Polyrhythm, Musical Theatre, and Hamilton

June 28, 2016


Today I’d like to explore a rhythmic thread in American Musicals which has been reinvigorated in the musicals In The Heights and Hamilton: polyrhythmic patterns. The specific polyrhythmic pattern I’ll be discussing was brought to America by Sub Saharan West Africans who came as slaves, and it grew to influence Central American Folk Music, Spirituals, Ragtime, Jazz, and many other forms of music. As the Habanera, the rhythm has been influencing classical music since the mid-19th century, and when Modernists began to incorporate jazz into their music in the early 20th century, it became part of the arsenal of rhythmic innovation that made the twenties such an interesting decade for music.

As the American Musical began to shed its European finery and take up a more local flavor, composers pulled many elements of black music, including this rhythmic idea. By this time the rhythm had become a fundamental part of the way Americans thought about constructing music. Irving Berlin and George Gershwin in particular devised melodies that expanded on a simple construction common to African music in order to play terrific mathematical games with phrase lengths. The culmination of this constructive complexity comes in the musicals of Leonard Bernstein, who used the device in such a sophisticated manner that he wore out the vein.

In the 1960s and 70s, the culture of Musical Theatre lost the taste for the exploration of these ideas melodically, but the Tresillo rhythm increasingly dominated accompaniment figures, especially in Sondheim and Schwartz.

More recently, the phenomenon that is Hamilton reintroduces a rhythmic play in the vocal line we enjoyed so much in the 1920s and 1930s, through the language of Hip-Hop, where artists have been consistently using these devices for a long time.

In this article I hope to show some of this development and trace just a little of its influence in Musicals, both from long ago, and from today. I am no expert on Hip Hop, but I’m going to try to connect that thread too, and show that Lin Manuel Miranda draws heavily on a musical culture that is linked to the same rhythmic heritage that enlivened the Jazz that once inspired Gershwin and Irving Berlin. Don’t worry, I’m going to do my best to keep it easy to understand.

Polyrhythm in American Music

The idea of more than one rhythmic grouping of notes happening at the same time is nothing new. Things like that were written in the Renaissance, and Mozart, Bach, and especially Beethoven liked to play games with rhythmic patterns. [Since first posting this, my buddy Vance Lehmkuhl turned me on to Haydn’s rhythmic games in his Symphonies too. Wow!] There’s a particular rhythm distinctive to West Africa called the Tresillo, which we see in a lot of Latin American music, particularly in the Habanera. It’s very similar to a hemiola, (the same amount of time divided into both three parts and two parts simultaneously). But while the main beat here is divided into 4 parts, there’s another thing going on which is almost divided into 3 parts: 123 123 12. (this illustration from Wikipedia) There are plenty of places online to see this kind of thing if you have the time to look, but check this video out and you can’t miss it, in the drumming. 12312312.

When Africans brought these rhythms with them, they took on a slightly different form, but the 3+3+2 pattern remained firmly rooted in the bones of the music: (try right around the 16:00 mark)

In Cuba, this same rhythm would become the heart of the Habanera, which would itself become an influence on Jazz, and Urban Blues, particularly for W.C. Handy and Jelly Roll Morton. In the United States, the rhythm embedded itself in many kinds of black music. Its inclusion in Ragtime helped to export it all around the world, and a critical concept emerged: A foreground musical idea could play a complex rhythmic game with a more regular background pattern. This is the heart of what Ragtime is all about. Here are two famous examples from The Entertainer by Scott Joplin. I’ve marked the groupings so you can see how the 3+3+2 pattern appears.Joplin 1

Joplin 2

European composers were delighted by these rhythms, which seemed to be a new way out of what had become a rather boring rhythmic palate for Western Music. Bizet famously took the color and exotic flavor of the Habanera rhythm for his 1875 opera Carmen, and Debussy in 1908 wrote a ragtime spoof in his Children’s Corner, cheekily quoting Wagner in the process. By the time Stravinsky got around to manipulating these ideas in 1917, he had already found by other means a way of detaching the various phrase lengths from their regular oom-pah partners, leaving the gears of accompaniment and melody free to link up in improbable ways with each other. (or against each other, as was more often the case)

