Phrases and forms

The construction transfers

Rhythm lesson 2 built the metric hierarchy by dividing a bar repeatedly and counting how many levels mark each position. It returned 5 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 for 4/4, which is the familiar strong-weak pattern, derived rather than asserted.

The figure below calls that same function with bars in place of beats. Nothing was adapted. It returns 3 1 2 1 for a four-bar phrase, which is exactly what theory teaching calls hypermetre: first bar strongest, third next, second and fourth weak.

The evidence does not

Getting the textbook answer out of an unmodified function is either a confirmation or a warning, and here it is a warning. Look at the seconds column.

Rhythm lesson 5 found that a cycle stops being something you can hold once it runs past a few seconds. At 120 beats per minute a bar is two seconds, so the gap between the downbeat of bar 1 and the downbeat of bar 3 is four seconds, and the whole four-bar phrase is eight. At a slow blues tempo the phrase is twelve seconds long.

Those are not spans you can tap. The reason metre was convincing in Rhythm lesson 2 is that a listener supplies the pulse and can demonstrate it by moving; the whole argument turned on the beat being something you do. Nobody taps hyperbeats.

So hypermetre is not the same kind of claim, even though it is the same arithmetic. It describes how the music is constructed, which is real and useful. It does not follow that a listener perceives a hierarchy over eight seconds the way they perceive one over two, and the shared formula is not evidence that they do.

To be fair to the idea: listeners plainly do notice when a phrase comes out the wrong length, and performers feel a four-bar unit strongly enough to argue about where it starts. Something is being tracked. The point is narrower - that whatever it is, it is not the same faculty that supplies a beat, and calling both of them metre hides the difference rather than explaining it.

And then there is the blues

The halving construction can only produce spans that are powers of two. Four, eight, sixteen. It cannot reach twelve at all, by arithmetic, no matter how the divisions are arranged.

Which is awkward, because the twelve-bar blues is arguably the most played musical form of the last century.

A form is a template with holes

Seven of the twelve bars are fixed. Five admit a choice, and the grammar in that figure admits 32 progressions in total. That is what a form is: not a piece and not a rule, but a template with holes in known places.

It is also why the form works socially. A listener can identify it from the first four bars because those are fixed, and a player can join a band they have never met and be right about bar 9 without being told. The fixed slots carry recognition and the open ones carry everything the players are actually choosing.

The grammar in the figure is a statement of the form, not the statement. Sources differ about which bars admit which substitutions, and a stricter or looser version would give a different count than 32. What does not change with the version is the shape of the answer: a handful of fixed bars, a handful of open ones, and a family rather than a progression.

The twelve bars, though, are not up for negotiation, and nothing about hearing explains them. Three four-bar groups is one story. Twelve as three phrases answering each other is another. Neither is derivable, and both are just descriptions of what the form does.

What forms are made of

Everything in this lesson is conventional in the strict sense used by this course: precisely stateable, learnable, powerful, and not derivable from anything.

That is not a complaint. A form is an agreement about length and return, and an agreement is exactly what you need if a listener is going to know where they are and a player is going to know what happens next. The blues does that with twelve bars and no theory of hearing at all, which is a decent argument that the theory was never what was doing the work.