Music with long ringing tails and dark spectra is rated calmer, and also less pleasant

People often reach for music with long, ringing sustain and a warm, dark tone when they want to wind down. We asked whether those two properties of the sound go with how calm and how pleasant listeners judge a clip to be, beyond loudness, genre and year. On 1,744 rated 45-second clips from the DEAM dataset, we measured how long each note rings after its onset and how far the spectrum leans toward low frequencies, and tested the link on 502 clips by 270 artists kept out of all fitting. A calm index built from a longer tail and a darker spectrum correlates -0.394 with rated arousal (95% interval -0.476 to -0.304), with loudness, genre and year held fixed.c1 Adding the two measures raises held-out explained variance in arousal by 0.110 (0.034 to 0.182).c2 We forecast that the same sounds would be rated more pleasant; they were rated less pleasant, -0.375 (-0.455 to -0.280), and -0.227 with arousal also held.c3 In these ratings, calm sits closer to subdued than to content.

The acoustic side of musical emotion has mostly been studied on single notes. Eerola, Ferrer and Alluri [2] had listeners rate isolated instrument sounds for valence, tension and energy and found that features such as attack time and spectral brightness tracked those ratings. Korsmit and colleagues [3] pooled several such datasets and found that some acoustic links held across them and others did not. These studies hold the musical context fixed by removing it.

Reverberation has its own small literature. Mo, Wu and Horner [4] added reverberation to eight wind and bowed-string sounds and found that its length shifted their emotional character, most strongly toward romantic and mysterious and less toward sad. Wilkie and Harrison [5] varied reverberation time in recorded music heard over headphones and found that longer reverberation raised ratings of sublimity, nostalgia and wonder while leaving unease and vitality about the same.

We asked a question one step further from the laboratory: in full mixed music by many artists, does a longer ringing tail after each note and a darker spectrum go with lower rated arousal, beyond loudness and genre, on artists the analysis never saw? We also asked, more tentatively, whether the same sounds would be rated as more pleasant. The decision this informs is which acoustic controls a music tool can trust to move perceived calm, and what else they move with it.

Searches run on 9 November 2026 found the DEAM benchmark paper [1], the studies above and related work on isolated tones. They returned nothing that measures an onset-locked tail in full mixed music. That is what the searches returned; it does not show that no such study exists.

The preregistrationDefinition: preregistration research method (metascience) A dated written plan for a study, fixed and hash-locked before any result is seen: the question, the data, the statistic, the controls, the forecasts and the kill conditions. Excludes a plan revised after looking at the outcome, and a protocol written only for the record after the run. full definition, a dated plan hash-locked before any result is seen, was written on 29 October 2026 and locked at 16:24 UTC. Acoustic features were extracted from the audio before the lock. No rating was joined to any feature before it; while checking copies of the annotation file, the first two rows (two clips) were seen and nothing else of the ratings.

The plan fixed the data, the measures that had passed an instrument check, the artist split, the controls, the predictions and the rule for each verdictDefinition: verdict research method (our usage) The pass or fail of one preregistered rule set against the run's numbers, read off by code. Excludes an interpretation written after reading the numbers. full definition, which is the pass or fail of one preregistered rule set read off by code. Every rule is fail-closed: a verdict passes only when all of its rules hold. The predictions were:

The forecasts written before the run were a P1 correlation near -0.15 (range -0.05 to -0.30) and a P3 correlation near +0.05, likely to fail. The same plan also held two questionnaire tests on music absorption and personality. Their values were seen before the lock through a test of the analysis code, so they are not blind tests, and they are left out of this paper.

One change came after the lock and before feature extraction: the audio loader switched from an FFT resampler to a polyphase one. The instrument check's synthetic clips are made at the analysis rate and never pass through the loader, so the check is unaffected.

The data are DEAM, the MediaEval Database for Emotional Analysis in Music [1]. It holds Creative Commons music from the Free Music Archive, Jamendo and MedleyDB, with ratings from crowd workers. The release is licensed CC BY-NC, non-commercial use with attribution; this paper reports statistics only and redistributes no audio or ratings.

The ratings are arousal and valenceDefinition: arousal and valence psychology of emotion (the circumplex model) Two rating scales for emotion: arousal runs from calm to excited and valence from unpleasant to pleasant. In DEAM each is a nine-point scale averaged over crowd raters. Excludes named emotions such as sadness or nostalgia, which the ratings place only as points on the two scales. full definition: arousal runs from calm to excited and valence from unpleasant to pleasant, each on a nine-point scale averaged over raters for each clip. They measure perceived emotionDefinition: perceived emotion music psychology The emotion a listener judges the music to express, as opposed to the emotion the listener feels. Excludes felt or induced emotion, physiological response and any change in mood or symptoms. full definition, what a listener judges the music to express, and not what the listener feels.

