Abstract
Learning and knowledge of transitional probability in sequences like music, called statistical learning and knowledge, are considered implicit processes that occur without intention to learn and awareness of what one knows. This implicit statistical knowledge can be alternatively expressed via abstract medium such as musical melody, which suggests this knowledge is reflected in melodies written by a composer. This study investigates how statistics in music vary over a composer’s lifetime. Transitional probabilities of highest-pitch sequences in Ludwig van Beethoven’s Piano Sonata were calculated based on different hierarchical Markov models. Each interval pattern was ordered based on the sonata opus number. The transitional probabilities of sequential patterns that are musical universal in music gradually decreased, suggesting that time-course variations of statistics in music reflect time-course variations of a composer’s statistical knowledge. This study sheds new light on novel methodologies that may be able to evaluate the time-course variation of composer’s implicit knowledge using musical scores.
Highlights
A multiple linear regression based on the stepwise method was carried out to predict the sonata opus numbers (i.e., Piano Sonata No.1 in F minor, Op.2-1 to No.32 in C minor, Op.111), based on the transitional probabilities of the 22 interval patterns in the first-order Markov chain
A multiple linear regression based on the stepwise method was carried out to predict the sonata opus numbers based on the transitional probabilities of the 12 interval patterns in the third-order Markov chain
A multiple linear regression based on the stepwise method was carried out to predict the sonata opus numbers based on the transitional probabilities of the three interval patterns in the fourthorder Markov chain
Summary
Implicit learning and knowledge is a ubiquitous phenomenon that occurs without the intention to learn and awareness of what we know [1,2]. In a series of psychological and neurological studies, the learning and knowledge of transitional probability in sequential information such as music and language—called statistical learning and statistical knowledge—have been considered implicit processes that could be performed domain-generally in both music and language regardless of sensory modalities. The terms implicit learning and statistical learning have been used interchangeably and are regarded as the same phenomenon [6], some researchers stated statistical knowledge and implicit knowledge may exactly not be same thing. In daily life, using the framework of statistical learning, we benefit immensely from artificial intelligence such as machine learning that gives computers learning ability similar to humans
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