Entropy, energy, and instability in music

Gündüz, Güngör

doi:10.1016/j.physa.2022.128365

Cited by 3 publications

(4 citation statements)

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“…Shannon Entropy is one of the concepts in information theory, which is used to measure the uncertainty and randomness of a piece of information, and has multiple meanings in physics, psychology and musicology. In cognitive psychology, the Shannon Entropy can be used to analyze the way people process information and their cognitive load in complex situations, such as information processing and decision-making behaviors; and in music, the Shannon Entropy has been used to measure the complexity of a musical piece and to differentiate between musical genres ( Febres and Jaffe, 2017 Gündüz, 2023 ).…”

Section: Methodsmentioning

confidence: 99%

“…The reason is that in piano performance, individuals are not able to unify the definition of difficulty and challenge for any type of work, so the number of notes in the piano score all over the piano becomes an objective measure of challenge, and the notes contained in the score are not subjective to the performer’s subjective influence of the challenge, so the study selects the SE as one of the measures of musical complexity. Following Gündüz (2023) , we randomly selected six musical compositions for the calculation of the SE based on the criteria of piano performance and cultural identity of the work (See formula below). Specifically, we include the notes contained in the score (except for ornamental notes that do not account for time values) in the data pool for calculation and define them as the Entropy of the piece.…”

Section: Methodsmentioning

confidence: 99%

“…Consequently, participants are encouraged to choose repertoire that not only aligns with their skill level but also presents a genuine challenge ( Kirchner, 2011 ). The Shannon Entropy algorithm emerges as a promising tool for extracting information about musical complexity and quantifying the challenge level ( Gündüz, 2023 ). This algorithm facilitates the derivation of musical information embedded in a piano performance, along with its complexity level, thereby enabling its integration into a quantitative analysis within a challenge and skill balance model.…”

Section: Introductionmentioning

confidence: 99%

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Flow and performance: a quantitative study of elicitation modeling in a piano performance perspective

Li,

Xu,

Wang

et al. 2024

Front. Psychol.

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IntroductionFlow, defined as a heightened state of consciousness characterized by intense concentration during an activity, is influenced primarily by the perceived challenge and the dynamic equilibrium of skills. This investigation focuses on the patterns of flow state attainment and its elicitation mechanisms within the context of piano performance among Chinese music college students.MethodsOur study establishes a framework for accessing flow, utilizing quantitative data from music ontology to gauge the level of challenge and the level of music acquisition to assess skills. Additionally, we integrate external factors such as music culture heterogeneity and demographic variables to elucidate the causes and moderating effects of flow on piano performance.ResultsThe findings reveal a positive correlation between flow and performance, with the model of challenge and skill induction partially explaining these results. Notably, melodic Shannon Entropy emerges as a potential indicator of challenge, suggesting its relevance in future studies on flow.DiscussionThis research provides multidimensional insights into the interplay between performance and flow in piano performance, guiding future investigations to explore the musical quantitative perspective more deeply.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Flow and performance: a quantitative study of elicitation modeling in a piano performance perspective

Li,

Xu,

Wang

et al. 2024

Front. Psychol.

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“…With the same purpose, cross-entropy (e.g., [12]) has been used to quantify stylistic similarity between two sequences [13]. An up-to-date review on entropy and other physical parameters applied to music is provided by Gündüz [14].…”

Section: Introductionmentioning

confidence: 99%

Partition Entropy as a Measure of Regularity of Music Scales

Cubarsi

2024

Mathematics

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The entropy of the partition generated by an n-tone music scale is proposed to quantify its regularity. The normalized entropy relative to a regular partition and its complementary, here referred to as the bias, allow us to analyze various conditions of similarity between an arbitrary scale and a regular scale. Interesting particular cases are scales with limited bias because their tones are distributed along specific interval fractions of a regular partition. The most typical case in music concerns partitions associated with well-formed scales generated by a single tone h. These scales are maximal even sets that combine two elementary intervals. Then, the normalized entropy depends on each number of intervals as well as their relative size. When well-formed scales are refined, several nested families stand out with increasing regularity. It is proven that a scale of minimal bias, i.e., with less bias than those with fewer tones, is always a best rational approximation of log2h.

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