New metre and rhythm page


After 11 years of having odd articles about rhythm and metre all over my old site at, 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.

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

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

It’s  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.

It’s things like this that make me dread trying to explain compound metres such as 6/8, coupled with the fact that the term “compound metre” (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.

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).

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?



Laptops in the classroom and multi-tasking


The case for banning laptops in the classroom is a blog by Dan Rockmore in the New Yorker on the surprising proposal by one of the lecturers to ban  laptops in programming classes  at Dartmouth.  I say ‘surprising’, but it doesn’t actually surprise me, since I’ve noticed that of all people, programmers and other exceptional thinkers in just about any field tend to regard notebooks or conversation as a more appropriate tool than computers for doing conceptual work (see earlier posts of mine praising [real] notebooks and even record cards).

But the main point about laptops in class is that they’re distracting. The message of one study on the subject “aligns pretty well with the evidence that multitasking degrades task performance across the board.” What I like about the guy that proposed the ban, apart from the fact that this blog adds to my growing list of articles busting the myth of multitasking is that he’s not blaming the youth of today for being distractible, but acknowledges that laptops distract him as well, so why would it be any different for the people he teaches? 

At a conference last year I looked round the lecture room during one of the presentations, and noticed that many of the big-name researchers, due to give papers later in the conference, had their laptops open. Some were blogging, some were tweeting, some were rejigging their PowerPoint presentations, others were editing papers, checking emails or on Facebook. One was googling a term that the presenter had just used, another was looking up the book that they had just referred to on a slide. One was checking the football results, another was actually watching a game. Oh yes, and one was organizing his albums in iPhoto.

Remember, these are professors I’m talking about (in the colloquial sense of high-end academics), not adolescent undergrads. Coming from the ballet world where a teacher wouldn’t let a bunch of 6-year olds behave like this, I was pretty appalled. But what appalled me was the lack of leadership and sense of collective responsibility. I wanted the conference organizer or the person chairing the session to stand up and tell the room to get a grip, put their laptops away, and give the person at the front 20 minutes of their attention for god’s sake. As for tweeting and blogging about conferences while you’re in them, isn’t this a form of Facebook-style snap-and-post narcissism? Look at me! I was there! I heard this! It was really cool! But while you were typing that, your focus necessarily drifted from the next few sentences, if it was ever there much in the first place.

I don’t think it’s the fault of the lecture as a form. I like lectures. People who speak well can inspire. The talk I attended by Ken Robinson  eight years ago still inspires me, and remains a model to aspire to. But it’s a relational thing - lectures depend on the attention of the audience as well as the attention-grabbing skills of the lecturer.  And if lecturers themselves can’t keep their minds off football, funny kitten pictures or email, then don’t expect students to fare any better.

That Czerny tarantella from Etudes – found but unidentified


Posters in an Italian piano forum have been playing the same game as me – trying to identify the Czerny studies used in Riisager’s ballet Etudes. In my post on the subject, I managed to trace all of them (leaving aside any short quotes that Riisager may have thrown in along the way that I failed to recognise as quotes).

The one that I couldn’t trace was the tarantella – but those Italians have found it. Or nearly. They’ve found a score of it, in an anthology of Czerny studies published by Presser in 1906, freely available at Open Library. The tarantella is on page 66-67. The only trouble is, Emil Liebling may have “revised, edited and fingered” the studies “with annotations”, but he didn’t bother to identify them. Someone (like me) has been through with a pencil, marking the opus numbers of each study, but (also like me) couldn’t identify the tarantella.

The Italians found my page on Czerny and posted a link to it, noting that I hadn’t – (unlike them) – found the tarantella. “Per solidarietà, potrei scrivergli e dargli il suo pezzo mancante” says one of the posters – out of solidarity, you could write and give him the missing piece (message 50).  Yes, out of solidarity, you could have done, that would have been very nice. But it would be even nicer if you could actually identify which book/opus number the study is.  







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.



What Schenker, Nicholas Cook & a food processor taught me about piano fingering

"Beyond the Score" and the implement that helped me understand Schenker's complaint about pianos and fingering

“Beyond the Score” and the implement that helped me understand Schenker’s complaint about pianos and fingering

By what turns out to be a happy coincidence, I managed this week to combine reading Nicholas Cook’s Beyond the Score: Music as Performance with an accident in which I sliced the end of the fourth finger on my right hand while I was washing up the blade of a food processor (see illustration on the left).  I picked it up and turned it so I could make it really nice and clean, and of course, in doing so, I made a little manual food processor in the sink, to which my finger fell victim.

Needless to say, for a pianist, this is bad news. Since it hurt so much to put any pressure on that finger, I didn’t even try until I really had to, which was a class & rehearsal last Thursday night.  One attempt to play on it during pliés  was all it took to realise that I’d have to play everything without a fourth RH finger. That made quite a difference to tunes that I usually play almost the same way every time: a lot more clarity and power in the phrasing, because you’re not weakening your tune-playing fingers by trying to do other stuff at the same time.

