We hear a few notes — and almost at once we begin to guess what comes next.
That is how perception works: the brain looks for patterns, remembers repetitions and continuously predicts what will happen the next moment. Music plays a subtle game with us — first it creates an expectation, then it confirms or breaks it.
But why do Mozart's works, familiar to humanity for more than two centuries, still retain a feeling of freshness? Why does the melody seem clear and natural — and at the same time constantly elude complete prediction?
An unexpected answer was proposed by the 18-year-old American researcher Linus Chen-Plotkin. He decided to examine Mozart's music not only as a historian or a performer, but also as a mathematician — and he discovered a feature that can be described almost paradoxically:
Mozart's music possesses a shorter statistical memory.
605 works and one question
29 September 2025 Linus Chen-Plotkin, Suman S. Kulkarni and Dani S. Bassett published a preprint of the study Predictability and Statistical Memory in Classical Sonatas and Quartets — “Predictability and Statistical Memory in Classical Sonatas and Quartets.”
The work received wide attention almost a year later — after the publication of a lengthy piece in The Guardian 16 September 2026.
The authors analysed 605 MIDI files of fragments of piano sonatas and string quartets by four composers:
- Wolfgang Amadeus Mozart;
- Joseph Haydn;
- Ludwig van Beethoven;
- Franz Schubert.
The researchers isolated the upper melodic voice and studied the note sequences using three mathematical approaches: Markov models of various orders, time-delayed mutual information, and analysis of distributed dependencies.
Behind the complex names lay a simple question:
how far into the past of a melody must one look in order to predict the next note?
What Is the Memory of Music?
Let us imagine a simple melody in which, after a certain sequence, almost always the same note appears.
The more often this pattern repeats, the easier it is for the listener — or for a mathematical model — to predict what comes next. Past events seem to be preserved within the musical phrase and to determine its further movement.
If a single preceding note is enough for an accurate prediction, we are dealing with a short dependency. If five, seven or ten past notes must be taken into account, then the music possesses a longer statistical memory.
This is not memory in the human sense, nor a characteristic of the composer himself. What is meant is a mathematically measurable dependency between successive musical events.
In Haydn, Beethoven and Schubert, models that took into account a longer history of the melody usually predicted the subsequent notes better.
With Mozart, something unusual happened.
Adding an ever longer context did not give the models the same advantage. His melodies depended less on extended sequences of the past and more often changed direction before the pattern became fully obvious.
In other words, Mozart's music seems to say:
“You have already understood where I am going? Then listen more closely.”
An Order That Does Not Become a Cage
Mozart's music is by no means chaotic. On the contrary, it is known for the clarity of its form, its balance and an almost architectural precision.
But it is precisely within this transparent structure that constant movement arises.
The melody manages to create a sense of regularity, yet does not allow it to harden. It offers the ear a support — and then gently alters its trajectory. The unexpected appears not as a sharp rupture, but as a natural continuation that a moment ago could not have been predicted.
Perhaps that is why Mozart's music seems at once comprehensible and inexhaustible.
If a work is entirely predictable, attention gradually weakens. If it is completely unpredictable, the listener may lose connection with what is happening. Mozart maintains a rare balance between recognition and discovery.
We manage to enter the musical pattern, but we do not manage to turn it into a habit.
The Brain as a Prediction Machine
Modern studies of perception regard the brain not as a passive receiver of sounds, but as a system continuously constructing predictions.
While listening, we unconsciously assess:
- whether the melody will continue upward or downward;
- when the phrase will end;
- which chord will follow next;
- whether a familiar rhythm will repeat;
- whether a resolution of tension will come.
When an expectation is confirmed, we feel coherence and order. When the music deviates slightly from the prediction, attention is renewed. And when the unexpected nevertheless turns out to be meaningful within the whole, the pleasure of discovery can arise.
The new study did not directly measure the brain activity of listeners and did not prove that short statistical memory by itself causes aesthetic enjoyment. But it does reveal a measurable feature of the musical material that is potentially capable of sustaining this play of expectations.
Mozart does not simply announce the next note.
He compels consciousness to remain in the present.
Mathematics Does Not Explain Genius Entirely
Headlines about the “solved mystery of Mozart” sound striking, but they call for caution.
The work is currently a preprint and has not undergone full journal peer review. The researchers analysed not all of the composers' works, but a specific set of sonatas and quartets presented in MIDI format.
Moreover, the model worked primarily with the sequence of the upper notes. It did not encompass the full richness of the music:
- harmony;
- inner polyphony;
- rhythmic organization;
- dynamics;
- articulation;
- timbre;
- large-scale forms;
- performing interpretation.
Statistical unexpectedness is likewise not equal to artistic value. An unpredictable sequence can be produced by chance, but it will not thereby become Mozart's music.
Therefore the study does not reveal the single formula of his genius. It discovers one important facet: a particular way of organizing melodic time.
It is precisely in this that the work is valuable. It does not replace musicology with mathematics, but adds to auditory perception yet another instrument of observation.
Can an algorithm write a new Mozart?
Linus Chen-Plotkin himself stresses that his aim is not to turn the discovered regularities into a machine for producing a “new Mozart.”
A mathematical model is capable of determining the statistical properties of a work, but it does not live through the cultural context, the intention, the risk and the inner necessity of a creative choice.
One can reproduce the frequency of unexpected transitions. One can create a melody with a similar length of statistical memory. But that still does not mean that music capable of surviving centuries will come into being.
Because creativity is not a set of deviations from the norm. It is the ability to feel which particular deviation the whole requires at a given moment.
Mozart does not violate expectation for the sake of effect. Every surprise sounds so natural, as if it were precisely the one that had always been meant to happen.
At this point, calculation meets mystery.
Why do we return to familiar music?
Usually it seems to us that repeated listening should diminish surprise. We already know the theme, remember the turns, and anticipate the finale.
But great works are constructed more intricately.
With each return, attention chooses a different path. Yesterday we followed the melody. Today we hear an inner voice. Tomorrow we notice a pause, a transition between keys, or a barely perceptible tension before a familiar phrase.
The music remains the same, but the point from which we perceive it changes.
Perhaps the short statistical memory of Mozart's melodies intensifies this property. A musical thought does not hold the listener inside too obvious a chain. Again and again it returns attention to the present moment—to where the next note has not yet become inevitable.
And a familiar work gains the chance to sound for the first time once again.
Between regularity and miracle
The most astonishing thing in this story is that the study was conducted by a person who, at the time of the fresh publication, was only eighteen years old.
While generations of musicologists described Mozart's beauty through form, harmony, and style, the young researcher asked a different question: but can the very capacity of a melody to surprise be measured?
The answer turned out to be not a final formula, but a new door.
Mathematics saw what the ear had long felt: Mozart's music creates order, but does not allow it to become motionless. It invites us to recognize the pattern—and in that same instant reveals a new direction within it.
Perhaps that is why Mozart does not belong only to the eighteenth century. His music happens anew every time—directly between the note that has sounded and the note not yet born.
We think we already know the continuation.
And the music smiles—and chooses freedom.
