Four bars of Mozart explains everything humans like in music

I’m not arguing here that everyone loves Mozart, or that I’m about to explain what all humans enjoy all the time. But I can say with confidence that this little bit of Mozart goes a long way toward explaining what most humans enjoy most of the time. The four bars I’m talking about are these, from “Eine Kleine Nachtmusik.”

What these four bars of music demonstrate is that humans like:

  1. Repetition
  2. Breaks in the repetition
  3. Repetition of the breaks in the repetition
  4. Breaks in the repetition of the breaks in the repetition
  5. Recursive layers of patterns of breaks and repetitions

In order to prove this to you, I’m going to talk you through these eighteen notes one at a time.

If you’d like to experience the kind of deep focus we’re about to perform together in real time, here are those first four bars one hundred times slower, thanks to the miracle of Paulstretch.

“Eine Kleine Nachtmusik” begins with the note G, played in unison by a string ensemble. There’s a lot of information packed into this very first note. To understand it, we need to do some physics of harmonic oscillators.

The vibration of a violin string is a complex squiggle made up of lots of different simple sine waves added together, and you hear each of those sine waves as a separate note. The loudest and lowest of these notes is G, produced by the string vibrating along its entire length. We call this one the fundamental. But the string is also simultaneously vibrating in halves, producing another G an octave higher than the fundamental. And the string is vibrating in thirds, producing a high, quiet D. As the string vibrates in quarters it makes yet another even higher and quieter G, and as it vibrates in fifths it makes a very high and very quiet B. There are more notes in there as you go up the harmonic series, but those are the most clearly audible ones in an acoustic instrument.

The overtone series

You can see the harmonics of the note G for yourself by playing the stretched track, opening this web page, and clicking the microphone icon. Each colorful horizontal stripe you see is a harmonic.

Okay, so the very first note in the piece includes a G, another G, a D, another G, and a B, each one higher and quieter than the last. So far, so good. Now we come to note number two. It’s a new one, a D. But it sounds very familiar, and it should, because you just heard it as the third harmonic of G. But here in note number two the D is much louder, and lower, and it comes with a whole overtone series of its own. Also, this D is only half as long as the G was.

Note number three is another long G. A pattern is starting to emerge. We started out “at home” on G. We left home, went on a little adventure down to D, and then we came home to G. This is a miniature version of the “hero’s journey” narrative that underlies all Western tonal music.

Note number four is another short D. Now the pattern is pretty obvious: long G, short D, long G, short D. You could play this pattern on a loop forever, it wouldn’t be terrible interesting, but it would make musical sense. The initial surprise of that D has been subsumed in the G/D/G/D pattern, which now sets our expectation for what comes next.

Note number five would appear to continue the pattern, since it’s yet another G, but there’s a twist: it’s short instead of long. Note number six is another D, but it comes sooner than the pattern has led you to expect. Note number seven is another short G. So it seems we’re still hearing a pattern of G/D/G/D, but now all the notes are short, more like a continuous stream of notes rather than the call and response we started with.

Note number eight continues the streaming rhythmic pattern, but it introduces a new pitch, a B. Only B isn’t a new pitch at all, it’s the fifth harmonic of G. So it’s a surprise, but not a total surprise, because you’ve already heard it, just quieter and higher and buried among a bunch of other overtones.

Note number nine is another D, an octave higher than the ones we’ve been hearing so far. Also, this D is long, like the first couple of Gs. As with everything that’s been happening, it’s sort of new, sort of familiar. This D is followed by a pause, the longest one we’ve heard so far. It feels like the end of a phrase or sentence. (We use silence to punctuate our speech in the the same way.) Together, the nine notes making up this first phrase have been jumping up and down the notes in a G major chord. Western listeners really like it when you take the natural overtone series and spell it out explicitly like this.

Now we enter the second half of this little tune, with note number ten. This is a brand new pitch, a C. Like all the others, it isn’t completely out of the blue. The third harmonic of C is our old friend G. Also, the interval from D to G is the same as the interval from G up to C. This new note that’s kicking off our new phrase thus makes a nifty parallel back to the very first note we heard. Note number eleven is another new pitch, an A. As you have come to expect, it isn’t totally new either–it’s the fifth harmonic of D. Notes ten through fifteen alternate C and A in the same rhythmic pattern as notes one through seven. It’s new pitch information, but in a familiar rhythmic structure.

Note number sixteen continues the rhythmic pattern, but introduces another new pitch, F-sharp. You will not be surprised to learn that it’s the fifth harmonic of D. There’s a new twist in melodic direction–the end of the first phrase went straight up to its conclusion. You might expect the end of this second phrase to fall straight down to create antisymmetry. But Mozart lightly violates your expectation here by having note number seventeen jump back up to A.

Note number eighteen concludes the second phrase on the low D we heard back at the beginning, with the silence afterwards indicating a sense of finality (a temporary one, anyway.) This second phrase has been rhythmically identical to the first one, but it spells out a different collection of pitches, a D7 chord. This chord is considered in Western tonal theory to be a tense, dissonant sound. Listening to blues, rock and jazz might have taught you to hear the chord as lively and interesting, rather than simply tense. Nevertheless, a lifetime of enculturation to Western music has taught us to expect a D7 chord to resolve back to a G chord, and that’s exactly what Mozart does in the next measure.

And from there, we’re off. In the rest of the piece, Mozart establishes new patterns, violates them, builds the violations into new patterns, violates those, builds yet more metapatterns, then exploits your memory of earlier events to refer back to the earlier patterns, encompasses those into metametapatterns, and on and on. I believe that this kind of scale-invariant self-reference is the thing we find the most gratifying in music, not to mention in art of all kinds, and in nature, which is full of recursion.

Gödel, Escher, Bach

Like I said at the top of this post, I’m not arguing that everyone loves Mozart or music that sounds like Mozart. Musical structures of repetition and novelty don’t need to use the Western tonal system at all. You can get the same kinds of effects using other scales and tuning systems, other methods of organizing time, other conventions of tension and release. You don’t even need to use pitched sounds; plenty of world cultures create beautiful recursive structures just using drums.

Everyone’s taste in music is different. The preferred balance of repetition to novelty will vary from person to person. Little kids like a lot of repetition, while older and more sophisticated listeners might prefer more novelty. Our preferences are strongly informed by our peers, our education, our environment, and a million other intangible factors. I picked this Mozart piece because it’s familiar to me, and probably to you, and because Mozart is unusually good at teaching you the structure of his music within the music itself. But there’s plenty of other very different music out there that builds up satisfying recursive loops. If we ever discover a universal formula for human musical taste, I would bet that it’s going to be a measure of the music’s recursiveness.

One thought on “Four bars of Mozart explains everything humans like in music

  1. cool example. I was just messing around with this and thinking: I definitely prefer short, repeating patterns, not too dense with notes and other “data”, with just the right smidge of deviation.

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