Mathematicians discover music really can be infectious
Dora Rosati, lead author of the study and former graduate in maths and statistics at McMaster University in Ontario, Canada along with colleagues, wondered whether they could learn anything about how songs become popular using mathematical tools that are more usually applied to study the spread of infectious diseases.
The team turned to a database of almost 1.4bn individual song downloads from the now-discontinued music streaming service MixRadio. Focusing on the top 1,000 songs downloaded in the UK between 2007 and 2014, they measured how well a standard model of epidemic disease, called the SIR model, fitted trends in song downloads over time.
这个团队以现已停产的音乐流媒体服务MixRadio中的近 14 亿首单曲下载量作为数据库，集中研究从2007年到2014年间在英国下载的前1000首歌曲，测量了流行病的标准模型（以下简称为 SIR 模型）与歌曲下载量随时间变化趋势的拟合程度。
The research, published in Proceedings of the Royal Society A: Mathematical and Physical Sciences, found the model performed just as well when describing song download trends as it did when describing the spread of a disease through the population.
Rosati said: "It implies that a lot of the social processes that drive the spread of disease, or analogues of those processes, might also be driving the spread of songs. More specifically, it supports the idea that both music and infectious diseases depend on social connections to spread through populations."
"With a disease, if you come into contact with someone who is ill, then you have a certain chance of catching that disease. With songs, it looks very similar. The big difference is that for songs, it doesn't necessarily have to be physical contact – it could be that my friend used this cool new song in their Instagram story, so now I'm going to go and find it."
Dr Thomas Rawson, a disease modeller at Imperial College London, said: "It's something that makes complete sense, when you consider that word of mouth is something that, much like disease, it will carry on via other people. The main difference is that there are more ways for music to spread."
Although this varied substantially within genres, they found that dance and metal had the lowest median R0 scores at 2.8 and 3.7. Pop music was more transmissible, but it was vastly outstripped by genres such as rock and hip-hop, while electronica – a form of electronic music intended for listening, rather than dancing – had the highest R0, at 3430. This makes it roughly 190 times more transmissible than measles, which has an R0 of about 18.
研究者们发现不同音乐类型的R0值差异很大，舞曲和金属乐的R0中位数最低，分别为2.8 和3.7；相比之下流行乐更具传播性，不过要是拿流行乐和摇滚乐、嘻哈音乐比，那它的传播性又远远不如后两者了。而电子乐（用来听而非跳舞的电子乐形式）的 R0 最高，为3430。要知道，麻疹的R0仅为18，那也就是说，电子乐的感染力是麻疹的 190 倍！
"The reason why we might see some really sky-high R0s for songs is that you can just make a tweet and you have already infected a hundred people. You can spread a song disease far quicker than you could an infectious disease." said Rawson.
Rosati said: "Maybe what those numbers are telling us is that electronica fans tend to be more passionate about their favourite songs … Or maybe the social network of electronica fans is more strongly connected."
"The biggest changes are likely to be in these more niche genres that wouldn't necessarily have been getting the radio play. I think they have a much better chance of spreading in our current situation of streaming and social media platforms," Rosati said.
If song popularity really is driven by the same contagious processes as disease, it could open new ways of predicting how new music releases could take off, and present opportunities to boost their spread.