Predictability and Uncertainty in the Pleasure of Music: A Reward for Learning?

Abstract

Music ranks among the greatest human pleasures. It consistently engages the reward system, and converging evidence implies it exploits predictions to do so. Both prediction confirmations and errors are essential for understanding one's environment, and music offers many of each as it manipulates interacting patterns across multiple timescales. Learning models suggest that a balance of these outcomes (i.e., intermediate complexity) optimizes the reduction of uncertainty to rewarding and pleasurable effect. Yet evidence of a similar pattern in music is mixed, hampered by arbitrary measures of complexity. In the present studies, we applied a well-validated information-theoretic model of auditory expectation to systematically measure two key aspects of musical complexity: predictability (operationalized as information content [IC]), and uncertainty (entropy). In Study 1, we evaluated how these properties affect musical preferences in 43 male and female participants; in Study 2, we replicated Study 1 in an independent sample of 27 people and assessed the contribution of veridical predictability by presenting the same stimuli seven times. Both studies revealed significant quadratic effects of IC and entropy on liking that outperformed linear effects, indicating reliable preferences for music of intermediate complexity. An interaction between IC and entropy further suggested preferences for more predictability during more uncertain contexts, which would facilitate uncertainty reduction. Repeating stimuli decreased liking ratings but did not disrupt the preference for intermediate complexity. Together, these findings support long-hypothesized optimal zones of predictability and uncertainty in musical pleasure with formal modeling, relating the pleasure of music listening to the intrinsic reward of learning.SIGNIFICANCE STATEMENT Abstract pleasures, such as music, claim much of our time, energy, and money despite lacking any clear adaptive benefits like food or shelter. Yet as music manipulates patterns of melody, rhythm, and more, it proficiently exploits our expectations. Given the importance of anticipating and adapting to our ever-changing environments, making and evaluating uncertain predictions can have strong emotional effects. Accordingly, we present evidence that listeners consistently prefer music of intermediate predictive complexity, and that preferences shift toward expected musical outcomes in more uncertain contexts. These results are consistent with theories that emphasize the intrinsic reward of learning, both by updating inaccurate predictions and validating accurate ones, which is optimal in environments that present manageable predictive challenges (i.e., reducible uncertainty).

Keywords: computational modeling; esthetics; music; predictive processing; reward.

Figure 1.

IDyOM model. We used the IDyOM model (Pearce, 2005, 2018) to systematically measure music unpredictability as IC and entropy. As configured here, IDyOM first builds a long-term model (LTM) of the statistical structure of a large training set of 903 melodies, represented as sequences of pitches and inter-onset interval ratios (IOIr). In a new stimulus melody with n notes, IDyOM then estimates the probability of each possible continuation x from an alphabet X, at each note index i based on the LTM and a short-term model (STM) learned dynamically within the current stimulus (i.e., from note 1 to note i). To combine the probabilities derived from the LTM and STM, IDyOM first computes a geometric mean (signified by '*') of the LTM and STM probabilities for pitch and IOIr separately, weighting each according to its entropy such that predictions based on higher-entropy models are less influential, and then multiplies these resulting pitch and IOIr probabilities. It then computes the note's IC as its negative log probability to the base 2, and its entropy as the expected value of the IC across all possible continuations (X). The result is a reliable computational measure of pitch unpredictability and uncertainty based on long- and short-term musical statistics. In the present studies, we averaged these note-by-note measures across each stimulus to represent each 30 s stimulus as one unit.

Figure 2.

Stimulus unpredictability and uncertainty distributions. Using formal mathematical modeling of musical unpredictability and uncertainty, we developed 55 stimuli, all excerpts of real, precomposed music, that varied across quantifiably wide ranges of mDW-Ent (i.e., the average entropy of all notes in a stimulus weighted by their durations) and mDW-IC (i.e., the average IC of all notes in a stimulus weighted by their durations). We standardized these measures with z scores to compare them, and so the standardized mDW-Ent and standardized mDW-IC are shown here. These features were positively correlated (Pearson's r = 0.44, p < 0.001).

Figure 3.