For Americans, though, the game has generally been to set up a fairly square and somewhat predictable accompaniment rhythm, over which the other musical lines play a game of syncopation. The trick to the particular kind of syncopation I’m discussing here, using patterns to emphasize a cross-rhythm, turns out to require a cheat in order to work. Because music (especially Western Music) tends to organize itself in symmetrical patterns of measures, you can’t just stack groups of three on top of groups of 4 without putting in a group of 2, or you’ll be out of sync. It’s kind of like Leap Year: We need an extra day every so often or the whole year winds up being off. The pattern we’ve been discussing was 3+3+2 to add up to the 8 needed to line up with the beginning of the next measure without just being off by an eighth note. But composers of novelty piano music in the 20s figured out ways to stretch that even further, to delay the re-alignment and keep the plates spinning, for example with a 3+3+3+3+2+2 pattern, holding off all the 2s until 2 full measures are up. This keeps the right hand pattern off kilter longer and makes the resolution even more amusing for the listener.  Zez Confrey’s biggest hit Kitten on the Keys, published in 1921, carries this idea to an even further extreme: 3+3+3+3+3+3+3+3+8 (with all the twos covered right at the end) He follows that with the traditional 3+3+2.


Irving Berlin and George Gershwin

It was only a matter of time before these syncopated games made their way to Broadway, and it makes sense that Irving Berlin would have had a hand in that, since his biggest early hit was Alexander’s Ragtime Band and since he had such a terrific ear for the interplay of multiple parts as evidenced by the many part songs he wrote throughout his entire career. He was an astute listener to things going on in the culture around him, including the newer developments in rhythm.

For 1921’s Music Box Revue, Berlin crafted a novelty number called Everybody Step. In the chorus of this song, he plays a very subtle rhythmic game. 3 quarters, 3 quarters, then a nesting pattern of 4 groups of 3 Eighth Notes to add up to a total of 4 groups of three Quarters. Through this ingenious figuration, Berlin arrives at symmetry after only 3 measures, so he takes a full measure with no melodic content to bring the pattern back into symmetry with a 4 measure unit:Berlin 1Berlin 2

At this point we’ve elevated the game from building patterns of threes and twos against a larger set of fours, and are now nesting smaller subsections of rhythm into the larger patterns.It’s kind of a miniature version of the large scale structure happening within one of the pieces of the other structure.

This kind of writing sets off a sort of rhythmic arms race: How unusual can the pattern be and still make a memorable and sensible melody? George Gershwin recognized Berlin’s acheivement and pointed to Everybody Step as an exercise for singers who wanted to learn Jazz. He would also launch the next salvo in the battle for rhythmic supremacy, in 1924, in a song he and Ira wrote for Lady Be Good. The title says it all: Fascinating Rhythm.

Fascinating RhythmGershwin has chosen a different game than Berlin: He uses 4 groups of 3 quarters just as Berlin did. But instead of building a nesting set of eighth notes inside the larger pattern, Gershwin innovates from the other direction. The corrective extra space isn’t all shuffled off to the end of the phrase. Instead, some of the four beats we need to complete the four measure phrase are inserted between the groups of three as eighth rests, leaving 2 and a half beats of correction at the end, after it’s all said and done. (That ‘I’m all aquiver’ line doesn’t count out exactly the same as the others, but in context I think it’s basically as I’ve divided it here, with the first eighth of ‘ver’ as part of the 3 pattern.)

I might also point out that this phrase is as much ‘phase’ music as Steve Reich’s Piano Phase or Clapping Music. Notice that each successive measure begins on the next note of the phrase. This happens because Gershwin’s extra eighth rest in the pattern makes the melody just one eighth note short of a measure long. Amazingly, the thing is singable by any random person on the street. That’s genius.

