Slashdot Mirror
The Geometry of Music
An anonymous reader notes a Time.com profile of Princeton University music theorist Dmitri Tymoczko, who has applied some string-theory math to the study of music and found that all possible chordal music can be represented in a higher-dimensional space. His research was published last year in Science — it was the first paper on music theory they ever ran. The paper and background material, including movies, can be viewed at Tymoczko's site.
Neanderthals had flutes and discovered the octave. If we are to assume music is linked to string theory, then the problem of where they all went is solved! They were the aliens all the time! (Seriously, the paper is interesting, but you can always describe a simple system with a complex one. I'd want solid evidence that this is the reduced form.)
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)
http://en.wikipedia.org/wiki/Sacred_geometry
http://www.spiritofmaat.com/archive/jan4/williams.htm
The Naked Scientist actully just had a Podcast [MP3 Link] about music and science. If you find music and science interesting, I think it is a good listen. Not quite on the string theory level, but non the less I think it is relivant.
Memory is deceptive because it is colored by today's events. - Albert Einstein
It's not the first time music has been represemted as mathematical equations, or even as a random events. Hell, even Bach experimented by throwing a pair of dices while composing some of his most popular baroque parts.
It's time to realise that Abble's products are the biggest abomination these days. Just say NO to the dumb iAbble way!!
Am I the only one who immediately thought of the computer scientist in Douglas Adams' Dirk Gently's Holistic Detective Agency?
...instead of having to play some of my own compositions on my nonexistent MIDI keyboard (my only MIDI device is my guitar amp effects controller), or manually entering the chords one by one, how about giving us the option to directly open MIDI files? MIDI files can be found for just about every equally-tempered piece of music you can think of, and it would be very interesting to see what they "look" like.
:)
Also, as a composer myself, I'd like to be able to see what they look like
Lots of people found out exactly this in the sixties.
...or, maybe it wasn't the music, but the copious amount of hallucinogens that were taking them to higher dimensions.
Just -1, Troll talking to another.
not to belittle the guys achievements, but isn't it so that any sequence of bits can be represented by any arbitrary higher dimensional space ?
The difficulty usually comes when trying to describe a higher dimensional space in a system with *less* dimensions, the other way around is trivial.
MP3 Search Engine
It would have been nice if the author had provided some examples of music that his model predicts. If I walk a circle in his four-dimensional space, what does it sound like?
This reminds me of the Aphex Twin track Windowlicker, which, when viewed via a spectrogram, shows hidden images - Richard D. James' face, and a spiral. This explains why the track sounds so weird in places - the music is being warped to generate the images.
"I bless every day that I continue to live, for every day is pure profit."
Musical DNA Software is actually doing something useful with mathematical patterns generated from music. Check it out.
Finally there's a hard piece of work that demostrates the usefulness of String Theory.... oh wait.... it doesn't.
Quit channeling Stockhausen ;).
The study of Music Theory is highly recommended (though I wouldn't recommend it for a career choice) for anyone of a technical nature who really wants to be challenged.
Beyond the simple technicalities of measure-by-measure analysis (what notes combine to find what chord? what notes form a pattern to yield what scale?) the body of known music as a whole forms a massive network of associations and references in the form of quotes, parody, mimesis, etc...it's almost as if music comments about other music.
This network, combined with various social and cultural studies, really provides a rich field of exploration (for example, the reason we concentrate on music by dead white europeans from 1700-1900 may include a cultural bias, not just technical).
The professional, academic fields of Music Theory, History, and Ethnomusicology are only now beginning to broaden the discussion, having been stuck in the early 1900s (I've known professors of music who will say, without irony, that there's nothing worth discussing since ca. 1915).
So, on your I-IV-V comment, it's true that there are about a zillion compositions that use this chord progression, so an interesting question would be "what makes each composition different in its use of this repetitive structure?"
The answers are always interesting, and can include discussions of different genres, barely-perceptible rhythmic features borrowed from other cultures, sound textures, audio effects, and on and on.
Fun times.
"Beware of bugs in the above code; I have only proved it correct, not tried it." -- Donald Knuth
I don't need no instructions to know how to ROCK!
I've never seen such a boring visual representation of music! While it may be accurate, even MS Media Player Visuals are better!
I was expecting to be blown up with something like this:
Flight 404 on Vimeo
Music and geometry have followed the same paths in western civilization since the days of Pythagoras.
If it did, It would be an improvement.
What if Tetris was invented by Nazis?
http://aboutscotland.co.uk/harmony/prop.html
This is emphatically NOT the first paper on music theory they have ever run. A cursory search turned up several other recent papers. I'm too busy reading Dmitri Tymoczko's report on "The Geometry of Musical Chords" to write any more ---Science 7 July 2006:
Vol. 313. no. 5783, pp. 72 - 74
DOI: 10.1126/science.1126287
"Will future ages believe that such stupid bigotry ever existed!" -- Ivanhoe
Only if the camera was pointed at Simon for the whole episode.
It's not paranoia when they really are out to get you.
It works like this: you use an algorithm that puts together in a very orderly fashion every possible note combination. Think of this as Serialism gone buttfuck crazy. If your system has only one note, and only one duration, then it can be represented in binary: 1 = note, 0 = silence. You can arbitrarily limit the duration (set definition) in question. So, let's say it's 8 measures.
So, every possible combination of 1 and zero becomes a number in this system, and so every melody can be identified.
Now, just multiply pitches, give it a number, and you get melody - 1,6,21,4,55, etc. Then you establish a simple number as your base "speed" (say, 120) and you can calculate the fastest possible repetition of a sound before it buzzes into a sound itself (something over 20 beats per second, so let's say 64th notes) and you then establish that as your "Planck" note duration. You then establish the number of possible pitches (the MIDI 128 will do for now) and then it's on to harmony.
