When will we run out of music?

This week, Katie Haylor has been sounding out this musical musing from listener Dennis...

Katie - Well Dennis, this question certainly got us Naked Scientists chatting!

Eva - I just wonder if the premise is correct i.e. are there a finite number of musical notes?

Adam - There's no limit unless you put other constraints on. You could play C forever, then a D.

Phil - You could put a time limit on it - like how long would it take for us to run out of 3min pop songs or something?

Katie - And you’ve been mulling this over too. Listener Skip reckons that over a googol of tunes are possible. That’s 1 followed by 100 zeros! To add up the answer for us, here’s creative computing expert Rebecca Fiebrink from University of the Arts London.

Rebecca - Let’s start really simple – ignoring harmony and rhythm completely, sticking to the really boring melodies that can just be played on one octave of 8 white keys on a piano. Let’s also just consider melodies of 14 notes– the length of the first phrase of “twinkle, twinkle.” There are 8 to the 14th combinations of such notes – over 4 trillion possible melodies. If we play 100 notes a minute, it would take us over 1 million, 170 thousand years to play all these melodies.

Then, if we add very simple rhythm – the ability to have eighth notes, quarter notes, or half notes as durations, this balloons to over 6 trillion years.

Let’s make this just a bit more realistic – say, the ability to play up to 4 notes at a time, with 8 possible common durations between a 16th note and a whole note, and the ability to play any of the 88 notes on the piano. Even when the harmony and melody notes are restricted to have the exact same rhythm as each other, we’ll need far more than a quadrillion quadrillion quadrillion quadrillion years to play all possible 14-chord-long sequences.

You might call this an overestimate, since most of these sequences won’t sound very musical. And some are going to sound identical after we shift them up or down in key or change their tempo. But we’re ignoring so many other meaningful musical variations here – longer phrases and musical structures, more realistic rhythms, varying instrumentation or adding drums or synthesisers or studio effects… By any estimate I make, you’d have plenty of variations still left to try out by the time the universe potentially ends in 200 billion years. And at that point, whatever life forms are around will probably have very different ideas about what music is, anyway.

Katie - So Douglas Adams’ restaurant at the end of the universe should have some great tunes then - excellent! Thanks Rebecca. Here’s the question we’ll be answering next time, and it’s from David...

David - Would a foetus develop differently in zero gravity conditions?