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Time Signatures: A Socratic Experiment September 19, 2010

Posted by contrapuntalplatypus in Music, Philosophy, Teaching.
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Dedicated to all those who “never totally got” time signatures in their childhood piano lessons…here is the explanation you were waiting for.


September has returned and with it a new year of piano teaching. I realized the other day that I haven’t yet posted a single entry on my teaching, even though it’s my career and (officially) one of my main blog topics! So, I decided it was high time to remedy that omission.

One of the questions I get asked a lot is: “What sort of method do you use?” I never quite know how to answer this, since there isn’t any convenient label (like “Suzuki method”) one can stick on it. I generally end up trying to explain that I have as many methods as I do students, and I use whatever technique will help the student get an in-depth understanding of the music and how it works – not simply get flashy “results” right away.

However, if anything I do comes closest to a “method”, it would be the “Socratic method”: teaching by asking questions. Though I’ve picked up many of my teaching techniques from my excellent university professors, I think the Socratic method is simply my default, intuitive way of teaching (I remember automatically doing this when I tutored children or explained concepts to my friends in school, before I’d even heard of Socrates).

The premise is simple: any student has, already, all the knowledge they need to understand any concept – though they might not be aware of it. (This tends to be true, I find, far more often than one might think.) The teacher’s job is merely to ask them the right sequence of questions – this will help the student put together the information in the right way to figure out the answer, rather than simply having it handed it to them on a silver platter, as so many teachers (music teachers in particular) tend to do

What is the advantage of this method? Wouldn’t it be more efficient just to feed the student the “facts” without all this intermediate, time consuming question-asking? I find there are two main problems with the “direct information transfer” approach. First of all, there’s no way to be sure the student really understood what you were saying without asking them at least one follow-up question to test their knowledge. But, more importantly, it’s simply boring. Nobody likes to be talked at. Socratic-style dialogue is engaging, often humorous, keeps the student involved and will stick in their memory far longer than dry, processed information. There’s a wonderful and highly entertaining illustration here of a math teacher who taught a class binary arithmetic in under 30 min using the Socratic method.

But (I can imagine the reader protesting at this point) math involves  a application of abstract laws that can be deduced through careful questioning. Music, though, is largely a human invention – surely it can’t be approached using this method of guided reasoning? Aren’t time signatures and rhythm and pitch notation merely facts to be systematically dispensed, one by one?


This summer a new family with three boys (5, 8 and 10 years old), joined my studio. They’re an attentive, enthusiastic and energetic bunch that enjoy competing (all in fun, of course) by playing all of one another’s repertoire – thereby totally confusing their teacher at times, but I certainly don’t discourage it!

One day, I was giving the oldest boy his lesson when we came to a new concept: the dreaded 6/8 time signature. Inwardly I groaned. Every time I had tried to teach this it had been a long, drawn-out process that often ended with the student looking utterly disoriented. Why were we suddenly using this strange-looking, flagged note as the “main beat?” Why was the measure now divided into six parts – or wait, was it two? Or three? What had happened to the good old quarter note which they’d understood perfectly, along with the nice familiar 4/4 time signature?

I thought back to how time signatures had been presented in my own childhood method books, starting with getting the student well-anchored in good solid 4/4 time, then 3/4 (a step that throws many of my students for a loop right away), then progressing to the thorny 6/8…and on to even more mysterious entities like 2/2 and 3/8 and 12/16, granted that the student hasn’t yet given up in frustration and dropped out. Which many do.

And suddenly a realization struck me: this was not the way to do it.

I wasn’t yet sure what the right way was, but I was absolutely certain it wasn’t presenting the student with time signatures to be learned, one by one, like capitals of the world or vocabulary words in a foreign language. All time signatures that had ever been created were produced by two simple, logical rules. Was there any simple way I could teach them the rules – in a way they understood – rather than trying to explain individual time signatures?

3. I called all three students over and we clustered around the coffee table in the middle of my teaching studio. “We’re going to talk about rhythm a bit,” I explained. (I’m wasn’t quite sure where I was going with this experiment, but had the feeling I should begin, at least, with something familiar.)

Step 1: Starting with the Familiar


“You’ve all seen this in front of most of your pieces, right?”

(Nods all around.)

“What does this “4” mean?” I point to the top number “4”.

“4 beats?” ventures the 10-year old after a bit of hesitation.

Me: “Good answer. But four beats where? Tell me more.”

8-year old: “Four beats in every bar.”

“That’s exactly right. We still don’t know very much about the beats, though. What kind of beats are they – this kind? Or this?”

(They answer “no” to both.)

“OK, can one of you draw me what the beat looks like?”

One of the boys takes the pencil and draws:

“That’s right. What kind of note is that called?”

“A quarter note.”

“Exactly! You (the two older boys) have done fractions, right? What kind of fraction has a 4 on the bottom, like this: 1/4)?”


“Can one of you draw out what a 4/4 bar will look like?”

