Universality and diversity in human song – Science Magazine

INTRODUCTION

Music is often assumed to be a human universal, emerging from an evolutionary adaptation specific to music and/or a by-product of adaptations for affect, language, motor control, and auditory perception. But universality has never actually been systematically demonstrated, and it is challenged by the vast diversity of music across cultures. Hypotheses of the evolutionary function of music are also untestable without comprehensive and representative data on its forms and behavioral contexts across societies.

RATIONALE

We conducted a natural history of song: a systematic analysis of the features of vocal music found worldwide. It consists of a corpus of ethnographic text on musical behavior from a representative sample of mostly small-scale societies, and a discography of audio recordings of the music itself. We then applied tools of computational social science, which minimize the influence of sampling error and other biases, to answer six questions. Does music appear universally? What kinds of behavior are associated with song, and how do they vary among societies? Are the musical features of a song indicative of its behavioral context (e.g., infant care)? Do the melodic and rhythmic patterns of songs vary systematically, like those patterns found in language? And how prevalent is tonality across musical idioms?

RESULTS

Analysis of the ethnography corpus shows that music appears in every society observed; that variation in song events is well characterized by three dimensions (formality, arousal, religiosity); that musical behavior varies more within societies than across them on these dimensions; and that music is regularly associated with behavioral contexts such as infant care, healing, dance, and love. Analysis of the discography corpus shows that identifiable acoustic features of songs (accent, tempo, pitch range, etc.) predict their primary behavioral context (love, healing, etc.); that musical forms vary along two dimensions (melodic and rhythmic complexity); that melodic and rhythmic bigrams fall into power-law distributions; and that tonality is widespread, perhaps universal.

CONCLUSION

Music is in fact universal: It exists in every society (both with and without words), varies more within than between societies, regularly supports certain types of behavior, and has acoustic features that are systematically related to the goals and responses of singers and listeners. But music is not a fixed biological response with a single prototypical adaptive function: It is produced worldwide in diverse behavioral contexts that vary in formality, arousal, and religiosity. Music does appear to be tied to specific perceptual, cognitive, and affective faculties, including language (all societies put words to their songs), motor control (people in all societies dance), auditory analysis (all musical systems have signatures of tonality), and aesthetics (their melodies and rhythms are balanced between monotony and chaos). These analyses show how applying the tools of computational social science to rich bodies of humanistic data can reveal both universal features and patterns of variability in culture, addressing long-standing debates about each.

Reducing the dimensionality of variation in musical behavior

To determine whether the wide variation in the annotations of the behavioral context of songs in the database (Text S1.1) falls along a smaller number of dimensions capturing the principal ways that musical behavior varies worldwide, we used an extension of Bayesian principal components analysis (84), which, in addition to reducing dimensionality, handles missing data in a principled way and provides a credible interval for each observation’s coordinates in the resulting space. Each observation is a “song event,” namely, a description in the NHS Ethnography of a song performance, a characterization of how a society uses songs, or both.

We found that three latent dimensions is the optimum number, explaining 26.6% of variability in NHS Ethnography annotations. Figure 2 depicts the space and highlights examples from excerpts in the corpus; an interactive version is available at http://themusiclab.org/nhsplots. (See Text S2.1 for details of the model, including the dimension selection procedure, model diagnostics, a test of robustness, and tests of the potential influence of ethnographer characteristics on model results.) To interpret the space, we examined annotations that load highly on each dimension; to validate this interpretation, we searched for examples at extreme locations and examined their content. Loadings are presented in tables S13 to S15; a selection of extreme examples is given in table S16.

The first dimension (accounting for 15.5% of the variance, including error noise) captures variability in the Formality of a song: Excerpts high along this dimension describe ceremonial events involving adults, large audiences, and instruments; excerpts low on it describe informal events with small audiences and children. The second dimension (accounting for 6.2%) captures variability in Arousal: Excerpts high along this dimension describe lively events with many singers, large audiences, and dancing; excerpts low on it describe calmer events involving fewer people and less overt affect, such as people singing to themselves. The third dimension (4.9%) distinguishes Religious events from secular ones: Passages high along this dimension describe shamanic ceremonies, possession, and funerary songs; passages low on it describe communal events without spiritual content, such as community celebrations.

To validate whether this dimensional space captured behaviorally relevant differences among songs, we tested whether we could reliably recover clusters for four distinctive, easily identifiable, and regularly occurring song types: dance, lullaby, healing, and love (54). We searched the NHS Ethnography for keywords and human annotations that matched at least one of the four types (table S17).

