Someone asked me last night what made me want to do a PhD in music in ballet training. I explained that one of the reasons came out of trying to teach time signature to trainee ballet teachers. It’s not that I think they ought to know about time signature, but I was filling in for someone who thought that they did. Trying to teach time signature did my head in, literally (you could say) to the extent that nothing but a PhD would really sort out the mess.
In the first class, I realised that the students knew more than I did about music theory, because they were studying for their ABRSM Grade 3 theory. In decades since I did that exam, I’d forgotten about terms like ‘melodic and harmonic minor’ (someone later asked me what ‘harmonic minor scales’ were for, and to this day, I don’t know). I’d also forgotten about simple and compound time signatures. As a musician, you look at a piece, see that it’s in 6/8, and play. There is no need to categorise it as ‘simple’ or ‘compound’. I bluffed my way through the first class, and then went away to quickly mug up on all the theory I’d forgotten.
I was confused. What is a compound time signature? Why is it called ‘compound’? What is simple about a simple time signature? Why does dividing a beat into three, rather than two, make it ‘compound’ rather than ‘simple’ (as most theory books tell you)? That leaves 3/8 in a rather odd position, because according to half of the theory, it should be compound, and to the other half, it should be simple. People argue about this on the internet, and one theorist says ‘Better to just remember that 3/8 is simple triple, for the exam’.
If (as other theorists tell you) compound time signatures are called compound, because they’re a compound of two or more bars of 3/8, then why logically, isn’t 4/4 also a compound time signature? It didn’t make sense to me, so how would I explain it to someone else? Then in 2002, I bought the newly published Cambridge History of Music Theory, and read Caplin (2002, p.661), where I discovered that some theorists in the 18th century did claim that 4/4 was a compound time signature, for exactly the reason that I thought they should. The main thing is, they argued and disagreed about what ‘compound metre’ meant, and which metres were compound.
In the years I’ve spent dealing with scores and music notation, and working with dancers, metre and time signature has never gone away as a problem or an interest, because contrary to appearances, it’s culture, not arithmetic. My latest joyful discovery is two articles on metre in Communication in Eighteenth Century Music, one by Danuta Mirka, the other by William Rothstein. Mirka’s article is about the way that composers in the eighteenth century would manipulate the metre of music without changing the time signature (she differentiates between the ‘notated’ metre and the ‘composed’ metre – ‘notated’ is what’s on the page, ‘composed’ is what you hear, after the composer has played around with your sense of metrical accent).
Here’s the bit that I like a lot: Koch and Marpurg (18th century theorists) say that if you’re listening to something that has been notated in compound metre (remember, that’s either 6/8 or 4/4), you can tell whether it’s ‘simple 4/4 or compound 4/4’ or ‘simple 6/8 or compound 6/8’ depending on whether caesuras (roughly speaking, the end of a short musical statement) come in the music. If the caesura comes in the middle of the bar, then it’s compound, if it comes at the beginning, it’s simple. Mirka’s article has several examples from Haydn that demonstrate this principle. One of them is the Adagio from Haydn’s string quartet in B flat major, Op. 50 No. 1 (arrangement for piano/cello from IMSLP here) where the first four bars are (in Koch/Marpurg’s terms) in simple 6/8 (because you only have one downbeat), and the last two are in compound 6/8 (because you’ve got two downbeats, and it’s effectively two bars of 3/8, notated as 6/8). The fascinating part here is that this can be construed as ‘balancing’ (in an aesthetic/theoretical sense) what appears to be an unbalanced (6 bar) phrase, because the first section is four bars of 6/8, the second is (effectively) four bars of 3/8. Whether you completely buy into that is a matter of theoretical position and interpretation – and Rothstein takes issue in his article in the same book (p. 114) with an analysis along the same lines by Maurer Zenck of a mid-bar cadence in Beethoven. Whatever position you take, the idea that there can be times when 6/8 or 4/4 are simple, and times when they’re compound, makes more sense than categorising 6/8 as “compound”, and 4/4 as “simple”.
