Math rock, but with actual math
January 14, 2018 6:52 PM Subscribe
The sound of space-filling curves. Herman Haverkort presents sonifications, or musical representations, of space-filling curves in various dimensions. (Sonification previously.)
A Rainbow In Space-Filling Curved Air
posted by Johnny Wallflower at 7:50 PM on January 14, 2018 [1 favorite]
posted by Johnny Wallflower at 7:50 PM on January 14, 2018 [1 favorite]
This is what the music that plays in M.C. Escher’s impossible palaces would sound like.
posted by acb at 8:02 PM on January 14, 2018 [1 favorite]
posted by acb at 8:02 PM on January 14, 2018 [1 favorite]
The first link under "Four dimensional" has a beautiful melancholy to it.
posted by umbú at 10:08 PM on January 14, 2018
posted by umbú at 10:08 PM on January 14, 2018
As someone who plays around with electronic music composition involving arpeggiators and pattern generators, I think techniques such as this have a lot of potential as textural elements. Especially in process-based areas of electronic music where one gets away from the idea of the composer being responsible for playing/placing each individual note/sonic event and instead goes to them being responsible for setting up and controlling the process from which the events emerge. Having a pattern generator which turns simple signals plus some kind of tempo into more complex patterns, and controlling the parameters of this, is no different than having a tape delay on a track and tweaking the feedback/mix of that.
I'm now wondering how to implement a space-filling curve/L-system-based generator in Max for Live. One problem is that a M4L MIDI effect only generates one voice's worth of notes, so architecturally it would be a bit of a mess.
posted by acb at 6:04 AM on January 15, 2018 [2 favorites]
I'm now wondering how to implement a space-filling curve/L-system-based generator in Max for Live. One problem is that a M4L MIDI effect only generates one voice's worth of notes, so architecturally it would be a bit of a mess.
posted by acb at 6:04 AM on January 15, 2018 [2 favorites]
Having endured many mathematical sonifications before, where the best you can hope for is an intriguing gimmick that gives all it's got quite quickly and then outstays its welcome, this is astonishingly good. Quite tiring, which I think is a function of the density of tones combined with the choice of voice; hearing some of these played by a string quartet would be quite something. Which is not to say that I don't appreciate the choices made in mapping notes to numbers (I guess you could call that mode?) - this is en excellent effort.
I do wonder how these would sound to someone who hasn't spent much time listening to minimalist music before, or with a penchant for analytical listening to longer orchestral pieces, where getting your ear in on how themes develop, reference and counterpoint each other unlocks a lot of what's going on and can be addictively rewarding. It's fascinating to think about how much of Bach works through the ideas of n-dimensional rotation of pattern sets (and to contemplate hearing some of this stuff on a museum dose...).
The illustration for the Gosper curve is an album cover in itself.
posted by Devonian at 6:39 AM on January 15, 2018 [3 favorites]
I do wonder how these would sound to someone who hasn't spent much time listening to minimalist music before, or with a penchant for analytical listening to longer orchestral pieces, where getting your ear in on how themes develop, reference and counterpoint each other unlocks a lot of what's going on and can be addictively rewarding. It's fascinating to think about how much of Bach works through the ideas of n-dimensional rotation of pattern sets (and to contemplate hearing some of this stuff on a museum dose...).
The illustration for the Gosper curve is an album cover in itself.
posted by Devonian at 6:39 AM on January 15, 2018 [3 favorites]
This is great, thanks for posting!
Devonian - It's fascinating to think about how much of Bach works through the ideas of n-dimensional rotation of pattern sets (and to contemplate hearing some of this stuff on a museum dose...).
Could you expand on this a bit, or suggest some search terms? It sounds fascinating.
posted by metaBugs at 7:55 AM on January 15, 2018
Devonian - It's fascinating to think about how much of Bach works through the ideas of n-dimensional rotation of pattern sets (and to contemplate hearing some of this stuff on a museum dose...).
Could you expand on this a bit, or suggest some search terms? It sounds fascinating.
posted by metaBugs at 7:55 AM on January 15, 2018
Yeah that sounds fascinating and 'well, duh' in a revelatory sort of way.
posted by Sebmojo at 1:04 PM on January 15, 2018
posted by Sebmojo at 1:04 PM on January 15, 2018
Motivated by this example, I have decided to use my free time to play with space-filling curves; so I coded up a quick implementation of the Gosper Curve in Haskell. It only draws the graphics as it stands (and only runs in the Haskell For Mac interactive playground IDE, though should be easy enough to build into a command-line program), but the intermediate representation is a 3-dimensional one which should map easily to note mappings or similar linear environments.
posted by acb at 3:17 PM on January 15, 2018 [1 favorite]
posted by acb at 3:17 PM on January 15, 2018 [1 favorite]
I don't have any cites, because it's something that occurred to me when I was listening to the FPP sounds. It is a 'duh!' sort of thought, to be sure, because you'd have to have an ear of purest tin not to be caught up in Bach's thematic patterns - and you probably couldn't stand listening if that didn't work for you - but as I've got older I'm finding that all those uncountable thousands of hours listening to engaging music has sunk in a bit and I have got better at following developments. With Bach, the parallels with mathematics are plain enough but go deep, not just in the mechanics but in those moments of revelation where a chain of logic suddenly results in unexpected beauty that's both obvious in retrospect and completely unguessable beforehand. Nothing sweeter.