Behavioral effects of unpredictability and uncertainty. Linear mixed-effects analyses revealed significant Wundt effects in Study 1. A, The optimal model of mDW-IC explained 26.3% of the variance in liking ratings (p < 0.001) with negative linear (β = −0.21, p < 0.001) and quadratic (β = −0.09, p < 0.001) effects. It also had significant random intercepts and slopes across subjects (intercept 95% CI = 0.54, 0.86, slope 95% CI = 0.11, 0.29). Red curve indicates the fitted model. Blue dots represent the mean liking ratings for each stimulus adjusted according to the model's random effects. B, The optimal model of mDW-Ent explained 19.1% of the variance in liking ratings (p = 0.03), with negative linear (β = −0.09, p = 0.009) and quadratic effects (β = −0.06, p = 0.003) and significant subject-varying random intercepts (95% CI = 0.54, 0.86). Red curve indicates the fitted model. Blue dots represent the mean liking ratings for each stimulus adjusted according to the model's random effects. C, We used k-means clustering to categorize our stimuli. Starting with six points (black diamonds) to distinguish low and high mDW-Ent along with low, medium, or high mDW-IC, this procedure yielded the six stimulus categories that we used for repeated-measures ANOVA. D, A repeated-measures ANOVA reaffirmed the main effect of mDW-IC (F_(1.70,69.63) = 34.45, partial η² = 0.51, p < 0.001, using Greenhouse–Geisser correction since Mauchly's test of sphericity was violated) but not mDW-Ent (F_(1,41) = 2.84, p = 0.10), and also suggested an interaction between the two on liking ratings (F_(1.71,70.21) = 3.17, partial η² = 0.07, p = 0.06). Planned comparisons reflected the Wundt effect of mDW-IC when mDW-Ent was low (high mDW-IC < low mDW-IC: p < 0.001; high mDW-IC < medium mDW-IC: p < 0.001; low mDW-IC vs medium mDW-IC: p = 0.35), but not when mDW-Ent was high, when liking ratings for low mDW-IC were significantly greater than those for medium mDW-IC (p = 0.01; high mDW-IC < low mDW-IC: p < 0.001; high mDW-IC < medium DW-IC: p < 0.001). Likewise, there was a significant preference for stimuli with high mDW-Ent over low mDW-Ent when mDW-IC was low (p = 0.001), but not when mDW-IC was medium (p = 0.60) or high (p = 0.85), implying that uncertain contexts amplify the pleasure of predictability. n.s. = not significant, *p < 0.05, ***p < 0.001.

Figure 4.

Individual differences in Wundt effects. Individual differences in the Wundt effects of Study 1 could be explained in part by musical sophistication, as measured by the Gold-MSI (Müllensiefen et al., 2014). A, We represented each participant's Wundt effect as a distribution of mean liking ratings across mDW-ICs by multiplying these measures together, resulting in flatter distributions for those with similar preferences across the mDW-IC spectrum, sharper distributions for those with more particular preferences, and so on. We then measured the kurtosis and skewness of each distribution, reflecting the sharpness and asymmetry of the participant's preferences, respectively. To illustrate this analysis, we show the distribution for Participant 7, on the left, who exhibits the greatest kurtosis and skewness of the sample, and Participant 43, on the right, who has the lowest kurtosis and second-lowest skewness. B, There was a significant positive correlation between Gold-MSI scores and the kurtosis of the Wundt effect, revealing sharper preferences for relatively more sophisticated participants (F_(1,41) = 7.43, p = 0.009, β = 0.02, R² = 0.15). C, There was also a significant positive correlation between Gold-MSI scores and the skewness of the Wundt effect, wherein more sophisticated listeners also had greater relative preferences for stimuli of lower mDW-IC (F_(1,41) = 4.76, p = 0.03, β = 0.003, R² = 0.10). In both cases, the Gold-MSI “Perceptual Abilities” subscale was the only one to survive follow-up stepwise regressions (kurtosis effect: F_(1,41) = 6.50, p = 0.01, β = 0.04, R² = 0.14; skewness effect: F_(1,41) = 5.89, p = 0.02, β = 0.009, R² = 0.13), indicating that music-listening skills drove these results. Kurtosis and skewness were also highly correlated (r = 0.94, p < 0.001), complicating the interpretations of these results. P7 = Participant 7, P43 = Participant 43.

Figure 5.

Behavioral effects of unpredictability, uncertainty, and repetition. Linear mixed-effects analyses revealed significant Wundt effects in Study 2. A, The optimal model of mDW-IC explained 41.6% of the variance in liking ratings (p < 0.001) with only a negative quadratic effect (β = −0.18, p < 0.001) and significant random intercepts and slopes across subjects (intercept 95% CI = 0.31, 0.58, mDW-IC slope 95% CI = 0.15, 0.29, mDW-IC² slope 95% CI = 0.10, 0.19, repetition slope 95% CI = 0.05, 0.09). Red curve represents the fitted model. Blue dots represent the mean liking ratings for each stimulus adjusted according to the model's random effects. B, The optimal model of mDW-Ent explained 34.9% of the variance in liking ratings (p < 0.001), with negative linear (β = −0.31, p < 0.001) and quadratic effects (β = −0.25, p < 0.001). This model also had significant subject-varying random intercepts (95% CI = 0.30, 0.58), slopes for mDW-Ent (95% CI = 0.26, 0.49), slopes for mDW-Ent² (95% CI = 0.82, 0.97), and slopes for repetition (95% CI = 0.05, 0.09). Red curve represents the fitted model. Blue dots represent the mean liking ratings for each stimulus adjusted according to the model's random effects. C, The best-fitting model of liking and repetition, which included an interaction term between mDW-IC and liking, significantly fit the data (R² = 0.42, p < 0.001), but not better than an alternative model that excluded the fixed effects of repetition (likelihood ratio test χ²(1, N = 27) = 3.42, p = 0.18). Even so, this model indicated that the Wundt effect did not significantly change across repetitions, as the interaction term was not significant (p = 0.38).