If you would like to participate in discussions, please sign in or register.

In this Discussion

Most Popular This Week

    Due to changing needs and technologies, the SMT Executive Board has decided to retire SMT Discuss (effective Nov. 9, 2021). Posts will be preserved for archival purposes, but new posts and replies are no longer permitted.

    Extended 4:3 examples in rock music

    Dear friends,

    In the textbook "From Music to Mathematics: Exploring the Connection" (Gareth Roberts, JHU Press 2016), there's a discussion on polyrhtyhms.  A song called "Fake Empire" by The National (2008) is mentioned as a song that involves a persistent 4:3 polyrhythm ().  The author says, "Fake Empire features a four-against-three polyrhythm throughout the entire piece, perhaps the first rock tune to ever accomplish such a feat."  (There is a footnote that says, "Other notable examples include 'First Tube' by Phish, 'Let Down' by Radiohead, and Frank Zappa's 'The Black Page.'")  

    Do any of you know an earlier example of a 4:3 polyrhythm persisting throught an entire rock song?

    Thanks for any help!


    Sign In or Register to comment.


    • 4 Comments sorted by Votes Date Added
    • Thanks for this thought-provoking query, Zac!

      1. First off, a correction to Roberts: "Let Down" is 5:4 (Osborn 2016, 74–76).

      2. More importantly, "Let Down" is different than The National example above in that it is indeed a grouping dissonance, where the five 8th notes and four 8th notes last different spans of time. So the terminological distinction must be made between a grouping dissonance (x and y share the same common denominator, yet last different spans of time) and what is happening in The National, which is what, I suppose, we could call a polyrhythm (x and y do not share the same common denominator, but last the same span of time)

      3. Now, finally, two examples. While entire grooves composed of 3:2 or 2:3 hemiola are so ubiquitous in rock as to be hardly worthy of mention, there are very few that constantly divide that 2 in half to give us a sustained 4:3 polyrhythm:

      Amiina, "Pusl" 

      Radiohead, "Bloom" (electronic percussion vs. acoustic percussion) 

      I'd love to know of others!

      -Brad Osborn



    • I don't, but am I understanding right that the author says "2008 is the first time this happens" but then says "Zappa also did it"?

      Or is the implication that Zappa is not rock (certainly an argument), in which case I'm confused by the inclusion of Phish...

      Megan L. Lavengood  |  Assistant Professor, George Mason University

    • Brad -- 

      Thanks for those examples.  Good stuff!  I was wondering about "Let Down," too -- I don't know the song, but when I listened to it for the first time, I didn't hear anything I'd call a polyrhythm (at least, not in the same sense as The National example he gives)...but I didn't listen more closely to the groupings.  The author doesn't address the difference between conflicting divisions of a shared time span and a grouping dissonance.  (I spent a little time in a YouTube wormhole this afternoon watching various drum set players explain their own "polyrhythmic" grooves -- and they seem to be similarly split over this)

      Megan --

      I also don't really get the footnote.  I hear it in the Phish example (though, the performance I heard has some pretty "loose" 4's...), and while there's polyrhythmic stuff in the Zappa, I don't hear that as pervasively 4:3.  But maybe I'm missing it.  I suspect that the footnote serves to just throw out a couple more examples...even though it seems like it should deal more explicitly with the chronology. 

      Thanks to both of you!


    • I don't know rock music, but there are actually a couple decent hip-hop examples:The bass line for "Can't Do Nuttin' For Ya Man" by Public Enemy (from Fear of a Black Planet (1989)), and the drum beat from "This is a D.A.I.S.Y. Age" by De La Soul (from 3 Feet High (1988)). Both of them feature a strong downbeat accent followed by a 4:3 rhythm that spans beats 2, 3, and 4.

      Of course they also both involve sampled music, so the beats aren't original with the hip-hop artists. Unfortunately, whosampled.com isn't any help, but there may be a way to track down the original music.