They draw:

Step 2: Tweaking the Familiar, Part 1


“Good. Let’s try something a little different. What if I change the number of the top to a 3, like here:  How many beats are in every bar now?”


“And what kind of beat are they?”

(After a bit of hesitation: “It’s still a quarter note.”)

“Right – the number on the bottom stays the same, so it’s the same kind of beat. Can one of you draw what this bar will look like?”

They draw:

“You’ve probably seen a lot too, but maybe not .” (From one of the boys: “It’s been in a couple of my pieces…”) “Ok, good. So what happens now that I’ve got a 6 on the top? How many beats are in every bar?”


“And what kind of beat are they?”

“They’re still quarter notes.”

“So this bar would look like…”

Step 3: Tweaking the Familiar (Getting Harder)


“Okay. Let’s go back to that 4/4 time signature, with 4 beats in every bar. Now I’m going to change it a little:  Is it still 4 beats in every bar?”


“What kind of beat are they? (Pointing to the bottom 2) Are they still quarter notes, or something different now?”

“Something different.”

“What kind of note will it be?” (For the first time they look unsure, so I decide to give them some clues.) “The quarter note had a “4” on the bottom. If it has 2 on the bottom, what fraction does that look like?”

(Tentative guess:) “A half note?”

“Yes! That’s right. This bar will have 4 half notes.” I draw it:

“It looks sort of weird, doesn’t it?”

(One of the boys starts to grin and says something like: “We’ve never seen a piece like THAT!”)

“Maybe not, but there are some pieces in 4/2 time. How about another weird one: 6/2 time?”

They draw it:

Step 4: 6/8 time – explained Socratically!


“Ok, let’s change the bottom number again. What if I make it an 8, so that we have 4/8?”

“It’s an eighth note.”

“How many eighth notes in every bar?”


“What if I put a 6 on the top? How many eighth notes are in every bar now?”

“There’s six notes now:”

(At this point we’d reached the original goal of explaining 6/8 time, but given how well this was going, I decided to try a few more exotic time signatures for fun…)

Step 5: And Now For Something Completely Different…


“Let’s try a really different one now. We don’t have to put just even numbers like 2 or 4 or 6 on the top. We could put 5 if we wanted!”

(“Five?!?” they ask incredulously.)

“Yes – what would it look like?”

(I clap it for them and tell them that one composer, Bartok, wrote lots of pieces with this time signature. Then:) “We don’t just have to pick small numbers either. We can put ANY NUMBER in the world on top. What if I put 21 on top and 8 on the bottom?”

“That means 21 eighth notes in every bar!” (All three boys have started grinning by now.)

Step 6: And So It Continues…


(At this point, to my delight, the boys start asking questions.)

“Hey, can you put ONE on the top?”

“Yes! Every bar would just have one note. The piece would go by very quickly, of course!”

We draw it:

(Another question occurs to me:) “Let’s say we wanted an even shorter note. Do any of you know what it looks like?”

(One of them suggests “A sixteenth note?”)

“Right, so if we decided to write, say, 7/16?”

(Another question from the boys:) “Is there an even shorter note than that?”

“That’s a good question. The next one is called a 32nd note.  I want you to guess what it looks like, though.” (I figure that, since they’ve seen two “flagged” notes already, they should be able to pick up the pattern and add a third flag.)

(Here comes an unexpected impasse. I hand the oldest boy the pencil and he stares at the paper nervously. He obviously desperately wants to get the “right” answer and is terrified of “not guessing right”, though he seems to have an idea of what it might be.)

“Well,” I say, “somebody had to make it up first. Suppose it’s way back in prehistoric times, your friends are off hunting woolly mammoths and you’re writing music on a cave wall somewhere…” (Grins and giggles from the other two at the picture.) “You need to invent a really fast note, and it’s up to you what it looks like. There’s no right answer. You can even do a star on it, or a smiley face…” (Laughter.)

(Eventually, after taking several tentative stabs at the paper, he draws the “right” answer:)

“Well done – that’s great!” (Look of immense relief from the boy). “Though really I would have been happy if you’d drawn a smiley face too.”

One last question from the boys: “Do you just keep adding flags? What about when you run out of room?”

My answer: “Yep, you just add another flag each time…but after about 5 flags it’s humanly impossible to play anything faster! (I demonstrate at the piano). You’d need to be a robot or a computer.”

4. At this point the structured “Socratic” part of the lesson ended and we went back to individual lessons. But, as I taught the oldest boy, I could hear the 8-year old going over the more complicated examples to the 5-year old in the background, who sat eagerly listening to his older brother’s explanation.


And then, when the dad came in during the middle boy’s lesson later (he would sometimes sit in on part of the lessons) both the oldest and youngest grabbed him and started enthusiastically explaining to him that now they knew how to write ANY time signature in the world!

None of the three boys has ever had any difficulty understanding or playing any time signature since.

It’s these experiences that make teaching truly worthwhile. 🙂

– The Contrapuntal Platypus