The Impact of the Complexity of Harmony on the Acceptability of Music

Abstract

In this article, we contribute to the longstanding challenge of how to explain the listener’s acceptability for a particular piece of music, using harmony as one of the crucial dimensions in music, one of the least examined in this context. We propose three measures for the complexity of harmony: (i) the complexity based on usage of the basic tonal functions and parallels in the harmonic progression, (ii) the entropies of unigrams and bigrams in the sequence of chords, and (iii) the regularity of the harmonic progression. Additionally, we propose four measures for the acceptability of musical pieces (perceptual variables): difficulty, pleasantness, recognition, and repeatability. These measures have been evaluated in each musical example within our dataset, consisting of 160 carefully selected musical excerpts from different musical styles. The first and the third complexity measures and the musical style of excerpts were determined by the first author using criteria described in the article, while the entropies were computed by computer using Shannon’s formula, after the harmonic progression was determined. The four perceptual variables were obtained by a group of 21 participants, taking their mean values as the final score. A statistical analysis of this dataset shows that all the measures of complexity are consistent and are together with the musical style important features in explaining the musical acceptability. These relations were further elaborated by regression tree analysis for difficulty and pleasantness after unigram entropy was eliminated due to high correlation with bigram entropy. Results offer reasonable interpretations and also illuminate the relative importance of the predictor variables. In particular, the regularity of the harmonic progression is in both cases the most important predictor.

A Computational Approach to the Detection and Prediction of (Ir)Regularity in Children's Folk Songs

“…Each pattern (p), either repeated at pitch or transposed repeated (t), was firstly annotated in the musical score. Secondly, based on the frequency distribution of patterns in each song, we computed the entropy of unigrams for each song (Mihelač & Povh, 2020b give details about computing the unigrams). The Welch two-samples t-test was used to compare the difference in mean values of unigrams between the irregular and regular children's folk songs.…”

“…No matter how internalization occurs, internal models of the (permissible) musical structures are generated and applied whenever listening to novel music (Deliège, 1987;Agres, 2019). If the internal models somehow confront the (prescribed) rules of the arrangement of the constituent parts of a musical structure, the structure is perceived not only as irregular, but also as more complex and less enjoyable (Sauvé & Pearce 2019;Mihelač & Povh, 2020b). This is because more effort has to be put into the listening process, as the learned musical syntax and its rules have to be adjusted in order to understand the novel structures (Kramer, 1988).…”

“…Several approaches have been used to measure (ir)regularity in musical structure, including subjective evaluation by listeners (e.g., Deutsch, 1980;Tillmann & Bigand, 1996;Mihelač et al, 2018;Mihelač and Povh, 2020b), measurement of neural response (mismatch negativity, MMN) and functional magnetic resonance imaging (fMRI) (e.g., Ulanovsky, Las, & Nelken, 2003;Grahn & Rowe, 2012;Yu, Liu, & Gao, 2015), or simulation of human perception of (ir)regularity using a computational system (e.g., Hansen & Pearce, 2014;Mihelač & Povh, 2020a). The current study uses a computational model to enable a novel approach to the examination of (ir)regularity in the musical structure of children's folk songs.…”

A Stimulus Set of 40 Popular Music Drum Patterns with Perceived Complexity Measures

“…The complexity of musical stimuli and its psychological effects on listeners (such as listeners' aesthetic appreciation or interest in the music, their groove experience, and many other kinds of music-evoked emotions) are a wide field of inquiry. Complexity has been shown to affect humans' appreciation of artifacts such as pictures (Nadal et al, 2010;Osborne & Farley, 1970;Vitz, 1966), narratives (Carney et al, 2014;Stokmans, 2003), music (Chmiel & Schubert, 2019), buildings (Imamoglu, 2000), advertisements (Cox & Cox, 1988), and websites (Mai et al, 2014;Nadkarni & Gupta, 2007; for a general overview, see Mihelačand Povh, 2020;Van Geert & Wagemans, 2020). A popular theory posited by Berlyne (1963Berlyne ( , 1971 claims that humans' preferences form an inverted-U function (also called a Wundt curve, see Wundt, 1874, p. 432) of stimulus complexity.…”

A predictive coding approach to modelling the perceived complexity of popular music drum patterns

“…The complexity of art or music has long been understood as an essential aesthetic dimension ([ [1] , [2] , [3] , [4] ]), and there is an abundant body of research that investigates the relationship between the complexity of artifacts and how much observers appreciate them (for an overview, see Refs. [ 5 , 6 ]). Researchers seem to agree that the complexity of an artifact can be expressed as a quantity (and thus measured), and that it is sensible to state that one artifact is more complex than another.…”