Tag Archives: rhythm

Steps in a polonaise rhythm: Rasmussen’s “Experiencing Architecture”

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Rhythm in architecture

A few years ago I was trying to write some study materials about “rhythm,” and tied myself in knots trying to connect all the different ways the word is used in different contexts: art, architecture, poetry, music: rhythm as repetition, rhythm as line, rhythm as flow, and so on. It’s an appealing thought to be able to talk about the rhythm of architecture, but what does that mean? Like many of the people I know working in music and dance, I want to be able to make enriching, useful connections like this, but don’t know where to look.

I was delighted, then, to find a wonderfully clear chapter on “Rhythm in Architecture” (pp. 127-158) in Steen Eiler Rasmussen’s Experiencing Architecture (1959/1964). The clarity comes from  Rasmussen’s honesty about the fact that rhythm is a fuzzy concept, and from a general tendency for scholars in the 1950s and 1960s to write more clearly and accessibly than they do now—in my view, at least. Having described the patterns of doors and windows in terraced houses in London and Venice, he says:

I am quite sure that most people would notice that all of these façades are rhythmically divided. And yet if you were to ask them what rhythm in architecture means it would be difficult for them to explain, let alone define. The term rhythm is borrowed from other arts involving a time element and based on movement, such as music and dancing. (Rasmussen 1964, p. 133)

He goes on to mention the importance of music and rhythm to the architects Eric Mendelsohn and Frank Lloyd Wright, in different ways:

For these two men, then, there is obviously a connection between architecture and music. But it still does not explain what is meant by rhythm in architecture. Architecture itself has no time dimension, no movement, and therefore cannot be rhythm in the same way as music and dancing are. But to experience architecture demands time; it also demands work—though mental, not physical work. . . .If you feel that a line is rhythmic it means that by following it with your eyes you have an experience that can be compared with the experience of rhythmic ice-skating, for instance. (p. 135)

In other words, the time element missing from architecture is supplied by you, the viewer, “reading” the building in time, as you might follow a score, or a dance. He describes the pattern of windows in the 15th century Calle dei Preti near Via Garibaldi in Venice thus:

As you glance across the front, from left to right, you experience something like a complicated dance rhythm; it could be played on four drums. (p. 132)

I can remember seeing either that row of houses, or one very like it in Venice, and being puzzled by the strange arrangement of windows, which he describes later as being “like the harmony of a four-part song.”

The Spanish steps of a polonaise

My favourite bit of all, however, is when he gets on to Piranesi’s Veduta di Piazza di Spagna (c. 1750), a detailed etching that includes a view of the “Spanish steps” in Rome.

Detail of

Detail of “Veduta di Piazza di Spagna” by Piranesi, circa 1750, similar to the one shown in Rasmussen (1964)

With its bends and turns, its design seems to have been based on an old-fashioned, very ceremonial dance—the Polonaise—in which the dancers advance four by four in a straight line and then separate, two going to the right and two to the left; they turn, turn again, curtsy, meet again on the large landing, advance together, separate once more to left and right, and finally meet again at the the topmost terrace where they turn to face the view and see Rome lying at their feet. (p.136)

Even if this is totally fanciful armchair theorizing, it’s a wonderful way to read those steps. The only problem for me is that he reads the dance going up the steps, whereas Piranesi’s drawing is from the bottom. Given that if stages are raked at all, the rake is towards the viewer, it would seem natural to consider the bottom of the steps, not the top, as the end point of the polonaise procession. I don’t think that particularly matters though: I’m quite convinced, now Rasmussen’s said it, that there is something very dancy about those steps, something, indeed, of the polonaise which looks so impressive as its lines divide and reform.

Nonetheless, as much as I love the idea, there’s a trace of what I have referred to elsewhere as they would have: They knew little about walking but so much more about the very ceremonious dancing of the period, and therefore they could move gracefully on those steps. . .” Rasmussen says (p. 136).  It’s a nice thought, and it’s true that that Piranesi’s drawing has lots of gallant looking people in farthingales and frock coats who look like they were made to process elegantly down that magnificent staircase. But Piranesi also shows people doing no such thing: on the left of the steps, there’s what might be a drunk, collapsed at the bottom. On the right, there’s what looks like a massive fight that’s ended in a pile-up. RIght in the middle of the central stairway, directly in the path of the elegant couple about to mount the stairs, a man is gesturing in angry desperation to what looks like a woman who absolutely refuses to move. She looks like she might be drunk and disorderly too, and maybe not even fully dressed, hence the exasperation of her partner. To the left of the piled-up gang on the right hand side is a man who looks like he might be taking a not very discreet piss against the walls. In short, “society” is as variegated in this picture as it would be on the Spanish Steps today (perhaps more so). The occupational hazard of working in dance and music for too long is that you tend to imagine the whole of society like a ballroom. 