We used the 1,744 clips of 45 seconds from the 2013 and 2014 rating rounds, by 899 artists. The 58 full songs from 2015 were left out because their length, rater pool and rating method differ. Genre comes from the dataset's metadata: 11 sampling genres, with one clip under another label pooled as Other.

The official host refused connections on the day of download. The audio came from a public mirror; the archive holds 1,802 files, the count the dataset paper gives, but there is no official checksum to compare it with. The per-clip annotations came from three independent public copies with identical bytes. The metadata is the official file, retrieved through the Internet Archive. The mirror's provenance is a limit, stated below.

Each clip was converted to mono at 22,050 Hz and cut to its first 45 seconds. The energy envelope is the root mean square over 256-sample windows at a 64-sample hop.

The onset-locked tailDefinition: onset-locked tail audio signal processing (our measure) For each note onset found in the energy envelope, the time constant of the envelope's decay from its peak to the next minimum, with the median taken over onsets. It follows whichever of the note's own decay and the room's decay is slower. Excludes the reverberation time of the room on its own, which this measure cannot separate in dense music. full definition is a decay time measured after each note onset. Onsets are envelope peaks at least 0.1 s apart and above the envelope's 60th percentile. For each onset, the log envelope from the peak to the next minimum is fitted by least squares against time, giving a slope $b_i$. Each onset with a negative slope gives a decay time constant in seconds,

and the tail $T_{\mathrm{tail}}$ is the median of ${\tau }_i$ over those onsets. This follows whichever of the note's own decay and the room's decay is slower. In dense music it cannot separate the two.

The spectral slopeDefinition: spectral slope audio signal processing The slope of log power against log frequency between 110 Hz and 5.5 kHz. A more negative slope means energy leans toward low frequencies and the sound is darker. Excludes pitch, loudness and the shape of the spectrum beyond its overall tilt. full definition $s$ is the least-squares slope of ${\log }_{}$ power against ${\log }_{}$ frequency from a Welch spectrum, between 110 Hz and 5.5 kHz. A more negative slope means a darker sound.

The calm index combines the two, with each measure standardised by its mean $\mu$ and standard deviation $\sigma$ on the training clips only:

A higher $C$ means a longer tail and a darker spectrum.

Artists were put in a random order with a fixed seed, and 30 percent of them, with all their clips, form the held-out test setDefinition: held-out test set statistics and machine learning Data kept apart from everything that was fitted or standardised, here every clip by 30 percent of the artists, so that a result on it is a check on new material. Excludes data used to fit the model, choose a threshold or compute a scaling. full definition: 502 clips by 270 artists. The other 1,242 clips are the training set. Every verdict reads the test set.

The controls in every confirmatory model are loudness in decibels relative to full scale, 11 genre indicators and rating year, with an intercept. The main statistic is the partial correlationDefinition: partial correlation statistics The correlation between two quantities after each has had the linear effect of a set of control variables removed by least squares. Excludes a causal effect, and any non-linear dependence on the controls. full definition: each of the two quantities is regressed on the controls by least squares, and the residuals $e_x$ and $e_y$ are correlated, with sums over the clips:

Residuals from a fit with an intercept have mean zero, so this is the ordinary correlation of the residuals.

The held-out R2 gainDefinition: held-out R2 gain statistics The share of variance in the test outcome explained by a model fitted on training data with the added measures, minus the same share for the model without them. Excludes the in-sample R2 of a fit, which can only grow as variables are added. full definition fits arousal on the training clips twice, once on the controls and once on the controls plus $\ln T_{\mathrm{tail}}$ and $s$, and scores both fits on the test clips:

where $y_{\mathrm{pred}}$ is a fit's prediction for a test clip, $y_{\mathrm{mean}}$ the mean test rating, $R_0^2$ the test score of the controls-only fit, $R_1^2$ that of the fit with the two measures, and $G$ the gain.

Intervals are 95% intervalsDefinition: 95% interval statistics The range that holds the middle 95 percent of the bootstrap or control draws for a number. We report it beside the number. Excludes a statement that the true value lies inside with 95 percent probability. full definition, the 2.5th to 97.5th percentiles of 2,000 cluster bootstrapDefinition: cluster bootstrap statistics A bootstrap that resamples whole groups, here artists with all their clips, so that clips by one artist count as one draw. Excludes a bootstrap over single clips, which treats one artist's clips as independent. full definition resamples of the test set, where whole artists are drawn with replacement.

Before the lock, every measure was run as a planted checkDefinition: planted check research method; called a positive control in experimental science Data built so that the right answer is known, run through the same analysis before the real data, to show that the analysis can see the effect when it is there. Excludes any check made on the real data, which cannot show what the analysis misses. full definition: synthetic music built so that the right answer is known. Each of 40 clips held 30 seconds of harmonic notes on a beat, with room decay time, note decay, attack, tempo, spectral tilt and wet mix set at random and varying at once. Each measure's median error was compared with the error of the same measure against shuffled targets. A measure counted as strong when it beat the shuffled targets' 5th percentile and its median error was at most half the shuffled median. The ratio of the two medians is in Figure 1.

