What is Musical Form?

Over a year ago I wrote a post on Form in Music that inspired some brilliant comments about the role of rhythm in jazz. It also inspired an email from a friend who said he didn't understand any of it! That post was intended to be the first of several on musical form, but I didn't follow up. My learned anonymous commentor made some excellent points and it is well worth going back and reading the whole post and the comments.

What I want to do here is restart the discussion by looking at form from an entirely different angle. In the previous post I talked about the basic structure of songs as that is something many people are familiar with. Today I want to take a different tack. There are three fundamental aspects of music: melody, harmony and rhythm. Every piece of music is a structure in which any one, two or all three are present--even John Cage's 4'33 which has a structure consisting only of rhythm, i.e. time. The form of a piece of music, that is, the articulation of it in time, is created by using any one, two, or all three of these aspects. That is so abstract that you are probably either scratching your head or rolling your eyes! Let me make it more concrete.

Let us imagine a simple musical context: a drumming circle. In Montréal when I lived there a group of drummers used to meet on Sunday afternoons in the park and drum together. Someone would start a simple beat then others would add various subdivisions and syncopations of the beat until a satisfactorily dense texture was created. This might go on until everyone was tired of it and then stop. Or, if it started to flag, someone might try and start an entirely new pulse, thereby launching a new section. If this just goes on until it peters out, then you have the form A (the first beat) followed by B (the second beat). If everyone then went back to the first beat then the form would be ABA. This is the very simplest musical form. Do something, then do something else, and if you are clever, then you return to the first thing again.

But the very first kinds of written down music in the West are both more complex than this but also even simpler. One of the earliest kinds of music in the West consisted of singing the psalms. Singing made the text a more sacred utterance. One person would first sing a few notes to establish the pitch, this is an "intonation", then the rest join in on a "reciting tone", just a repeated note. This reciting tone can go on as long as needed for the text. It can be punctuated if needed to indicate a division in the text. This punctuation was called a "fluxus". Then you return to the reciting tone. To end, there is another few notes that fall in pitch, called a "cadence" which means falling or "cadere" in Latin. Don't mix this up with the cadence in common practice harmony, which refers to a structure of two or more harmonies.

I suppose that what I have just described is very roughly ABA, but it is really a kind of musical prose, where the form is very loose and while originally there is just enough melody to encourage people to sing a text, the tendency over time is to add more and more decoration. Here is an example of this kind of psalm setting, one of the early favorite texts "Justus ut palma" from Psalm 91:

This kind of form is so loose that it is almost impossible to describe. A lot of music composition consists in giving form to what was originally formless. So a meandering melody like this, only organized in terms of a reciting tone and a final tone, composers are going to replace with a melody with a clearer structure. I'm not going to work my way through music history here, instead, I'm just going to jump to a different kind of melody that is very organized. Here is the original subject from the Art of Fugue that Bach will transform in various ways:

This subject is both very simple and highly organized. It is the very opposite of the loose, meandering kind of melody found in Gregorian Chant. The first two measures state the tonic harmony, D minor, as simply as possible. Then the next measure states the dominant harmony. The last measure allows for ambiguity as it can be harmonized in different ways, but it returns to the tonic at the beginning of measure five. Notice that there are two measures of arpeggiation followed by two measures of a scale. Notice also that the rhythm speeds up over the four measures. This extremely simple, highly organized theme will serve as the material with which Bach will construct a whole series of fugues, fourteen in all, and four canons. Here is a performance of the first fugue, which uses the theme exactly as I have given it above:

You will notice that as each voice enters, it does so with the same theme. This is one way of structuring a piece of music with melody. Though, of course, as soon as you have more than one voice, then the harmonic structure becomes hugely important as well. But let's leave that aside for the moment and just note how this simple melody ties the whole piece together. You can look at the structure of fugues in various ways, but the most salient aspect is that theme: it is what generates the structure, that is, the form.

In a more mechanical way, the contemporary composer Steve Reich has done something very similar: use a single theme to generate the structure of a piece. He does it by creating a short theme for piano and then, with two pianos playing that theme together, one "slides" ahead rhythmically bit by bit, a process he calls "phasing". Here is what that sounds like:

UPDATE: Here is a complete version of the piece:

In between the basic subdivisions, i.e. when the notes don't "line up", there is considerable rhythmic tension that is released when the two pianos slip back into alignment,  though, a different alignment! The piece ends when the whole set of alignments has been traversed and the two pianos are back in the original relationship.

