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 I 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.
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.
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.
There’s a kind of allegro that’s in 6/8 that needs music like this. I don’t really know what to call it, except “a six eight allegro.” The canonical example for me is “Sempre libera” from La Traviata (below):
The trouble is that there’s only about 16 useful bars of that aria, and for this kind of exercise that comes forward in multiple groups, you need at least a hundred. Most of the things I know that fit the bill are equally short, or turn out to have too many notes to keep up the necessary speed without wilting. Also, the exercise usually needs lift and movement in particular places, so I usually end up improvising – until I found this piece from Jerusalem.
Tip: Useful is not always interesting, and interesting is not always useful
I was going to skip this in favour of something that looks more interesting on paper, but when I came to play it, it felt and sounded better as performed music than it does on the page, and it’s also very handy because it goes on for ages. Even though I can hear a score in my head by reading it, there is often – as with this piece – a chasm between what it feels and sounds like as a physical experience, and what it looks like on paper. I’m certainly influenced by just how useful this is, so maybe a normal pianist (rather than a ballet pianist) wouldn’t feel that way.
What I love about this piece, the more I hear it and play it, is its constantly changing rhythmic shape. I wouldn’t have noticed this so much, or had the words to talk about it, had it not been for two instances recently where I was supposed to be teaching pianists, and learned something myself.
The first occasion was in Ljublana, (photo gallery here) leading a weekend seminar for ballet teachers and pianists at the Conservatoire for Music and Ballet. A question came up about battements tendus with the accent in or out: how much does that affect the music that you should play? I wasn’t giving answers, it was a discussion between teachers and pianists. After nearly 30 years of playing for ballet, I noticed something for the first time: teachers, when they want to stress the accent in, appear to give more “accent” to the out preceding it. That figures logically, because if you want to chop a log harder, you lift it higher before it falls, and you have to show that the leg is out before it comes in on one. But it really messes with your metrical head, because you hear “accent in” as a verbal instruction, then you hear “AND a 1″ as a musical cue. Also, “accent in” doesn’t (I think) mean accent in the sense of chopping logs, but of where the close is in relation to the musical metre.
Franco-Italian hypermeter in the ballet class: try it, you’ll like it (and so will they)
So maybe this is a case for pieces that exhibit what Rothstein explains as “Franco Italian hypermeter” (see previous post) I tested the theory by playing this piece (playing card 46) which has more than half a bar anacrusis (which is one of the requirements), and asked teacher Tom Linecar-Boulton during a London Amateur Ballet class to see if it did the trick. It seems to, and it illustrates a fascinating thing about the incommensurability (in my view, at least) of musical accent with ballet accents. There’s a lightness and accentuation about this which has a very different kind of body to it than non-ballet music, and “anacrusis” in music has too many implications about downbeat that may not work for dance. What it has is a long “and,” not a heavy one, and the one has an accent which is not to do with volume or weight, but – I don’t know how to describe it – where it is. It’s like saying “I’m going to put this here, and that there,” without shouting about it.
Try this (at a slow speed) for tendus with the accent in. It’s fun.
Franco-Italian hypermeter in a six eight allegro
The second occasion was yesterday, when I was talking to some music students who were going to have a go at playing for ballet classes. They were asking if it’s acceptable to have a stock of chord sequences that you improvise over. I said yes it was, and that it’s surprising how much a simple repeated sequence can be masked by the detail that you hang over it. I took this Verdi piece as an example. It’s in 6/8, but as Danuta Mirka would say, the “composed meter” varies – that is, the first two bars are indeed in duple with triple subdivision, but then the next bars, with the little grace notes, and the emphasis on each beat, are effectively in 3/8. As the piece goes on (I’ve sewn two together and done a bit of reworking to try to make enough for several groups), there are many variations on the rhythm of the phrase (with an anacrusis, or on the beat, with a half-bar anacrusis, or a short one) even though the basic duple structure is maintained. My favourite is this one:
That triple forte is the upbeat to the next “1”
“A bit lighter please” — try meter, not dynamics
This to me solves a conundrum with a certain kind of jump that jumps before the 1, yet mustn’t be heavy. When a teacher I played for recently kept saying “a bit lighter” I thought he meant just “quicker” but I think he really did mean lighter – but in the sense of not thumping either downbeats or upbeats, but maintaining a kind of tension between the two, as in this wonderful example.
