Sjeltur

Maybe this question sounds absurd to you. Maybe you think there’s no limit on new musical pieces that can be created. But this can’t be true, limitations on human hearing puts constraints on the number of possible sounds we can hear. Since not all sound is music, it follows that the number of all possible musical pieces must be smaller than the number of all possible sound pieces. Today humans are still the creators of good music, their music is superior to music created by computers. Computer technology changed the way how composers create new musical pieces, but the computer is a “dumb” tool in most cases. It’s a great tool to create new sounds and to compose music with those sounds, but the creativity of the composer is still needed to produce new good music that’s perceived by listeners as such. This may change, though.

How many sounds are out there we can hear? There are limitations on human hearing, putting an upper limit on this number. To make an estimate on the number of possible sounds we can hear, let’s assume digital sound systems can produce all these sounds. This assumption is justified, digital sound systems are actually capable of producing sounds well beyond the limits of human hearing. Humans are able to hear sounds with a frequency in the range of 20 Hz to 20,000 Hz (20 kHz) and with a wide range of intensity, from barely noticeable sounds to very loud sounds that make your ears hurt. Digital systems nowadays are capable to produce sounds with high frequencies, much higher than humans can hear, and they are capable of producing sounds with very high accuracy way beyond the pain threshold of human hearing. The number of all possible sounds these digital systems can produce is larger than the number of sounds humans can hear.

Imagine a digital sound system capable of producing all possible sounds with the same limitations as human hearing. In other words, the digital sound system produces all possible sounds that humans can hear. The highest frequency that can be heard is 20 kHz and the maximum dynamical range, from barely noticeable to the pain threshold, is about 130 dB. Then the digital system would be a 22 bit/40 kHz system. Now we can calculate the number of all possible sounds a human can hear within a given time frame. Suppose we take a time frame of one second, then the number of possible sounds a human can hear is about 2 x 10^264906. This is a very, very large number: it’s a two followed by 264,906 zeros!

Perhaps surprisingly, it’s very easy to write a computer program that’s able to produce all possible sounds, the entire sound space. But although the computer gives us the exact solution of all possible sounds, it will take a very long time for a computer to complete this task, an amount of time far beyond astronomical time scales, even for short sound pieces. So this is nowhere near practical. And after the computer has finished, it will turn out that most of these sounds are not very interesting. Most of these sounds would appear as random noise, with no structure at all. The number of sounds that actually make sense is considerably smaller. The number of sounds that’s perceived as music is even smaller. On a human scale the number of possible musical pieces might be large, but compared to all possible sounds it’s probably a very small number. Musical structures seem to put tight constraints on the sound space of all possible sounds to be perceived as music by humans.

For example, we can estimate the number of all possible “melodies” that can be played within a given time frame. Known limitations of human hearing can provide an estimate on this number. Humans can distinguish about 200 notes per octave and are able to distinguish about 50 notes per second. The result will grossly overestimate the number, because “music” close to the limitations of human hearing isn’t perceived as music at all. In reality humans like music with tighter constraints on the number of available notes per octave and the maximum number of notes played per second. But this estimate provides a usable upper bound. Within the frequency range humans can hear, the number of all possible “melodies” we can play during one second is about 7 x 10^100, a seven followed by 100 zeros. Compare this number to the number of all possible sounds calculated, it’s a very small number. Because this number is grossly overestimated, the number of melodies musically meaningful to humans is a lot smaller in reality. The constraints musical structures put on the sound space are very tight.

Is it possible for a computer to calculate only that small part of the entire sound space containing musical structures? So far it turns out to be very difficult. Some progress has been made in this direction, but music created by computers is still inferior to music created by humans. On the other hand, computer technology is growing fast. With the increase of computational power it becomes possible to use new algorithms that are not just crunching numbers with exact solutions, but instead mimic processes found in nature that can approximate solutions. The solutions are new and interesting, bypassing most of the noisy solutions that make no sense. A genetic algorithm is an example of this. The algorithm starts off in a random, disordered state and produces noisy sounds with no structure. It then evolves gradually, away from the noisy solutions to solutions with structure, sounds that make sense. Eventually it moves to solutions that’s perceived as music by humans.

But we’re not there yet. These algorithms require a lot of computational power, today’s computers are just too slow. To get an idea how far scientists are with genetic algorithms and sound, here an example. It’s not producing a new sound, but the algorithm tries to copy a given, existing sound. First you hear the target sample, a sound fragment the algorithm tries to copy. The next fragment is the result after iterating the algorithm for about 800 generations, then after 6,500 generations, 10,000 generations and finally after 19,000 generations. Although not perfect, the final result is a good approximation of the original sample. These algorithms need a lot of computational power, for results only lasting seconds the processing time is many hours with computers we have today. We can improve the quality of the copy some more, even to the point they are indistinguishable, but this requires so much computational power making it impractical at the present time. And it should be noted, this is just copying an existing sound, not creating a new sound, let alone a new sound perceived as music.

But with increasing computer capabilities we should see the first practical applications of this approach not too far in the future. Now it takes hours to copy a given sound fragment that lasts only seconds, but given Moore’s Law it should be possible to do this real-time in, say, 10 or 20 years from now. After that, real-time synthesis of new sounds using these methods shouldn’t be far behind, followed by systems that can produce new sounds, as a musically meaningful structure.

If we don’t hear this, the attempt has failed. Perhaps it turns out computers are not able at all to produce music and humans remain the creative source behind all new musical pieces. Then we will not run out of music anytime soon, because the number of all possible musical pieces is still large on a human scale.

When we do hear musically meaningful structures then perhaps it turns out computers can provide structures, but only humans can put these structures together in a way that’s perceived by most people as good music, and music created by humans continues to be distinguishable from music created by computers. This scenario is likely to be favored by composers of the early 21st century. The computer becomes a great tool producing structures, a composer can edit these structures in a way contemporary composers can hardly imagine. In this scenario we will not run out of new music anytime soon either, humans are still the creative source and this puts an upper limit on the pace humans can create new musical pieces.

Or computers eventually leave human composers obsolete. Perhaps the computer provides us a map of the entire music space. Although such a map would be very interesting to explore, the consequence is that there would be not much left for human composers to create. When a human composer creates a new piece, the computer creates a whole new genre of music. Contemporary composers probably view this picture of the future as downright pessimistic. It even gets worse, perhaps the tight constraints that turn sound into music puts a limit on the number of possible musical pieces low enough for a computer to produce all these pieces within a reasonable amount of time. Then there’s nothing new left for humans to discover and humankind truly runs out of new music.

We don’t know how likely these scenarios are. We don’t know how much music is out there, perhaps the music space is large enough that even computers can’t produce all music within a reasonable time frame. A suitable model of musical structures might give us an upper and lower bound on the number of all possible music pieces one day, this would provide us more insight on this question. Given the development of computer technology, the question if computers are able to produce good music by human standards should at least partially be answered sometime this century, with a glimpse of what might be possible already in the decades to come.