How I found Rasmussen 

Sometimes I wonder how much detail is too much when you’re documenting your sources. For me, the route is one of the most important parts: it shows respect to those whose work pointed you in the right direction, but if you’ve found something truly wonderful, it might also provide clues as to how to conjoin the right kind of search terms in future. But where do you stop—how many steps should you retrace? 

In this case, I was re-(skim)reading Bachelard’s The Poetics of Space, and noticed his reference to rhythmanalysis (long before Lefebvre) which I hadn’t before, and to the name that I remembered from  Lefebvre’s book, Lúcio Alberto Pinheiro dos Santos—the Portuguese philosopher who first introduced the term rhythmanalysis in 1931. I was wondering how I had managed to miss Bachelard’s reference the first time round, so I googled dos Santos and rhythmanalysis as search terms, and came across Giovanni Campus’s doctoral thesis “The City as Theatre: The Performing Space.”  In the section of the thesis about rhythmanalysis, I found a discussion of Rasmussen, buildings and rhythm which set me on the path to this post. Thank you Giovanni. 

As I said in a recent post, sometimes I wonder how it is that you can fail to discover really useful resources for such a long time: surely, when they’re that good, or that close to your interests, Google will just find them? Well, no. When I tried to find the Campus’s thesis online again, I couldn’t. Then I remembered that when I first googled dos Santos and rhythmanalysis, I had misspelled what I could remember of the first names—Pinero, rather than PInheiro. Only when I googled <pinero dos Santos rhythmanalysis> could I find Campus’s thesis again—why? Because Campus himself misspells the name.  When Google can be so precise about not delivering relevant results to you for the sake of a simple misspelling, you wonder what else you might be missing. 

Footnote on dos Santos and rhythmanalysis

And all of that makes me as suspicious as I ever was about the benefits of Google unless you have something to bring to the search box yourself. Once I’d got Bachelard, Pinheiro dos Santos, Rhythmanalysis, and Lefebvre as search times, the useful results multiplied. Especially useful was this article by Jonas Rutgeerts, where in a footnote he explains what I was already beginning to surmise about dos Santos, from the lack of literature available: 

The Portuguese professor in literature and psychology Lúcio Alberto Pinheiro dos Santos allegedly coined the term rhythmanalysis in 1931, when he wrote La Rythmanalyse. However, up until today the theoretical relevance of this work remains unclear, as the book was never published and the original manuscript is lost. The only in-depth reference to the text can be found in Gaston Bachelard Dialectics of Duration. Moreover, as Bachelard neither intends “to give an over-all view of these nor to describe all the many lines of development,” it is virtually impossible to make claims about dos Santos’s own theory. (p. 99)

In the end, I begin to wonder whether talking about rhythm in architecture is just something refined people do as part of elegant conversation: a kind of linguistic curlicue that is decorative rather than providing useful insights. It seems every time someone wants to use the trope, they have to explain what they mean, at the same time as saying that what they mean is difficult to define. That to me is God telling you to use a different metaphor, or just say what you mean without resorting to metaphor at all. 

References

Steen Eiler, R. (1964). Experiencing architecture. Cambridge, Mass: MIT Press.

Research on marching music and dotted rhythms

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Nice to see an article about marching music, one of the weird, esoteric topics  that perplex ballet pianists like me: a 2018 conference paper by Niels Hansen, Nicholas Shea & David Huron called Do Dotted Rhythms Increase Performance Precision: Why Marches Have Dotted Rhythms (free to download from Academia.edu, but you’ll need to sign in with Google or Facebook, or create an account). 

Read it for yourself, but the take home point is that although we’re prone to believe that marches have a dotted rhythm, a carefully selected sample of 200 pieces from IMSLP that are categorized as marches appear not to fulfil the stereotype. I think what the authors are getting at is that there are many reasons from a perceptual-motor point of view why marches would be better off having dotted rhythms: it’s easier to synchronize to a beat when it’s divided thus, particularly in the preparation for a downbeat. Despite this, the numbers just don’t stack up when you take a sample of marches from IMSLP, so the roots of the “conjectured propensity” for marches to have dotted rhythms lie in culture, rather than practical, physical concerns.

The march as  musical topic

An example (mine, not theirs) of such a cultural source for the idea can be found in Raymond Monelle’s  The Musical Topic: speaking of  a march in an 18th century opera Monelle notes that “the musical figures are in a dotted rhythm, like marches in all ages” (p. 161). Here’s another: dance and music historian Marian Smith in “The Forgotten Cortège,” in Bewegungen zwischen Hören und Sehen: Denkbewegungen über Bewegungskünste (2012, pp. 405-416)

“The Opèra procession’s sense of immediacy was enhanced by its music, for the march (the usual type of music used)—in real life and on the stage—attracted its listeners physically. After all, it was a genre intended to inspire and sustain walking; to supply the energy of forward motion. This attraction was achieved mainly by its rhythms (which typically included triplet figures and dotted rhythms), whatever the tempo or mood—though the tempo was always (by definition) walkable.” (p.411).

