Zipf-Mandelbrot Scaling in Korean Court Music: Universal Patterns in Music
Byeongchan Choi, Junwon You, Myung Ock Kim, Jae-Hun Jung

TL;DR
This study demonstrates that Zipf-Mandelbrot scaling laws, previously observed mainly in Western music, also apply to Korean court music, suggesting a universal pattern in musical structures across cultures.
Contribution
It provides the first evidence that Zipf-Mandelbrot law applies to non-Western music, specifically Korean court music, and explores how musical evolution influences these scaling laws.
Findings
Korean court music fits Zipf-Mandelbrot law well, especially for pitch-duration pairs.
Musical evolution over centuries smooths variations, reinforcing Zipfian patterns.
Joint distributions of independent Zipfian data sets also follow Zipf-Mandelbrot law.
Abstract
Zipf's law, originally discovered in natural language and later generalized to the Zipf-Mandelbrot law, describes a power-law relationship between the frequency of a Zipfian element and its rank. Due to the semantic characteristics of this law, it has also been observed in musical data. However, most such studies have focused on Western music, and its applicability to non-Western music remains not well investigated. We analyzed 43 Korean court music pieces called Jeong-ak, spanning several centuries and written in the traditional Korean musical notation Jeongganbo. These pieces were transcribed into Western staff notation, and musical data such as pitch and duration were extracted. Using pitch, duration, and their paired combinations as Zipfian units, we found that Korean music also fits the Zipf-Mandelbrot law to a high degree, particularly for the paired pitch-duration unit. Korean…
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Taxonomy
TopicsMusic and Audio Processing · Language and cultural evolution · Neuroscience and Music Perception
