Tag Archives: 18th century theory

Meter vs subdivision: An easy solution to the ballet and time signature problem?

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In the course of writing an article about the problems of ballet and time signature recently, I read a lot of books and articles about 18th century theories of meter. I’ve already blogged about that several times recently, as I found a lot of it helped to answer queries I’ve had for years.

As the dust has settled on the thoughts that I had for the article, I have come to a conclusion, for now at least, that “mixed meter” as the 18th century theorist Koch used that term, offers a really useful way of understanding meter and time signature problems in ballet teaching. I began to formulate that idea in And now for something completely sextuplebut I could say it even more simply now.

The problems I’m talking about are almost exclusively to do with triple meter, and the fact that in the kind of music that you get in ballet classes (i.e. predominantly 8-count or 8-bar phrases) there is always a possibility of counting in 2 or 4 rather than 3 – and if trainee ballet teachers have to learn about time signature, they often have difficulty understanding why something should be classified as a 3 or a 6 when it seems more natural to count it in 4.

If Koch were to come back to earth and teach such courses, he probably  wouldn’t say  “you’re wrong, it’s a 6,” he would have said “this is a tripled 2,” or “mixed meter” – you’re right, it is four, because the tune is moving predominantly in a 1,2, 1,2, fashion, rather than diddeley diddeley diddely diddely style, like a double jig, or Schumann’s Der wilde Reiter/The Wild Horseman.  Koch’s point was that these things that sound like fours, are fours, but you write them in compound time like 6/8 because it’s notationally easier. A true 6/8, or truly triple meter, is one where the movement of the tune coincides with the “6” in the top of the time signature.  The exceptions – and they have to be learned – are the triple jig, the polonaise, and the sarabande, and very slow versions of either minuet or mazurka (and of course, many other styles of music that are not so commonly used in ballet).

To put it another way, what matters about time signature if you’re trying to make a bridge between movement and music is not how many beats there are in a bar, but which beats carry the motion. This rather 18th century way of looking at it helps to distinguish meter from subdivision. If you define time signature only as how many beats there are in a bar, without also looking in individual cases at what  happens  in the melody or most salient part of the musical surface, then meter and subdivision get confused. That’s the kind of class where hapless students try to count “12” in a bar of 12/8 where Koch would have said, “Don’t count 12, because this is mixed meter, it’s really a 4, written in 12 for the sake of notational simplicity.”

It’s rather a shame that I’ve only just realised this at the point in my life where I no longer have to teach it, but that’s why partly why I keep a blog – to atone for my past conceptual sins.

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?