As I was playing, I thought of a passage in Beyond the Score where Cook describes Schenker’s disdain for the ‘cult of velocity’ and the 19th century idea of all-purpose fingering systems. Schenker argued that each piece had it’s own ‘special fingering’ and ‘special dynamics’ (Schenker 2000:77, cited in Cook 2013: 41). His own fingerings were apparently aimed at bringing out the sense of the music rather than being convenient physically. He (Schenker) was critical of Broadwood’s English action, saying that

perfect evenness of touch has arrived. Simultaneously, music training has for decades striven for perfect evenness also of the fingers. Thus, we are faced with evenness of fingers and keys. We could be pleased by this development if – what irony! – precisely the opposite were not the crux of the matter: unevenness! The fingers, by nature uneven, must play unevenly: all effort in practicing is in vain if it does not aim at unevenness in performance. (Schenker 2000: 77, cited in Cook 2014: 42) [scroll to the end for references]

I remember having a mental jolt when I read that, given that my entire pianistic life has been spent in the pursuit of exactly what Schenker criticised. I don’t think my teachers drummed it into me – two of my teachers, Trissie Cox and Antony Saunders, would often suggest unusual fingerings like playing a motif in the left hand with your thumb to give it oomph, or sliding from a black key to a white one with the same finger, and then there’s the trick of fingering mordents 1-3-2.  But the aim for evenness of touch is all around you – Czerny, Hanon, and those endless scales and arpeggios that you learn for ABRSM exams.

I thought no more of it until last Thursday night when I had to play the reel from La Sylphide, which, I can tell you, is pretty hard without a fourth finger. When it got to the B flat section, I realised with the clarity that only having sliced your finger with a blade gives you, that Schenker was brilliantly right about this. Previously, I’d have done the physically convenient thing, and started this passage with my 3rd finger, which makes the whole bar lie under one hand position. But there was no way I could do that this time, and in the heat of the moment, I came out with the fingering below:

Reel from La Sylphide

How I fingered this bit of the reel without a fourth finger. It works.

This section looks so much fun on paper, but it never sounded as good as I wanted it to until I put this “emergency” fingering into action. It’s a bit messy – especially the hopping over your own thumb to play the quaver B flat on the second half of the second beat in the first bar – but it sounds a whole lot better musically than starting with 3-4-5 and using the same hand position for the whole bar. If you finger the slide up to the F with 1-2-3, you get a real punch out of the F and a lot of ring out of the appoggiatura. By hopping from 1 to 1 on the C and D on beats 3 and 4, you get a much better staccato than fingering it 2-4-3-5.  And that hop over the thumb to play the B flat with 2 results in a light staccato for that note – whereas with the ‘convenient’ fingering, this relatively weak beat/note gets the whole weight of your thumb.

Another insight was chord voicing. The standard pattern for a big chord in the RH is an octave with two filler notes. By the time I’d accidentally hit my injured finger a few times during the piece, there was no way I was going to hit it again for the sake of a major third that was already present in the bass (the chord was a first inversion F major in the right, ACFA, with an octave F in the left) so I missed it out. I realised then that trying to play four-note chords because you can is pretty pointless. Including the fourth finger weakens the attack that you can give to your fifth. The 4th is weak, so you don’t get a lot of sound out whatever note is under it. So, frankly, why bother? Why not try different voicings, and if missing out a note actually sounds better, do it.

Next on the playlist was “Snowflakes” from The Nutcracker, and for the first time in my life, those twiddles in the right hand actually sounded like a piccolo, because I had to play all of them 1-3-1 rather than sort out how to avoid using my 4th finger. Interestingly, one of the only places where Taneev indicates fingering is during this massive countermelody in the bass – for which he suggests a thumb on every note. Combine that with 1-3-1 for the right hand notes (forget about the lower octaves – they add little, compared to what leaving them out enables you to do, I discovered), and this begins to sound a lot more like an orchestra.

Taneev's fingering for part of Snowflakes.

Taneev’s fingering for part of Snowflakes.

So the happy part of the coincidence is that this embodied-knowledge encounter with a food processor blade, combined with Cook’s wonderful scholarship,  made Schenker’s thoughts on pianism come to life in fascinating, practical ways. It’s rather a messy, bloody and painful way to enlightenment, though. Save yourself the trouble – take Schenker’s word for it, and discover what relying on the unevenness of your fingers can do for making your playing sound more musical.


Cook, Nicholas. 2013. Beyond the Score: Music as Performance. New York: Oxford University Press.

Schenker, Heinrich. 2000. The Art of Performance. Heribert Esser, ed., Irene Schreier Scott, trans. New York: Oxford University Press

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.

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?