Hemiola: It's Not Just For Hemophiliacs!

I think my title is a pun in Greek! Hemiola and hemophilia both come from ancient Greek, but from different words. Hemiola comes from ἡμιόλιος meaning "one and a half" and it refers to the practice of putting three beats where there would normally be two. Hemophilia comes from the Greek haima αἷμα 'blood' and philia φιλία 'love' and refers to a medical condition where the blood does not clot properly.

So someone who was in love with hemiola would be a "hemiolaphiliac". Or something.

Hermiola is a very interesting rhythmic effect that comes from changing the grouping of beats. We first start seeing it in Spanish music in the 16th century. It usually occurs in triple time as follows. This is from a Baxa de contrapunto by Luys de Narvaez published in 1538:

 

The hemiola occurs in the third and fourth measures when tieing the A over the barline turns two measures of 3/4 into one measure of 3/2. This became a popular way of signalling a cadence in the Baroque. But the hemiola became quite ubiquitous in Spanish music. A famous example is this Canarios by Gaspar Sanz from the 17th century:

Instead of just appearing at the end or a cadence, this alternation between two groups of three beats and three groups of two beats, shown in the example by the changing time signature from 6/8 to 3/4, happens throughout the piece. We find this a typical rhythmic effect in Spanish music. It appears at the beginning of the famous Concierto de Aranjuez for guitar and orchestra by Joaquin Rodrigo:

There are a couple of nice things about this deceptively simple opening. First of all, it is a three-measure phrase, which is unusual. It has an urgency about it that comes from squeezing the last two measures of a theoretical four-measure phrase into one. The first two measures are a typical hemiola. The third measure is a compressed version of the same hemiola! Let's listen to that opening:

Very nice. Do you hear how that third measure throws us forward? The unusual rhythmic patterns of flamenco underlie a lot of Spanish music. The history of flamenco is somewhat obscure, but undoubtedly some of its unusual handling of rhythm and timbre, by European standards, comes from the long occupation of Spain--some 700 years--by the Moors. One hemiola-related pattern in flamenco is this one:

The two layers are often clapped, but for some reason, my percussion example didn't want to be embedded. As you can see the one player keeps a steady pattern that is in 6/8 while the other plays alternating measures of 6/8 and 3/4. The effect is quite remarkable. We find this kind of pattern in, for example, the bulerias:

This is Sabicas, a real master of the bulerias. He is not actually playing the pattern I have shown above, except in bits, but you will find that you can clap it along with him.

So, that's the hemiola.

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Footnote to Taruskin

As I said, I just finished reading all five volumes of Taruskin's monumental Oxford History of Western Music and occasional musings sparked by that have popped up here from time to time--and will again! It is really above and beyond any quibbling I might engage in, but here are a couple anyway. It is not possible that a book of this kind will be free from error, but I noticed very, very few. One was the claim that Berlioz, who played the guitar, wrote no music for guitar. Well, of course he did, but nothing terribly significant.

There was one particularly comic moment that I enjoyed. Throughout the book, Taruskin adopts the historian's neutrality, even though he often quotes strong opinions from others, critics and composers, as important historical evidence. These quotes are, of course, footnoted. But on one occasion, when he quotes a particularly scathing review of the opera by John Adams, The Death of Klinghoffer, accusing the composer of "moral blankness and opportunism", if one turns to the footnote one finds that the critic in question is none other than Richard Taruskin. Mind you, he does say that the review was "possibly overwrought". Heh!

There is really only one hobbyhorse that I have my doubts about. Taruskin has long been known for making the counterintuitive point that the revival of early music and its austere mode of performance ("no vibrato!") was in fact just one manifestation of modernism. We like early music and we like it performed that way because it fits our taste. Not to detract from the truth of that,  but I think he takes it too far when he says that the rigid, metronomic tempos typical of some manifestations of the early music movement (and of music by, among others, Stravinsky and other moderns) is specifically a modernist quirk. I think that most music in most times and places has been composed and played in a range of rhythmic modes. Some of these are fluid and with a lot of rubato, while others are motoric and have a real groove. I think this was as true in 1500 as it was in 1700 as it was in 1900. Sure, there are historic trends, but music with rhythmic precision and drive was not a discovery of the modernists.