Annoyingly, I cannot remember where I read it — possibly in Eric McKee’s book on the waltz, maybe in one of Lawrence Zbikowski’s many articles on music, dance and meaning—but someone more scholarly than me has made an important point that the more music is composed as a recollection, a souvenir or representation of dancing, as opposed to music practically intended for dancing, the more prominent are the rhythmic patterns that signal the dance in question.  Listening to music for aesthetic enjoyment, watching an opera, you are being presented with the idea of other people marching, you aren’t doing it yourself, nor is there probably much marching going on on the stage—there isn’t room, or a large enough cast.  The responsibility for signalling “this is a march” thus lies more on the music than on the physical movement.  

By the same token, many different dance/music forms—polkas, reels, rags, marches, hornpipes, galops— will suffice if you want to do a polka as long as it’s roughly the right tempo, but if you are in the Wigmore Hall and you want to titter behind your fan at your neighbour and gesture knowledgeably “Oh what a pretty little polka the pianist is playing!” then you’re going to need big signals from the rhythm of the music that it’s a polka that the composer wanted you to hear (so it’s likely to be a tune with a rhythm that sounds like “potato chips”). And it won’t particularly matter about the tempo either (which is why you’re unlikely to find ballet pianists by going to the Wigmore Hall). 

The conclusions of the conference paper don’t undermine Monelle’s point, which is that  the dotted rhythm is a kind of musical-literary symbol of a march and the military, regardless of what people actually march to—rather like his other concept, the cheval écrit: a horse represented in music, not a horse-horse. Similarly, even as early as Stravinsky’s Petrushka (1911), there was a  musical symbol for “ballerina” (slow, tinkly waltz) which persists today, though Stravinsky surrounding it with music which itself defied the stereotype while real ballet was going on. 

Perhaps it was a little reckless for Monelle to say “like marches in all ages,” and perhaps he was seduced in that regard by the proliferation of dotted rhythms in the musical literature that he specialised in, but he was talking about soldiers and the military as a topic in music, not a genre of music for marching to. It’s not altogether surprising  that in  music that was actually intended for marching, dotted rhythms are somewhat redundant and unnecessary. For one thing, you’re already marching, so the rhythm of your step is doing half the work. Marching to a tune that sounds like it’s marching is like buying a dog and barking yourself. . . kind of. 

 These relatively simple questions—about what makes a march a march, and how is listening to a march as a cultural signifier different to actually marching—are quite basic to choosing repertoire for ballet classes, and ought to be lesson one in talking about dance rhythms in the context of ballet, yet it’s rare to see them raised or discussed in a scholarly context, supported or challenged by empirical research. I have some issues with the sampling procedure: the collection of music on IMSLP is to my mind a strange place to look, given that what is there is dependent on what is out of copyright, and what people around the world have decided to upload. I’d be more interested to see data drawn from, say, recordings of march music made by bands that actually march or play for marching. 

Keeping in time in real-life marching

William McNeill’s book on marching and drill (Keeping Together in Time: Dance and Drill in Human History)  is frequently cited whenever an author wants to quickly make a scholarly reference to the joys of being together in time. Less well-known is the excited flurry of expert argumentative correspondence that followed a review of the book in The Times Literary Supplement in 1996 (I’m indebted to the detailed footnotes in Kate van Orden’s 2005 book Music, Discipline, and Arms in Early Modern France for pointing me towards this wonderful exchange of views.) The debate on those pages is inconclusive, but eye-opening.  A particularly interesting one was  from 6th September, by John Keegan, who argued that drums might serve a number of purposes in troops, including frightening the enemy, but keeping in time was problematic: 

“Music can detract from precision drill. The explanation was suggested to me recently by a former adjutant of the Scots Guards, who revealed that the end of a column, if it marches to the received beat of the band, will be out of step with the head of the column. Guardsmen therefore learn to carry the pace in their heads, and actually march off the beat they hear, when they know that the speed of the sound through the air is misleading them. (The Times Literary Supplement (London, England), Friday, September 06, 1996; pg. 17; Issue 4875.) 

As a result, he concludes that  “soldiers had, from about 1760 onwards, to programme themselves to the idea of a cadenced step” —that is, I suppose, it’s something they had to do themselves, based on judgement and skill, not by synchronizing to an external beat.  I recognize that sensation: in the days when I used to be an organist, there was one church that had a “choir” organ in a side chapel. The delay in sound was about half a second, so to keep in time you had to pay attention to the rhythm and tempo of your hands on the keyboard, and ignore what you were hearing.  As an accompanist, there’s a kind of reversal of this in class: you clearly can’t accompany everyone at the “right speed,” and even in a solo, you have to look at a dancer and judge the tempo that you think they really want overall, rather than the one they appear to be giving in the moment—they may be rushing, or lagging, or have tripped over themselves. I imagine that for dancers it must be similar: if the tempo of the accompaniment is unstable, they have to find a way of being more or less in time, without being pulled hither and thither by the music. 

