The Geometry of Music 170
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.
Hmmmm. (Score:4, Insightful)
Related: (Score:2, Insightful)
http://www.spiritofmaat.com/archive/jan4/williams.htm [spiritofmaat.com]
Re:Hmmmm. (Score:2, Insightful)
but this goes for any stream of information (Score:4, Insightful)
The difficulty usually comes when trying to describe a higher dimensional space in a system with *less* dimensions, the other way around is trivial.
Does it work backwards too? (Score:2, Insightful)
Re:but this goes for any stream of information (Score:4, Insightful)
The article is light on mathematical details, but it seems that the achievement is that this space of points has been characterized in a useful way. The story is not that now it can be done with even more dimensions (which as you point out would be trivial). Rather, the story is that now this space of points has been characterized at all, and this description just so happened to require several or many dimensions.
Since this paper is the first ever on musical theory to be published in Science, which is a highly prestigious peer-reviewed journal, we can assume that the paper is saying something interesting within its field. Specifically, we can assume that this is not just a question of fitting some standard statistical model to some data points.
Re:Hmmmm. (Score:5, Insightful)
Re:Actually (Score:5, Insightful)
You're right. Plato did it in the Timaeus about 2500 years ago.
It's nice to see folks eschewing traditional Western culture and then 'discovering' things the same Western tradition developed over two millenia ago.
Sonny Bono owns you (Score:4, Insightful)
Re:Watched the .movs (Score:4, Insightful)
Melodies are just as finite (Score:3, Insightful)
Grr... (Score:2, Insightful)
/rant
Pitch is Boring -- study rhythm (Score:3, Insightful)