Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Perspectives and Interpretations: Weighted Power Law Analyses of Three Short Works for Piano

Version 1 : Received: 24 January 2022 / Approved: 27 January 2022 / Online: 27 January 2022 (12:34:26 CET)

How to cite: Scott, D. Perspectives and Interpretations: Weighted Power Law Analyses of Three Short Works for Piano. Preprints 2022, 2022010421 (doi: 10.20944/preprints202201.0421.v1). Scott, D. Perspectives and Interpretations: Weighted Power Law Analyses of Three Short Works for Piano. Preprints 2022, 2022010421 (doi: 10.20944/preprints202201.0421.v1).

Abstract

Power law relationships, which describe scaling relationships of data, are powerful information theoretic descriptive tools in many empirical contexts, including that of music. Zipf’s law (pink noise) describes the optimum case of a power law relation where observations are exactly inversely proportional to their rank. Descriptions that approximate a pink noise signature can be said to maximize the amount of information in a signal, and is thus suggestive of a richness of an understanding. This information density of pink noise signatures is not, however, necessarily a desirable quality for explanations in general, which, by definition, “flattens out” some data while highlighting others, ideally those most relevant to an interpretation. The privileging of data most relevant to comprehension corresponds to a red noise relationship, as opposed to the pink noise of Zipf’s law or the white noise of a description that highlights nothing in particular. Here, I explore and evaluate this concept of red noise explanations in the form of analyses of three comparable short piano works: Robert Schumann’s “Von fremden Ländern und Menschen” (no.1 from Kinderszenen op. 15, 1838), Frédéric Chopin’s Prelude op. 28 no. 20 (1838-9), and Felix Mendelssohn’s “Venetianisches Gondellied” (no. 6 from Lieder ohne Worte op. 19b, 1829-30).

Keywords

Music, Power laws, Zipf’s law, Noise profiles, Timescape, Wavelet, Schumann, Chopin, Mendelssohn

Subject

ARTS & HUMANITIES, Music Studies

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