Tag Archives: rhythm

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


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


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)

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 [zotpressInText item=”{MA7Z3TTP}”].

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:


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New metre and rhythm page


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


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?


After a previous post about triple metre and waltzes, 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.

From the little I know from having worked with him, the last thing he wanted was to have to wait in music – 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.”

I’m not saying that Chopin couldn’t write a waltz, or that his embodied sense of what waltzing was 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 autonomous compositional technique in the ways that I’ve described it above, but a difficulty in shaking off an ingrained Mazurka habit.



More on the rareness of the truly triple waltz


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?