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. Preprints2022, 2022010421. https://doi.org/10.20944/preprints202201.0421.v1
Scott, D. Perspectives and Interpretations: Weighted Power Law Analyses of Three Short Works for Piano. Preprints 2022, 2022010421. https://doi.org/10.20944/preprints202201.0421.v1
Scott, D. Perspectives and Interpretations: Weighted Power Law Analyses of Three Short Works for Piano. Preprints2022, 2022010421. https://doi.org/10.20944/preprints202201.0421.v1
APA Style
Scott, D. (2022). Perspectives and Interpretations: Weighted Power Law Analyses of Three Short Works for Piano. Preprints. https://doi.org/10.20944/preprints202201.0421.v1
Chicago/Turabian Style
Scott, D. 2022 "Perspectives and Interpretations: Weighted Power Law Analyses of Three Short Works for Piano" Preprints. https://doi.org/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 and Humanities, Music
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.