Tonality Tunes the Statistical Characteristics in Music: Computational Approaches on Statistical Learning.

Tatsuya Daikoku

doi:10.3389/fncom.2019.00070

Abstract

Statistical learning is a learning mechanism based on transition probability in sequences such as music and language. Recent computational and neurophysiological studies suggest that the statistical learning contributes to production, action, and musical creativity as well as prediction and perception. The present study investigated how statistical structure interacts with tonalities in music based on various-order statistical models. To verify this in all 24 major and minor keys, the transition probabilities of the sequences containing the highest pitches in Bach's Well-Tempered Clavier, which is a collection of two series (No. 1 and No. 2) of preludes and fugues in all of the 24 major and minor keys, were calculated based on nth-order Markov models. The transition probabilities of each sequence were compared among tonalities (major and minor), two series (No. 1 and No. 2), and music types (prelude and fugue). The differences in statistical characteristics between major and minor keys were detected in lower- but not higher-order models. The results also showed that statistical knowledge in music might be modulated by tonalities and composition periods. Furthermore, the principal component analysis detected the shared components of related keys, suggesting that the tonalities modulate statistical characteristics in music. The present study may suggest that there are at least two types of statistical knowledge in music that are interdependent on and independent of tonality, respectively.

Highlights

Prediction and Production in the Statistical LearningThe brain is innately equipped with statistical learning (SL) machineries that model external phenomena as a dynamical system that encode the probability distributions
Statistical knowledge formed in cerebral cortex may be sent to the cerebellum that is thought to play important roles in prediction of sequences (Lesage et al, 2012; Moberget et al, 2014), motor skill learning (Ito, 2008), habit learning (Friston et al, 2016), generalization or abstraction based on transitional probabilities (Shimizu et al, 2017), efficient performance in a learned context (Balsters et al, 2014)
This study aimed to examine how the statistical structure interacts with tonality

Summary

Introduction

Prediction and Production in the Statistical LearningThe brain is innately equipped with statistical learning (SL) machineries that model external phenomena as a dynamical system that encode the probability distributions. Statistical knowledge formed in cerebral cortex may be sent to the cerebellum that is thought to play important roles in prediction of sequences (Lesage et al, 2012; Moberget et al, 2014), motor skill learning (Ito, 2008), habit learning (Friston et al, 2016), generalization or abstraction based on transitional probabilities (Shimizu et al, 2017), efficient performance in a learned context (Balsters et al, 2014) These findings may suggest that the internalized statistical model affects production of music (i.e., composition) (Daikoku, 2019a), the creativity (Wiggins, 2018), and individuality of artistic expression (Daikoku, 2018b) as well as the prediction and perception (Daikoku, 2019c). Unknown how the acquired statistical knowledge influences the production of music

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