Although each song type can appear throughout the space, clear structure is observable (Fig. 2): The excerpts falling into each type cluster together. On average, dance songs (1089 excerpts) occupy the high-Formality, high-Arousal, low-Religiosity region. Healing songs (289 excerpts) cluster in the high-Formality, high-Arousal, high-Religiosity region. Love songs (354 excerpts) cluster in the low-Formality, low-Arousal, low-Religiosity region. Lullabies (156 excerpts) are the sparsest category (although this was likely due to high missingness in variables associated with lullabies, such as one indicating the presence of infant-directed song; see Text S2.1.5) and are located mostly in the low-Formality and low-Arousal regions. An additional 2821 excerpts matched either more than one category or none of the four.

To specify the coherence of these clusters formally rather than just visually, we asked what proportion of song events are closer to the centroid of their own type’s location than to any other type (Text S2.1.6). Overall, 64.7% of the songs were located closest to the centroid of their own type; under a null hypothesis that song type is unrelated to location, simulated by randomly shuffling the song labels, only 23.2% would do so (P < 0.001 according to a permutation test). This result was statistically significant for three of the four song types (dance, 66.2%; healing, 74.0%; love, 63.6%; Ps < 0.001) although not for lullabies (39.7%, P = 0.92). The matrix showing how many songs of each type were near each centroid is in table S18. Note that these analyses eliminated variables with high missingness; a validation model that analyzed the entire corpus yielded similar dimensional structure and clustering (figs. S1 and S2 and Text S2.1.5).

The range of musical behavior is similar across societies

We next examined whether this pattern of variation applies within all societies. Do all societies take advantage of the full spectrum of possibilities made available by the neural, cognitive, and cultural systems that underlie music? Alternatively, is there only a single, prototypical song type that is found in all societies, perhaps reflecting the evolutionary origin of music (love songs, say, if music evolved as a courtship display; or lullabies, if it evolved as an adaptation to infant care), with the other types haphazardly distributed or absent altogether, depending on whether the society extended the prototype through cultural evolution? As a third alternative, do societies fall into discrete typologies, such as a Dance Culture or a Lullaby Culture? As still another alternative, do they occupy sectors of the space, so that there are societies with only arousing songs or only religious songs, or societies whose songs are equally formal and vary only by arousal, or vice versa? The data in Fig. 2, which pool song events across societies, cannot answer such questions.

We estimated the variance of each society’s scores on each dimension, aggregated across all ethnographies from that society. This revealed that the distributions of each society’s observed musical behaviors are remarkably similar (Fig. 3), such that a song with “average formality,” “average arousal,” or “average religiosity” could appear in any society we studied. This finding is supported by comparing the global average along each dimension to each society’s mean and standard deviation, which summarizes how unusual the average song event would appear to members of that society. We found that in every society, a song event at the global mean would not appear out of place: The global mean always falls within the 95% confidence interval of every society’s distribution (fig. S3). These results do not appear to be driven by any bias stemming from ethnographer characteristics such as sex or academic field (fig. S4 and Text S2.1.7), nor are they artifacts of a society being related to other societies in the sample by region, subregion, language family, subsistence type, or location in the Old versus New World (fig. S5 and Text S2.1.8).

We also applied a comparison that is common in studies of genetic diversity (85) and that has been performed in a recent cultural-phylogenetic study of music (86). It revealed that typical within-society variation is approximately six times the between-society variation. Specifically, the ratios of within- to between-society variances were 5.58 for Formality [95% Bayesian credible interval, (4.11, 6.95)]; 6.39 (4.72, 8.34) for Arousal; and 6.21 (4.47, 7.94) for Religiosity. Moreover, none of the 180 mean values for the 60 societies over the three dimensions deviated from the global mean by more than 1.96 times the standard deviation of the principal components scores within that society (fig. S3 and Text S2.1.9).

These findings demonstrate global regularities in musical behavior, but they also reveal that behaviors vary quantitatively across societies, consistent with the long-standing conclusions of ethnomusicologists. For instance, the Kanuri’s musical behaviors are estimated to be less formal than those of any other society, whereas those of the Akan are estimated to be the most religious (in both cases, significantly different from the global mean on average). Some ethnomusicologists have attempted to explain such diversity, noting, for example, that more formal song performances tend to be found in more socially rigid societies (10).

