Differences in regional music show up in statistical analyses via symbolic dynamics

Traditional music from different cultures seems to differ greatly in tonality, rhythm and composition. To test whether these perceived differences in musical characteristics and complexity can be quantified analytically, Basios et al. compared Western and Japanese classical pieces parameterized as a series of “ups,” “downs” and “sustains.”

“Music evokes emotions directly and is universally meaningful, across diverse cultures and epochs. Music pieces can move people independent of origin, gender and education,” said author Vasileios Basios.

Because musical text is meant to be read in one direction, it can be encoded using variables that represent sequential changes. Each note can be compared with the previous note and expressed as an “up” if the tone rises, “down” if it falls, and “sustain” if unchanged. Thus, an entire musical composition can be depicted as a series of just three descriptors.

“The alphabet of ‘ups-downs-sustains’ captures the physicality of tones and musical phrases without referring to scales, which are quite arbitrary and different between musical traditions,” Basios said.

Mapping out Beethoven’s Sonata Op. 31 No. 2 and two classical Japanese pieces, Rokudan no Shirabe, by Yatsuhashi Kengyoo, and Chidori no kyoku, by Yoshizawa Kengyoo II, the group compared the probabilities of each type of tone change and the block entropies – an analytical tool used in statistical mechanics for 1-D dynamical systems – of the two musical traditions. They found the technique can distinguish the clear auditory and tempo differences and quantify the statistical framework that otherwise hides in the background.

The researchers have additional studies underway for understanding complexity, timing, semantics and other contextual properties, and hope additional statistical and analytic tools can uncover new connections.

Source: “Symbolic dynamics of music from europe and japan,” by Vasileios Basios, Thomas Oikonomou, and Robin De Gernier, Chaos (2021). The article can be accessed at https://doi.org/10.1063/5.0048396 .