I’d like also to point out that Ira evidently had a very difficult time writing a lyric for this tune. The freestyle rap culture we’ll come upon later is a lyric driven rhythmic game. The game in the early 20th century is driven by the fingers, and the lyric has to do the best it can to keep up after the fact.

Irving Berlin’s next bit of mastery is one of his most famous songs, Puttin’ on the Ritz, which he wrote in 1927, but which didn’t find its way into a musical until the 1930 film of the same name. Berlin embeds the extra four in the middle of the pattern, for a 3+3+4+3+3 idea. He also nests a syncopation which is a kind of three grouping inside two of the threes.

Ritz 1

Ritz 2

It’s really ingenious, very singable, and also phases similarly to the Gershwin we just examined. Watch that F. It’s in beat 1 the first time, on the and of 4 the second time, on 4 the third time, then on the and of 3 the fourth time.

Because all that rhythmic interest is compressed into 4 measures, the remainder of the phrase plays out with only a handful of notes for the following 4 measures.

Leonard Bernstein

After Gershwin died in 1937, we don’t see a lot of this kind of rhythmic play in popular music or on Broadway, with one notable exception: the music of Leonard Bernstein. Bernstein’s music includes a lot of Jazz ideas, and I hear in his music the strong influence of Gershwin and Stravinsky. In Bernstein’s lectures about Mozart, he spends some time talking about Mozart’s exquisite sense of balance, so we know that Bernstein thought this way about all kinds of music, not just showtunes. In his shows in the 1950s, Lenny introduced some real rhythmic innovations; equal parts Gershwin and Stravinsky. By the time Candide rolls around, Bernstein is playing such fascinating phrasing games that he seems to be tying together the threads of Post-ragtime experimentation and Viennese waltz Hemiola. Some of it doesn’t even sound like Jazz anymore.

The first Bernstein example I want to explore is The Wrong Note Rag from Wonderful Town in 1953. It only takes 5 seconds or so to hear that Bernstein is taking the examples I’ve listed above one step goofier and more off-kilter. He frontloads the two counts, and then runs 4 3s in a row, which leaves the rhythmic resolution of the phrase until the very end of the 8 measure unit.The next 8 measures use Berlin’s trick from Puttin’ on the Ritz and embeds a smaller syncopation into the same count set of 2+2+3+3+3+3.

Wrong Note Rag

I’m not even going to begin to discuss what is happening in terms of key here, but it’s further out than anything you would have heard in Musical Theatre in the 30s and 40s.

What’s new here? Bernstein is using the same rhythmic elements pioneered decades earlier by Confrey, Berlin, and Gershwin. What I hear is a new expression of irony. In the introduction, he quotes a very commonplace cliche that he later embeds into the melody itself, and unlike his predecessors, Bernstein is pushing the edges of listenability for comic effect. The lyric is self-referential and mocks the tune. Once a style of music can be parodied in this way, it’s probably not possible to make it function the old way; it has passed into nostalgia and camp.

1956’s Candide is where Bernstein takes that idea of varying phrase-length so far into the classical realm that it one no longer hears jazz in it. There are many examples of this in Candide, but we’ll look at a passage here from Bon Voyage. Bernstein’s intentions here are clear, he marks the meters on the score:Candide corrected


(Bernstein marks the first measure of each 3/2, cut time, and 3/4 meter. I’ve continued marking it for clarity. Yes, notation nerds, I know I’m breaking some rules here to conserve space) 

Note that the first half of the first measure of accompaniment is blank, which makes the listeners unsure whether they are hearing a full measure of 3/2 or a measure and half of cut time. Note also the use of both patterns of 3 half notes and three quarters: it’s Irving Berlin’s game writ large. This is by no means the only example in Candide of this kind of writing, and West Side Story, written right around the same time, also has this kind of thinking in it.

At this point, Bernstein has so internalized this rhythmic interplay that it has simply become part of his musical language. But he’s also playing the game at a level so much more sophisticated than his peers writing musicals that they basically conceded the field to him.