The tail recovered the slower of note and room decay with an error ratio of 0.12 and a rank correlation of 0.95; the spectral slope recovered the planted tilt with 0.21 and 0.99.c4 The library's reverb-size measure failed in dense music (0.81), and the tail against room decay alone failed too (0.80), so room reverberation cannot be separated from note decay with these tools and enters no verdict. The best attack measure reached 0.55, short of strong, so attack enters no verdict either. A constant estimator, included as a false-success check, scored 1.00 and failed, as it must.

Each controlDefinition: control statistics and experimental design A version of the data with the structure under test removed (for example shuffled or pooled), scored the same way as the real data, so the real score has something to beat. Excludes a comparison with a different dataset or with a published number. full definition removes the structure under test and is scored the same way as the real data. For P1 and P3, the calm index was shuffled across test clips 1,000 times and the partial correlation recomputed each time; the spread of those draws is the null distributionDefinition: null distribution statistics The spread of scores a control gives over many random draws. Its 95th percentile is the bar a real score must clear. Excludes a theoretical distribution assumed rather than drawn from the data. full definition. For P4, the tail and slope rows were shuffled within the training set and within the test set, 1,000 times, and the whole fit repeated. Table 1 gives the bars.

Figure 2 and Table 2 give the confirmatory results on the 502 test clips. A calm index built from a longer tail and a darker spectrum correlates -0.394 with rated arousal (95% interval -0.476 to -0.304), with loudness, genre and year held fixed.c1 That is far outside the shuffle range and about 2.6 times the size forecast. Each measure carries the link on its own: the tail at -0.301 and the slope at +0.324, where a higher slope means a brighter sound.

Adding the two measures raises held-out explained variance in arousal by 0.110 (0.034 to 0.182).c2 The controls alone explain 0.160 of the test variance. With tempo and spectral entropy added to the controls, the calm index still correlates -0.343 with arousal.

We forecast that the same sounds would be rated more pleasant; they were rated less pleasant, -0.375 (-0.455 to -0.280), and -0.227 with arousal also held.c3 P3 failed on all three of its rules. This is an honest nullDefinition: honest null research method (our usage) A working test that found no effect beyond a stated bound, a forecast that failed, or an error of our own found and fixed, reported with the same weight as a positive result. Excludes a void run, and a result left unpublished because it was negative. full definition of the forecast, reported with the same weight as the passes: arousal and valence correlate 0.54 on the test clips, so part of the valence drop rides on arousal, and the rest (-0.227, interval -0.312 to -0.123) does not.

The following were run after the verdicts and carry no verdict. In busy music the next onset cuts each tail short, so the tail could stand in for note rate. Note rate has a median of 4.9 events per second and correlates -0.17 with the log tail. With note rate added to the controls, P1 is -0.370 (-0.444 to -0.284) and the tail alone -0.285; with note rate, tempo and entropy all added, P1 is -0.324.

Inside each of the 11 genres, on the 1,743 clips they hold (one clip tagged Other is left out), the calm index correlates negatively with arousal, from -0.25 in hip-hop to -0.62 in international music.c5 Figure 3 shows each genre.

On the whole sample, P1 is -0.414 and the valence correlation -0.395. Among exploratory measures on the test clips, the failed reverb-size measure reads in the same direction as the tail (partial correlation with arousal -0.237), and so does the envelope's autocorrelation decay (-0.198); neither can be read as room reverberation. Rise time shows no relation (0.024), which is a null of a weak instrument and says nothing about attack itself.

The arousal result agrees with what single-note studies found for brightness [2] [3] and extends it to full mixes by many artists, on artists held out from fitting, with a tail measure checked on synthetic music before use. The size, about -0.39, is larger than we forecast. It survives tempo, spectral entropy and note rate, and holds inside every genre.

The valence result is the more interesting one. A reader might expect calm music to be rated pleasant. In DEAM it is rated less pleasant, and the drop is not only the shared variance with arousal. Wilkie and Harrison [5] found that longer reverberation raised sublimity and nostalgia and left unease and vitality about the same, and Mo, Wu and Horner [4] found reverberation moved instrument sounds toward romantic and mysterious and, less strongly, sad. Both fit a reading in which long dark tails carry a wistful or melancholy calm.

For a music tool, the practical reading is that a sustain or darkness control may move perceived calm and lower perceived pleasantness together, which a test that changes the sound would have to confirm. A tool that offers calm through these controls should say so.

The tierDefinition: tier our publication register How ready a finding is to publish: A candidate, B signal worth expanding (B* strong), C internal, D honest null worth reporting, E not reliable as it stands. Excludes a measure of how large or how true an effect is. full definition B* places this as a strong signal worth expanding. Three things would raise it: a second rated corpus, a listening test that changes the tail with instrumentation held fixed, and ratings of felt calm.