The first music composed by computer considered good enough for top-class musicians to play is to be performed to mark the 100th anniversary of Alan Turing's birthTake our own musical Turing test here

As soon as you see the title of Iamus's composition Transits – Into an Abyss, you know it's going to be challenging, modernist stuff. The strings pile up discords, first spooky, now ominous. But if your tastes run to Bartók, Ligeti and Penderecki, you may like it. At least you have to admit this bloke knows what he's doing.

But this bloke doesn't know anything at all. Iamus is a computer program. Until the London Symphony Orchestra was handed the score, no human had intervened in preparing the music.

"When we tell people that, they think it's a trick," says Francisco Vico, leader of the team at the University of Malaga who devised Iamus. "Some say they simply don't believe us. Others say it's just creepy." He expects that when Iamus's debut CD is released in September, performed by top-shelf musicians including the LSO, it is going to disturb a lot of folk.

You can get a taste of Iamus's oeuvre before then, because on 2 July some of Iamus's compositions will be performed and streamed live from Malaga. The event is being staged to mark the 100th anniversary of the birth of Alan Turing, the man credited with more or less inventing the concept of the computer. It was Turing who devised the test to distinguish human from artificial intelligence made famous by the opening sequence of Blade Runner. The performance will itself be a kind of Turing test: you can judge for yourself by taking our own musical Turing test here.

Iamus – named after the son of Apollo who could understand the language of birds – composes by mutating simple starting material in a manner analogous to biological evolution. The compositions each have a musical core, a "genome", that gradually becomes more complex.

"Iamus generates an initial population of compositions automatically," Vico says, "but their genomes are so simple that they barely develop into a handful of notes, lasting just a few seconds. As evolution proceeds, mutations alter the content and size of this primordial genetic material, and we get longer and more elaborated pieces." All the researchers specify at the outset is the rough length of the piece and the instruments it will use.

"A single genome can encode many melodies," explains composer Gustavo Díaz-Jerez of Musikene, the Higher School of Music of the Basque Country in San Sebastian, who has collaborated with the Malaga team since the outset and is the pianist on the new recordings. "You find this same idea of a genome in the western musical canon – that's why the music makes sense."

The computer doesn't impose any particular aesthetic. Although most of its serious pieces are in a modern classical style, it can compose in other genres too, and for any set of instruments. The Darwinian composition process also lends itself to producing variations of well-known pieces or merging two or more existing compositions to produce offspring – musical sex, you might say.

Using computers and algorithms – automated systems of rules – to make music has a long history. The Greek composer Iannis Xenakis did it in the 1960s, and in the following decade two Swedish researchers devised an algorithm for creating nursery-rhyme melodies in the style of the Swedish composer Alice Tegnér. In the 1980s, the computer scientist Kemal Ebcioglu created a program that harmonised chorales in the style of Bach.

As artificial intelligence and machine learning became more sophisticated, so did the possibilities for machine music: now computers could infer rules and guidelines from real musical examples, rather than being fed them to begin with. The computer scientist John "Al" Biles devised an algorithm called GenJam that learns to improvise jazz. A trumpeter , Biles performs alongside GenJam under the name the Al Biles Virtual Quintet, but admits the algorithm is a rather indifferent player. The same is true of GenBebop, devised by the cognitive scientists Lee Spector and Adam Alpern, which improvises solos in the style of Charlie Parker by "listening" to him and iterating its own efforts under the ultimately less-than-discerning ear of an automated internal critic.

One of the most persuasive systems was the Continuator, devised by François Pachet at Sony's Computer Science Laboratory in Paris. In a Turing test where the Continuator traded licks with an improvising human pianist, expert listeners were mostly unable to guess which was playing.

But these efforts still haven't shown that a computer can make tolerable music from scratch. One of the best known attempts is Emily Howell, a program created by the music professor David Cope. Yet Howell's bland, arpeggiated compositions sound like a technically skilled child trying to ape Beethoven or Bach, or like Michael Nyman on a bad day: fine for elevators but not for the concert hall.

Iamus is different. This seems to be the first time music composed by computer has been deemed good enough for top-class performers to play. Díaz-Jerez says the LSO were "a little bit sceptical at the beginning, but were very surprised" by the quality of what they were being asked to play. The soprano Celia Alcedo, he says, "couldn't believe the expressiveness of some of the lines" she was given to sing.

"I felt it was like a wall of sound," says Lennox Mackenzie, the LSO's chairman. "If you put a colour to it, this music was grey. It went nowhere. It was too dense and massive, no instrument stuck out at any point. But at the end of it, I thought it was quite epic."

"The other thing that struck me," Mackenzie adds, "was that it was festooned with expression marks, which just seemed arbitrary and meaningless. My normal inclination is to delve into music and find out what it's all about. But here I don't think I'd find anything." But he's far from discouraging. "I didn't feel antipathy towards it. It does have something. They should keep trying, I'd say."

What is disconcerting is that Iamus can produce this stuff endlessly: thousands of pieces, fully notated and ready to play, and "many of them great", according to Díaz-Jerez. Such profligacy feels improper: if it's that easy, can the music really be any good? Díaz-Jerez thinks the pieces are often better than those produced by some avant-garde composers, which revel in their own internal logic but are virtually impossible to play. Crucially, people have different favourites – it's not as if the program occasionally gets lucky and turns out something good.

How does a performer interpret these pieces, given that there's no "intention" of the composer to look for? "Suppose I found a score in a library without knowing who wrote it," says Díaz-Jerez. "I approach these pieces as I would that one – by analysing the score to see how it works." In that respect, he sees no difference from deducing the structure of a Bach fugue.

You can compare it with computer chess, says the philosopher of music Stephen Davies, of the University of Auckland in New Zealand. "People said computers wouldn't be able to show the same original thinking, as opposed to crunching random calculations. But now it's hard to see the difference between people and computers with respect to creativity in chess. Music, too, is rule-governed in a way that should make it easily simulated."