…

vinaypai 4y ago
I think it's more then that, there is a sort of base rhythm that has variations built on it.
wyager 4y ago
> Even then though the 12 tone scale is an interpretation of tonality from western music I hear this a lot, but this is a pretty uncharitable description of the 12-tone scale. The 12-tone scale is pretty easy to derive from first principles - the only non-mathematically-"obvious" part is the weird behavior of the multiplicative group generated by 2^(1/12) approximating lots of low-entropy rational numbers. The rest of it (identifying integer powers of 2, group properties of C12, etc) are relatively "obvious" to justify mathematically/physically. It's not just "what western people are used to" or something like that.
- jablongo 4y ago
  Thanks for this comment. I mostly agree with you. A music theory professor used to lazily say that "nature says so" when asked why a major 3rd sounds better than an augmented 4th (i.e. tritone). Lacking a better explanation I assumed this had to do with consonant chords having notes whose wavelength had a lesser common multiple, but am not entirely sure. Can you provide some citations or resources describing the mathematical justification for a 12-tone basis for tonal music in more detail? I know there was a group theory element to some of Schoenberg's compositions but aside from that I have not been exposed much to this idea.

jasonjayr 4y ago

https://www.oocities.org/vienna/9349/ https://www.oocities.org/vienna/9349/ This reminded me of this way back page on the internet, from the time where phone ring tones could only be Midi files. (Sony Ericsson T610). I used "rabbit.mid" on that page as my ring tone, which gave my phone a very unique sound. That page is but one of many different ways of mapping functions/fractals to sounds + music, while trying to build something artistic + aesthetically pleasing to the ear.

iamtedd 4y ago
For anyone wondering, it's the link next to The Golden String.

motohagiography 4y ago

This is pretty cool, even if by good it just means consonant. I happen to use fractals a fair bit in my own musical experiments, and I do it with a specific synth module called a fractal sequencer from Bloom. It takes a scale, a sequence length, a root sequence, and then various depths of mutations and iterates them. There is something about the way our minds select and sort information from noise that it's just complex enough to entrain the listeners attention where it seems predictable but it isn't, and it has just enough texture to create satisfying tension and release. My use of it has been pretty coarse and I just record live sessions without any composition, but as I get more competent with it, I could see some formal fractal techniques emerging. Technically it's noise, but 1/f or recursive noise, and consonant instead of the dissonant noise we think of when we hear random music.

raydiatian 4y ago

Do it chromatically.

raydiatian 4y ago

Do it microtonally.

bitwize 4y ago

It sounds like it could be part of a leitmotif from Zelda, which is interesting because the Triforce is the first iteration of Sierpinski.

blululu 4y ago

Nice. Shameless plug, but I once did something like this with a Sierpinski triangle back in the day: https://www.youtube.com/watch?v=72FmQAfQv1E https://www.youtube.com/watch?v=72FmQAfQv1E When you start to think about it, there are really a lot of different ways you could turn the Sierpinski triangle into sound. They generally have something interesting about them since the fractal pattern has a nice balance of same but different. I would personally recommend trying to make sound from a fractal as a good exercise to do if you have a Jupiter (or Colab) notebook handy.

2-718-281-828 4y ago

i'm not a music expert by any means but this strikes up strong association with "indian" music. maybe played on the sitar?

robinsonb5 4y ago
What it brought to mind for me was John Adams' "China Gates".

ilyt 4y ago

It's because author added extra spacing so the notes happen to land in musical intervals ?