You’d have to pick your moment to play this – if the dancers need the music to tell them what to do on every step, then avoid it – but if they know what they’re doing, the subtle shifts of grouping over the phrase bring all kinds of lightness and accent to it, in a way which is definitely Franco-Italian, and not German: what you have to avoid is obeying the (Germanic) rule that every downbeat has to have an accent. Think about Italian or French poetry, with its end-accented lines, and swoop over the bar lines, resisting the accents until the final bar.
I can’t find a recording of this that is at a tempo which I think would work for class, so I’ve done a very rough one here – my apologies for the botched job, but I’m sight reading, and the piece has only just come out of my musical oven. Teachers, I’d love to know what you think about this, and whether I can give a name to this (is it particularly good for a certain kind of jump?).
The point of posting stuff like this is not to bring back Verdi’s Jerusalem because it’s the best thing for allegro, but to offer models for either improvising or finding other repertoire, and the changes of accent, metre, phrasing, rhythm, grouping and so on in this offers all kinds of ideas.
From Wilson’s 1820 “A Companion to the Ball Room” available at IMSLP
I was tempted to put the ballet-class equivalent of the Holy Family on the 25th of this advent calendar, to finish off the series with a heart-warming sentimental twist that starts “… in spite of all these things that make me anxious, I love playing for ballet, and these little things are what makes it exciting and interesting.” But just in time to save you from such a sugary end, I remembered the 9/8. This list of anxieties wouldn’t have been complete without it.
Now I’m not talking about the kind of 9/8 that’s just a 3/4 in disguise, that is, a tune that’s in three with a lot of “diddly diddly diddly” underneath it (see earlier post). I mean a proper 9/8 where the tune itself goes diddly diddly diddly diddly diddly diddly, without stopping for breath. I mean those 9/8s that are weird in the same way that the polonaise is weird, where phrases finish on the weakest possible (final) beat; where the end of the phrase feels like you’ve leapt on to the tube as the doors were closing, and just managed to pull your coat free as you got inside. Look at the example above – what kind of music ends on a little note like that? That’s like finishing a sentence with a comma,
I never trust myself to improvise them, because I have so often got hopelessly lost in the middle of them in class. It goes so well for so long, but it only needs one beat to go wrong to mess the whole class up, and once you’ve slipped up in a slip jig (another name for the 9/8), it’s hard to pick yourself up again. I’ve got a few in my head that I keep for special occasions, and stick to what I know.
It’s a strange pocket of ballet behaviour, the 9/8. It’s relatively rare in music*, but it seems someone once thought that it would be a good thing if ballet teachers learned about it, like you’d learn about the two-toed sloth, or photosynthesis. So the 9/8 crops up occasionally in class like a trick question, just when you least want or expect it. I rather like them, but they make me nervous.
*Justin London wrote a paper called “The Binary Bias of Metric Subdivision and the Relative Complexity of Various Meters, or, Why is 9/8 so Rare?” given at the 4th International Conference on Music Perception and Cognition, Montreal, Quebec, August 1996. The background to the theory is also explained in his book Hearing in Time(second edition) on pp. 44-45.
One of the reasons that I’m very sympathetic to anyone who says they don’t “get” time signature, is that my own hearing and sense of metre can play strange tricks on me. The most bizarre of these is when I accidentally play the “wrong” thing for an exercise, and it turns out to be OK, because there’s some kind of metrical equivalence that I had never thought of before (there’s a diagram coming to explain that).