I thought of this whole topic as I was re-reading an interview with a conductor talking about the way that you conduct the front desk of the violins, but the ones at the back are following the movement of the bows in front of them;  if you conduct for the back desk, then the ones in the front are going to be ahead, and so on. And that’s leaving aside the fact that people hear and respond to beats differently.  

And finally, the “ballet march”

Over the years I’ve played for ballet, I’ve come to realise that there are dance rhythms that are particular to ballet class: the habañera/tango that is so slow, it almost grinds to a halt; the ronds de jambe waltz that is like stirring a vat of porridge with an oar; the medium allegro 6/8 that is neither a jig nor a waltz; the “waltz” for grand allegro that is so big and fat you could fell trees to it. And then there’s the Grands Battements March, which I’ve already written about in an earlier post. People of my generation used to refer to this as “stripper tempo,” referring to the David Rose tune The Stripper of 1962 [NSFW], but even that tempo sounds too jaunty for the 21st century grand battement.  

Interestingly, though, the rhythmic model of that grands battements march, often sung (slowly) by ballet teachers is Non più and’rai from The Marriage of Figaro, or the march from The Thieving Magpie, both of which have the dotted rhythm-to-downbeat rhythmic figure that the authors of this research refer to, yet tend not to find in their survey of the IMSLP marches. That illustrates their point again, that the figure is probably a cultural phenomenon, rather than one occasioned by the needs of marching itself. At the same time, the ballet example perhaps indicates one of the routes through which such cultural work is done: the tune comes out of the opera house and into the ballet studio, and tends to stay there. Play Colonel Bogey or The Liberty Bell and it won’t feel like a “marchy march,” even though those tunes are probably much more common as actual marching music.  But play the much more recent Darth Vader theme from Star Wars (the “Imperial March“) and there is that dotted rhythm again, illustrating once more the resilient potency of musical topics—which was exactly what Monelle was writing about. 

Music theory for (ballet) dancers, the last word for now? Grant’s “Beating Time and Measuring Music in the Early Modern Era”

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Roger Grant's book "Beating Time and Measuring Music"

I’ve just added Roger Grant’s Beating Time and Measuring Music in the Early Modern Era as my top choice for books on music theory for those interested in music-dance relationships (see my metre and rhythm page for a brief bibliography on  that topic). I don’t want to say too much, because it figures largely in a chapter in my PhD, and it’s too detailed and scholarly a book for me to summarize hastily. Suffice it to say, if you want to know what think about time signature and meter and movement, it’s all in this book. I’m glad I hadn’t read it when I was writing How Down is a Downbeat?, a journal article on music, ballet teaching and time signature that I wrote a few years ago; it would have tempted me to rewrite the whole thing. On the other hand, I wish I had read it when I first started teaching music for dance teachers back in 2000. However, some of the significant books and articles that Grant refers to in building his theory were published some years later than that. Is theory even the right word? I’m not sure: it’s history, but in order to understand the history, you have to change your ideas about what you thought was music theory. It’s amazing that in the 21st century, we’re still solving the problems unexamined or hidden by “rudimentary” music theory, e.g.—to name but one— why is a 6/8 called a compound time signature? What’s compound about it? 

The biggest problem with what is conventionally called “music theory” is that it presents as simple and straightforward (a matter of counting two or three) something which is exasperating in its complexity, not least because “time signature” as a subject leaves out the people who use it and the way they interpret it, but it is virtually meaningless without the (changing) practice in which it is embedded. I’ve hinted at this in many of my more recent postings on triple meter and Rothstein’s theory of  “Franco-Italian hypermeter.”   Grant discussed the way that the meaning of beat as movement has gradually disappeared, morphing into the concept of time as a endless stream of motionless, durationless ticks. This in fact was exactly how I used to teach music theory and meter, without realising the entailments or history of my own beliefs about what meter or musical time was. 

I am in awe of the way that Grant makes sense of such a complex assemblage of notation, musicians, practice, ideas, primers, teachers, and so on. It’s only when you’ve struggled to sort out some of these problems yourself that you realise how courageous and hard-working someone else has been at grappling with similar issues.  

 

Musicology, ballet teaching and time signature

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A proud day for me, my first proper article published in Empirical Musicology Review. “How Down is a Downbeat? Feeling Meter and Gravity in Music and Dance?” came out of a single teaching session, when about 12 years of trying to teach about meter and time signature finally imploded in a discussion with students. For people who wonder why I’m doing a PhD, and what I’m writing about, this will give you an idea – not of the subject, but of the problem.