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The Tyranny of the Backbeat

People used to talk about the tyranny of the barline which came from the very useful invention of the barline to organize ensemble music. When the barline, or rather the beat associated with the downbeat, or first beat of the bar, became all-controlling, then it started to be called the "tyranny of the barline". A related complaint was directed against the indiscriminate use of the metronome leading to a rigid sense of the beat. One writer wrote:

A good performance is so full of these minute retardations and accelerations that hardly two measures will occupy exactly the same time. It is notorious that to play with the metronome is to play mechanically - the reason being, of course, that we are then playing by the measure, or rather by the beat, instead of by the phrase. A keen musical instinct revolts at playing even a single measure with the metronome: mathematical exactitude gives us a dead body in place of the living musical organism with its ebb and flow of rhythmical energy. It may therefore be suggested, in conclusion, that the use of the metronome, even to determine the average rate of speed, is dangerous.

— Daniel Gregory Mason; The Tyranny of the Bar-Line

Alas, it seems that skirmish, at least in some areas, is long lost... If you combine a little metronomic beat with the tyranny of the barline and add in a characteristic accentuation that comes from rock n' roll, then you get a structure that underlies an amazing amount of the music we hear every day. I call it the "tyranny of the backbeat". What's a backbeat? Nearly all popular music these days, certainly all that derives from rock, is in 4/4 meter, meaning that beats come in 4 beat packages. Normally the first beat is stressed, which helps to define the package. In rock, the 2nd and 4th beats are stressed instead. This is a kind of syncopation in that it places the accents in an unexpected place. But it is so ubiquitous now, that it is like a rigid Procrustean bed that all music is forced to lie on. Well, a lot of music at least! Here is the locus classicus:

Just let me hear some of that rock'n'roll music

Any old way you choose it

It's got a backbeat, you can't lose it

Any old time you use it

There are exceptions, but they are amazingly few. Here is a rock song where the stresses are reversed. The effect is to restore the feeling of syncopation! Neophyte drummers are so programmed to stress 2 and 4 that they sometimes have difficulty with this song:

Do you hear it? It sounds like the beat is oddly shifted--not because it is, 1 and 3 are stressed--but because the backbeat has become so ubiquitous that it is ingrained into us, at least with this type of music. Let's choose some random examples from YouTube to see how prevalent it is.

I almost thought my brilliant theory was going to be undercut by the first clip, but no, around the 53 second mark it settles into a backbeat.

Yep, more backbeat. Oh, by the way, I am finding these by going to YouTube and typing in a single letter to see what comes up. I started with 'L'. Here's another:

Now that's a particularly aggressive example. The backbeat is bad enough, but when it is delivered by a drum machine, I like it even less. Another:

Yep, but at least this time it's a real drummer. I've done 'l', 'm', 'n', and 'o'. How about 'p'?

That's the first one with a slight divergence from the backbeat. While two is heavily stressed, they mess around with 4 a bit.

But I think you get my point. And my impression is that with the generic stuff you often hear out in public, in malls and restaurants, it is even worse. AAAAAAGGGGGHHHHHH!!!!!!!!!!!!!

I have this vision of generations of impressionable young minds and ears growing up permanently infected with the backbeat, unable to feel and appreciate the subtle expression and rubato that we have enjoyed for centuries if not millennia.

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Syncopation

This is a rhythmic technique that is widely used. The definition, "If a part of the measure that is usually unstressed is accented, the rhythm is considered to be syncopated" may seem a bit obscure, like the definition of ontology in philosophy: "the study of being qua being." Here is the fairly good Wikipedia article on syncopation. The problem with terms like syncopation or harmony or ontology is that they are so fundamental that they are very difficult to define in terms of anything else.


Let's go right to some examples. Rock and roll is partly based on a very simple kind of syncopation. In a measure of four beats the normal ones to stress are one and three: ONE two THREE four. In rock and roll, instead the two and four beats are stressed. This is known as the "back-beat". Here is an example:

It would be a creative thing to try and do a rock song that didn't do this and in fact Cream did. Here is "Sunshine of Your Love":

What gives it its primal effect, apart from the 'lick', is the strong beats on one and three, possibly inspired by Ginger Baker's interest in African drumming. Neophyte rock drummers are sometimes very puzzled to play this one because they are so thoroughly programmed into putting the stress on the backbeat.