What Happened After Bernstein?

For all intents and purposes, Bernstein disappears from the Musical Theatre landscape after he takes the directorship of the New York Philharmonic. (although if you want to see the rhythmic master at work in his later years, you must have a listen to this. About 40 seconds in, each phrase is slightly longer than the last)

There are some outliers like Burt Bacharach who do really creative things with rhythm, but they are no longer playing the same game as those earlier composers. Bacharach loves to really break up the phrase lengths, but the melodic ideas are not playing a balancing act against the accompaniment; they’re in lock step. Think of a song like Promises Promises in 1968 from the musical of the same name. The time signature changes keep the melody in step with the accompaniment at each juncture.

The 3 against 4 patterns didn’t disappear by any means, but they moved into the accompaniment. In a way, this was a return to their home; patterns of three come very naturally on the piano or guitar, but they do not occur as naturally to a singer. In the 1970s, Sondheim favored Latin bass lines, which often approximate the rhythm I discussed earlier because they’re descended from the same African source. But it’s in the right hand that we find the interplay we’ve come to expect from these earlier experiments, demoted now to the function of providing a bed of eighths or sixteenths over which the singer provides melody:

Another Hundred People (1970) is perhaps the archetype of this accompaniment style:

Company 1970 1

Marry Me A Little, cut from CompanyCompany 1970

Stephen Schwartz also favors this kind of pattern:

From Corner Of The Sky in 1972.

Pippin 1972

Meadowlark from The Baker’s Wife in 1976:

Baker's Wife 1976

Other examples would include Patterns from Maltby and Shire’s 1983 musical Baby, parts of  You’re Nothing Without Me from Cy Coleman’s 1989 City Of Angels, No More from Marvin Hamlisch’s 1993 the Goodbye Girl,  Stars and the Moon from the 1995 Songs for a New World by Jason Robert Brown, and a host of others.

Note that in these patterns, the number grouping is usually the same, (3+3+3+3+2+2) and that the note patterns are for the most part metronomic and unvarying, which is only right. After all, this is an accompaniment, not a foreground figure. It really shouldn’t be too interesting. These patterns appear frequently in mainstream Musical Theatre from the 1970s onward. In fact, I think these kinds of piano finger-picking patterns are one of the truly distinctive features that mark mainstream modern musical theatre after rock began to be introduced. One doesn’t find this kind of accompaniment many other places, and when one does find it in the occasional choral octavo, it often sounds ‘like Musical Theatre’. Even though the style contains an echo of the earlier patterns, this is a far cry from the kind of metric playfulness we had seen 40 years earlier. The vocal melodies we hear from the 1970s onward in most Musical Theatre are generally fairly square, rhythmic interest coming from back-phrasing or from simply singing very very fast, or with long notes at the end of an otherwise busy phrase. I’m not arguing here that this writing is bad, I’m only pointing out that the interests of the writers lay elsewhere. On occasion, we find examples of people using the older styles in a pastiche mode, for example in Ragtime or Thoroughly Modern Millie. But the fact that they’re employed to evoke the earlier time simply proves my point.

Enter Lin-Manuel Miranda

Look AroundSo far I have only been discussing the mainstream Musical Theatre written mostly by white composers playing out ideas that originated in black culture. The Musical Theatre written by people of color over the last hundred years has consistently brought in elements from Blues, Jazz, Latin Music, Soul, Hip Hop, R&B, Gospel, and other related forms. Because these popular forms are more closely connected to the source of black music, they often contain elements of rhythmic play that mainstream white musicals haven’t been interested in exploring. This incredible culture of black musicals has intrigued white audiences, but never in such an overwhelming way as the recent reception of Lin-Manuel Miranda’s work.

The opening number of Miranda’s 2008 In The Heights begins with the son clave rhythm, which includes the tresillo, and is the lifeblood of Afro-Cuban music. As an urban Latin groove unfolds, Miranda, singing himself as the character Usnavi, raps:Usnavi

(this iteration comes from the piano vocal selections, the cast recording is slightly different.)