Here’s an example: the other day, I did something in class that I don’t think I’ve ever done in 28 years of playing for ballet. The teacher marked a ronds de jambe à terre exercise, a bog standard 3/4 one, no surprises, no tricks. But as I was watching, the music that started playing in my head was What a wonderful world. It’s against all the unwritten rules of ballet (ronds de jambe must be on a dirgy 3, or – once, in about 1976, on a slow 4) that I hardly dared do it. But it went almost unnoticed, which is to say, nobody died, and everyone did the exercise, and the teacher didn’t stamp the floor and look shocked. So it does work.
If you think about it (which I did, for a few seconds before, to see whether it could possibly work in theory, and a long time afterwards, to explain why it did in practice) one bar of a 4/4 ballad-y thing like that, with triplets in the left hand, is at some level equivalent to a bar of 2 bars of 3/4. One reason why it’s not immediately obvious is because those six quavers are split down the middle in the 4/4, and into 3 lots of 2 in the 3/4. Another reason is that when you think “6/8”, “3/4” or “4/4”, you think certain kinds of music or tune, you don’t think about imaginary metrical levels that might connect them in a metric-theoretical universe.
Potential metrical alignments between three time signatures/tunes
The diagram above shows – metrically – how a 4/4 ballad with triplets, a tune in 3/4, and a tune in 6/8 could be used for the same exercise. Imagine the 6/4 written out in 6/8 with semiquavers instead of quavers, and played half speed. I’m not offering this as a handy tip for solving problems in class – like I said, it’s taken me almost my entire career to work this out, and it makes my brain hurt to look at that diagram. I discovered the trick only this year, when playing for adages – when teachers mark something in what sounds like an impossibly slow 3/4, you can play a 4/4 ballad. I couldn’t work out the theory, I just found it worked.
One of the things that enabled me to work it out, was (mis)hearing a teacher counting a bar of 6/8 in a rehearsal – I couldn’t tell whether she was grouping the notes in threes or 2s, so it sounded sometimes like 3/4, sometimes like 6/8. This connects eventually with my last post on the perils of being too “musical” as a pianist – ballet teachers are sometimes much “cleaner” and stricter in tempo than us musicians, and that’s why I was able to mis-hear what she was singing. The trouble (for pianists) with thinking in 3/4 (as in Santa Lucia in the diagram), is that under the influence of the tune or the main metre, the quaver accompaniment begins to slide into fancy “musical” performance. If, on the other hand, you mentally imagine that you’re grouping the quavers as 3+3 instead of 2+2+2 (as in the bottom line of the diagram) you slip out of the 3/4 tendency, and it becomes the steadier, more reliable undercurrent that is better in adage.
All of this makes me think that Justin London’s “Many Meters Hypothesis” is absolutely bang-on. Metre isn’t a neutral grid that you can just lay over or extract from music, so that all 3/4s are in some way equivalent. Quite the opposite – within the range of things that are in 3, for example, there are repertoires which have particular qualities of threeness, and you’ll recognise and parse these to a greater or lesser extent, depending on your musical enculturation. The proof of this, to me, is that the theoretical (metrical) equivalence of the three things that I’ve shown in the diagram is so strained as to still appear unusual and unintuitive, even when you see it written down and “proved” on paper. Each of those pieces has a particular feel which cannot be reduced to a unifying metrical level.
As chance would have it, I was skimming through Prausnitz’s Score and podium: a complete guide to conducting book on conducting (recommended to me by Gavin Sutherland, thank you very much, sir), and came across this terrific quote on page 115:
A timely caution: one good subdivision does not necessarily deserve another. Given the fact that most music is made between beats, it follows that the fewer the beats, the more music making can take place.
That to me sums up the hazards of marking adages for the pianist. Teachers are encouraged to indicate musical subdivision to musicians, and sometimes, it’s good that they do. But in adage, the more they prescribe the subdivision, the less chance there is that you as the pianist can think laterally about how to fill the space between the beats. And for the teacher, those subdivisions are less significant, it seems to me, than they are for the pianist – but you have to be a brave soul to take the risk and play something other than was marked, in case the teacher really did want that thing she asked for. Nine times out of ten, I don’t think it matters. I’ll run and hide now.
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).
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.
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?