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Cool stuff... could be even cooler if they'd map it to anything but whole tones.

Looks cool, but like this guy ^ I can't play midis... The link on his page http://turbulence.org/Works/song/index.html is interesting too, and you can play stuff there. I did some music visualization stuff too with spectrum analysis here - http://robosexual.typepad.com/glob/science/index.html.

I second the mp3 request too.

I think this is awesome. We always knew that there was a mathematical relationship going from music to math (the beats and counts of a note, etc) -- but this establishes a relationship going from math to music.

+Digg^2 from this math geek.

(Also, instead of turning in analysis homework, I'll just bring an electronic piano to class and play the proof for my professor.)

Some of these are better than most songs on the radio today...

Sounds like in Dirk Gently's Holistic Detective Agency

FTA: "...a proof's tree structure, which is inherently suggestive of a musical score..."

Maybe to somebody who knows more about math than music. I suppose he sees tree structures in everything, including his scrambled eggs.

its strange that they make a nice music.... id like to see answers with numbers along with the song...

This is a very non-complete approach to attempt to connect mathematics and music.

If this area interests you, consider looking into the music of Milton Babbitt: http://en.wikipedia.org/wiki/Milton_Babbitt .

It is almost infinitely more difficult to comprehend, but as a result, is an almost infinitely more interesting and complete system.

As a CS major with a strong interest in both math and music (one of my recent projects was a cellular automaton based on chord progressions from the Common Practice Period).. this is pretty cool.

The following is more of a translation from architectural space to musical space, but Iannis Xenakis, who's theory of meta-art - the concept that an artistic expression can be realized mathematically in any artistic medium - is somewhat related to this study.

For more info, Wikipedia has what you need:
http://en.wikipedia.org/wiki/Iannis_Xenakis

His most famous work, "Metastaseis"...
http://en.wikipedia.org/wiki/Metastasis_%28Xenakis_composition%29
...is ear-splitting to listen to, but is intriguing nonetheless.

"Essentially, the musical notes correspond to the depth of the proof tree as the proof is constructed by the proof verifier"

Can I just say... wtf?

I'm seriously loving this. Thanks to whoever posted it.

if you like this you should read 'godel, esher, bach' i'm surprised he didn't even reference it somewhere. that book has all this kind of stuff and much more in it and it was published over 20 years ago.

i was expecting complex deep sounding piano but most of the stuff sorta sounds like a bad ragtime song.

Anyone remember the episode of Voyager where the doctor performed opera to a new race, but it turns out they were only interested in the music's mathematical relationship? They started to ask him to perform something that involved the intersection of two fractals http://www.space.com/sciencefiction/tv/voyager_613_spoilers_000127.html

I loaded some of these files into Fruity Loops and played them with Native Instruments Absynth - some of them sound pretty cool.

this is cool. I even think it sounds good.

I have a musical project in the IDM vein (autechre, squarepusher, kid 606) where I use alot of constants for melody and drum programming, check it out if you like. http://www.garageband.com/ccommand

Reminds me of King Crimson... Especially those crazy guitar solos robert fripp would go on.. Interesting indeed!

This is actually really cool. When I learned all those theorems I thought they were useless... go figure.. ;)

Anybody here ever read Douglas Hofstadter's "Godel, Escher, Bach: An Eternal Golden Braid"? This kind of stuff has been talked about and done ad nauseum for at least 25 years.

wow, cantor's theorem actually sounds like an expressionist piece. zorn's does too, and i rather like how it trickles up and down a little bit, and every so often there's that bold lower note. with a little work, these things really could end up being something significant to the cannon of music.