What is interesting about this is that he uses only a simple rhythmic device to generate the whole piece from that original theme.

There is a lot more to say about how musical form can be created, but I'll save it for next time!

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The Most Audacious Composition of the 20th Century

The title of this post is itself a most audacious claim, is it not? After all, if there is one thing true about 20th century composition it is that it consists of wave after wave of composers and performers trying to outdo one another for sheer audacity. The reason for this lies in the ideology behind the notion of modernism and the avant-garde. Art must be progressive, that is to say, each new composition must be truly new in some significant way and that has usually been interpreted as new in technique. This approach really began with the New German School of Liszt and Wagner in the mid-19th century, but it steadily accelerated in the 20th century and fewer and fewer composers were able to resist it. Perhaps the last hold-out in Western Europe was Jean Sibelius and he found his ability to compose slipping away by the mid-1920s after which he wrote no more large-scale works. One of the most important figures in the progressivism of 20th century compositional technique was Arnold Schoenberg who arrived at his final method of composition with twelve tones--serialism--by 1923. I would speculate that the fact that this coincides with Sibelius ceasing to compose might not be entirely a coincidence!

Historian Richard Taruskin captures some important aspects of modernism in music by referring to it as "maximalism". More and more, once the traditional structures were broken down and cast aside, the one sure path to the future for most composers was greater and greater and greater complexity. I'm not talking so much about length or the sheer size of the orchestra, both those were well under way in the 19th century with the operas of Wagner and symphonies of Bruckner and Mahler. No, the complexity extended to the saturation of harmonic space with acceptable harmonies containing not just three or four notes, but seven or even ten! The degree of dissonance was constantly being increased. When Schoenberg finally came upon a way of setting aside the entire concept of consonance, new ways of structuring music had to be found. Again, it was always in the direction of greater and greater complexity and ways were found to structure tone rows, those building blocks of twelve-tone music, that involved complex kinds of symmetry. New and complex vocabulary was also invented so that we can talk about mysterious things like "hexachordal combinatoriality" and be talking about a piece of music, not mathematics!

These trends just went on and on to ever higher and higher levels of complexity. That wasn't the only thing that was happening, there was also the greater inclusion of new kinds of sounds, more percussion instruments and the use of new performing techniques. But the basic trend was always toward greater complexity. You start to see the problem, I think? Just as if you throw all the colors on the canvas and mix them together, you always end up with greyish-brown, if you constantly have a high level of dissonance combined with great rhythmic complexity, all orchestral music starts to sound a bit the same. Then what do you do? People like Karlheinz Stockhausen just kept adding more: by the late 1950s and early 60s he was writing enormously complex and dissonant music for three and four separate orchestras.

Ok, that's the back story. Now I will tell you how I ran across what I think is the most audacious piece of the 20th century. As an undergraduate at McGill in the mid-70s I would sometimes go to the listening library during a free period and just try and listen to some new stuff. I would wander randomly down the shelves and grab a few discs that looked like they might be interesting. Usually they would be pieces of newer music because that was a special interest of mine at the time. I don't recall much of what I would listen to, but this would be pretty typical:

• Ligeti
• Boulez
• Stockhausen
• Nancarrow

As I only had forty minutes or so, I would often just put on the beginning and if something didn't grab me pretty quickly, I would move on to the next disc. Let's recreate the experience. First some Ligeti, Continuum for harpsichord:

Not a well-known piece, but one I was listening to at the time. Next is an excerpt from Le Marteau sans Maitre by Pierre Boulez:

Here is Gruppen for three orchestras and three conductors by Stockhausen:

Notice that the complexity level is very high for all these pieces--and if you study the scores, you will just see more complexity! But this complexity was not just restricted to big orchestral music, as we saw with the harpsichord piece. One composer managed to find a way to create music for piano that was simply too complex to be performed and he did it by directly cutting piano rolls. Here is a piece by Conlon Nancarrow:

So imagine me in the library, listening to some or part of various pieces and then, I put this on, Drumming by Steve Reich:

In a context where EVERYTHING is designed for a great degree of complexity, this is simply astonishing. I was bracing myself for -- what? And then this, a single beat on a drum? Honestly, I nearly fell off my chair. You see, doing just what everyone else is doing, but just a little more, or doing it in a different medium is just not all that audacious, now is it? But if everyone else is writing fiendishly difficult music using hexachordal combinatoriality and you go out there and hit a little drum with a little stick, well, that's audacious! I'm sorry I can't put up the version I was listening to, on Deutsche Grammophon, but it is not on YouTube. Another audacious thing is that the whole piece is one hour and twenty-four minutes long, divided in four parts. The first part is nothing but those little drums and the development of one simple rhythm. Then he does it all over again with marimbas, then with xylophones and then puts them all together. Simple. And, to my mind, absolutely devastating to the musical aesthetic that says that the only road forward is to keep adding layers of complexity.

There are rare times in music history when all should be swept aside and composers need to return to the absolute fundamental basis of music. That was what Steve Reich was doing in 1970 when he wrote this piece, the most audacious composition of the 20th century.

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Ligeti: Poème Symphonique for 100 metronomes

I see on Alex Ross' blog that Ligeti's piece for 100 metronomes is about to be performed in New York. This piece dates from 1962 and therefore predates the similar work by Steve Reich titled Pendulum Music. Wikipedia has articles on both pieces here and here. In both cases the idea is to start a physical process that generates sound and to wait for the process to complete. In the piece by Ligeti the process is to wind up 100 of the old-fashioned metronomes, set them to different tempi and let them go simultaneously. At first there is a collision of many different ticks, but as they run down, slowly, we end up listening to just one metronome which finally stops. In the Steve Reich piece, several microphones are suspended above speakers pointing up and the levels are set so that there will be feedback when the microphone is just above the speaker. Then the microphones are set swinging. The piece ends when they have all stopped swinging and there is a continuous feedback. Here is the Ligeti piece:

And here is the one by Steve Reich:

Depending on the microphones, the speakers, the microphone chords and the amplifier, you can get different results:

Ligeti composed his piece as a criticism of trends in contemporary music. He said:

What bothers me nowadays are above all ideologies (all ideologies, in that they are stubborn and intolerant towards others), and Poème Symphonique is directed above all against them.

Steve Reich's piece, however, was an experiment in rhythm and, along with a couple of pieces using tape loops, led him to some new rhythmic possibilities. Both pieces are, I would suggest, neither interesting aesthetically, nor any sort of human expression in music. Well, that was the point, of course! It is somewhat ridiculous to find oneself in the audience watching a performance of this sort. It is equally ridiculous, I suggest, to sit in the audience listening to a piece of electronic music. Why is this? I think it is because a musical performance requires one or more human beings expressing something to other human beings. In other words, despite the bad press artistic intention has garnered in recent decades, it is in fact necessary to art that human beings intend to express something to other human beings. You might reply, that in the two pieces discussed above, the composer definitely had intentions. Well, ok, but they were not really expressive intentions, were they? In other words, while these might be justifiably considered experiments, they do not seem to have what I would term aesthetic content. Neither does Cage's 4'33 which I talk about here. Neither do any of Cage's pieces where the notes were chosen with chance procedures. The common element in all these pieces is the removal of any possibility of human aesthetic expression.

I think this was a phase that was mercifully brief. What surprises me is that people keep scheduling 'performances' of this stuff. Like some jokes, they are amusing once, but not for a second time. Ironically, since these pieces are emphatically not about expressing something aesthetic, what they really do is express an ideology. I say "ironically" because of Ligeti's comment. They all want to 'free' music from the human element. If you don't want to hear human expression in sound, you can go down to the freeway and listen to traffic sounds, or listen to the wind in the trees, or the surf crashing on a beach. One electronic piece I have heard was called Hurricanes and that was what it sounded like. Ok, but IT'S NOT INTERESTING!! Sorry to shout, but without intentional human expression, art has no more significance than a sunset. So what was the significance of this phase? Was it a sort of throat-clearing as a preface to post-modernism? There are some clues in this interesting essay on the phenomenon of post-modernism. After tracing the history of post-modernism and discussing some exemplary works the author points out that the strength of post-modernism was to remove the idea of a central narrative with accompanying aesthetic values. Edward Docx describes what happened next:

because postmodernism attacks everything, a mood of confusion and uncertainty began to grow and flourish until, in recent years, it became ubiquitous. A lack of confidence in the tenets, skills and aesthetics of literature permeated the culture and few felt secure or able or skilled enough or politically permitted to distinguish or recognise the schlock from the not. And so, sure enough, in the absence of any aesthetic criteria, it became more and more useful to assess the value of works according to the profits they yielded. Capital, as has been said many times before, accommodates all needs. So, paradoxically, we arrive at a moment where literature itself has become threatened, first by the artistic credo of postmodernism (the death of the author) and second by the unintended result of that credo, the hegemony of the marketplace. What then becomes sought and desired are fictions that resonate with the widest possible public: that is, with as many discourses as possible. This public can then give or withhold approval measured in sales.
In other words, increasingly, artistic success has become about nothing except money; and, increasingly, artists have come to judge their own success that way, too. This is the reason today that we feel the genre writer’s cry “I sold millions” so powerfully, even though in truth it can say little about the art form other than “it sold millions.” Changing disciplines, if we take this commoditisation of art to its natural limit, we arrive at Damien Hirst’s diamond encrusted skull, For the Love of God (2007). Commoditisation has here become the only point. The work, such as it is, centres on its cost and value and comprises also (I would say mainly) the media storm surrounding it: the rumours that it was bought for £50m, or that Hirst himself bought it, or that he offset his tax bill by claiming diamonds as tax deductible artistic materials, or that he didn’t buy it at all, or that nobody has bought it… And so postmodernly on. The paradox being this: that by removing all criteria, we are left with nothing but the market. The opposite of what postmodernism originally intended.

The author concludes by seeing a new phase beginning in which authentic aesthetic values are returning. Well, yes, that's my impression as well. No-one writes pieces for 100 metronomes any more. If there was a point to it, there is no longer. As the author indicates, "Gradually we hear more and more affirmation for those who can render expertly, the sculptor who can sculpt, the ceramist, the jeweller, even the novelist who can actually write." And, presumably, the composer who can actually compose music. For actual instruments. Played by actual performers. Requiring training and skill. And human expression...

UPDATE: Something I should have brought out is how seriously we are meant to take these pieces. I think the Ligeti is obviously a satire: Poème Symphonique for 100 metronomes? Really? The title itself is a satire and the image of an audience sitting in a hall listening to 100 metronomes run down is itself hilarious. The piece by Steve Reich is simply an experiment--he doesn't seem to have a sense of humor. John Cage however, does. I suspect that most of his music is actually meant to be funny, 4'33 not least of all. I can just see Cage sitting in his apartment wondering to himself, just how much absurdness can I get away with? A piece for 18 radios tuned in and out randomly? A piece for water sounds including a duck call? How about a piece that is just silence!!! Heh. Never forget to entertain the possibility that the composer is just out to make fun of us.

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Harmony Revisited, Part 3

I've published quite a few posts on harmony. The reason is that harmony is, I think, the big problem for composers at this moment. Why? The period from the 12th century up until a little after 1900 saw a long and fairly consistent development of harmony. It started with the most basic fundamentals, simply learning how to combine two voices and what intervals were consonant and what dissonant. There was a long see-saw between the differing demands or possibilities of harmony (the vertical) and counterpoint (the horizontal) but there was, until some time in the 19th century, a continual development in the sense of the composer learning to handle more and more possibilities. Then, in the late 19th century the system simply became overloaded and ultimately broke down entirely as Schoenberg called for the "emancipation of the dissonance" which meant the end of harmony as true harmony depends on a relationship between consonance and dissonance. Well, so does counterpoint, actually. This situation did not last very long. For one thing, audiences fairly decisively rejected atonal music and for another, in the late 60s and early 70s a number of composers, the so-called 'minimalists', revived harmony. This was not, and still is not, entirely successful, though. Today, I'm going to try and show you the reason why.

First, here is an excerpt from a score by Steve Reich, the slow movement of Electric Counterpoint written in 1987:

Click to enlarge

And here is a performance of this movement. The excerpt above appears about 1'05 into the performance.

All through this piece, Steve Reich is doing fascinating things with rhythm as he always does.  As one would expect from the title, the counterpoint is also rich. What we see on the page excerpted is one motif beginning with a falling fourth and with a rising third decoration in sixteenth notes. This is heard in different voices starting at different places in the meter and on two different pitches. It begins on either E or B.