Despite this variation, a song event of average formality would appear unremarkable in the Kanuri’s distribution of songs, as would a song event of average religiosity in the Akan. Overall, we find that for each dimension, approximately one-third of all societies’ means significantly differed from the global mean, and approximately half differed from the global mean on at least one dimension (Fig. 3). But despite variability in the societies’ means on each dimension, their distributions overlap substantially with one another and with the global mean. Moreover, even the outliers in Fig. 3 appear to represent not genuine idiosyncrasy in some cultures but sampling error: The societies that differ more from the global mean on some dimension are those with sparser documentation in the ethnographic record (fig. S6 and Text S2.1.10). To ensure that these results are not artifacts of the statistical techniques used, we applied them to a structurally analogous dataset whose latent dimensions are expected to vary across countries, namely climate features (for instance, temperature is related to elevation, which certainly is not universal); the results were entirely different from what we found when analyzing the NHS Ethnography (figs. S7 and S8 and Text S2.1.11).

The results suggest that societies’ musical behaviors are largely similar to one another, such that the variability within a society exceeds the variability between them (all societies have more soothing songs, such as lullabies; more rousing songs, such as dance tunes; more stirring songs, such as prayers; and other recognizable kinds of musical performance), and that the appearance of uniqueness in the ethnographic record may reflect underreporting.

Listeners accurately identify the behavioral contexts of songs

In a previous study, people listened to recordings from the NHS Discography and rated their confidence in each of six possible behavioral contexts (e.g., “used to soothe a baby”). On average, the listeners successfully inferred a song’s behavioral context from its musical forms: The songs that were actually used to soothe a baby (i.e., lullabies) were rated highest as “used to soothe a baby”; dance songs were rated highly as “used for dancing,” and so on (54).

We ran a massive conceptual replication (Text S1.4.2) where 29,357 visitors to the citizen-science website http://themusiclab.org listened to songs drawn at random from the NHS Discography and were asked to guess what kind of song they were listening to from among four alternatives (yielding 185,832 ratings, i.e., 118 songs rated about 1500 times each). Participants also reported their musical skill level and degree of familiarity with world music. Listeners guessed the behavioral contexts with a level of accuracy (42.4%) that is well above chance (25%), showing that the acoustic properties of a song performance reflect its behavioral context in ways that span human cultures.

The confusion matrix (Fig. 5A) shows that listeners identified dance songs most accurately (54.4%), followed by lullabies (45.6%), healing songs (43.3%), and love songs (26.2%), all significantly above chance (Ps < 0.001). Dance songs and lullabies were the least likely to be confused with each other, presumably because of their many contrasting features, such as tempo (a possibility we examine below; see Table 2). The column marginals suggest that the raters were biased toward identifying recordings as healing songs (32.6%, above their actual proportion of 23.7%) and away from identifying them as love songs (17.9%), possibly because healing songs are less familiar to Westernized listeners and they were overcompensating in identifying examples. As in previous research (54), love songs were least reliably identified, despite their ubiquity in Western popular music, possibly because they span a wide range of styles (for example, the vastly different Elvis Presley hit singles “Love Me Tender” and “Burning Love”). Nonetheless, d-prime scores (Fig. 5A), which capture the sensitivity to a signal independently of response bias, show that all behavioral contexts were identified at a rate higher than chance (d′ = 0).

Are accurate identifications of the contexts of culturally unfamiliar songs restricted to listeners with musical training or exposure to world music? In a regression analysis, we found that participants’ categorization accuracy was statistically related to their self-reported musical skill [F(4,16245) = 2.57, P = 0.036] and their familiarity with world music [F(3,16167) = 36.9, P < 0.001; statistics from linear probability models], but with small effect sizes: The largest difference was a 4.7–percentage point advantage for participants who reported that they were “somewhat familiar with traditional music” relative to those who reported that they had never heard it, and a 1.3–percentage point advantage for participants who reported that they have “a lot of skill” relative to “no skill at all.” Moreover, when limiting the dataset to listeners with “no skill at all” or listeners who had “never heard traditional music,” mean accuracy was almost identical to the overall cohort. These findings suggest that although musical experience enhances the ability to detect the behavioral contexts of songs from unfamiliar cultures, it is not necessary.

