Can Music Ever Run Out of New Melodies?
What are young people listening to these days? That question popped into my mind recently when I realized that our two teenagers love and listen mostly to music that was popular when I was their age. That was a surprise, as younger generations used to “revolt” against their parents by completely refusing the popular music their elders grew up with. So what happened?
In this post, I don’t want to criticize recent popular genres, nor do I want to complain about music industry greed. I also won’t dive deep into the cultural shifts causing audiences to stop looking for fresh solutions.
Instead, I want to look at the numbers. I decided to tackle a straightforward mathematical question: Is it possible to run out of melodies? Simply put, can we exhaust music if measured purely by quantity? As I am surely no mathematician, I decided to ask and use Artificial Intelligence. Isn’t this exactly the kind of heavy lifting computers and software should handle?
Let’s find out!
My exploration started with a simple prompt:
“How many new (unique) music melodies can really be produced? This is a mathematical question. If we have a diatonic system with 12 tones, some 30 typical key signatures, 8 or 16-bar format, 5 typical note lengths (16th, 8th, 1/4, 1/2, 1), pauses, accents, repetitions, harmony… are all variables to be considered – for simplicity. Just when looking at this, I am sure the final number will be huge. But still – is it possible that music will exhaust all new possibilities? Or have we already, as current music seems to be stagnating and younger listeners are re-discovering popular music from 40–60 years ago?”
And, as we’ve come to expect from AI, the answer came promptly and reassuringly:
“The quick answer is: mathematically, no—we will never run out. The number of possible melodies is effectively infinite for human purposes.”
That’s it! We are fine!
Or are we?
Obviously, it is never that simple. And, as almost always happens with AI, there was a crucial catch:
“However, your observation about modern music feeling stagnant and listeners retreating to hits from 40–60 years ago touches on a profound distinction: the difference between combinatorial possibilities and perceptual/cultural resonance.”
So I had to start digging deeper. If the following numbers and conclusions sound suspicious or debatable to you, please don’t blame me – it is all the AI! Remember, mathematics is certainly not my forte. But here is what I found.
The Math: An Astronomical Playground
Even under severe constraints, the math explodes exponentially. Let’s look at a heavily simplified example:
- Imagine a brief, single-line 8-bar melody in $4/4$ time, giving us 32 total quarter-note beats.
- Assume each beat can contain one of 12 chromatic tones or a rest, giving us 13 choices per beat.
- Ignore pitch range, octaves, rhythm subdivisions, accents, dynamics, and harmony for a moment.
Just assigning pitch to those 32 rhythmic slots yields:
13³² ≈ 1.26 × 10³⁵ possibilities
That is 126 decillion melodies!
To put it into perspective: if every human on Earth composed 10,000 new 8-bar melodies every single day, it would take humanity roughly 43 × 10²⁰ years to exhaust just that basic 8-bar pitch grid.
When you re-introduce rhythm (eighth and sixteenth notes, dotted rhythms, triplets), performance nuances (accents, articulations, swing), phrasing, and harmonic context, the combinatorial space expands far beyond the number of atoms in the observable universe (10⁸⁰). If you wonder what is the name of such a large number – it is officially named unoctogintillion and corresponds to one followed by 80 zeros, formally classified in extended naming schemes like the standard Conway-Wechsler system. It is famously referenced in astrophysics as the estimated total number of fundamental particles (protons) in the observable universe (known as the Eddington number).
The Human Filter: Why Infinity Doesn’t Equal Art
So, if the math guarantees an endless well, why do we feel like we are running dry?
While mathematics allows for wild pitch jumps and erratic, chaotic rhythms, the human brain only accepts a tiny fraction of those combinations as an actual “melody.” We have physical and psychological filters:
- Conjunct Motion: We need step-wise, flowing movement rather than jarring leaps.
- Symmetry and Resolution: We rely on predictable phrasing, repetition, and a sense of emotional tension and release.
- The Breath Limit: We are physically bound by the human vocal range and the limits of the human breath.
When you apply these biological filters, they shrink the practical pool of pleasant melodies down by over 99.999%.
Music, Math and Lawsuits
Now look at this from a different perspective, and add a legal view. The tension between finite melodic mathematics and intellectual property law has produced some of the most fascinating experiments and contentious legal battles in modern music history. Because copyright law treats melodies as unique “property,” a finite mathematical space inevitably leads to conflict.
In 2020 Damien Riehl and Noah Rubin put together the All the Music Project. Their goal was to protect musicians from “subconscious copying” lawsuits by proving that short melodies are statistically inevitable. They wrote an algorithm that systematically generated every possible 8-note, 12-beat melody within an octave. The system generated 68 billion melodies (and later expanded the search parameters up to 471 billion pitch variations). They output every sequence as MIDI data, saved them to a physical hard drive (satisfying the legal requirement of “fixation”), and released them all into the Public Domain under a Creative Commons Zero (CC0) license. Under copyright law, if an expression is already in the public domain, future authors theoretically cannot claim exclusive ownership over that exact note sequence.
The mathematical reality of finite melodies became a crisis in the courts because copyright law traditionally uses two criteria: Substantial Similarity and Access. If a melody sounds similar and you could have heard it, you can be found guilty of infringement – even if you created it independently without realizing it.
I don’t want to get here into various subsequent lawsuites like Williams v. Gaye (2015), or Gray v. Perry (2019 – 2022). What is important from today’s perspective is, that ultimately the judge ruled that the 8-note pitch sequence was merely a basic “building block” of music – a fundamental unit of the finite musical scale that cannot be monopolized by any single artist.
While Damien Riehl’s project is a brilliant conceptual point, legal scholars point out two major hurdles in court:
1. The Human Authorship Requirement: The US Copyright Office explicitly rulse that purely computer-generated works without human creative intervention cannot be copyrighted. While Riehl put the files in the public domain, courts may rule that automated data dumps do not constitute prior artistic creation in a way that invalidates human originality.
2. Context and Expression: Courst evaluate songs based on how a “lay listener” lerceive the full piece – including rhythm, timbre, lyrics, and harmonic context – not just raw MIDI pitch grids in a vacuum.
Projcets like All the Music highlight that when law treats basic 8-note building blocks as private property, it treats pure mathematical probability as theft.
Looking Beyond the Grid
We will never truly run out of melodies. The mathematical universe of music is so vast that every possible combination of notes could be written a trillion times over, and we would still only scratch the surface.
If contemporary music feels repetitive or uninspired, the problem isn’t a lack of raw numbers. The exhaustion isn’t in the math – it is in our habits, our production shortcuts, and our surrender to algorithmic loops that prioritize quick attention spans over deep musical narrative.
True novelty doesn’t come from discovering an untouched mathematical sequence hidden in a computer grid. It comes from breathing human life, organic phrasing, and real emotional intent into simple, timeless shapes – the kind of melodies that stay with us for decades.