What I’m really chuffed about is that both Arnie Cox and Robert Hatten agreed to write commentaries on the article (see Arnie Cox’s here, and Robert Hatten’s here).

It would be nice to think that perhaps this might open up a conversation about the musical components of dance teaching courses, but I somehow doubt it will – and for as long as that’s the case, I guess dance teachers will keep saying “By the way, I don’t do time signatures,” and be perfectly justified in doing so, in my view.

I’m still hopelessly behind with the 52 cards, which is annoying me, but I’ve not given up yet.

A year of ballet playing cards #18: Another 6/8 allegro – by Auber (5h)

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Music for allegro in six eight (6/8)

Click to download the score

This music for allegro in six eight is what I call an “assemblé 6/8” because it’s often in assemblé exercises that teachers ask for a 6/8, or what seems like a waltz. Once the exercise starts, you realise that it’s neither a waltz, nor the kind of 6/8 that grows on trees. I call it “one of those 6/8s” (see  recent post for another example), or an “assemblé 6/8” – you can also use it for some battements glissés exercises at the barre.

In music for ballet, less is often more

The longer I’ve played for ballet, the more I’ve come to appreciate pieces like this. On the surface they appear to do nothing – the bass line barely moves for the whole piece. But as a rule, taking stuff away rather than adding it seems to work well in ballet class. Structurally, too, the middle section with its upward motion and drama is all the more exciting for being set off by rather static stuff either side. What also looks like musical dullness – the same note in the bass for most of the piece, also acts like a drum, and a musical “floor” for the person doing the exercise. It’s easy to denigrate 19th century ballet music for being samey, but it works, and what the hell, Uptown Funk doesn’t suffer from having too many of the same notes in the tune either.

Well-designed music for allegro in six eight keeps you in time

This piece is a good example of music that has physical constraints in its design that prevent you from snatching a few milliseconds in the middle of the bar as you might in a waltz or jig-like rhythm. Those two semiquavers in the central beat (punctuated by horns in the orchestration) keep this in a genuine three, and make you hold your tempo. I borrowed the idea of physical constraints as a design feature  from Donald Norman’s The Design of Everyday Things .

The value of physical constraints is that they rely on properties of the physical world for their operation; no special training is necessary. With the proper use of physical constraints there should be only a limited number of possible actions – or, at least, desired actions can be made obvious, usually by being especially salient.  (Norman, 1989, p. 84)

An example of this in everday life would be a door that had a push-plate on one side, and a handle on the other. You simply couldn’t pull the door on the push side by accident because there’s nothing to grab, and you would naturally go to pull the door on the pull-side. In this music, those semiquavers are the physical constraints, they prevent you from squeezing the tempo in the middle of the bar. The same principle works like a dream when you use polka-mazurka types for a pirouette – it’s almost impossible to get out of time.

About the arrangement

Despite it’s simplicity, this piece was difficult to reduce for piano, and I’m still not happy with it, after several revisions.  It’s hard to capture the bouncy lightness of the orchestration on a piano with only two hands, so this would probably make a nice duet. In three places, I’ve missed out one beat, in order to drag the piece into a meter that works for class. The start of it comes from Act 1 (should start automatically start in the right place when you click, but if not, drag the slider to 6:11)

The A minor section comes from Act 5 (starts at 16:17, again, should start there automatically on click, but drag to the right time if not). Altogether, this week’s score has four variants of 6/8 for allegro, one of which will probably work for the exercise. It’s handy to have a piece that keeps changing rhythmic emphasis like this, because then you can see which particular variant works. You’ll notice that the final section also removes the constraint that I wrote about in the F major section – which will be either a good or a bad thing, depending on the exercise.

The Auber in the Tchaikovsky

I can’t say I was much of an Auber fan before this week, but the more I listen, the more I like it. There are some really bizarre, tender and wonderful moments of orchestration.  I also began to realise how much Tchaikovsky’s dance music resembles Auber at times (the Tchaikovsky pas de deux female variation could have been written by him, in places, and there’s a bit that sounds straight out of a march in Swan Lake.

There’s also a strong resemblance between this last A minor section from Act I, and Tchaikovsky’s “August” (Harvest song) from The Seasons which is used in the pas de trois after the duel in Onegin. There seems to be a worldwide competition to play this as fast as possible, until the rhythm just blurs into rabid prattle of notes, but I do rather like this orchestration, which makes the piece sound a lot better than it is:

Bibliography

Norman, D. A. (1989). The design of everyday things. London: MIT Press.

New metre and rhythm page

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After 11 years of having odd articles about rhythm and metre all over my old site at jsmusic.org.uk, I decided it was time to reduce it all down to a page of the books and articles on rhythm that I got most of it from, rather than try to rewrite it to a standard that I’ll be happy with.

