The Procrustean Bed

In Greek mythology, Procrustes was a bandit preying on travelers between Athens and Eleusis. He had an iron bed and compelled people to lie on it. No-one ever quite fit so for those who were too tall he amputated the extra and those who were too short he stretched to fit. Theseus, on his way to Athens, solved the problem by serving Procrustes with his own medicine. As commentators like Fil from Wings of Pegasus and Nick Beato have been pointing out, commercial pop music has become something of a Procrustean bed. Let's listen to Fil:

I think this is enough to get the idea. From different angles Fil is pointing out that much of what we see and hear in these kinds of videos is processed or, to be a little more blunt, fake. Rick Beato was making a similar point in the video I just put up yesterday. Here it is:

Now let me connect this to R. G. Collingwood, Professor of Philosophy at Oxford. His essay "Good Art and Bad Art" is found on page 536 in Art in Theory. Here are some quotes:

Art is community's medicine for that worst disease of the mind, the corruption of consciousness.

...a work of art is an activity of a certain kind; the agent is trying to do something definite, and in that attempt he may succeed or he may fail. It is moreover, a conscious activity; the agent is not only trying to do something definite, he also knows what it is that he is trying to do; though knowing here does not necessarily imply being able to describe, since to describe is to generalize, and generalizing is the function of the intellect and consciousness does not, as such, involve intellect.

A work of art, therefore, may be either a good one or a bad one. And because the agent is necessarily a conscious agent, he necessarily knows which it is. Or rather, he necessarily knows this so far as his consciousness in respect of this work of art is uncorrupted; for we have seen that there is such a thing as untruthful or corrupt consciousness.

A bad work of art is an activity in which the agent tries to express a given emotion, but fails. This is the difference between bad art and art falsely so called. In art falsely so called there is no failure to express, because there is no attempt at expression; there is only an attempt (whether successful or not) to do something else.

To give some examples: if Paul McCartney were to sing "Hey Jude" very badly, out of tune and poorly phrased, that would be an example of bad art. If his performance of "Hey Jude" were to be pitch-corrected and rhythmically quantized, that would be "art falsely so called" because it would not be the truthful expression of emotion.

A bad work of art is the unsuccessful attempt to become conscious of a given emotion: it is what Spinoza calls an inadequate idea of an affection. Now, a consciousness which thus fails to grasp its own emotions is a corrupt or untruthful consciousness.

In my view, music that is pitch-corrected, autotuned or quantized is the product of a corrupt consciousness. A lot of what J Dilla did with his beats was an attempt to insert human expression into otherwise mechanized rhythms.

A person who is capable of producing bad art cannot, so far as he is capable of producing it, recognize it for what it is ... To mistake bad art for good art would imply having in one's mind an idea of what good art is, and one has such an idea only so far as one knows what it is to have an uncorrupt consciousness; but no one can know this except a person who possesses one. An insincere mind, so far as it is insincere, has no conception of sincerity.

Art is not a luxury, and bad art not a thing we can afford to tolerate.

I recommend reading the whole thing. I'm something of an Aristotelian myself and from the first sentence of the Collingwood I got the sense that he was one as well. So when you read him, do so slowly and carefully.

I suppose that we can thank the purveyors of rhythmic quantization and pitch-correction for showing us exactly what a corrupt consciousness in music consists in these days.

Just a footnote: every good singer I have worked with has intentionally bent the pitch of certain notes in one direction or the other for the sake of emotional expression. And phrasing, of course, is nothing but the pushing of rhythm in one direction or the other for the same reason. I learned these things from my first voice teacher. 

 

 

 

 

 

In the Groove?