Now that we have all learned what an important and capable writer Miranda is, these words seem like an introduction, a statement of purpose, and a demonstration of methodology. He claims a multifaceted ethnic heritage and his intention to return to it, along the way playfully phrasing 3 and 2 beat phrases at the level of the eighth and the quarter note, and even splitting the eighth into triplets. This way of playing the foreground against the background is still a rich vein in hip-hop, but we haven’t seen it so convincingly and pervasively applied in Musical Theatre since Bernstein, and then it contained a rich admixture of Stravinskian modernism.

Much has been made elsewhere of how well Miranda has managed to fuse the values of Hip-Hop and the well-made musical, and that’s very important. But here I want to examine the re-infusion of rhythmic play. Even though I’m certain Miranda knows this thread of Bernstein’s theatre music very well, his expression of it is not a throwback to Bernstein at all, but a re-connection to a much deeper thread via the language of Hip-Hop, where these African ideas have never left the conversation.


In an interview with Jon Caramanica,  Miranda talks about his influences, and the kind of music he listened to as a child. He actually describes a listener exactly like me in this interview:

“..they hear a polysyllabic rhyme, and they go, ‘oh! Eminem!’, because that’s the only polysyllabic rapper to which they are exposed. If you only have like, a toe in that water, that’s all you’re gonna know.”

Intuitively, of course, I know that there’s a deeper culture of that kind of rapping; I just haven’t encountered it in my daily listening habits. So I was interested to hear some of the places he first encountered the kind of quick internal rhyming I’m talking about.

“When I discovered Big Pun, I mean everything… everything turned upside down. Just ’cause, you know I’d heard, I’d listened to Rakeem, I’d listened to, you know, Kool G Rap, but to hear [raps] ‘Dead in the middle of Little Italy, little did we know that we riddled some middlemen who didn’t do diddly…’ I literally didn’t know that was possible. Even Musical Theatre had never given me internal rhyme like that.”

He’s right. Internal rhyme in traditional Musical Theatre is incredible, but the balance is between the perfection of the rhyme and the exact placement in the scansion of the rhyme. One of my go-to internal rhymes is this knock-out from Sondheim’s Follies:

Sally dear, now that we’re man and wife

I will do wonders to make your life

Soul stirring, and free of care

If we fight, and we might, I’ll concede

Furthermore dear should your ego need

Bolstering, I’ll do my share.

The wonder of Sondheim’s rhyme, (which is goofing on Ira Gershwin’s style) is that the dear-we’re, do-to, fight-might, …more-your internal rhymes land like clockwork at the same foot in the scansion, that the impressive bolstering-soul stirring rhyme sits unexpectedly at the top of each last line as a bonus, and that there are no near-rhymes, only perfect ones. Despite the mechanical brilliance, it also sounds like something somebody might actually say; there are no Yoda-isms. This is how good traditional Musical Theatre rhyming works. But the example Miranda raps from Big Pun is playing Scott Joplin’s old game, with the accents punching out 3+3+2+3+2+2+3+3+2+2+3+2+2. It was awesome when Stravinsky heard it, and it’s still awesome now. (I understand that this is super old news for Hip-Hop fans, but you’ll bear with me)

It would probably be impossible to list every time this device happens in Hamilton; once you hear it working, you won’t stop noticing it all over the showWashington

It’s all over the rap passages:

My Shot 1


My Shot 2

It’s also in the accompaniments, like this figure in My Shot:My shot Accompaniment

Sometimes it’s in both at the same time. This example has most of that old Habanera bass line, and then in the next measure we hear the Tresillo rhythm twice as fast as it was in the previous measure. At the end of the following two measures, we get the sped up sixteenth version twice in a row, with accents to make sure we don’t miss it. But it’s also up in the vocal line.

Satisfied Example

And then this moment, where Miranda runs 6 threes in a row over a barline:Satisfied Example 2

I don’t know about you, but these excerpts and others like them are among the most thrilling moments in the musical; they’re what make it distinctive for me as a listener.

