Author Correction: The role of harmonicity on listeners' ability to hear out voices in polyphonic music

Correction to: Scientific Reportshttps://doi.org/10.1038/s41598-025-16404-8, published online 28 August 2025 The original version of this Article contained an error in the calculation of the Sensitivity index, d'. Upon a review from the Authors, the identified error affects a subset of the data from Experiment 2, where performance was at the ceiling or floor, in which case the value of d' was erroneously set to 0. The differences between the originally presented and reanalysed data do not affect the main results or conclusions as stated in the Abstract. As a result, in the Analysis section, where: “A d’ value of zero implies chance performance (i.e., 50% correct), a d’ value of 1 implies about 69% correct, and a d’ value of 2.5 implies about 90% correct, all assuming unbiased responding.” now reads: “When the hit or false alarm rate was at ceiling (1) or floor (0), the corresponding value was replaced with 1-1/(2N) or 1/(2N), respectively, where N represents the number of trials on which the proportion is based ⁵⁵. A d’ value of zero implies chance performance (i.e., 50% correct), a d’ value of 1 implies about 69% correct, and a d’ value of 2.5 implies about 90% correct, all assuming unbiased responding.” In addition, under the Results section, where: “A linear mixed-effects model indicated that only the number of voices significantly affected bias [χ2(3) =12.89, p = 0.005], with no significant effect of harmonicity [χ2(2) =0.28, p = 0.871], and no interaction [χ2(6) =4.98, p = 0.546]. Even the effect of the number of voices on bias was not systematic, with post hoc pairwise comparisons showing that the difference in bias between two and four voices was significant [χ2(1)=12.34, p = 0.003], as well as the difference between three and four voices [χ2(1)=5.79, p = 0.048], but no other differences in bias reached significance. Overall, the mean bias value of β=0.95 suggested no clear preference for ‘same’ over ‘different’ responses, or vice versa. (A value of β=1 implies no bias.).” now reads: “A linear mixed-effects model indicated no significant effect of number of voices [χ2(3) = 7.05, p = 0.07], harmonicity [χ2(2) = 1.45, p = 0.49], or their interaction [χ2(6) = 4.77, p = 0.57] on bias. Overall, the mean bias value of β = 0.99 suggested no clear preference for ‘same’ over ‘different’ responses, or vice versa. (A value of β = 1 implies no bias.).” Where: “Considering first only the results of the main experiment (solid lines), our analysis revealed main effects of harmonicity [χ2 (2) = 20.86, p < 0.001] and number of voices [χ2 (3) = 43.13, p < 0.001] on d', but no significant interaction [χ2(6) = 8.57, p = 0.199]. Thus, unlike the findings from Experiment 1, inharmonicity influenced performance consistently across all numbers of voices rather than showing a varying effect depending on the number of voices. Post hoc pairwise contrasts confirmed a significant difference between all three levels of harmonicity [harmonic and inharm10 conditions: χ2(1) = 15.43, p < 0.001; harmonic and inharm30 conditions: χ2(1) = 60.63, p < 0.001; inharm10 and inharm30 conditions: χ2(1) = 14.89, p6.20, p < 0.05] in all cases. Regarding the results from the control experiment alone, performance was generally poor but above chance, with d’ values averaging around 0.5.” now reads: “Considering first only the results of the main experiment (solid lines), our analysis revealed main effects of harmonicity [χ2(2) = 36.35, p < 0.001] and number of voices [χ2(3) = 60.35, p < 0.001] on d’, as well as a significant interaction [χ2(6) = 16.09, p = 0.01]. Thus, as in Experiment 1, the influence of inharmonicity on performance depended on the number of voices. Post-hoc contrasts revealed that differences between all harmonicity levels were significant with 2 and 3 voices (p < 0.04 in all cases), but none was significant with four voices (p > 0.06). At five voices, a significant difference was found between the harmonic and inharm30 conditions (estimate = 0.50, 95% CI [0.13, 0.87], p = 0.004), but not between harmonic and inharm10 (p = 0.08) or between inharm10 and inharm30 (p = 0.2). Therefore, the significant interaction reflects a greater effect of inharmonicity at low voice counts than at high voice counts. Regarding the results from the control experiment alone, performance was generally poor but above chance, with d’ values averaging around 0.6. Where: “We found a significant main effect of experiment [χ2(1) = 24.73, p < 0.001], harmonicity [χ2(2) = 23.83, p < 0.001], and number of voices [χ2(3) = 49.28, p < 0.001], as well as an interaction between experiment and number of voices [χ2(3) = 19.55, p < 0.001]. The other interactions, including the three-way interaction, failed to reach significance (p > 0.134 in all cases). Following up on the interaction between experiment and number of voices, we found significant differences between the two experiments for each voice level (p < 0.003), except for five voices [χ2(1) = 0.15, p = 0.7]. We find a progressively smaller context benefit as harmonic structure was reduced. For example, at two voices, the difference in d' between the main and control experiments was 0.89 in the harmonic condition, 0.76 in the inharm10 condition, and 0.64 in the inharm30 condition.” now reads: We found a significant main effect of experiment [χ2(1) = 36.94, p < 0.001], harmonicity [χ2(2) = 42.71, p < 0.001], and number of voices [χ2(3) = 70.92, p < 0.001], as well as an interaction between experiment and number of voices [χ2(3) = 27.47, p < 0.001], and an interaction between number of voices and harmonicity [χ2(6) = 18.9, p = 0.004]. The other interactions, including the three-way interaction, failed to reach significance (p > 0.06 in all cases). Following up on the interaction between experiment and number of voices, we found significant differences between the two experiments for each voice level (p < 0.004), except for five voices [χ2(1) = 0.30, p = 0.58]. We find a progressively smaller context benefit as harmonic structure was reduced. For example, at two voices, the difference in d’ between