We had a discussion in the comment section recently about the steady pulse found in popular music, which was referred to as a "groove," and the compatibility with classical music. Now, of course, there is a whole very popular genre of classical music that very much has a groove. This is often called "minimalism" but I'm not sure that has ever been a very good label. Steve Reich used to call what he does "process music" and that might be a little better. In any case, this music is very much "in the groove." Take Music for 18 Musicians, for example:

This music has very distinctive energy that, while it shares something with pop music, is actually quite different. Compare "Gimme Shelter" by the Rolling Stones:

Or more recently "Jesus Walks" by Kanye West:

https://www.youtube.com/watch?v=f9wJBdFy6sQ

But there is an awful lot of classical music that would suffer enormously from being forced into a rigid beat. For example this performance of the Chopin Nocturne op. 9 no. 2 by Arthur Rubinstein:

No, it is not just Romantic repertoire that would suffer. Here is an unmeasured prelude by Louis Couperin that is an extreme example of music that is not intended to have a regular pulse:

Mind you, if I were to put up examples of 18th century music by historically informed performance ensembles we would hear a lot of quite strict rhythms. In Classical music there has always been a spectrum of expression between the more lyrical and free songlike side and the more physical dancelike elements. For example, taking two examples from the same suite by Bach, played by the same performer, here is Hilary Hahn with the Sarabande from the D minor Partita followed by the Gigue from the same suite:

But even in the Gigue with its strongly dancelike character there are subtle rhythmic inflections.

As a performer, while I see the powerful appeal of a rhythmic groove, I also see it as a potential rut preventing you from having some kinds of musical expression.

Additive Rhythm, and Meter

I have been wrestling with some problems with notating rhythms recently. Perhaps I should say I have been exploring rhythmic possibilties? In my String Quartet No. 2, I decided that I wanted a particular effect in the first movement where the last beat of the measure would be slowly expanded to give a sort of limping meter. At first I wanted to do this with just a text instruction: "Repeating the chordal passage sixteen times, expand the last beat of the measure from a quarter note value to a half note value incrementally." My violinist suggested notating this precisely so I ended up with this:

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That is just part of the passage. Each measure is repeated four times. The last beat of the measure grows from a quarter note, to a quarter tied to a sixteenth, to a quarter tied to an eighth and so on, until the last beat becomes a half note. The latter part of this process is shown above. Now there is no doubt that this is notationally ugly! I soon realized that the composer that had really explored this technique, known as "additive rhythm" was Olivier Messiaen. What inevitably happens if you use additive rhythms is that you destroy the meter; this kind of music is "ametric." I discovered this looking at Messiaen scores and seeing that he simply omits meter entirely. Here is an excerpt from his Catalogue d'oiseaux, "Le Chocard des Alpes."

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Even where, as in the beginning of the piece, the meter is clearly 2/4, he shows no meter and there are many passages like this where there is no regular meter. Unfortunately, not showing or more importantly, not having a regular meter, is not an option in my music software, so for my most recent piece, I simply notate everything in 4/4, but the bar lines are actually irrelevant. In this passage the violin is doing a "subtractative" rhythm while the guitar does an additive one:

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Deal with that, copyright bots!

Two Symphonic Openings, part 2

The reason that the Symphony No. 2 by Sibelius also came to mind when I was reading about the interesting rhythmic aspects of the opening of the Symphony No. 40 by Mozart is that I recollected that there is something odd about the meter there as well. Let's just have a listen first.

Let's pretend we are taking it down in dictation. How would you notate that opening? Some kind of compound duple time, right? Either 6/8 or 6/4. Here are a couple of possibilities:

These are taken from the essay "Meter in the opening of the Second Symphony" by Tapio Kallio published in Sibelius Studies, ed. by Timothy L. Jackson and Veijo Murtomaki, Cambridge University Press, 2001. Tapio Kallio suggests that what we actually hear is the second version. The first version is how Sibelius notates it in the published score. Mr. Kallio offers some interesting evidence for his interpretation taken from the original manuscript held in the Sibelius Museum in Turku. Above is the original version from the manuscript and below is the final version:

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Sorry about the teeny tiny image. If you click it should be big enough to read. Kallio's example goes on for three more pages, but I think this opening gives us enough to talk about. Essentially, Sibelius moved the opening to later in the measure. What I hear is that in Kallio's hypothetical rebarring, the listener hears the barlines as being where the top of the chord rises from F# to G. It is also natural to hear just one rest instead of several. Notice this, though: in Sibelius' rebarring it is the F# and A that fall on the strong beats and the crescendo is delayed accordingly. Kallio offers some interesting commentary suggesting that the opening could be heard as a 2/2 meter instead of a 6/4 meter. Here is his analysis:

That doesn't look or sound like 2/2 to me, but maybe I'm missing something as he is relating it to the following woodwind theme. But I could certainly hear the opening in 3/2 instead of 6/4, despite the indicated phrase groupings. Actually, I think a lot of performers, myself included, try out different metric groupings when we are learning a piece. It gives you different perspectives and can add to your interpretive understanding. It seems as if what Sibelius is up to with his revised metric notation is to make the character of the opening more ambiguous, more tentative, to create a narrative in which the ambiguity of the opening leads to a later unfolding. Kallio mentions that the horns seem to contradict the meter when they come in.

