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What Math Actually Sounds Like
cellophane writes "If Verdi had a math fetish and a computer, would he be John Greschak? Greschak composes music based upon the mathematical properties of various mathematical objects (e.g. a six-sided die or pentominoes). He writes computer programs to realize devised algorithms and uses the results of these processes as source material for musical pieces. Greschak's newest addition, Platonic Dice: Dodecahedron for 12 woodwinds, was created by using musical material derived from the mathematical properties of one of the Platonic dice. Well, its not Verdi, but its definitely interesting."
It's not as good at the latest crazy town album, but in case it's slashdotted -- it sounds very strange, twangy, almost random, and VERY, VERY dissonant. However, it's quite beautiful.
Fractal Music is quite interesting, as well, and oddly it still sounds more orderly than Platonic Dice.
Music has mathmatical patters, that does not mean math makes good music. People have been trying to discover algorithims which can generate music for years, and this guy has not advanced the science any.
True enough. The only good overlap I've seen between mathematics and music has been the use of math to analyze music written by humans. For an example of such analysis, please refer to the landmark work by Meloon and Sprott.
Yes, Bach was mathematical, but only in the formulaic sense. Mozart's tabular melodic composition system, on the other hand, was pure mathematical genius.
Sometimes I wonder what people are thinking. The musical system is, as it is, very heavily mathematical (resonance and harmonics etc)...
We are looking at this from the wrong way around, people should be looking for incredible mathematical leit-motives and patterns in already existing music such as Mozart or whatever...
All of these attempts to show that math is beautiful (or just attempts to make math an auditory experience) seem kind of ridiculous to me... kind of like if someone tried to make paintings using the vertex rendering methods used in Quake 1... sure it's a noble idea, but the hill to climb is in the other direction: to make vertex renderings that look like Van Gogh.
As for the music I heard on that page. It's 'curious'... nothing more. If you really want odd sounding yet beautiful harmonics, listen to some Joe Zawinul on piano...
sigh. all this, in IMHO (tm).
...the music of Arnold Schoenberg. He was a german composer in the early 20th century who wrote very atonal pieces using what he called "tone rows" - a particular note could not be used again until all of the other 11 notes in the chromatic scale had been used.
Didn't Douglas Adams come up with this idea? It was a program called Anthem, which turned a company's financials into music, rather than geometric shapes, but the idea's the same.
Politas
I would propose making monsterously huge speakers and blasting this into Iraq, but in my oppinion it would be a violation of the Geneva Convention.
Actually, we've done stuff like that before
GMD
watch this
Even if software was written to create music that fooled people into believing a human wrote it, would people want to listen to it? When I listen to music, I want to know there's a real person behind it, who is going through the human experience just as I am. Maybe if a robot, or even body-less artificial life, some day composes music it will be worth listening to, but true human-composed music will always have some appeal to it.
Schoenberg tried the same sort of thing in 1921 or so. He invented the "twelve tone" system, in which the twelve chromatic tones were arranged according to mathematical sets. He even remarked to one of his students that he had come up with an idea that would, "ensure the domination of German music in the 20th century."
The basic idea was neat in that it removed conscious choice from the equation and resulted in melodic and harmonic combinations that wouldn't normally occur to a composer. Serialism, as it's called, is still being taught and used to this day, even if I find it tiresome myself. Basically, this is just another facet of that serial system.
It has a unique kind of icy, remote quality, but music isn't really meant to be appreciated on an intellectual level so much as an emotional one. True enough, you can have a satisfying balance of both (like Bach's Well-Tempered Clavier), but purely intellectual stuff like this just isn't all that interesting outside of certain circles. Schoenberg's students, Alban Berg and Anton Webern did a much better job of writing listenable music with the system, mostly because they allowed some human influence in the model.
THE GOOD HUMOR MAN CAN ONLY BE PUSHED SO FAR
Bart Simpson on chalkboard in episode 2F18
You are wrong! Nothing is based on math, we actually use math to explain something, not the other way around.
Former blues players in Mississipi didn't have a clue about math. And fractal was invented in order to study plants, and it's a well known fact that plants were around way before human being could count their 10 fingers.
If you want to listen to math in a raw uninterpreted form, try mathematical proofs set to music on the Metamath Music Page.
This is simply wrong. It is *very* possible to write an equation to describe the chords for an entire song. This is what music theorists do, and it's nothing new. The same mathematical system used to quantify harmony in Bach's day is still in place today, still required (for two years at most schools) at nearly every music school for all students.
This is not completely relevant, but people here might be interested in the converse question: What does music look like when viewed as a sequential, mathematical structure. This guy has analyzed a number of musical pieces and shows their structure. He also shows what sequential data look like.
John Greschak probably should do a bit more research on the subject of "Platonic Dice". What he is referring to are the Platonic solids.
In order for a solid to be a Platonic solid, it needs to be convex and have all its vertices (corners) to have the same number and size of regular polyhedrons touching them. For example, a cube is a Platonic solid because all of the vertices have 4 of the same size squares touching. There are only 5 Platonic solids possible: the Tetrahedron (4 sides), the Hexahedron (cube, 6 sides), Octahedron (8 sides), Dodecahedron (12 sides), Icosahedron (20 sides).
There is also a class of related solids called Archimedian solids where the solids are convex, all vertices are identical, all faces are regular polygons, but not all of the faces are identical to each other.
Sapere aude!
The aesthetic qualities you hear in music are all in the functions you use to map a mathematical pattern to sound. One that corresponds to your aesthetics will sound good. One that doesn't won't.
I've been doing this sort of thing since high school, on and off. The conclusion that I came to about five years ago is that there might actually be a reason why most scales/tonal systems people have come up with have some basis in the harmonic series. Since then, it's been interesting trying to come up with algorithms that work with it.
Why am I not posting links? Because this is done in my spare time, and what I've come up with is still crummy. But I think the idea might be significant...
Libertarianism is rich wolves and poor sheep playing gambler's ruin for dinner.