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

What is it about?

In this paper, we contribute to the longstanding challenge of how to explain a listener’s acceptability for a particular piece of music, using harmony as one of the crucial dimensions, and that is among the least examined. We propose three measures for the complexity of harmony: (i)the complexity based on the usage of 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 perceptual dimensions for the accept-ability of musical pieces, including difficulty, pleasantness, recognizability, and repeatability. These measures were evaluated in each musical example within our dataset of 160 carefully selected musical excerpts from different musical styles. The first and third complexity measures and the musical style of excerpts were manually determined using the criteria described in this paper, while the entropies were computed using Shannon’s formula after the harmonic progression was determined. Data for the four perceptual variables were obtained from a group of 21 participants, with the mean values taken as the final score. A statistical analysis of this dataset showed that all measures of complexity were consistent, and together with the musical style, were important features in explaining musical accept-ability. These relations were further elaborated upon using regression tree analyses for difficulty and pleasantness. The results provided reasonable interpretations and also illuminated the relative importance of the predictor variables. In particular, the regularity of the harmonic progression was the most important predictor for both perceived variables.

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Photo by Mitchell Griest on Unsplash

Photo by Mitchell Griest on Unsplash

Why is it important?

We have introduced three measures for the complexity of harmony, (i) usage of basic tonal functions and parallels in the harmonic progression, (ii) entropy of the harmonic progression and (iii) (ir)regularity of the harmonic progression. The irregularity of the harmonic progression is of particular interest because it evaluates the interaction between harmony and other musical dimensions (e.g., rhythm).

Perspectives