The paper by Kallio goes into a lot more detail, so please seek it out if you are interested. In the meantime, enjoy the whole symphony. The last movement is a particularly successful symphonic finale in my view!

This is Leonard Bernstein and the Vienna Philharmonic. Notice that he beats all the rests of the opening measure!

Two Symphonic Openings

As a child of the 60s I grew up, musically, surrounded by rock n roll and ragas, the Rolling Stones rhythm section and Alla Rakha on tabla. So I had a special interest in rhythm, even more than melody and harmony. The instrument I wanted to start on was the drums, but I got switched onto bass guitar instead. All this is by way mentioning that in recent decades interest in the rhythmic structure of music has grown more and more. Some older theorists, like Heinrich Schenker, tended to diminish the role of the rhythmic structure of music into mere surface activity, having little real importance. It makes one long for a Schenkerian analysis of Drumming by Steve Reich!

I got to thinking along these lines from reading Matthew Riley's recent book The Viennese Minor-Key Symphony in the Age of Haydn and Mozart in which he looks into the rhythmic structures quite thoroughly. The book finishes up with a magnificent discussion of the Symphony No. 40 by Mozart in which he goes a long way to explaining both why this symphony is so compelling but at the same time, so confusing. Here is how he describes the opening of the first movement:

The idea that this opening is a sped-up gavotte that has been overlaid with the breathless repetitions of an aria agitata and then squeezed into the form of the main theme of a fast symphony movement (statement-response presentation) accounts for the sense of something strange in a recognizable guise.

I'm going to have to explain all of that, but you can see that the foundation of the analysis rests on rhythmic character.

All this, in turn, reminds me of another symphonic opening that also has considerable rhythmic sophistication, the beginning of the first movement of the Symphony No. 2 by Sibelius. I had a lot of enjoyment a while back looking into all the different ways Sibelius found to end his seven symphonies. In today's post, I won't have any real original research, I am going to just talk about two brilliant analyses of two great symphonic openings.

First, let's listen to the two movements. This is The Chamber Orchestra of Europe conducted by Nikolaus Harnoncourt playing the first movement of the Symphony No. 40 by Mozart:

Here is the first movement of the Symphony No. 2 by Sibelius conducted by Charles Mackerras:

What the two openings share is a deceptive or misleading presentation of meter and phrase.

The opening of the Mozart, now that I come to think of it, has always bothered me and it is mostly because of the accompaniment that starts just before the theme. You don't quite know what just happened.

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It opens with the strings alone, piano, which is itself mysterious. But while the accompaniment starts on the downbeat, the theme begins on the upbeat. While rare, it was not unprecedented for the first movement of a symphony without a slow introduction to begin quietly. Beginning with this sort of accompaniment figure is unusual for a symphony at this time, but again not totally unprecedented. Let's let Riley isolate what is really unusual:

There are three genuinely distinctive aspects of the opening of K. 550/i: topic, accompaniment figuration, and rhythmic and metrical organization. The first is the buffa idiom of the aria agitata. A short rhythmic motive is repeated continually, as though breathlessly, in a way that would support a fast, syllabic text setting. [p. 251]

What he is referring to here is the eighth-note motive in the violins and its resemblance to a typical brisk aria from an opera buffa. It has long been noticed that a good part of the classical style owes a lot to the vivacious sparkle of opera buffa. Follow the link for the Wikipedia article on opera buffa which will give you some context. The innovation of the composers in the classical style was to humanize their instrumental music by giving it the bounce and immediacy of the opera buffa style.

