Rock Hemiolas

When I was in sixth grade, I had a band – a power duo with my best friend Bill who played drums, called The Rolling Pebbles. Bill did most of the singing, but I had a couple of vocal features, and one was “Subdivisions” from Rush. Bill and I were nuts about Rush, and that was the title track of their latest record at the time, and the first single. “Subdivisions” was the first song I played that used the odd time signature of 7/4. It planted the seed of all things “7” in my brain and I followed up much later, exploring that rhythmic meter in the jazz format with my trio.

For the non-musicians: Much of Occidental music is rhythmically written and felt in continuous groups of 2 (TUM-tum TUM-tum), 3 (TUM-tum-tum TUM-tum-tum) or 4 (TUM-tum-tum-tum TUM-tum-tum-tum) beats. Other rhythmic groupings – like 5, 7, 9 or even 11 – are common in folk music from the Balkans, Indian ragas, flamenco music, and other music, but are not the norm in western classical, jazz and pop/rock music. “Odd” rhythmic meters, as they are called, do indeed crop up in those genres: 20th Century composers like Bartok and Prokofiev use them, and jazz musicians like Dave Brubeck popularized them. For me though, the portal into that rhythmic world when I was ten was Rush.

The appeal of “Subdivisions” for me is the way it simultaneously has a “large” and “small” 7 feeling. (The whole song is not in 7; it switches between the odd meter and a straightforward 4/4 meter throughout – a favorite device of prog-rockers.) We could write the opening synth-bass figure that drives much of the song like this:


How we write that should depend on how we feel the song. The figure itself is 7 beats long; so one might ask, why write it the first way? Why put two of those seven beat figures in one bar, subdividing the bar awkwardly in the middle? (I wonder if the double-entendre of the song’s title was intentional on lyricist Neil Peart’s part.) Why not simply let the length of the figure dictate the meter, so that it starts logically at the beginning of the bar, as with the 7/8 meter of the second example?

I myself favor the first notation, though, because it corresponds to what I’m feeling, which is two things at once. On the one hand, I’m feeling these groups of seven that continually repeat. On the other hand, I’m simultaneously feeling a larger, slower seven – I’m feeling the quarter notes of the 7/4 in the first example. That is for me what makes the groove not merely complex but also pretty fat. There is symmetry at play: The large seven is split into two smaller groups of sevens. Because seven is an odd number, though, it must split between the third and fourth beat. This rub of something resembling a downbeat landing on an upbeat gives a very cool feeling in the body.

This phenomenon has a name in classical music – it is called a hemiola (yes, it sounds like a blood disease). Brahms loves them, and will keep them going for a long time, creating wonderful rhythmic tension. A hemiola in classical music is usually understood as a repeated pattern of four in the context of a meter of three or six – for instance, in a 6/8 meter, groups of phrases that last 4 beats. But it could involve more unorthodox, odd numbered patterns. One of my favorite hemiolas is at the end of Brahms’ Capriccio, the fifth piece from the Opus 76 Klavierstücke, when he places five-beat groupings into the 6/8 meter:


The effect is great and full of drama, like a big wheel that has fallen off its axle, careening wildly towards some poor soul. This piece of Brahms is huge for me. It’s chock full of hemiolas and 2 against 3 patterns; one could say that hemiolas are the “subject” of the piece. Note the more traditional hemiolas in groups of two as well in the right hand.

When I learned about fractions and their common multiples and denominators, I think in third grade, we had rectangular blocks of different colors and different lengths. If you lined them up, two longer red ones would be the same distance as 3 green ones, or four shorter blue ones, etc. The fun of hemiolas is not just where they overlap, but also where they meet again, and when my teacher, Ms. Hurwitz, showed me what they were for the first time in a piano lesson, I thought of those colored blocks.

This phenomenon has a name in rock too: “Kashmir”. Led Zeppelin’s classic groove on that song from Physical Graffiti, demonstrates why its members are truly rock gods: We usually think of Led Zeppelin as proto-heavy metal, leading the way for head-banging, but with “Kashmir” they instigated a solidly prog gesture, one that bands like Rush would expand upon, and later, prog-inspired metal bands like Dream Theater will exploit. Here is the grandfather of modern rock’n’roll hemiolas, the vamp on “Kashmir”:


Even though drummer John Bonham plays a relentless rock beat in 4/4, no one would say that this song is simply in 4/4, because the riff played by the guitar, mellotron, etc. is in groups of three. That riff unto itself, though, is twofold: It suggests a quicker 6/8 meter, as it repeats that ostinato rhythm every six 8th notes, but also implies a larger, slower 6/4. The single D that ends each bar above is subtle but very important – it makes us feel the end of a bar; it wordlessly instructs us to feel the 3 note ostinato in groups of two, and thus ultimately hear Kashmir as a slow, strange 6/4. So there are really three implied grooves at once: the quicker 6/8 meter suggested in the figure played by the guitar, the 4/4 of the drums, and the final marriage of the two – the 6/4 as it is written above – or at least that’s how I feel it.

As with Rush’s “Subdivisions”, the play between quick and slow meters in Kashmir is a big part of its design. In Both the Led Zeppelin and Rush, the drummer is holding down the fort, so to speak, providing the slower backbeat that passes over the barline, like a cement roller smoothing over cracks in pavement. This approach pays off for the same reason in both songs: Both of them shift to a regular 4/4 groove, making an actual time signature change, but when they do, there is no hiccup – the drummer is already there, grooving.

The metaphor for the feeling that hemiolas give is often one of physical motion, and with “Kashmir”, I’m led – undoubtedly by the back story of the song as well, which was inspired by a journey through Morocco – to visualize way a camel and its rider move across a desert – slowly, stately, powerful, but with a bounce and a shake on each step, with a constant funky jerkiness that mingles with the backbeat of the camel’s slow trudge.

When I went to write “Boomer” for my trio with Jorge Rossy and Larry Grenadier, which we recorded on an album called House on Hill, both “Subdivisions” and “Kashmir” were informing it: Jorge, a la John Bonham, plays a slower rock beat in 4 which passes through the barline and then meets up again with the quicker meter, and the 7/4 bar is split into to equal halves of 8 eighth notes, like in Rush’s “Subdivisions”. Here is the piano ostinato figure of Boomer, the bass root-motion, and a simplified sketch of the drum beat under it:


A little more of that third grade math will tell us that the first common multiple between the 7/4 meter and Jorge’s implied 4/4 is 28. So it takes 28 quarter- notes – or four bars, like the four bars shown here – until Jorge’s bass drum cycles around to land on the downbeat of the bar, as it does on the following bar.

Larry, Jeff Ballard and I explored this idea a little further on our version of Oasis’ “Wonderwall” a few years later. On that one, Jeff and I played in regular 4/4 meter, but Larry played a truncated bass line:


That line would immediately repeat itself starting on the 8th note upbeat of beat two of that fourth bar, and similarly thereafter, giving us a repeating pattern that was 27 8th notes in length, against the backdrop of the 4/4 meter. Did we all meet up eventually in the right place? I’m not even sure anymore!

© Brad Mehldau, All Rights Reserved