THE Stones or the Beatles? That, as any baby-boomer knows, is the most important question in music. But for American boomers it raises a second question. Were those two bands really responsible for the revolution of 1963 and 1964, which those west of the Atlantic call the British Invasion, and those to its east just think of as the beginning of modern popular music?

Matthias Mauch of Queen Mary, a part of the University of London, and Armand Leroi of Imperial College decided to attack this second question and other, similar ones, in a scientific manner. As they report this week in Royal Society Open Science, they took their data from the Billboard Hot 100, the standard music-industry chart for singles in America. They used Last.fm, a music-streaming service, to collect 30-second clips from 17,094 songs (86% of the total) that were in this chart between 1960 and 2010. Then they attacked each clip with sonic analysis and statistics.

They found that they could extract what they describe as “topics” from the music. These were coherent harmonic and timbral themes which were either present in or absent from a clip. Harmonic topics, of which there were eight, captured classes of chord change, or their absence (eg, “dominant 7th-chord changes” and “major chords without changes”). Timbral topics, of which there were also eight, were things like “drums, aggressive, percussive” and “female voice, melodic, vocal”.

As might be expected, different genres (as defined by the way tracks were tagged by users of Last.fm) were over-represented in certain topics. Songs tagged “jazz” or “blues”, for example, had a high frequency of topic H1 (that pertaining to dominant 7ths). H3 (involving minor 7ths) is most common in funk, disco and soul. T3, a timbre topic described as “energetic, speech, bright” is found especially in hip-hop.

As might also be expected, the rise and fall in frequency of these topics tracked the rise and fall of genres. But Dr Mauch and Dr Leroi thought they could do better than just following human-assigned genres. By applying a statistical technique called principal-component analysis to the distribution of topics, they were able to divide modern, popular music into 13 genre-straddling “styles” (one, for example, draws from “rock”, “classic rock”, “pop” and “new wave” while another draws from “rock”, “hard rock”, “alternative” and “classic rock”). They could then follow the waxing and waning of these styles over the years.

Further statistical processing, which looked at how the mix of styles in a given quarter differed from those in previous and future quarters, revealed when that mix was shifting rapidly and when it was stuck in a rut.

As the chart shows, there were three periods of rapid change. The first is from 1963 to 1964—the period of the British Invasion. Though this appears to be the smallest, that is probably an illusion caused by there being few previous quarters to compare it with. The second is in the early 1980s. The third is around 1991. These revolutions do all correspond with times musical critics would have said change was happening (classic rock, new wave, and hip-hop respectively), but this analysis suggests other apparent novelties, such as the punk of the 1970s, were not the revolutions that their fans might like to believe. The principal-components technique can also answer the question of whether, and to what extent, British bands drove the revolution of the early 1960s. Dr Mauch and Dr Leroi looked at the styles of Hot 100 songs by the Beatles and the Rolling Stones, who between them made 66 appearances in that chart before 1968. Their conclusion, paraphrased, is that although the British did not start the revolution, they were perhaps its Bolsheviks—pushing it to a conclusion it would otherwise not have reached. Signs of change are perceptible before the Beatles and the Stones arrive on the scene. But when they do arrive, they bring with them styles characteristic of the subsequent era: styles that other bands took time to adopt. Dr Mauch and Dr Leroi seem, then, to have devised a useful way of analysing cultural evolution. They are now applying it to popular music back to 1940, and to folk music, and it is possible to imagine it being applied to non-musical fields, too, if ways of quantifying elements of those fields (the cut of clothes, for example) can be devised.

Of course, their method is not all-powerful. It cannot, for example, answer the question posed at the beginning of this article. Luckily, science is not needed for that one. It’s obviously the Stones.