Riley points out that the theme has a lot more motivic repetition than is usual. The basic idea is four measures, what I quoted above from the score. (It begins on an upbeat and goes to the second beat of the fifth measure.) That little E flat to D motive is repeated three times in the presentation phrase (the first two measures). What is unusual here is that buffa allusions are more usual in the subordinate theme, not the main one which is more likely to be in seria style (see the Wikipedia article on opera seria).

Typical of the first movements of minor-key symphonies is a "stormy" kind of texture that Mozart suggests with the busy accompaniment figure in the violas.

The whole presentation of the theme takes eight measures. I quoted the first four above. Here is the whole phrase:

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The time signature is alla breve, or with the half note as the beat, but Riley argues, citing the theorist William Caplin, that an eight-bar presentation in Classical period music is typically a standard four-bar presentation with the meter renotated. That makes this opening in 2/1, not 2/2 (for the whole argument, see Classical Form by William E. Caplin, Oxford University Press, 1998, p. 35). There is another twist: underlying this surface meter is the rhythm of a gavotte, a formal, aristocratic dance form. Here is how Riley analyses this:

Hypermeter is when you have the "real" meter at a higher level than the notated meter. There are fast movements, for example, in 3/4 time where the actual meter is one beat per bar. The actual felt meter might consist of three or four of these notated measures. This why, by the way, there are instances of compositions that end with a blank measure--it was needed to complete the hypermeter. Looking at the sketch above, we see the 2/1 meter in the bass notes, one per bar. Then, looking at the speculative gavotte rhythm at the top, this clarifies how we should hear that theme. The first little motive is really an "upbeat to an upbeat" as the gavotte itself starts with an upbeat. The first big downbeat here is really the beginning of measure three. The organization of the theme bears this out. Go back and listen to that movement a few times.

I think I will just post this part as it is and leave Sibelius to tomorrow.

Musical Time

That recent award, number 43 on the list of the top 100 music education blogs, reminds me that I ought to do the occasional post on, you know, music education. After the series of Stravinsky posts and a scattering of posts on aesthetics (which I will continue) the blog has strayed into some political issues. My defense of that on this determinedly non-political blog, is that when politics makes inroads into our beloved realm, we need to occasionally push back.

But today I am going to talk about the rhythmic aspect of music. Music is a "time-art" meaning that not only does it, like theater, take place in time, but even more, everything about music is about vibrations:

These vibrations take place on multiple levels. Most obviously, music tends to organize itself around a recurring pulse:

But let me back up a bit and tell you what I used to tell my students: even though music is a time-art, when we talk about the "timing" of music, that only refers to the duration of a piece. When you look at a CD cover or the second column in your iTunes playlist you see the time or timing of each piece in minutes and seconds. Time and timing are not musical terms, though. In music we have three separate terms, none of which is time or timing. The first is "pulse."

Pulse is related, of course, to your pulse and for a lot of music history the typical pulse of most pieces was not far from the range of the human pulse. We like pulse in music as it is the simplest and most compelling way of organizing time. Steve Reich has written pieces that use pulse in a very primal way:

The "trick" in that piece is that the pulse that you hear, which in the absence of any context you hear as the downbeat, actually turns out to not be the downbeat, but an upbeat. When the downbeat finally arrives, if you have been listening closely, you almost fall off your chair in surprise. This is a "metric" effect and "meter" is our second musical term. You see, in music those pulses come in packages: there are stronger ones, downbeats, and weaker ones, upbeats. There is a correspondence with the raising and the putting down of the foot in dance. The two basic kinds of meter are duple and triple. In Drumming, the whole piece is based on a simple pattern in 3/2 6/4. Here is the composer's note from the score:

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And here is the beginning of the score. As you can see, that first beat is not the downbeat:

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Those numbers at the beginning tell you the meter. The 3/2 means "each measure (or package) has three beats and each beat is notated as a half note." The alternate meter of 6/4 means that "each measure has six beats and each beat is notated as a quarter note." Why the ambiguity? Steve Reich plays with meter in his music, constantly re-interpreting how the meter can be felt.

