Let’s take a closer look at rule seven of my rules for melodies from the beginning of chapter ten:
7. After a big step, the next step will probably be smaller and in the reverse direction.
Rule six states that big leaps, or skips, in the pitch of a tune tend to be upwards, and rule seven says that these big upward leaps are usually followed by a smaller step downwards. For example, a big jump up from A to F will probably be followed by a smaller jump downwards, to a note between A and F. Similarly, on the rarer occasions where there is a big leap downwards in pitch, the next note tends to be a smaller step upwards.
This phenomenon is called post-skip reversal and it’s common throughout much of the world’s music. Because it is so widespread, musicians and musicologists have until recently assumed that there is some deep psychological/musical driving force behind post-skip reversal.* Perhaps some emotional longing to return to safer ground after a big leap?
Well, I’m afraid the psychology of music has nothing to do with it. The actual reason why post-skip reversal is so common was discovered by music psychologists Paul von Hippel and David Huron in the late 1990s.1 After a lot of work studying the folk songs of Europe, South Africa, Native America, and China, they found out that post-skip reversals are simply a matter of probability:
• Each song has a bottom note and a top note.
• The notes used most frequently in a song tend to be somewhere in the middle of this range.
• Just before a large leap upwards, you are likely to be somewhere in the middle of the range.
• So when you hit the top note of your upwards leap, you are likely to be near the top of the range of notes for your tune.
• After the leap you will be producing one of the highest notes in the range of the tune, and there is only a small chance that the next note will involve moving upwards again, to one of the rarely used upper notes. But there is a bigger likelihood of moving downwards to one of the frequently used mid-range notes.
• So a step downwards is very probable.
The same argument is true for a large downward leap: it’s likely to be followed by a smaller step upwards.
The statistical principle behind all this is called “regression to the mean,” and it holds true in lots of situations. For example, if a shopkeeper has just served a very tall person, the chances are that the next customer will be closer to the average height, simply because very tall people are rare.
In the case of post-skip reversal, the tall person is the equivalent of a high note—and the next note is likely to be closer to the average pitch of the tune.
Von Hippel and Huron then extended their study to look at tunes with big leaps upward that start from a very low note. According to their “return to mid-range” theory, a big leap upwards from a very low note would not necessarily be followed by a smaller leap downwards. If the leap took you up to a note in the mid-range of the song, then the tune could go either up or down from there. And this, to their great satisfaction, is what they found.
“Baa, Baa, Black Sheep” is an example of this. The first note, “Baa,” is the lowest note in the whole song; the next “baa” is the same note again. Then there is a big jump up to “black,” but this jump just takes us to the middle of the range of this song, so the next note could be up or down or the same note repeated. In fact the tune repeats the same note for “sheep” and then continues upwards—not a post-skip reversal in sight.
Going back to our shopkeeper, this is the equivalent of serving a very short customer followed by an average-height customer. The third customer is equally likely to be a bit taller, or a bit shorter, or the same height as Mr. Average.
So although post-skip reversal does exist, the cause is not musical/psychological. It all comes down to the statistical fact that notes at the extreme range of any melody are rare (because they are more difficult to sing), and notes in the middle of the range are common.
Only one more of my rules for melodies has a straightforward explanation: rule four states that there are far more small steps than big jumps in most melodies. The obvious reason for this is that small steps are easier to sing than big jumps. Music originated from singing, and so our tunes will tend to involve a lot of easy-to-sing small steps.