Musical Theatre, like other kinds of popular culture, needs a kind of blood transfusion from other art forms to keep from slipping into a coma of repetition. In the 1920s and 30s, the infusion came from Jazz. In the 60s, it came from Rock, in the 80s, we suddenly got very interested in what the British had to say. In this century, one lifeline seems to be coming just in time from the Hip-Hop community, reflecting ideas as old as America itself, and rich with a complex and conflicted racial past. It remains to be seen whether other writers can make the same kind of compelling musical arguments, or whether Miranda will be the only master. It’s tempting to think that every significant new show will speak this new language, but the important thing is that new musicals keep pulling in people and ideas from other genres and cultural experiences and using them authentically and compellingly in the service of a good story.

I’ll let Lin-Manuel Miranda have the last word, from that same interview:

“What I like about Hip Hop is what I like about Musical Theatre, which is we can absorb any genre and flip it and make it our own. That’s the thing the two genres share, even though there isn’t a ton of overlap. You can have a musical that absorbs disco music like David Byrne did with Here Lies Love, and use it to tell a story. You can use Emo to write Bloody Bloody Andrew Jackson; it takes whatever it needs. Jay Z’s biggest hit sampled Annie. Hip Hop has that same thing, of we will take what we need to get our message across, and that’s what I love about both genres.”





  1. I cannot thank you enough for this!

    As a student of both classical and jazz music who was recently thrust into music directing Lin-Manuel’s In the Heights, I cannot even begin to describe how much I enjoyed your exposition on this rhythmic theme… Brilliant. As much as I love your music directing show guides, I would really love to see more articles such as this one! Thank you again for the research you’ve done.

  2. This is a marvellous post, and I’m equal parts grateful and jealous. If you’ve not seen this clip of Hugh Laurie and Stephen Fry, as Bertie Wooster and Jeeves, I think you’ll enjoy it: https://www.youtube.com/watch?v=zO9axGrzDE0

    I wanted also to put in a vote for the opening vamp of ‘Don’t Rain On My Parade’ as a contributor to the demise of 3+3+2. Not because it’s self-referential, but because it was such a thumping great hit that the vamp became a cliche. I read somewhere – and I can’t find a source, but that just makes it a better story – that Jule Styne was asked “What time is that song in?” “It’s time is Broadway,” he replied.

    Lastly, when the Tony-nominated songwriters sang “Tomorrow” together in this year’s Tonys broadcast, what did Lin-Manuel Miranda tap out while they all sang the final held note? So – o – on Cla – ve, So – o – on Cla – ve.

    • Mr. Casey- I had not seen the Wooster and Jeeves clip. Fabulous! It sent me down a path listening to a whole bunch of them.

      And thank you also for mentioning Jule Styne. He flew under my radar, but yes! He loved that rhythm, didn’t he? He does the 3+3+2 rhythm in the melody of I Met a Girl from Bells are Ringing, and there are plenty of interesting things in Gypsy too, 3+2+3 in the melody of Some People, All I Need Is The Girl, and Together Wherever We Go, the whole “all the sights that I gotta see yet” figure is like, 3.5 and 4.5, isn’t it? And the Momma’s Talkin’ Loud portion of Rose’s Turn is a classic 3 against 4 with 10 3s before she breaks down! He was a great writer. Somebody needs to do a full musical survey of his output.

      Glad you liked the post! If I think of anything similarly interesting, I’ll write about it.

  3. Brilliant! As someone with only moderate knowledge of music theory, I can’t tell you how incredible it was reading this. I’ve been trying to find the words to describe that kind of syncopated accompaniment that I love hearing in Soundheim and Bernstein and William Finn and other works of musical theatre.

    I’d been searching ever since seeing this Seth Rudesky video, in which he mentions how the orchestra sounds “so musical theatre:” https://m.youtube.com/watch?v=tSrhEFDX3Fw

    I’m so happy I found this essay! Excellent research and excellent writing!

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