Tuesday, February 28, 2012

Math Rock: The Jacob's Ladder Code

I've got symbols and secret codes on the brain from preparing for the A-Z Challenge, and recently I've also been listening to songs by a band that's known for them: Canada's prog-rock power trio Rush!

The idea of encoding secret messages in music is not the newest idea in the world, of course, but I've always enjoyed the geeky ebullience of how it was done by progressive bands of the 1970s and 1980s.  (And there were sometimes messages hidden in not just the music, too!)  Rush famously used the Morse code call-sign of their hometown Toronto airport in their instrumental song YYZ.  They also played around with binary ASCII code in "The Body Electric" from the Grace under Pressure album.  Their tour book for the Roll the Bones tour contained the encoded phrase "Remember Death" in a pattern of skulls.

The one song that always seemed (to me!) like it contained some kind of complex code was "Jacob's Ladder" from the Permanent Waves album. Brimming with strange time signatures and rapid changes in mood, this song was kind of a tone poem that takes the listener through the changing moods of a thunderstorm... first the gathering gloom, then the dark rumbling, then finally the emergence of the Sun from the clouds as the storm dissipates. Neil Peart, the songwriter and drummer, was also no stranger to the multiple allusions of the phrase "Jacob's Ladder" -- the Biblical vision, the meteorological phenomenon, the high-voltage electrical arc, and so on.

The entire song is quite complicated, but it's the introduction to the ending verse that's always fascinated me.  It's just 6 bars long, but it merits special attention in this youtube drumming video where the narrator stops the song (at about 7:13 in the video) and discusses the complexity just as this "ending" part is about to begin.  In fact, that video is the only place I've found on the Internet that describes the ending in such detail.  It consists of several sections of F-sharp staccato rhythms in the following pattern:


In other words, a sequence of 5 beats, followed by a rest, then 4 beats, then a rest, then 4 more beats, and so on.  Pretty random looking -- but with JUST enough regularity to hint at hidden meaning!  One of the commenters on the youtube video calls it "mayhem" to learn and play.  Here's the section scanned from my copy of the Rush Complete score book...

I've long wondered if the random-looking sequence of numbers has any meaning, and I've never been able to find any.  One could translate the numbers into letters using their position in the alphabet (i.e., A=1, B=2, C=3, etc), and one would get: 


If you ignore the L, these could be musical notes, but I can't tell if there's anything significant there.  Just recently, I dug a little deeper into the score scanned above and realized that the beats and rests aren't all of the same length.  Most of the beats are either eighth notes or "triplets" (three notes crammed into the space of 2 eighth notes; they are essentially "twelfth notes"), and just a few are sixteenth notes.  Since my mind doesn't naturally think in terms of musical notes, I translated it into something that makes more sense to me.  In the following chart, the numbers are proportional to the lengths of the notes (in bold colors) and the surrounding rests (in unbolded black):

Click to enlarge

I chose these numbers as a sort of least common denominator.  If one wants to represent eighth notes, twelfth notes, and sixteenth notes as integers, one needs to break up a bar (containing one whole note) into 48 parts.  That way, the eighth note is "6", the twelfth note is a "4", and the sixteenth note is a "3".  Nothing smaller will do it.

I wish I could report that this activity yielded a solution to the elusive secret code.  But no dice!  If anyone sees any order crystallize out of the above chaos, please let me know.

Unfortunately, the only thing more annoying than not being able to solve a puzzle is not KNOWING whether there really is a puzzle there or not!


  1. This is why math scares me off in popular physics books.

    1. Well, this is a good data point for me to have in my head, as I think about moving forward writing popular articles on science.

      But in this case, I'm starting to suspect that there is no underlying "math" here, just something random that Neil thought sounded cool, but with no real meaning! :-)