Harmony (harmonies, triads, and chords, clusters, etc.) is simply melody stacked on top of itself. So, you then put some upper limit on the number of "voices" you wish to consider. An orchestra has 80+ voices, so let's make it a nice number like 100. So, you then take one melody.
So, now we have to calculate all the possible (128) pitches and silences for 8 measures for one melody. That gives you a number. Then you calculate it for each voice in sequence, and that gives you another number. Keep calculating. You will end up with a VERY large number of numbers, but you will be able to calculate EVERY POSSIBLE melody, harmony, triad and chord, in EVERY POSSIBLE rhythm within the parameters of your system (which, at 64th notes at 120bpm with a range of 128 notes, is REALLY FREAKIN' HUGE).
Except for primes, all numbers are the products of two smaller numbers greater than 1, so, one could then arrive at an equation of simple numbers arranged in additions and multiplications that would provide the given number to express a given piece of music. In fact, it would, in essence, express ALL music, as a given song would consist of a number expressing 8 measures, which is then followed by another number expressing 8 measures, etc. It's completely linear.
So, the first 8 bars might be [(a+b+c)(df)+g] which is then followed by [h(ij)+(kl)] which describes the next 8 measures, etc.
The computer would do the calculations themselves on demand. And this is where the EVIL FUN begins:
What you do is with this system, ANY piece of notated music could be fed into the computer, and it would then "find" that music inside the system, and ALL SONGWRITERS would have to PAY royalties on the music the computer has generated.
"Buh buh buh I'm an artist and I wrote this song. It goes Gm / Gm7 / A / D / G for eight bars and then..." Buh buh bullshit buddy: you song is located RIGHT HERE in my MASTER MUSIC PLAN. It's number consists of 10^42 digits and starts with "234895230498000345600045345" and ends with "3489000234502340523065023045604004506340" See? Right there.... Now PAY UP MOTHERFUCKER...
"buh buh buh..."
"ALL YOUR SONGS ARE BELONG TO ME!!!! now PAY UP!!!! I make the RIAA look like a bunch of GIRL SCOUTS!!! PAY UP!!! NOW!!!!"
See? We don't need "multidimensional systems" to describe music - it can be done linearly. And it can make the guy who builds this damn thing filthy fucking rich.
RS
Shoes for Industry. Shoes for the Dead.
The only remarkable thing about this man's research (at least what I can tell from the superficial article) is that he got published in Science. Music theory scholars study all kinds of mathematical models with strong resemblances to his multi-dimensional lattices. There's a whole branch of music theory devoted to graphical, parsimonious chordal analysis and derivatives thereof.
Neo-Riemannian theory centers around a triangularly-tiled toroidal space (usually represented as a flat plane) in which chords, represented as whole triangles, typically move one vertex at a time, flipping across the space along adjacent sides.
I realize this is probably whiny of me, but it would have been nice if he hadn't built his entire freaking page as a Flash object. Since I run Firefox3 on 64bit Linux, the only way to see swf content is through an ugly hack that rarely works. This is one case where it does not: I just get a big white page. Is there another link to the article?
/rant
That, says Princeton University composer Dmitri Tymoczko, "is why, no matter where you go to school, you learn almost exclusively about classical music from about 1700 to 1900. It's kind of ridiculous."
/. discussion.
"Kind of ridiculous?" It's abhorrent. Think about all of the musical innovation that has happened since 1900. It's off the collegiate music curriculum. Try doing that in the field of engineering or medicine and see how the public reacts. But since it's just music, it's OK. We can all thank the NASM, the organization through which most music schools are accredited, for keeping us, figuratively, in the dark ages.
The public usually thinks of high standards as forcing everyone to do equally well. Unfortunately, they often result in everyone doing equally poorly; there are only so many hours available in a day, and so many credit hours available towards a degree. We need more diversity in music education, especially in higher ed. Perhaps Dmitri Tymoczko's work will help.
And now, back to your regularly scheduled
Spoon not. Fork, or fork not. There is no spoon.
Music theory is miles deep in frequency analysis, throw this one on that slag heap. I do congratulate him on proving that pitch is boring though: since his chordal (i.e., pitch-based) analysis manages to lump vastly different musics together, ironically he's shown that the vast majority of what makes them different from each other must be something else.
The claim this is the first paper in Science regarding music theory is wrong. There have been others, including some on music theory and the physiological basis of music perception.
The use of the circle to described musical perceptions is not new. It's been used to describe among other things the "ascending/descending" illusion. However, the use of other topological/dimensional concepts is novel, and pretty damn awesome. I've studied musical perception and its physiology, and a circle is definitely insufficient. More dimensions are required, as the waveforms involved are never (as early as the ear, much less in neural processing) sine waves. A simple example is the fact that inclusion of noise improves reception. The ear itself introduces noise, quite possibly for this purpose. Another is the multimodal (ie. harmonics) nature of most musical instruments. For instance, look inside a piano. The "notes" have more than one string. Even a single string vibrates in a complex set of harmonic frequencies. Now consider that the complex harmonics alone can be used to recreate the missing fundamental (the "main") note in perception, and possibly even in the instrument. Many different multimodal waveforms can create the same result. That requires different approach paths to the solution, and that requires more dimensions.
Sadly, very few in the relevant psychological fields are prepared to understand and incorporate this theory into their work. I still can't find more than a handful that can understand nonlinear statistics above 2 dimensions, even though they often use them for such as fMRI (the vast majority team up with biophysicists who do understand it). When they do manage to grasp the concepts in TFA, or find enough people from a relevant field who do with whom they can work, the results will be damn interesting.
"I may be synthetic, but I'm not stupid." -- Bishop 341-B