German composer Baroque Johann Sebastian Bach has produced so scrupulously structured music that it is often compared to mathematics. Although few of us are emotionally affected by mathematics, Bach's works – and music in general – soft. It's more than sound; It's a message. And now, thanks to the tools of information theory, researchers are starting to understand how Bach's music transmits this message.
By representing scores as simple points networks, called nodes, connected by lines, called edges, scientists have quantified the information conveyed by hundreds of Bach compositions. An analysis of these musical networks Posted on February 2 Physical examination revealed that the numerous musical styles of Bach, such as choirs and toccatas, differ considerably in the amount of information they communicated – and that musical networks contained structures which could facilitate the understanding of their messages for human listeners.
“I have just found the really cool idea,” said physicist Suman Kulkarni from the University of Pennsylvania, principal author of the new study. “We have used physics tools without making hypotheses on musical pieces, simply starting with this simple representation and seeing what this can tell us about the information that is transmitted.”
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The researchers quantified the content of the information of everything, from simple sequences to tangled networks using information entropy, a concept introduced by the mathematician Claude Shannon in 1948.
As its name suggests, information entropy is mathematical and conceptually linked to thermodynamic entropy. It can be considered as a measure of the surprising of a message – where a “message” can be everything that transmits information, from a number sequence to a piece of music. This perspective may feel counter-intuitive, since, among information, information is often assimilated to certainty. But the key key to information entropy is that learning something you already know is not at all learned.
A conversation with a person who can say only one thing, like the character Hodor in the television series Game of Thrones,, Who only says “Hodor” would be predictable but non -informative. A conversation with Pikachu would be a little better; The Pokémon cannot say that the syllables in its name, but it can reorganize them, unlike Hodor. Likewise, a musical piece with a single note would be relatively easy for the brain to “learn” or reproduce with precision as a mental model, but the piece would find it difficult to convey any message. Looking at a coin with a double head piece would not provide any information.
Of course, the packaging of a message full of information is not very well so no matter – or anyone – recovers that it cannot precisely understand this information. And with regard to musical messages, researchers always determine how we learn what music is trying to tell us.
“There are a few different theories,” said cognitive scientist Marcus Pearce of Queen Mary University of London, who was not involved in the recent Physical examination study. “The main thing, I think, for the moment, is based on probabilistic learning.”
In this context, “learning” means constituting precise mental representations of the real sounds that we hear – what researchers call a model – through an interaction of anticipation and surprise. Our mental models predict to what extent it is likely that a given sound will then come, depending on what preceded. Then Pearce says: “You find out if the prediction was good or bad, then you can update your model accordingly.”
Kulkarni and his colleagues are physicists, not musicians. They wanted to use the tools of information theory to browse music for information structures that may have something to do with the way humans gleaned the sense of melody.
Kulkarni therefore summarized 337 Bach compositions in canvases of interconnected nodes and calculated the entropy of information from the resulting networks. In these networks, each note of the original score is a node, and each transition between the notes is an edge. For example, if a piece included a note followed by a C and a G played together, the node representing E would be connected to the nodes representing C and G.
Networks of transitions of notes in the music of Bach have packed more information punch than the networks generated randomly of the same size – the result of a greater variation of nodal degrees of the networks, or the number of edges connected to each node. In addition, scientists have revealed a variation in the information structure and the content of the many styles of composition of Bach. The choirs, a type of hymn intended to be sung, gave networks which were relatively sparse in information, although even richer in information than the networks generated randomly of the same size. Toccatas and preludes, musical styles which are often written for keyboard instruments such as organ, harpsichord and piano, had higher information entropy.
“I was particularly excited by higher surprise levels in the Toccatas than in choral work,” explains the co-author and physicist for the Dani Bassett study of the University of Pennsylvania. “These two types of parts feel different in my bones, and I was interested in seeing that the distinction is manifested in composition information.”
Network structures in Bach compositions could also allow human listeners to learn these networks with precision. Humans do not learn the networks perfectly. We have biases, says Bassett. “In a way, we do not know some of the local information in favor of seeing the largest information image throughout the system,” they add. By modeling this bias in the way we build our mental models of complex networks, the researchers compared the total information of each musical network to the amount of information that a human listener would glean.
Musical networks contained clusters of transitions of notes that could help our biased brain to “learn” music – to accurately reproduce the music information structure as a mental model – without sacrificing a lot of information.
“The particular type of which they capture learning is quite interesting,” explains Peter Harrison of the University of Cambridge, who was not involved in the study. “It is very reductive in a certain sense. But it is quite complementary to the other theories that we have there, and learning is a rather difficult thing to master.”
This type of network analysis is not special for Bach – it could work for any composer. Pearce says it would be interesting to use the approach to compare different composers or look for informational trends through the history of music. For his part, Kulkarni is delighted to analyze the informational properties of scores beyond the Western musical tradition.
Music is not only a sequence of notes, however, notes Harrison. The rhythm, the volume, the stamp of the instruments – these elements and more are important dimensions of musical messages which have not been taken into account in this study. Kulkarni says that she would be interested in including these aspects of music in her networks. The process could also work in the other direction, adds Harrison: rather than boiling musical features to a network, it is curious to know how the functionalities of the network are translated into things that a musician would recognize.
“A musician would say:” What are the real musical rules, or the musical characteristics, which lead this? Can I hear this on a piano? “” Said Harrison.
Finally, it is not yet clear how, exactly, the network models identified in the new study result in the lived experience of listening to a Bach piece – or any music, says Pearce. Settling who will be a question for musical psychology, he continues. Experiences could reveal “If, in fact, this kind of thing is perceptible by people, then what effects they have on the pleasure that people have when they listen to music.” Likewise, Harrison says that he would be interested in test experiences if the types of learning errors of the network modeled by researchers in this study are in fact important for the way people learn music.
“The fact that humans have this kind of imperfect and biased perception of complex information systems is essential to understand how we are committed to music,” explains Bassett. “Understanding the information complexity of Bach's compositions opens up new questions concerning the cognitive processes that underlie the way in which we each appreciate different kinds of music.”
