What makes music sound "good?"*

Let's turn randomness into music.

We begin with random notes, three at a time at a constant rhythm. I've added some random dynamic variation to ease the monotony. Now constrain the notes of each chord to move by short distances to the next. This music exhibits efficient voice leading. Alternatively, we can require that all our chords belong to the same type. Here I've used the stack of fourths, which music theorists would call an "027 chord." This music exhibits harmonic consistency but not efficient voice leading. Now combine efficient voice leading and harmonic consistency. It already sounds much more musical. I change chords during the excerpt: major triads enter at about 9", we return to fourths at 12", we get more crunchy chords (014s, or C-Db-E) at 15", and then we end by returning to fourths.

Macroharmonic Consistency

When listening to music, however, we are not just listening to a series of disconnected instants. Instead, the way things sound depends on the notes we have heard. In other words, we integrate over time. One of the most important functions of a musical scale is to limit the overall pitch content of what we're hearing over short spans of time, ensuring what I call macroharmonic consistency. Consonant scales produce more consonant macroharmony, while dissonant scales produce dissonant macroharmony.

I find it remarkable how musical the final result sounds. Using just a few simple constraints, we've turned randomness into something recognizably musical. It wouldn't win any composition prizes, but it is satisfying (and indeed, "tonal") in some elemental way. This table illustrates the relative contributions of efficient voice leading, harmonic consistency, and macroharmony.

Voice Leading, Harmonic Consistency, and Macroharmony

Scale Random notes Efficient voice leading only Harmonic consistency only Efficient voice leading and harmonic consistency Chromatic (very dissonant macroharmony) A1 A2 A3 A4 Octatonic (moderately dissonant macroharmony) B1 B2 B3 B4 Acoustic (moderately consonant macroharmony) C1 C2 C3 C4 Diatonic (very consonant macroharmony) D1 D2 D3 D4

In the classical period, chords were also constrained to move in certain specific ways. Here are two examples of random progressions generated using a second-order Markov model whose transition frequencies come from an analysis of all of Mozart's piano sonatas. These samples have something of an "uncanny valley" effect: as the chords get more human-sounding, the disconnect between pitch and rhythm becomes more irritating; it is as if the music has become too close for comfort to being human, without being human enough.

Click here to compare tonal and twelve-tone strategies of musical organization.

Towards Composition

Here are two examples that show how these ideas could be used in a composition. Both add some fancy timbre and rhythm, but are essentially still random.

Repeated, echoing chords. A more complex gestural texture. The piece begins in G melodic minor, with E as the primary pitch. It moves to a more chromatic sound-world, before returning to G melodic minor, with D as the primary pitch.

*That is, "good" to typical Western listeners.