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.
Regularity in musical structure is experienced as a strongly structured texture with repeated and periodic patterns, with the musical ideas presented in an appreciable shape to the human mind. We recently showed that manipulation of musical content (i.e., deviation of musical structure) affects the perception of music. These deviations were detected by musical experts, and the musical pieces containing them were labelled as irregular. In this study, we replace the human expert involved in detection of (ir)regularity with artificial intelligence algorithms. We evaluated eight variables measuring entropy and information content, which can be analysed for each musical piece using the computational model called Information Dynamics of Music and different viewpoints. The algorithm was tested using 160 musical excerpts. A preliminary statistical analysis indicated that three of the eight variables were significant predictors of regularity (E cpitch, IC cpintfref, and E cpintfref). Additionally, we observed linear separation between regular and irregular excerpts; therefore, we employed support vector machine and artificial neural network (ANN) algorithms with a linear kernel and a linear activation function, respectively, to predict regularity. The final algorithms were capable of predicting regularity with an accuracy ranging from 89% for the ANN algorithm using only the most significant predictor to 100% for the ANN algorithm using all eight prediction variables.
We examine (ir)regularity in the musical structure of 736 monophonic children's folk songs from 22 European countries, by simulating and detecting (ir)regularity with the computational model, IDyOM, and our own algorithm, Ir_Reg, which classifies melodies according to regularity of their musical structure. IDyOM offers a range of viewpoints which allow observation and prediction of various musical features. We used five viewpoints to measure the information content and entropy of musical events in songs. Analysis across the data shows absence of irregular musical structure in children's folk songs from Croatia, Serbia, Turkey, Portugal, Hungary, and Romania. Conversely, absence of regular structure in children's folk songs was found in Great Britain, Norway and Switzerland. Further analysis of (ir)regularity, by individual country, revealed the importance of patterns repeated at pitch in regular songs, and a higher occurrence of transposed repeated patterns in irregular songs. Principal component analysis (PCA) shows the salience of pitch and pitch intervals in the perception of (ir)regular structure. Neither rhythm nor contour affects the perception of regularity. Recurring pulse/meter and arch-like melodic structure were found in the majority of children's folk songs. The study shows that irregularity exists in children's folk songs, and that this genre can be complex.
The paper presents a manual classification model, the Classification Model for the categorization of Children’s Songs (Model CMCS) for the selection of children’s songs based on the proposed criteria found in studies about the selection of children’s songs, on music theoretical background, and on findings from cross-cultural studies about (dis)similarities in children’s songs. A step-by-step procedure comprising four levels for the classification of songs is explained and applied in the first testing, employing two musical experts for the evaluation of three different songs. The results have shown that the Model CMCS is transparent (understandable), applicable, and useful and will be tested in the next stage on a larger number of songs and involving more musical experts. An improved version of the Model CMCS could be used in the future as a framework for an automatic classification model for the selection of children’s songs.
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