Rothstein’s article “National metrical types in music of the eighteenth and early nineteenth centuries” is probably one of the most fascinating and enlightening articles about metre and time signature I’ve ever read. His theory is that barring music is a matter, to some degree, of what he calls ‘national metrical types’. ‘Broadly speaking’, he says:
Italian and French composers were more likely in the nineteenth century to place cadences on the first beat of a bar, whereas German composers often placed them later. Conversely, phrases in German music were less likely to begin in mid-bar, beginning instead on the the downbeat or with a short anacrusis, one-third of a bar or less in length. (Rothstein 2008, p.113)
I’ll try to summarise as briefly as possible, with inevitable loss of detail and accuracy – better to read the article yourself, don’t take my word for it: In compound metres, he distinguishes between French, Italian and ‘neutral’ barring. French compound metre is where you get half-bar anacruses, and cadences on a downbeat, and it’s rare in the late 18th century onwards. Bach’s Badinerie from the Suite in B minor is written in 2/4, with a half bar anacrusis, but he could have written it as a French compound 4/4, i.e. so that you have a 3-beat anacrusis – because that’s effectively what the music does. German compound metre is where you get a short or no anacrusis, and cadences are on the second beat of the bar. ‘Italian‘ is where you might just as well have written it in 3/8 or 2/4 (what Mirka calls compound 6/8 or compound 4/4, in reference to Marpurg & Koch).
This has finally solved a mystery for me that bugged me all the time I was preparing the scores for the RAD’s new Grades 4-5 syllabus. There were two pieces, one by Verdi (E03b, Canzone Greca from the ballet music from Otello), and one by Bizet (E5a, prelude to l’Arlèsienne) where the melody begins on the half bar, where I nearly rebarred the music so that the downbeats fell on ‘one’, because it sounds like ‘one’. But then I realised that this made the cadence land in the middle of the bar, and that looked wrong. So I ended up having to just write a big ‘1’ underneath the half bar in the music, so that there wouldn’t be any arguments in the studio. I can’t say for sure what the answer is, but in the case of l’Arlèsienne, it seems to me that this is a clear case of French compound metre – the point is to get that final cadence on a downbeat (just as many French words are end-accented), and not make such a big deal about the metrical accents in between: it’s long jump, rather than hurdles. Otello, I’m inclined to think is somewhere between French and Italian compound, in Rothstein’s terms, because you could rewrite the beginning in 2/4, but when the long legato melody that comes in in the middle, it begins with almost an entire bar anacrusis, and it cadences on the downbeat. If you rewrote this in 2/4, you’d lose those long lines. It’s precisely the ambiguity of this music that I suspect makes it so effective for fondus, because you never got a strong sense of either up or down, it’s in a constant state of fluid tension.
So, 15 years after I started teaching, and now that I have stopped teaching, I finally know something about compound metre that makes sense. Unfortunately, I don’t think we’ll ever escape the tendency on teaching courses to reduce knowledge about time signature to a catechism of partial truths, like the notion that there is a fixed, categorical difference between 2/4 and 4/4, or that 6/8 always sounds different to 3/4. The answer to the question “What’s the difference between a 2/4 and a 4/4” for the moment will have to remain “What does your teacher say you have to say it is to pass the exam?”
If you’re a music theorist (like Mirka, Rothstein or Caplin) and you’re reading this thinking “Why on earth is someone who doesn’t understand all this, trying to teach music to ballet teachers?” then you’ve got a good point. Hands up, people like me shouldn’t be trying to teach time signature when they don’t understand it themselves, but they do. Or maybe we shouldn’t be trying to teach about time signature at all, if in fact it’s so darn complicated that you need a PhD to understand it properly. Or maybe we should just stick to basic ‘facts’, and not get into this kind of detail. But you can’t do that with dancers, because they’ll ask the kind of awkward questions that lead you straight back into complex theory of metre. And that, roughly speaking, is one of the things that got me into this PhD.
Rothstein, W. 2008 National metrical types in music of the eighteenth and early nineteenth centuries In D. Mirka & K. Agawu (eds.) Communication in eighteenth-century music. Cambridge UK; New York: Cambridge University Press, 112–159.
Rothstein, W. 2011. Metrical Theory and Verdi’s Midcentury Operas. Dutch Journal of Music Theory, Vol. 16 No. 2, pp 93-111. Available online at