Musicologists have long studied how musical styles change over time. They can see that new styles emerge from musical traditions, sometimes by combining two or more styles.
That brings to mind the process of evolution. Is it possible that this powerful process has shaped the musical landscape using the same well-known laws of transmission that shape the biological landscape? Or is it just that musical evolution is the result of the idiosyncratic behavior of composers and so defies more general characterization?
Today we get an answer, in part thanks to the work of Eita Nakamura at Kyoto University and Kunihiko Kaneko at the University of Tokyo. They have carried out a large-scale study of Western classical music and say it reveals for the first time a number of evolutionary laws at work. Their results have implications for the understanding of other cultural phenomena, such as the evolution of language, fashion, and science.
First, some background. Evolution is an algorithmic process applied to populations of individuals. These individuals must differ in some way—in appearance or behavior, for example. They must be able to pass on specific traits to a new generation of individuals, and they must exist in an environment that selects for certain traits while culling others. Finally, there must be a process of iteration that repeats these steps many times.
The fine details of this process lead to some subtle differences in the way evolution occurs. When features are successful—like antibiotic resistance—they can spread rapidly through a population in ways that follow precise statistical patterns.
And in recent years, with the emergence of large genetic databases, statisticians have begun to study these patterns and to discover the mathematical laws of evolution that govern them.
So an interesting question is whether the same approach could work with music. Nakamura and Kaneko decided to find out by studying a database of 9,996 musical compositions by 76 composers working during the period from 1500 to 1900. Each piece consisted of a MIDI (musical instrument digital interface) file that the researchers interrogated to produce an ordered sequence of pitches and the intervals between them.
One challenge with cultural phenomena is to find units of inheritance that can be tracked. In biology, these units are genes, and the way they spread through populations has become straightforward to follow.
But in music, units that play a similar role are much harder to define. So Nakamura and Kaneko identified several rare musical events, such as the appearance of dissonant intervals called tritones, and used them as units of inheritance. They then studied how often these units occur and how they have spread over the centuries.
Tritones are defined as two notes played at the same time separated by three whole notes. They are generally thought of as dissonant and are rare in musical compositions from the 16th century. But they have become more common over time.
Musicologists have long hypothesized that to be successful, new compositions must be both novel and linked with existing musical tradition. So they must contain novel or rare musical events along with typical ones.
In this way, rare musical events can spread. And that is exactly what has happened with tritones. “The mean and standard deviation of the frequency (probability) of tritones steadily increased during the years 1500–1900,” say Nakamura and Kaneko.
But an important question is whether this spread is the result of a general mechanism of transmission or the idiosyncratic behavior of individual composers.
To find out, Nakamura and Kaneko developed a mathematical model of evolution that can distinguish between these circumstances. And they say the way this frequency has increased follows precise statistical rules, called a beta-like distribution, that governs transmission.
That’s interesting work that has important implications for our understanding of the way music evolves. Nakamura and Kaneko say their findings suggest that evolution occurs through the general mechanisms of transmission and selection of cultural style. “We conclude that some trends in music culture can be formulated as statistical evolutionary laws rather than by the circumstances of individual composers,” they say.
What’s more, the same approach can be used to tease apart the evolution of other cultural phenomena. “The balance between novelty and typicality can be important for other types of culture, and the present model can be useful for analyzing not only music data but also other cultural data,” say the researchers.
Various teams are already looking at the evolutionary dynamics of language, other genres of music, and even scientific topics. It’ll be interesting to see how this form of cultural evolution has influenced science and engineering and where gaps might exist for future work.
Ref: arxiv.org/abs/1809.05832 : Statistical Evolutionary Laws in Music Styles