So now we know what pulse and meter are. The third word used by musicians is "rhythm" and it is used in a couple of senses. First, it can be used as a kind of generic term referring to all the elements of music that are time-related. "Ya gotta have rhythm!" But it is used in a specific sense as well. Rhythm is the pattern of notes of different durations that we hear as the surface of the music. The rhythm of Drumming as Reich shows it in his note is "three eighth notes, eighth note rest, eighth note, eighth note rest, three eighth notes, eighth note rest, eighth note, eighth note rest." So you see why we invented notation! The rhythm is always changing (yes, and repeating as well), but the pulse and the meter are the same.

But everything in music is a kind of vibration, not just the rhythmic aspect. Each musical note or pitch is a collection of vibrations at different frequencies. You have heard the term "A = 440?" This refers to a specific pitch, the note A, one example of which vibrates 440 times per second. This creates a particular pitch, one that musicians typically use to tune to. So each note in a melody is actually a specific vibration. Harmony? Well, harmony is just different pitches as they sound together so harmony is also a collection of vibrations. Everything in music is vibrations!

Let's listen to a particularly felicitous collection of vibrations by one of those dead white guys. This is the Symphony No. 39 by Joseph Haydn in a spirited performance by The English Concert directed by Trevor Pinnock:

UPDATE: I replaced my original Drumming clip with a different performance that makes my point better.

Metric Textures

You may be astonished to hear this, but the term I have chosen for the title of this post is of my creation/invention. At least, if we can believe Google. The only similar uses they turn up have to do with image textures, not musical ones. So let me define my term!

Metric textures are a category of musical devices and practices having to do with rhythm, specifically meter, in music. Let's just review some basic terms. In music we talk about time in various ways. The timing of a piece of music refers to its duration in minutes and seconds: "what is the timing of the first track on the disc?"

Pulse refers to the repeating beat underlying the music, akin to the pulse created by our heartbeat.

Meter refers to how the pulses are grouped. This is indicated in a musical score by the time signature which in simple meters usually consists of two numbers: the upper one tells us how many pulses make up the metric group and the lower one what rhythmic value counts as a pulse. A typical example is the ubiquitous 4/4 time signature indicating four beats or pulses in each metric group with each beat a quarter note. There is another kind of time signature used for compound meters where there are two levels of grouping. In these meters the sub-group is usually three notes instead of the usual two, making the larger group a dotted note. Examples of these are 6/8 and 12/4. In musical scores the metric groups are normally divided off with barlines.

Rhythm refers to the pattern of short and long notes that we hear as the surface of the music. For example, each pulse or beat can be divided up into shorter notes that create subdivisions. The varying of these subdivisions is the rhythm of the piece.

There are certain music techniques that use layers of different meters to create interesting rhythmic effects. One of these is called hemiola and was a favorite way for Baroque composers to clinch an important structural cadence. It depends on re-grouping the meter. A typical example would be to turn the recurring dotted quarter pulse of a piece in 6/8 temporarily into 3/4 by rewriting the rhythm to group the patterns into quarter notes instead of dotted quarters. This changes the basic pulse. In flamenco a similar technique is used to create a polyrhythm or polymeter where we hear the two groupings simultaneously instead of sequentially. This is used in the flamenco palo known as bulerías. It is a bit tricky to show in notation, but it can look like this:

Or follow the link to the Wikipedia article.  On one level, a measure of 6/8 is followed by a measure of 3/4, but on the other level a quick 3/8 continues throughout. Here is how bulerías sounds like in performance. What you hear are various slices of the metric texture, which is always present in the background, but not in the foreground.

This idea, of combining two different metric groupings, is an example of a metric texture. It is found in flamenco music, in African drumming and is the technique used in a lot of music by Steve Reich. Layering different meters creates a kind of sustained tension that enables him to write quite long pieces that seem to hover, almost without change, for long stretches. It is the built-in tension of the metric texture that makes the music exciting to listen to in the absence of the usual harmonic and melodic devices that music has traditionally used.

The first kind of metric texture used by Steve Reich came about through experimenting with tape loops. If you run the same tape loop at slightly different speeds, you get some interesting results as we can hear in the early tape pieces like Come Out from 1966:

As this technique, called "phasing" by Steve Reich, involves infinitesimal changes, it resembles a kind of metric calculus! Reich soon discovered that it could be adapted to use in compositions for live performance and Piano Phase is a simple example:

This is performed by two pianists both playing this pattern at the beginning together. Then one pianist slightly speeds up until he is one sixteenth-note ahead, at which point the two pianos synchronize their sixteenths. Then this process is repeated. What happens is a metric texture is created through minute tempo changes. Here is what that sounds like:

In another post I will look at some other examples of metric textures in Steve Reich.