Although it might not seem like much, it’s a significant day in my life, and of my online life, because it signals the end of my belief that there is anything simple to say about meter and rhythm as soon as it gets outside of its comfort-zone of music notation for the purpose of reproducing music (mainly of the Western art music tradition).  That’s not to say that you couldn’t teach the subject from an elementary entry point upwards  – but what you’d start with would be very different to conventional music “theory” in the sense of time signatures and so on (I’d probably start with the tensions between time-discrete and time-continuous concepts of meter).

Anyway, if you’re interested, you can read some of it yourself, on my Metre and Rhythm page.

And now for something completely sextuple

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This variation by Mozart on “Ah, vous dirai-je maman”, K.265/300e has turned out to be a real life-saver in class for one of those ballet exercises where you need a 6/8 that gives you six quavers in a bar (click here to hear it). If you’re thinking “But that’s not a 6/8,” hold on, I’m coming to that, in this discussion of compound meter.

Compound meter in all but name in Mozart's "Ah, vous dirai-je maman"

Ah, vous dirai-je maman’, K.265/300e, Variation 3

The Mozart is useful for class, but it’s also an example of a particular kind of 6/8 that does what you’d think it would do, i.e. articulate six quavers that you can hear and count. Not that you’d want to count them, but they’re there, so you can hear why it’s called a six. Many pieces in 6/8 don’t go like that (they just jig along rumpty-tumpty fashion, so they sound barely distinguishable from a 2, so to see why it’s a six, you have to imagine the beats that you can’t hear.

What is compound about compound meter?

It’s things like this that make me dread trying to explain compound meters such as 6/8, coupled with the fact that the term “compound meter” (or “compound time signature”) does not convey anything useful or hearable in the “compound” part. The meaning that “compound” once had in this context is rarely taught in music theory  – that a 6/8 was at one time a way of writing two bars of 3/8 as compound bar, thus halving the number of barlines you had to draw.

Well, that’s part of the the story, at least. In Danuta Mirka’s Metric Manipulations in Haydn and Mozart,  she explains that the eighteenth century theorist Koch viewed 6/8 sometimes as a “compound metre” in this sense, and sometimes as a “mixed meter” or a simple meter of “tripled beats”. That is, some 6/8s are basically just 2/4s with triplets (and some 9/8s are just 3/4s with triplets), but for notational ease, you might sometimes write the “tripled” 2/4 as 6/8.

The difference is crucial – one is triple subdivision (tripled 2/4), the other (compound 6/8) is triple meter, even if they’re both notated as 6/8. Which brings us back to a well-worn topic on this site, truly triple meter. It’s truly triple rather than sextuple, because to Koch, it’s a compound of two 3/8 bars (with equal weight in both halves of the bar, and quavers establishing the meter. That in turn is one reason perhaps why Mozart didn’t write this as 6/8. It’s clearly duple, rocking between stronger and weak beats in each bar.

Is compound meter really just about subdividing beats into three?

This is why it’s so hard to teach about compound time signature as a concept to those (like dance teachers) who are trying to understand how it relates to hearing music. To recap a previous post: If you look at many music primers, they’ll tell you that compound time signatures are where the beats are divided into three, and simple are where they are divided into two. Nothing about the term “compound” suggests “divided into three”, and if you’re looking at a time signature like 6/8, unlike the simple meters, there is no visible beat to be divided, it’s already been divided as part of the time signature. It makes no sense, unless you  explain what I’ve explained above, which also explains what is simple about simple meters – not that the beat is divided into two, but that the bars are single units, not joined together as in compound signatures. But also, “compound time signature” only describes one concept of 6/8, and one which does not continue into the 19th century and beyond, where we describe it as if it were a duple metre with triple subdivision.

That is the why the Mozart piece is relatively unusual, and so useful. It is duple with triple subdivision, but it tips over into the realm of a truly triple meter because the movement that one hears, clearly on the musical surface, is of a continuous triple meter. It is hard to retain tripleness in the metrical slipstream of a piece which is duple at another level, but Mozart does it. Tears for Fears’ song “Everybody wants to rule the world” does it some of the time – there’s a constant, steady, truly triple 6/8 going on in a lot of the music, but the vocal line  exerts a strong duple pull.  Mozart’s advantage is that the tripleness is centre-stage in the melody, it’s not a support act. In “Everybody wants to rule the world”, it’s not exactly melody and accompaniment, they are simultaneous, equally salient layers of the music which both draw your attention (incidentally, the song’s time signature as published is notated in 12/8 with (4/4) in brackets).