This is syncopation on the basic level of style or genre. Another example would be the Baroque sarabande, a slow dance in 3/4 time. Normally in triple time the first beat is stressed, the second beat is neutral and the third beat lifts--the 'upbeat' (meaning that in a dance, the dancer would typically lift their foot on this beat so as to put it down on the first beat). But in the sarabande, it is the second beat that is stressed: one TWO three. An example:

The common metric technique based on syncopation is called 'hemiola' and involves turning two measures of 3/4 into one measure of 3/2 by using syncopation: ONE two THREE one TWO three. This was often used at final cadences in Baroque music.


But syncopation is found on all rhythmic levels, even within beats. So it is not only a metric technique, but also a rhythmic one on the level of melody and a harmonic one as well, as intense harmonies are often placed on weak beats. In the following example, the third movement of a Beethoven quartet, the first variation uses some intense accents on the weak parts of the beat at the end of the first section. The effect is around 1:53 in this clip:

The only kind of context in which you cannot use syncopation is one where there is no context of strong and weak beats and hence no expectation to play with. This is the problem with the jagged rhythmic textures of high modernism because they are so fragmented that the listener has no sense of a regular beat. Ironically, these pieces that look extremely 'rhythmic' on paper, really have little rhythmic effect because they sound random.

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Dance, Music and Rhythm

I usually try to post about something I know something about, but this one is a bit of a mystery to me. On several occasions I have taught adult beginners who have had considerable background in dance--one was a professional dancer. Now one might expect that they would have a special sensitivity to or head start on rhythm. But it turned out not to be the case. In most cases, the students with dance background turned out to have more problems with rhythm than the average student. Their background in dance turned out to be of no advantage and possibly a disadvantage.

Now why is this? It seems counter-intuitive, after all, rhythm is rhythm whether you are following it with your legs or with your fingers, right? But it seems not. If anyone has any thoughts on this, I would be interested to hear them. I would speculate that the way dancers feel and execute rhythms in their bodies is quite different from the way musicians do. I can't quite put my finger on it... Is it that they are moving weight in space while we are placing moments in time? I really have no idea. But it is an interesting mystery.

And musicians seem to be notoriously bad dancers!

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The Case of Sibelius

Continuing on from my previous post, let's have a closer look at Sibelius' 4th Symphony. A lengthy analysis would be tiresome and, uh, lengthy, not to mention unbloggy! But we can look at just the opening of the 4th Symphony. Alex Ross, in his excellent book The Rest Is Noise writes as follows:

Sibelius finished his first two symphonies in 1899 and 1902 respectively. On the surface, these were typical orchestral dramas of the heroic soul, although Sibelius' habit of breaking down themes into murmuring textures sounded strange to many listeners... In [ ] the Fourth, Sibelius presented his listeners with music as forbidding as anything from the European continent at the time ... The first few bars of the symphony extrapolate a new dimension in musical time. The opening notes, scored darkly for cellos, basses and bassoons, are C, D, F-sharp and E--a harmonically ambiguous whole-tone collection.

"A new dimension in musical time"... wait, doesn't that sound familiar? Haven't some other composers been doing that more recently? Here are those opening bars in my reduction:

(click to enlarge) 

Hmm, what do we have here? A pedal that decelerates, moving between the dominant and the raised sixth degrees; rhythmically displaced outlining of the tonic and then dominant minor chords; strong modal feel. You know, these techniques of modified modal harmonies combined with repetitive rhythmic structures sound a lot like what the minimalist composers Steve Reich, Philip Glass and John Adams evolved into after a while. They got tired of the excessively simple harmonies of the early pieces and started writing music that isn't so terribly different from this. Here is the Sibelius 4th Symphony again:

And here is some music by Philip Glass:

I think the main difference between the two is that the Sibelius is more interesting. Here is the opening of Shaker Loops by John Adams:

What do you think? Did composers steer a wide berth around this kind of harmonic writing only to return to it in the 1970s? Was Sibelius doing interesting things rhythmically that would be echoed in music several decades later?

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