the main and control experiments was 1.14 in the harmonic condition, 0.93 in the inharm10 condition, and 0.64 in the inharm30 condition. Where: Our analysis revealed a significant main effect of voice location [χ2 (1) = 18.74, p < 0.001], an interaction between voice location and number of voices [χ2 (2) = 9.07, p = 0.011], as well as a significant three-way interaction with harmonicity [χ2 (4) = 11.4, p = 0.022]. Post hoc pairwise comparisons indicated that edge voices were associated with significantly higher d’, meaning participants performed better when they were cued to follow an edge voice throughout the passage. This edge advantage was significant (p < 0.05) for all combinations of number of voices and harmonicity level, except for five voices in the harmonic condition (estimate = 0.11, 95% CI [− 0.025, 0.46], p = 0.55),and four voices in the inharm30 condition (estimate = 0.17, 95% CI [− 0.18, 0.53], p = 0.34). now reads: Our analysis revealed a significant main effect of voice location [χ2(1) = 5.73, p < 0.02], and a significant three-way interaction with number of voices and harmonicity [χ2(4) = 13.47, p = 0.009]. Post hoc pairwise comparisons indicated that edge voices were associated with significantly higher d', meaning participants performed better when they were cued to follow an edge voice throughout the passage. This edge advantage was significant (p < 0.05) for all combinations of number of voices and harmonicity level, except for three voices in the inharm10 condition (estimate = 0.28, 95% CI [-0.09, 0.65], p = 0.14), and four voices in the inharm30 condition (estimate = 0.11, 95% CI [-0.26, 0.48], p = 0.57). And where: “The full model provided a significantly better fit [ΔAIC = 2.6, χ2(11) = 24.60, p = 0.01], although moderate multicollinearity was observed for several interaction terms. Significant main effects were found for number of voices [χ2(1) = 13.06, p < 0.001] and for musicianship [χ2(1) = 10.20, p = 0.0014], as well as significant interactions between number of voices and musicianship [χ2 (3) = 9.35, p = 0.025] and between harmonicity and musicianship [χ2(2) = 14.61, p < 0.001]. These results suggest that musicianship is associated with better accuracy (higher d’), and that the extent of this benefit varies depending on both the number of voices and the level of harmonicity. However, although we found two significant interactions (between musicianship and number of voices, and between musicianship and harmonicity), post hoc pairwise comparisons revealed no statistically significant differences between musicians and non-musicians at any individual level of number of voices or harmonicity after correction (all p > 0.05, FDR-corrected).” now reads: The full model provided a significantly better fit [ΔAIC = 12.4, χ2(11) = 34.4, p < 0.001], although moderate multicollinearity was observed for several interaction terms. Significant main effects were found for musicianship [χ2(1) = 16.48, p < 0.001], as well as significant interactions between number of voices and musicianship [χ2(3) = 12.68, p = 0.005] and between harmonicity and musicianship [χ2 (2) = 20.86, p < 0.001]. These results suggest that musicianship is associated with better accuracy (higher d'), and that the extent of this benefit varies depending on both the number of voices and the level of harmonicity. However, although we found two significant interactions (between musicianship and number of voices, and between musicianship and harmonicity), post hoc pairwise comparisons revealed only one statistically significant difference between musicians and non-musicians in the harmonic condition (χ2(1) = 6.28, p = 0.04), but not atany individual voice count (all p > 0.05).” Furthermore, in the Discussion section, where: “In contrast to what was found in Experiment 1, the interaction between harmonicity and number of voices was not significant, suggesting that the effect of inharmonicity on accuracy was similar across different voice counts. Taken together with results from Experiment 1, this pattern suggests that listeners’ ability to follow voices is generally impaired by inharmonicity, and that the reduced effect of inharmonicity in Experiment 1 at four and five voices may have been due to listeners basing their judgments on overall perceived density of components, rather than number of perceived voices.” now reads: “Consistent with what was found in Experiment 1, the interaction between harmonicity and number of voices suggested that the effect of inharmonicity on accuracy was greater for lower than for higher voice counts. Taken together with results from Experiment 1, this pattern suggests that listeners’ ability to follow voices is generally impaired by inharmonicity, with greater effects observed at lower voice counts.” And where: “The drop in d’ between harmonic and inharmonic conditions for two-voice stimuli in Experiment 2 supports this interpretation, with accuracy falling from 1.68 (harmonic), to 1.02 (inharm30) in the main experiment, and from 0.79 (harmonic) to 0.38 (inharm30) in the control.” now reads: “The drop in d' between harmonic and inharmonic conditions for two-voice stimuli in Experiment 2 supports this interpretation, with accuracy falling from 1.83 (harmonic) to 1.02 (inharm30) in the main experiment, and from 0.79 (harmonic) to 0.38 (inharm30) in the control. Moreover, Fig. 6 was updated with the updated data. The published incorrect Fig. 6 and its legend appear below. (Figure presented.) Mean sensitivity (d’) as a function of the number of voices. Colors and shapes indicate the level of harmonicity. The solid lines indicate the results from the main experiment, while the dashed and slightly transparent lines indicate the results from the control experiment. Error bars represent ± 1 standard error of the mean across participants. And finally, a new reference was added to the Reference list as ‘Reference 55’: Macmillan, N. A., & Kaplan, H. L. (1985). Detection theory analysis of group data: Estimating sensitivity from average hit and false-alarm rates. Psychological Bulletin, 98(1), 185–199. https://doi.org/10.1037/0033-2909.98.1.185. The original version of this Article has been corrected.