But I want to just look at the harmony. If we look at any one beat, say for example, the first beat in the excerpt, we find the following notes from bottom to top (considering the whole beat): B, E, F#, B, E. The second beat is B, E, F#, B, E. Third beat: D#, F#, G#, C#, D#. Fourth beat: G#, D#, B. This can't really be analyzed in traditional ways at all. But the effect is a shimmering and pulsing harmony of E major blended with B major with the C# as a kind of 'non-harmonic' tone. This fits with the counterpoint as the C# looks like a decoration there too. The only thing I want to point out is that this harmony is static and remains so for long periods. Later on, the bass puts an A underneath this, but the upper voices remain pretty much the same. In the absence of cadences or other structural load points, we accept this constellation of notes as 'tonic' harmony. So, tonic blended with dominant all the time.

Now, let's compare this with a piece from the days when harmony was at its best.

This is the sarabande from the First Partita for solo violin. This is my own transcription for solo guitar and I have modified the bass line slightly and added one bass note, but that will have nothing to do with the point I will be making. If you notice in the score above, I have inserted boxes here and there. These boxes are the only places in the score where Bach has tonic harmony. All the rest is devoted to non-tonic harmony. For example, in the first few bars he moves from i to iv to V of III to VI before having a weak cadence in measure 5. The first half ends with a half cadence. There are 32 measures in the whole movement for a total of 96 beats. Of these 96 beats, tonic harmony occupies a mere 12 or 12.5%. Seven-eighths of the piece is taken up with other harmonies that are related to the tonic either directly or indirectly. For example, as telegraphed in measure 1, in the second half there is a significant modulation to the subdominant minor, E minor, with a full cadence in that key in mm 16-17. Bach does not need to belabor the tonic because he is working within a harmonic system where he doesn't have to. It is like a delicately calibrated solar system with all the planets orbiting the tonic sun. Steve Reich on the other hand, has to really sit on the tonic because the system of relationships between tonic and other chords has been wiped out. I think that further examination will show that most composers writing tonal music now seem to cling to the tonic with little of the harmonic freedom that composers enjoyed in the days of "common practice" harmony, from about 1600 to 1900.

Here is a performance of the Bach Sarabande:

So the question is, if your 'harmony' consists in sitting on the tonic all the time, is that really harmony?

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Glass vs Reich: A Music in Process

The two big names in so-called minimal or process music (even though Philip Glass now calls himself a classicist) are Philip Glass and Steve Reich. Can we compare them? Should we compare them? How could we not compare them?

Here is the first piece on YouTube by Philip Glass:

And here is a piece by Steve Reich that is as similar as I could find:

Very different, of course, but the point is to observe the differences. What about string quartets? Here is one by Philip Glass (I recommend not watching the distracting video):

Now that's interesting. It sounds a bit like Glassworks in the two against three rhythmic patterns, but here and there is a sequence that almost reminds you of Vivaldi. Now for some Steve Reich. Unfortunately we don't have a simple string quartet by him, so I've chosen the first movement of his Triple Quartet for string quartet and two pre-recorded quartets:

That is certainly more complex than the piece by Glass. It ends abruptly because it goes without pause into the second movement. How about a large ensemble? Here is the first movement of Glass' Cello Concerto:

Steve Reich does not write for conventional orchestra, but here is a piece for largish ensemble:

So what do you think? My impression, without having studied the scores to any of these pieces, is that harmonically and rhythmically Philip Glass is consistently more tied to the past, especially when he takes on larger forms. The two against three of Glassworks for solo piano, the first excerpt, is something we find in a lot of previous composers, along with the fragmentary voice-leading. Steve Reich has an approach that is less easy to find precedents for. His idea of form is additive. His harmonies tend to unfold whereas, in shorter pieces, Glass' are static. In the string quartets there seem to be more interesting, and more difficult to understand, harmonies in the Reich piece. In both the string quartet and the cello concerto, Glass tends to revert back to harmonies and textures that we might find in Vivaldi or a host of orchestral pieces. But in the pieces by Reich, it is hard to hear previous music--at least from the Western world. Additive techniques and layered textures such as in the Music for 18 Musicians remind you more of gamelan than anything else.

The conclusion? We probably have to wait at least fifty to a hundred years, but my intuition is that while both are writing some fascinating and beautiful pieces, there seems to be more substance in Steve Reich. Just a preliminary feeling...

What do you think?

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