6/8: two meters/time signatures masquerading as one

Disambiguating 6/8s into those which are characterised by triplet subdivision, and those which are truly triple meter seems to me to solve the problem, because it’s how people in the real world hear this music. You could argue that you should teach basic time signature before these more complex topics, but to my mind, teaching “compound time signature” by saying it “means” dividing a beat into 3, is oversimplifying the case to the point where it becomes difficult to understand because it doesn’t make sense. Koch’s theory isn’t simple, but it makes sense, and it reflects clearly the fact that 6/8 is not a single concept, but, echoing Justin London’s “many meters hypothesis”, it is a structure that has multiple expressions in real music.  A differentiation between two types of 6/8 is partially clarified in Labanotation and Benesh Notation, because you have to say what level of the beat you’re using as your pulse. However, the issue here is not about the pulse that you count or sense as being the main beat, but level of beat where the musical action happens. Music could be truly sextuple (i.e. triple x 2) compositionally, but whereas a dancer might not count it that way if it’s fast, the composer on the other still writes it that way, because that’s how the music moves.

It would be good if in ballet teaching we had words to describe different kinds of 6/8, at least at the point at which you learn about time signatures, so that you can account for the fact that some don’t sound like six at all, and some do. We need something like a “triplety-two” and “truly sextuple” and a “swingy two” for those things like 6/8 marches that barely reveal any of their sixy undergarments, and possibly a few more. Dance rhythms are handy – but only if both parties (teacher and musician) have the same shared vocabulary and understanding, and only up to a point. It would be nice to be able to have something that was like a 6/8 march metrically, but wasn’t a 6/8 march culturally (or is that impossible?).  Any ideas for some new terms?

More on “truly triple meter” – are Chopin’s waltzes really mazurkas?

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I’m not saying that Chopin couldn’t write a waltz, or that his embodied sense of  waltzing was too fragile to be able to incorporate it in music. But I wonder if the inherent tripleness of his waltzes is not a question of pure compositional technique, but a difficulty in shaking off an ingrained Mazurka habit. In other words, are Chopin’s waltzes really mazurkas in all but name? 

This thought came out of a previous post about triple metre and waltzes, after which some pianist colleagues and I had an ongoing discussion about particular pieces. According to our (my) definition, for a waltz-like piece to be classed as ‘truly triple’, cadences have to fall on the second main beat of a 6/8 bar, or, in 3/4, on the 8th bar of the phrase (otherwise it’s 3/4 “masquerading”, so to speak, as 6/8).  One musician cited Chopin’s Grande valse Op. 18 No. 1 (the finale of Les Sylphides) – is this truly triple, she asked? Well, yes it is. And so are most of the other waltzes. 

As I mentioned in our Facebook discussion, my composition teacher Malcolm Williamson once praised Chopin’s treatment of the harmony in his waltzes, that is, he’s careful to make sure that it changes in every bar. At the time, I don’t think either Malcolm or I knew enough about waltzing to discuss this from a metrical point of view, the point he was making was about maintaining harmonic interest.  One of Malcolm’s own great waltz tunes (he would probably not thank me for that, since he didn’t want it extracted from the opera as a single number), “Thank You, Saint Seraphina,” from Our Man in Havana was itself truly triple, which probably reflected his concern for both metric and harmonic interest.

Conversations with Malcolm lead me to think that he didn’t like to wait in music, in the sense of harmonic or metric inertia. And that’s the thing about 6/8s, once you know that you’ve arrived on 7, all you’re doing is just waiting for that extra beat. That can be OK sometimes, but in allegro, it’s not great.  Which brings me back to Chopin and the waltz. The  epigraph to chapter 6  of Eric McKee’s Decorum of the Minuet, Delirium of the Waltz is an interesting quote from Chopin

“I have picked up nothing that is essentially Viennese. For example, I can’t dance a waltz properly – that speaks for itself! My piano has heard nothing but mazurkas.”

In the light of this comment, those waltzes make rather more sense to me viewed as mazurkas, or waltzes with a mazurka feel, at the very least. 

 

More on the rareness of the truly triple waltz

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In my last post, I said “Truly triple waltzes are an impossibility. They shouldn’t exist, and they don’t”. Less than 48 hours later, while I was playing Ich weiß nicht zu wem ich gehöre for a warm-up tendu, I realised I was wrong. There are examples of waltzes in truly triple metre, and I’d just played one. These useful, slow, “English” waltzes are very common in German 1930s songs for some reason – Vom Kopf bis Fuß (Falling in love again), Ich weiß es wird einmal ein Wunder geschehen,  Leben ohne Liebe kannst du nicht. Truly triple songs in English include The boy next door (from Meet me in St Louis), Would you? (from Singing in the Rain), What’ll I do. 

But how many of those examples can we say are truly truly triple metre? If you take the position of cadences as the giveaway (i.e. for it to be truly triple, they must come on 8, not 7), then only Falling in Love Again qualifies (though Would you? meets the criterion in the first three lines). Their feel is more triple than other waltzes, but it’s only a feel, not a structural fact.  Look more closely at Vom Kopf bis Fuß, the only truly truly triple ‘waltz’ of the ones I listed, and you’ll see that the cadences fall on the second beat of the bar, mazurka-style (or more appropriately, given the tempo, kujawiak-style). So the truly-triple-waltz turns out, in fact, to be more like a kujawiak, which we knew was triple already.

