The Entropy of K-Pop songs

Year: 2014 Authors: Daeun Cheong; Jaewon Cheong; Mi Ju Kim; Jae Hee Park; Jeong Mi Park

Core claim

Selected K-Pop songs show lower informational uncertainty than selected American Pop songs by entropy measures, except for phrase entropy.

Topics

music entropy, K-Pop analysis, comparative pop music

Domains

information theory, Shannon entropy, probability, music, popular culture

Methods

sample probability, song selection, entropy calculation, comparative analysis

Media

K-Pop songs, American Pop songs, chords, tones, rhythms

Paper text

The text below is the locally extracted OCR/Markdown version of the paper. Raw PDF files remain local and are not published here.

Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture

The Entropy of K-Pop songs

Daeun Cheong¹, Jaewon Cheong², Mi Ju Kim², Jae Hee Park³, Jeong Mi Park⁴ 1, Jinsun Girl’s High School, 27, Seolleung-ro 85-gil, Gangnam-gu, Seoul, 135919, South Korea 2, Hana Academy Seoul, 535 Yeonseo-Ro, Eunpyeong-Gu, Seoul, 122200, South Korea 3, Gyeonggi Science High School for the Gifted, 135, Suil-ro, Jangan-gu, Suwon-si, Gyeonggi-do, 440800, South Korea 4, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151742, South Korea E-mail: daeun_26@naver.com, jaewon28@naver.com, logicalmjk@hana.hs.kr, udmji@snu.ac.kr, mensa92@hanmail.net

Abstract

We compared the entropy of K-Pop songs with the entropy of American Pop songs. The results show that K-Pop songs tend to have lower entropy in respect of chords, tones, and rhythms, but have higher entropy in phrase. This implies that the uncertainty of K-Pop song is lower than that of American Pop songs.

Introduction

Korean popular music (K-Pop) has gained popularity in the world market in recent years. We tried to find the differences between K-Pop songs and American Pop songs in respect of informational theory. Shannon and Weaver systematized the information theory and defined the entropy as the quantity of information implicit in signals or events [1]. Let X be a discrete random variable $\{x_1,x_2,\dots ,x_n\}$, then the entropy of X, $H(X)$ is defined as follows:

where $p(x_i)$ is the probability of $X$ being $x_i$.

In informational theory, entropy implies the amount of information included in signals or events, which measure the uncertainty of a random variable. Pinkerton used the entropy to measure the uncertainty of tones of some children’s songs [2] and Youngblood compared the entropy of tones in different genres of music [3]. The uncertainty of music comes not only from the distribution of tones, but also from the distribution of various factors such as chords, rhythms, phrase, and so on. In this research, we measured the entropy of 5 K-Pop songs and 5 American Pop songs based on the distribution of chords, phrase, tones, and rhythms.

Methods and Results

Most of the popular K-Pop songs are dance music and are written in minor keys, so we selected only dance music written in minor keys among the most popular songs released from 2007 to 2013 for fair analysis. We first shift all songs to C minor and calculated the entropy based on chords per 2 beats, frequency of tones, phrase of chords per 16 beats, and patterns of rhythm per 4 beats. In practice, to determine the probability we use the sample probability with each song, for example, for the probability

Cheong et al.

of a C chord in a given song, we used the fraction of all chords per two beats of all chords in that song which are C chords per two beats. The title, singer and year released of each song and entropy based on each factor are shown in the table 1. A Similar approach can be found in [4], though the factors and coding scheme are different from ours.

Table 1: The Entropy based on each factor

Conclusions

It turned out that by this method of analysis, in the songs we selected, K-Pop songs tend to have lower entropy. We expect that the higher the entropy, the more uncertainty and complexity is typically present. The results suggest that the uncertainty of K-Pop songs is lower than that of American Pop songs in respect of chords, tones, and rhythms, but not phrases. However this analysis of limited data does not show if these differences are statistically significant in general. Future work may explore these questions in more detail.

References

[1] Shannon, C. E., & Weaver, W. (1949). The Mathematical Theory of Communication. University of Illinois Press. [2] Pinkerton, R. C. (1956). Information theory and melody. Scientific American, 195(2), 77-86. [3] Youngblood, J. E. (1958). Style as information. Journal of Music Theory, 2(1), 24-35.4 [4] Alexander, P. J. (1996). Entropy and popular culture: product diversity in the popular music recording industry. American Sociological Review, 61(1), 171-174.