Modulation in background music influences sustained attention

Referee: [Methods] Methods (stimulus generation): The abstract states that stimuli were 'musically and acoustically identical except for a peak in the modulation spectrum.' To support the claim that performance differences are caused by the 16 Hz / depth manipulation rather than uncontrolled changes in RMS level, loudness, spectral tilt, or musical phrasing, the manuscript must provide quantitative verification (e.g., measured modulation spectra, loudness matching data, or acoustic feature tables) showing that only the intended modulation peak differed across conditions.

Authors: We agree that explicit quantitative verification is necessary to rule out confounds. The original stimuli were generated with the explicit intent of isolating the modulation spectrum peak while holding other acoustic and musical properties constant, but the manuscript did not include the supporting measurements. In the revised version we will add (1) measured modulation spectra for all conditions, (2) a table of RMS levels, estimated loudness (LUFS), and spectral centroid values, and (3) confirmation that musical phrasing and tempo were identical across tracks. These additions will be placed in the Methods section and referenced in the Results. revision: yes

Referee: [Results] Results (statistical reporting): The non-monotonic benefit at 16 Hz and higher depths is the load-bearing finding. The manuscript should report the exact statistical tests, degrees of freedom, effect sizes, and any multiple-comparison corrections used to establish that neighboring rates and depths produced reliably null effects.

Authors: We accept that fuller statistical reporting is required. The original manuscript presented the primary ANOVA and selected post-hoc contrasts but omitted exhaustive reporting of all pairwise tests and effect sizes for the null neighboring conditions. In revision we will expand the Results section to list, for every rate-by-depth comparison: the exact test statistic, degrees of freedom, p-value, effect size (partial η²), and the multiple-comparison procedure applied (Bonferroni). This will make the non-monotonic pattern and the null results at adjacent parameter values fully transparent. revision: yes

Referee: [Discussion] Discussion (task interpretation): The central claim attributes gains to modulation-driven changes in sustained attention. The manuscript should explicitly address whether SART performance differences could instead reflect changes in response inhibition, arousal, or other processes, and whether any convergent measures (e.g., error types, RT variability) were examined to support the sustained-attention interpretation.

Authors: We appreciate the call for a more nuanced task interpretation. The SART is conventionally interpreted as a sustained-attention measure, yet commission errors also index response inhibition and overall error rate can reflect arousal. The manuscript did not previously discuss these alternatives or report secondary metrics. In the revised Discussion we will (1) explicitly consider alternative accounts (response inhibition, arousal, motivational effects), (2) present analyses of commission vs. omission errors and intra-individual RT variability where available, and (3) acknowledge that the design cannot fully dissociate these processes. If certain secondary measures were not recorded, we will state this limitation and propose targeted follow-up experiments. revision: partial