rotational energy

I’ve been playing with the EchoNest remix API, reimplementing some of the MEAPsoft composers. Right now I’m doing lots of experiments with beat rotation. Gary Marcus and I are starting on a project that will involve permutations of segment order, so I’m playing with different kinds of rotations to get a feel for how displacement of beats affects the perception of different kinds of music.


rotation takes three arguments: how far to rotate, which beat to start rotating on, whether to rotate every measure or whether to skip n measures between each rotation.


Assuming the music is in 4/4 for now, the original beat order is (showing 4 bars):


1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4


The basic rotation, where we rotate by 1 beat, start rotating on beat 1, and rotate every measure (indicated by 1_0_0, meaning rotate by 1 beat, skip zero beats, skip zero measures), gives us:


2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1


Next we do rotate by 1 beat, start rotating on beat 2, and rotate every measure (1_1_0):


1 3 4 2 1 3 4 2 1 3 4 2 1 3 4 2


Finally we do rotate by 1 beat, start rotating on beat 2, and rotate every other measure (1_1_1):


1 3 4 2 1 2 3 4 1 3 4 2 1 2 3 4


1_0_0 is curiously inert on strongly pulsed music, like reggae. That’s because once you’re a few beats in your sense of where the 1st beat is has shifted. Even though the song starts on a 2, you get the original 1 2 3 4 beat pattern starting on the 3rd beat. It’s not the _right_ 1 that’s there, but in reggae it’s going to be similar to the other 1s, so it fits in well. 1_1_0 breaks that pattern up, so it’s more disruptive of strongly pulsed music. 1_1_1 is more subtle, since 1/2 of the bars are in their normal order and the reordering sort of sneaks up on you.


A bunch of examples:


Bob Marley, “Zion Train”: 1_1_0 does a pretty good job of changing the feel, shifting the beat. 1_0_0 doesn’t have much effect at all.




King Tubby & Lee “Scratch” Perry, “Right Yo Dub: the production on this is a lot wackier than on the Marley, so the effect of 1_1_0 is less pronounced. I don’t think people would necessarily realize that these have been rotated. There’s a nice repeating bit where a reverb tail is cut off and displaced by a beat, but if I didn’t know it was rotated I would have assumed it was an effect that Perry applied.




Ricky Skaggs & Friends playing Bill Monroe, “Big Mon”: these are all pretty convincing as originals, given the unrelenting pace and complexity of the melodies.




Bebel Giberto, “Sem Contencao”: generally tracks with lyrics are distracting, since the vocal discontinuities overwhelm the other effects of the rotation. Using a less familiar language helps even things out, although it of course depends on which languages the listener is familiar with! I think that’s generalizable into styles/genres as well. These are all fairly convincing as originals:




Squarepusher, “Come On My Selector”: music with quickly changing textures, tempos, and meters is going to sound great no matter what you do to it! There’s no way to tell that these have been rotated:



Bootsy Collins, “The Pinocchio Theory”: 1_1_0 is still kinda funky, but it can never quite take off. It’s not obvious where the rotations are, but the pulse is broken…





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