Melody

Three kinds of claim

Almost everything said about melody falls into one of three categories, and they get presented in the same tone of voice, which is the problem.

• Perceptual. Facts about hearing. They do not have to be learned, they hold for people with no musical training, and they are measurable in a laboratory.
• Statistical. Real regularities in what people write, which turn out to follow from something other than the principle they are usually credited to.
• Stylistic. Conventions of a repertoire, learned by exposure, genuinely powerful, and not laws of anything.

This lesson has one figure for the first, one figure for the second, and prose for the third, which is roughly the ratio of how much can be demonstrated in each.

What is actually perceptual

The strongest result in the field is auditory streaming. Play two pitches alternately and your hearing decides whether they are one thing or two, and the decision depends on how far apart they are and how fast they are going, together.

Slow and close, you hear a single line bouncing up and down. Fast and far apart, the line splits into two independent streams and you can attend to either one on its own. Van Noorden mapped the boundary in 1975 and it is a property of the auditory system, not a musical convention: it works on people who have never heard the music it appears in.

Which explains the one real rule

Melodies overwhelmingly move by small intervals. Count them in any tradition you like and you will find seconds and thirds dominating, with leaps comparatively rare. That is about as close to a universal as this subject has.

Streaming explains it. A line that moves by small steps stays inside one stream and is heard as one thing. A line full of large leaps fragments into several streams, and then it is not a melody any more, it is a texture. So the preference for steps is less an aesthetic rule than a precondition: it is what it takes to be perceived as a single voice at all.

The exceptions are the proof. Bach's solo violin and cello writing implies two or three voices from an instrument playing one note at a time, by leaping between registers fast enough to force the split. That is the streaming boundary being used deliberately as a compositional device, three centuries before anyone measured it.

And now a rule that mostly is not one

Here is the standard teaching: after a large leap, a melody tends to turn round and come back by step. It is called gap fill, it is in every textbook, and the statistical claim is entirely true. Melodies really do behave that way.

The explanation is where it goes wrong. Gap fill is presented as an aesthetic principle, something composers do because the leap opens a hole that wants filling. Von Hippel and Huron pointed out around 2000 that you get the same behaviour with no such principle at all, purely from melodies staying in a register.

The figure below is that argument, running live. The generator picks an interval size from a fixed table and a direction by coin flip. Nothing in it consults the previous interval. The only other thing it does is stay inside a register.

What that figure shows

Unbounded, the reversal rate sits at 50%, which is what having no tendency looks like. Confine the walk to two octaves and it rises to about 54. To a tenth, 58. To a single octave, 64. The tighter the register, the stronger the effect, and at no point does the code know what a leap is for.

The mechanism is unglamorous. A large leap tends to land near the edge of the register, and from an edge most of the available room is back towards the middle, so the next move goes that way more often than not. It is regression to the mean, and it produces the textbook tendency without anybody intending it.

This does not prove composers never fill gaps deliberately. It proves that observing the tendency is not evidence that they do, because a process with no such intention produces it too. That is a weaker and far more useful statement than the one usually made.

Worth being careful about what has been shown. The simulation reproduces the direction tendency, not everything gap fill is said to cover, and real melodies do exceed the reversal rates here in some corpora. The honest reading is that a large part of the effect is statistical, that the residue may well be real, and that the textbook version attributes all of it to intention without checking. Von Hippel and Huron did the checking; this figure only reproduces the cheap half of it.

What is left is style, and it is not lesser

Everything else usually taught about melody belongs in the third category. That the leading tone should rise to the tonic. That a phrase should be four bars. That a melody should have a single high point. That it should end on a stable degree.

These are real and they are strong, in the sense that music which violates them sounds wrong to listeners raised on music that obeys them. What they are not is derivable. They are conventions of a repertoire, they differ between traditions, and they have changed inside Western music several times.

Calling them conventions is not a demotion. Language is convention and it is not thereby arbitrary or unimportant: a shared convention is what makes an expectation possible, and an expectation is what makes it possible to satisfy or deny one. Almost every effect in music worth having is built on that, and none of it would work if the rules were laws.

The reason to sort the claims carefully is not to rank them. It is that treating a convention as a law makes you unable to hear the music that declines it, and treating a perceptual fact as a preference makes you think you can compose your way around your own ears.