It Don't Mean a Thing if it Ain't Got That 12/32 Swing!

Way back in 1931 Duke Ellington wrote a tune called "It Don't Mean a Thing (If It Ain't Got That Swing)". The title was an oft-expressed sentiment at the time among jazz musicians even though the "swing" era was a couple of years in the future. Here is a 1943 recording.

Nice tune, nicely done. But jazz musicians did not actually invent 'swing' --wait a minute, just what the heck is 'swing' anyway? Here is the Wikipedia article. Here is the section on the specific rhythmic technique:

A "swung note" or "shuffle note" is a performance practice, mainly in jazz-influenced music, in which some notes with equal written time values are performed with unequal durations, usually as alternating long and short. Music of the Baroque and Classical notes inégales era follow similar principles. A swing or shuffle rhythm is the rhythm produced by playing repeated pairs of notes in this way.

Yes, that is quite correct, the notes inégales of the French baroque was basically the same technique, though in a somewhat different context. Here is an allemande by Rameau with lots of notes inégales:

Of course, the idea of playing notes written as even notes unevenly predates the Baroque, though in the Renaissance it was regarded more as an optional way of ornamenting. The French made it more systematic. Pretty much any piece in 3/4 with flowing eighth notes could be played inégale.

But for a really stunning example of rhythmic virtuosity and swinging rhythms, we look to the last piano sonata of Beethoven, the Sonata in C minor, op. 111, composed in 1822. The last movement is an Arietta adagio molto semplice e cantabile: slowly, very simply and singing. It certainly starts that way. But the rhythms get more and more complex. This is one of Beethoven's great sets of variations. Here is that theme and the first variation:

The notes of the theme are certainly simple enough with an absolutely diatonic theme in regular note values. But the time signature is a bit unusual: 9/16. Mind you, unless you are following in the score you are hardly going to notice that this is a compound time signature. Just those couple of times when you have an eighth followed by a sixteenth. But the basic beat here, and in all compound time signatures, is not a simple note value, but rather a dotted note value. So when, in the first variation which starts in the middle of the page, we get the beat subdivided, we suddenly realize that the beat consists of three notes. We might even think we are hearing triplets. The feeling of subdividing the beat in three parts moves us to another rhythmic level, propelling us forward. The second variation takes this to another level. Here we can see the end of the first variation followed by the second variation:

As you can observe, the second variation is the same tempo ("L'istesso tempo") as the first, which was the same tempo as the theme. But now Beethoven moves to yet another level of division where the notes are exactly half as long as in the first variation. The eighth/sixteenth pairs are replaced by sixteenth/thirty-second pairs. It starts to sound a bit "jazzy", something one would not have expected from the original theme. But Beethoven is just getting started. The next variation really goes to town:

Again, same tempo, and again, a halving of the note values. The sixteenth/thirty-second note pairs are now replaced by thirty-second/sixty-fourth note pairs! Notice the change of time signature to 12/32. This is another compound time signature. Where the original signature 9/16 had three beats, each beat consisting of a dotted eighth, this one has four beats, each one consisting of a dotted thirty-second. I can't actually recall another similar time-signature in a piece by Beethoven--or anyone else up to this time, for that matter. From here on things get rather more complicated and the variations tend to flow into one another. But I want to pick out two more examples from the coda. After a great deal of thickly-textured rhythms, everything quietens down and we have a recall of the original theme in the bass in the original note values:

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We have since returned to the 9/16 time signature. There are actually three levels here: a bit of the theme in the bass (with echoes in the tenor), a counter melody in the soprano and a trill in the alto. The trill moves up and up into the stratosphere and then the triplet subdivision returns (not really triplets, of course, just to the ear). This is all on the dominant of E flat major. Beethoven works around a few different keys: C major, A minor, C major again, before arriving at the last page:

What is extraordinary about this is the rhythm again. He has three absolutely separate levels: first, the trill on G that goes on for a long time. Then the melody, in dotted eighths as in the original theme. Finally a rumbling decoration in the bass in thirty-second notes. This performs the function of somehow uniting all the various rhythmic levels of the movement. The ending is simplicity itself, with the original theme, split up between treble and bass, in the simplest of cadences.