Adieu - Romance sem palavras by Ernesto Nazareth. Bars 6-8 of the tune.

Adieu – Romance sem palavras by Ernesto Nazareth. Bars 6-8 of the tune.

So apart from the waltz-which-is-really-a-kujawiak, are there any truly triple waltzes, contrary to what I said in my earlier post? One very strong contender is Nazareth’s Adieu – Romance sem palavraswhich we used for pliés in the RAD’s new Grade 5. It works wonderfully for Adages in a very slow 3, because it’s calm and measured, and wears its three-ness on the surface, so you get a clear sense of timing. And it really is in three – the cadences are on 8, not 7. Adieu is a strange example, though. The first four bars of the melody strongly suggest a 6/8 hypermeter, but the next four emphasise each bar individually, and reverse the accentuation of the hypermeter established in the preceding phrase, so that the weakest bars now receive the strongest accent. What’s more, whereas the harmonic change happened over two-bar spans in bars 1-4, in bars 6 and 8, that change is compressed into a single bar in a weak position. That’s a lot of metrical interest for an 8 bar phrase, and is perhaps why it works so well for complex ballet exercises where a lot is happening in a short space of time.

Update (26/9/14) Re-reading what I’ve written about Adieu, I think it’s hard to make a case for it being “truly triple” except for the fact that the final cadence is on 8 rather than 7. Otherwise, though, it’s hypermetrically duple. The feeling that it is triple comes, I think, from the fact that the harmony frequently changes every bar, or at times, within the bar at quarter-note level.

The chorus of Feed the Birds from Mary Poppins is truly triple, apart from the middle eight, but I can’t think of many more – can you?

Playing for ballet class tips day 19: read the feet, divide the beat

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There’s nae luck aboot the hoose, Good King Wenceslas, and a sample of a step rhythm. It all fits, but the top one is better.

In petit allegro, it’s a useful rule of thumb to listen to the rhythm of the exercise as the teacher sets it, and look very carefully at the feet as it’s being marked. Work out what the rhythm is that they make, and then divide it by half in the melody line.  If it’s a bit slow, swing or dot the melody.

So for example, let’s say that the rhythm the feet make is roughly like the bottom line in the example above (except that perhaps you wouldn’t have a step on every quaver beat), then you’d play something like the top line, There’s nae luck aboot the hooseThere are dozens of slightly different versions of this tune, depending on what it’s for and who’s playing it, but the main thing is, you can see that the tune divides the rhythm of the step, it doesn’t copy it.

Merely copying the rhythm of the step creates a beat that is effectively half the speed of the exercise.  It’s not that this beat isn’t present somewhere in There’s nae luck, but this tune also has subsidiary beat levels, and most importantly, all those semiquavers give you room to slightly stretch the beat, therefore making space (that subject again) for dance. This breathing space and contingency is the reason that fiddle tunes, quadrilles and rags work so well for petit allegro. With Good King Wenceslas, you have none of that. You can also see that the difference betweeen time signature, perceived beat, the rhythm of the step and the rhythm of the music illustrate that you might as well forget about time signature and focus on rhythm instead.

I haven’t got a name for the concept, but the principle is explained partly by the psychology of beat induction. When you hear two evenly spaced sounds in succession, your brain predicts when the third one will come, and if it does indeed fall there, then your brain goes ‘aha’ and begins to build a picture of a beat-framework where the beats you just heard are organized by another layer of  beats at half this speed . Thus, in the carol Good King Wenceslas, the middle line of the example above, the beat that you feel is at the level of the quarter note, because the repeated quavers predict it. Conversely,  whatever constitutes the beat-level of the exercise your teacher has set, you need to help your dancers to perceive that beat by subdividing it in some way. There’s Nae Luck Aboot the Hoose  does this, and the dotted rhythm (which you can take or leave, depending on the speed of the exercise) uses the additional factor of length to create the feeling of a beat at the quaver level (the actual note values are immaterial here, it’s the proportion of the durations that matters).

If you look the musical problem set out in those three lines above, you’ll see that we’re back to Riepel and his zweyers and vierers.  The rhythm of the exercise consists of two zweyers and a vierer, and that’s reflected in the fiddle tune, whereas Good King Wenceslas is two zweyers, but at half the speed of the exercise. If you merely copy the rhythm of the exercise with the melody of your music, then you may well end up playing music that perceptually speaking is half speed. This is often what dancers mean when they say that music is ‘heavy’ for an allegro exercise. it’s not that it’s entirely wrong – it fits, after all – but the perceived pace of the music as at a higher (slower) hypermetrical level, so it doesn’t support the dance well.

For petit allegro, the tip I’ve shown usually works like a dream, but there are cases at the barre where you might want to avoid it and do the opposite – but more on that tomorrow.