5,850 views

Watch
- Search Videos
  
  Advanced search »
- Submit a New Video
Discuss
About
- Try clicking on the various channels to see videos posted to that channel - if you're into music you can click the Music channel to get more music sifts - go on and explore! Use the "hotness" when you have opened the channel link to get videos that have gotten a lot of votes, or use "newness" to have a look at the new sifts.
  When browsing sifts you like, have a look at the Related Posts list to see other related videos, click the tags under the video title to see more sifts tagged with the same tags or have a look at other sifts from the same user in the More Posts By list. If the sifted video is in a play list, have a look at the play list to see other interesting videos the Sift users have linked together.
  Enter the Sift Lounge to chat with online sifters about anything and everything, or read interesting posts in the Sift Talk forum.
  The Top New Videos list is always full of interesting, current videos. It is always recommended that you have a look through the Top New Videos, but also have a look at these:
  - Upcoming Unsifted Videos - active video submissions that neither are published to the front page nor archived to the submitter's personal queue
- Have you seen a really funny, surprising, scary, interesting, cute or in any other way extra good quality video?
  Post and share it here - VideoSift is the best video aggregator on the Web, where we share, discuss, promote, and interact with the best videos out there on the web. Post it here, and share it with the large community of video-interested users. And - you are guaranteed to find more very good videos here already!
  Mind you, we only share videos you discover that someone else has made; if you "self link," by posting a video you have made, have posted or have interests in, you risk the ban hammer - read the posting guidelines before posting. The sift is NOT for promoting your own videos - it is for sharing videos others have made.
  Submit a Video Now »
Login

The Geometry of Music (Chopin)

submitted by doremifa

1 decade 7 years 8 months 2 weeks ago

Dimitri Tymoczko recently published an article in Science (313,72-4, 2006) about Western music chord cadences set to equations of string theory. There is another video which shows chord choices as intervals (2 different notes) and the 2-dimensional geometry superimposed. He uses Deep Purple's "Smoke on Water."

http://video.google.com/videoplay?docid=9174364106511581362&q=tymoczko

http://www.time.com/time/magazine/article/0,9171,1582330,00.html

http://www.sciencemag.org/cgi/content/full/313/5783/72

The article's abstract:

The Geometry of Musical Chords
Dmitri Tymoczko

A musical chord can be represented as a point in a geometrical space called an orbifold. Line segments represent mappings from the notes of one chord to those of another. Composers in a wide range of styles have exploited the non-Euclidean geometry of these spaces, typically by using short line segments between structurally similar chords. Such line segments exist only when chords are nearly symmetrical under translation, reflection, or permutation. Paradigmatically consonant and dissonant chords possess different near-symmetries and suggest different musical uses.

Department of Music, Princeton University, Princeton, NJ 08544, USA.