There are hosts of books about Beethoven from just about every angle: his biography, spiritual development, sketches, harmony, handling of form and on and on. But I don't know of a single one that really has a thorough look at his handling of rhythm--just as important in my view.

So there you have it, a brief look at the rhythms of one movement of one of his piano sonatas, in which he did a number of things that no-one had done before (or since). One writer, on hearing that third variation proclaimed that Beethoven had invented jazz! But of course it only sounds that way to us because we know jazz and ragtime. One wonders what the listeners at the time thought of it.

Let's listen to this movement, which is about fifteen minutes long. Here is Maurizio Pollini live in Lucerne in April 2012:

Musical Texture

This is not something that they really talk about much in theory classes, but it is one of the most distinctive features of a piece of music. I can recall an interview with David Byrne where he said that when he wrote a song, he always started with the texture. Here is an example of one of his textures:

The bass has a quick dactyl (dum, da, da) and the guitar an iamb (da, dum) with the drums giving isolated punctuation. This is a rhythmic texture and it is rhythm that distinguishes most textures. Here is a prelude by Bach in which there is a nearly constant flow of sixteenth-notes, but layered against this is a staccato rising theme. These two layers often change places, but it is the layering that creates the unique texture of this piece:

The Rolling Stones have always had, propelling their songs, probably the best r&b rhythm section in the business. The bass and drums are a tightly integrated unit that drives the song. Over top of this they layer guitars, keyboards, harmonica and voices. Listen to how they build up this texture in the beginning of this song, "Gimme Shelter" from the 1969 album Let It Bleed. It starts with the guitar, some isolated percussion, voices and finally the bass and drums.

For a comparison, listen to this song by George Harrison from the year before, "While My Guitar Gently Weeps" from The White Album. The texture is much sparer and suspended rather than driving. Ringo's drumming is placed, crafted, rather than constantly pushing onward. The bass is very distinct and solid. Listening to the textures of the two songs side by side is quite illuminating!

Going back to classical music, the second movement of Beethoven's quartet op 59 no 3 is an unusual texture. In 6/8, with the violins and viola flowing along in arc-like melodic shapes, it is the cello that is the odd man out, playing pizzicato nearly the whole time. The throbbing cello part is a textural contrast with the other instruments.

But for some really extraordinary textures, we should look at the piano sonatas. The late sonata in E major, op 109 is in three movements and ends with a theme and variations that starts with the most tender and simple theme that becomes more and more involved. The theme itself is just over two minutes long (the length of a whole early Beatles' song). It is a very simple song in 3/4. Each variation is a different textural spinning out of the theme, sometimes in 2/4 or 9/8 or 2/2. For Beethoven, variation technique has a great deal to do with rhythmic texture. Here is Alfred Brendel with the first part of the movement:

It continues with a change of tempo from andante to allegro in a more contrapuntal texture, then for the final section, it returns exactly to the original theme and tempo, but this time starts a process of rhythmic division that turns the simple quarter notes of the theme into 32nd notes combined with trills and triplet eighth notes! It seems almost a miracle, that he can find his way back to the simplicity of the theme at the very end.

With all the scores of books on Beethoven I am still surprised that more has not been written about his rhythmic ingenuity. Sometimes it is all about texture...

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: UPDATE: I fixed a misprint in the flamenco example. Hmm, well now I can't get the example to show at all. I'll have to leave it out until I can figure out what the problem is...

UPPERDATE: I finally got around to redoing this example. This is a flamenco rhythmic pattern, called a compas, that has twelve beats. I have notated it in 6/8. Here are two iterations:

The two layers are often clapped. 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. It does not quite work written in ordinary notation because the downbeats aren't downbeats, but I don't know of another way of writing it down. 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.

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.

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:

UPDATE: Due to link-rot that clip had vanished. If this one goes to, the clip in question is "Sunshine of Your Love by Cream which, due to the inventive drumming of Ginger Baker, does NOT have a backbeat, but instead, heavy stresses on 1 and 3.

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.

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.