This study investigates the role of extrinsic and intrinsic predictors in the perception of affect in mostly unfamiliar musical chords from the Bohlen-Pierce microtonal tuning system. Extrinsic predictors are derived, in part, from long-term statistical regularities in music; for example, the prevalence of a chord in a corpus of music that is relevant to a participant. Conversely, intrinsic predictors make no use of long-term statistical regularities in music; for example, psychoacoustic features inherent in the music, such as roughness. Two types of affect were measured for each chord: pleasantness/unpleasantness and happiness/sadness. We modelled the data with a number of novel and well-established intrinsic predictors, namely roughness , harmonicity , spectral entropy and average pitch height ; and a single extrinsic predictor, 12-TET Dissimilarity , which was estimated by the chord’s smallest distance to any 12-tone equally tempered chord. Musical sophistication was modelled as a potential moderator of the above predictors. Two experiments were conducted, each using slightly different tunings of the Bohlen-Pierce musical system: a just intonation version and an equal-tempered version. It was found that, across both tunings and across both affective responses, all the tested intrinsic features and 12-TET Dissimilarity have consistent influences in the expected direction. These results contrast with much current music perception research, which tends to assume the dominance of extrinsic over intrinsic predictors. This study highlights the importance of both intrinsic characteristics of the acoustic signal itself, as well as extrinsic factors, such as 12-TET Dissimilarity, on perception of affect in music.
IN THIS PAPER, WE INTRODUCE A SMALL FAMILY OFnovel bottom-up (sensory) models of the Krumhansl and Kessler (1982) probe tone data. The models are based on the spectral pitch class similarities between all twelve pitch classes and the tonic degree and tonic triad. Cross-validation tests of a wide selection of models show ours to have amongst the highest fits to the data. We then extend one of our models to predict the tonics of a variety of different scales such as the harmonic minor, melodic minor, and harmonic major. The model produces sensible predictions for these scales. Furthermore, we also predict the tonics of a small selection of microtonal scales-scales that do not form part of any musical culture. These latter predictions may be tested when suitable empirical data have been collected.
Models of the perceived distance between pairs of pitch collections are a core component of broader models of music cognition. Numerous distance measures have been proposed, including voice-leading [1], psychoacoustic [2][3][4], and pitch and interval class distances [5]; but, so far, there has been no attempt to bind these different measures into a single mathematical or conceptual framework, nor to incorporate the uncertain or probabilistic nature of pitch perception. This paper embeds pitch collections in expectation tensors and shows how metrics between such tensors can model their perceived dissimilarity. Expectation tensors indicate the expected number of tones, ordered pairs of tones, ordered triples of tones, etc., that are heard as having any given pitch, dyad of pitches, triad of pitches, etc.. The pitches can be either absolute or relative (in which case the tensors are invariant with respect to transposition). Examples are given to show how the metrics accord with musical intuition.
Tonal affinity is the perceived goodness of fit of successive tones. It is important because a preference for certain intervals over others would likely influence preferences for, and prevalences of, "higher-order" musical structures such as scales and chord progressions. We hypothesize that two psychoacoustic (spectral) factors-harmonicity and spectral pitch similarity-have an impact on affinity. The harmonicity of a single tone is the extent to which its partials (frequency components) correspond to those of a harmonic complex tone (whose partials are a multiple of a single fundamental frequency). The spectral pitch similarity of two tones is the extent to which they have partials with corresponding, or close, frequencies. To ascertain the unique effect sizes of harmonicity and spectral pitch similarity, we constructed a computational model to numerically quantify them. The model was tested against data obtained from 44 participants who ranked the overall affinity of tones in melodies played in a variety of tunings (some microtonal) with a variety of spectra (some inharmonic). The data indicate the two factors have similar, but independent, effect sizes: in combination, they explain a sizeable portion of the variance in the data (the model-data squared correlation is r 2 = .64). Neither harmonicity nor spectral pitch similarity require prior knowledge of musical structure, so they provide a potentially universal bottom-up explanation for tonal affinity. We show how the model-as optimized to these data-can explain scale structures commonly found in music, both historical and contemporary, and we discuss its implications for experimental microtonal and spectral music.
There is an uncountable number of different ways of characterizing almost any given realworld stimulus. This necessitates finding stimulus features that are perceptually relevant -that is, they have distinct and independent effects on the perception and cognition of the stimulus. Here, we provide a theoretical framework for empirically testing the perceptual relevance of stimulus features through their association with recognition, memory bias, and aesthetic evaluation. We deploy this framework in the auditory domain to explore the perceptual relevance of three recently developed mathematical characterizations of periodic temporal patterns: balance, evenness, and interonset interval entropy. By modelling recognition responses and liking ratings from 177 participants listening to a total of 1,252 different musical rhythms, we obtain very strong evidence that all three features have distinct effects on the memory for, and the liking of, musical rhythms. Interonset interval entropy is a measure of the unpredictability of a rhythm derived from the distribution of its durations. Balance and evenness are both obtained from the discrete Fourier transform (DFT) of periodic patterns represented as points on the unit circle, and we introduce a teleological explanation for their perceptual relevance: the DFT coefficients representing balance and evenness are relatively robust to small random temporal perturbations and hence are coherent in noisy environments. This theory suggests further research to explore the meaning and relevance of robust coefficients such as these to the perception of patterns that are periodic in time and, possibly, space.
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