I suppose the first time I really thought about this was when I read Gödel, Escher, Bach: An Eternal Golden Braid in the early 1980s. Our generation's Zen and the Art of Motorcycle Maintenance, I guess. It's just that some things you read when you're young, even if you see that they're true and interesting, can only really be incorporated in your consciousness by living long enough and sifting enough krill.
posted by Devonian at 6:57 AM on January 16, 2018 [4 favorites]
I suppose the first time I really thought about this was when I read Gödel, Escher, Bach: An Eternal Golden Braid in the early 1980s. Our generation's Zen and the Art of Motorcycle Maintenance, I guess. It's just that some things you read when you're young, even if you see that they're true and interesting, can only really be incorporated in your consciousness by living long enough and sifting enough krill.
posted by Devonian at 6:57 AM on January 16, 2018 [4 favorites]
Dammit, I knew I slept on this link too long! But I'm glad someone other than me was interested in posting musical space-filling curves to the blue, because I was delighted when it crossed my path last week. I was really impressed with how well some of it sounds like legitimate (if distracted and wandering) musical writing; there's something in the alternating stepwise movement of voices against each other that just does feel musical, feel in some way composed in the way that just throwing an RNG at a melody line doesn't tend to.
It's fascinating to think about how much of Bach works through the ideas of n-dimensional rotation of pattern sets
Yeah! As someone who can't even dig in very far on that (so please do!), I still found myself thinking about stuff like Bach et al using essentially mathematical transformations on motifs to generate huge complex figures out of a simple part. Take a four note melody, shift it in time against itself, stretch it in time against itself, shift it up or down; invert the melody on a scale, reverse the melody in time; roll all that up into a ball of voices moving against one another to find that perfect arrangement that marries a bunch of deliberately technical futzing into a nonetheless harmonious whole. There is a lot of math in music, historically, so why not music in math?
Someone threw a related link my way the other day, to this 3blue1brown video about space-filling curves, which also touches on the idea of sonification though the focus there is more on the property of Hilbert curves and related objects and their capacity to retain local position for a given point along the curve even as the dimension of the curve changes. Which is itself a fascinating thing, and is exploited in e.g. Google's S2 cells system for organizing a literal world full of map data efficiently. (About which maybe there has never been a post? I learned about it from this comment from radwolf76.)
posted by cortex at 8:24 AM on January 19, 2018 [2 favorites]
It's fascinating to think about how much of Bach works through the ideas of n-dimensional rotation of pattern sets
Yeah! As someone who can't even dig in very far on that (so please do!), I still found myself thinking about stuff like Bach et al using essentially mathematical transformations on motifs to generate huge complex figures out of a simple part. Take a four note melody, shift it in time against itself, stretch it in time against itself, shift it up or down; invert the melody on a scale, reverse the melody in time; roll all that up into a ball of voices moving against one another to find that perfect arrangement that marries a bunch of deliberately technical futzing into a nonetheless harmonious whole. There is a lot of math in music, historically, so why not music in math?
Someone threw a related link my way the other day, to this 3blue1brown video about space-filling curves, which also touches on the idea of sonification though the focus there is more on the property of Hilbert curves and related objects and their capacity to retain local position for a given point along the curve even as the dimension of the curve changes. Which is itself a fascinating thing, and is exploited in e.g. Google's S2 cells system for organizing a literal world full of map data efficiently. (About which maybe there has never been a post? I learned about it from this comment from radwolf76.)
posted by cortex at 8:24 AM on January 19, 2018 [2 favorites]
This image of a space filling series of staircases from another page is so interesting. Tantalising? I don't know the word for it.
posted by lucidium at 8:05 AM on January 20, 2018 [2 favorites]
posted by lucidium at 8:05 AM on January 20, 2018 [2 favorites]
Lots more renderings here. It's like that "so cute I want to eat it" thing but for climbing around a space.
posted by lucidium at 9:10 AM on January 20, 2018 [2 favorites]
posted by lucidium at 9:10 AM on January 20, 2018 [2 favorites]
This image of a space filling series of staircases from another page is so interesting. Tantalising?
cortex: "I'll be in my bunk."
posted by Johnny Wallflower at 11:09 AM on January 20, 2018 [1 favorite]
cortex: "I'll be in my bunk."
posted by Johnny Wallflower at 11:09 AM on January 20, 2018 [1 favorite]
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posted by Sebmojo at 7:12 PM on January 14, 2018 [2 favorites]