Quantitative representations of musical forms accurately predict behavioral contexts of song

If listeners can accurately identify the behavioral contexts of songs from unfamiliar cultures, there must be acoustic features that universally tend to be associated with these contexts. To identify them, we evaluated the relationship between a song’s musical forms [measured in four ways; see Text S1.2.5 and (12, 31, 32, 91–93) for discussion of how difficult it is to represent music quantitatively] and its behavioral context. We used a cross-validation procedure that determined whether the pattern of correlation between musical forms and context computed from a subset of the regions could be generalized to predict a song’s context in the other regions (as opposed to being overfitted to arbitrary correlations within that subsample). Specifically, we trained a least absolute shrinkage and selection operator (LASSO) multinomial logistic classifier (94) on the behavioral context of all the songs in 29 of the 30 regions in the NHS Discography, and used it to predict the context of the unseen songs in the 30th. We ran this procedure 30 times, omitting a different region each time (table S23 and Text S2.3.2). We compared the accuracy of these predictions to two baselines: pure chance (25%) and the accuracy of listeners in the massive online experiment (see above) when guessing the behavioral context from among four alternatives (42.4%).

We found that with each of the four representations, the musical forms of a song can predict its behavioral context (Fig. 5B) at high rates, comparable to those of the human listeners in the online experiment. This finding was not attributable to information in the recordings other than the singing, which could be problematic if, for example, the presence of a musical instrument on a recording indicated that it was likelier to be a dance song than a lullaby (54), artificially improving classification. Representations with the least extraneous influence—the expert annotators and the summary features extracted from transcriptions—had no lower classification accuracy than the other representations. And a classifier run on combined expert + transcription data had the best performance of all, 50.8% [95% CI (40.4%, 61.3%), computed by corrected resampled t test (95)].

To ensure that this accuracy did not merely consist of patterns in one society predicting patterns in historically or geographically related ones, we repeated the analyses, cross-validating across groupings of societies, including superordinate world region (e.g., “Asia”), subsistence type (e.g., “hunter-gatherers”), and Old versus New World. In many cases, the classifier performed comparably to the main model (table S24), although low power in some cases (i.e., training on less than half the corpus) substantially reduced precision.

In sum, the acoustic form of vocal music predicts its behavioral contexts worldwide (54), at least in the contexts of dance, lullaby, healing, and love: All classifiers performed above chance and within 1.96 standard errors of the performance of human listeners.

Musical features that characterize the behavioral contexts of songs across societies

Showing that the musical features of songs predict their behavioral context provides no information about which musical features those are. To help identify them, we determined how well the combined expert + transcription data distinguished between specific pairs of behavioral contexts rather than among all four, using a simplified form of the classifiers described above, which not only distinguished the contexts but also identified the most reliable predictors of each contrast, without overfitting (96). This can reveal whether tempo, for example, helps distinguish dance songs from lullabies while failing to distinguish lullabies from love songs.

Performance once again significantly exceeded chance (in this case, 50%) for all six comparisons (Ps < 0.05; Fig. 5C). Table 2 lays out the musical features that drive these successful predictions and thereby characterize the four song types across cultures. Some are consistent with common sense; for instance, dance songs differ from lullabies in tempo, accent, and the consistency of their macrometer (i.e., the superordinate grouping of rhythmic notes). Other distinguishers are subtler: The most common interval of a song occurs a smaller proportion of the time in a dance song than in a healing song, which suggests that dance songs are more melodically variable than healing songs (for explanations of musical terminology, see Table 2). Similarly, it is unsurprising that lullabies and love songs are more difficult to distinguish than lullabies and dance songs (97); nonetheless, they may be distinguished by two features: the strength of metrical accents and the size of the pitch range (both larger in love songs).

In sum, four common song categories, distinguished by their contexts and goals, tend to have distinctive musical qualities worldwide. These results suggest that universal features of human psychology bias people to produce and enjoy songs with certain kinds of rhythmic or melodic patterning that naturally go with certain moods, desires, and themes. These patterns do not consist of concrete acoustic features, such as a specific melody or rhythm, but rather of relational properties such as accent, meter, and interval structure.

Of course, classification accuracy that is twice the level of chance still falls well short of perfect prediction; hence, many aspects of music cannot be manifestations of universal psychological reactions. Although musical features can predict differences between songs from these four behavioral contexts, a given song may be sung in a particular context for other reasons, including its lyrics, its history, the style and instrumentation of its performance, its association with mythical or religious themes, and constraints of the culture’s musical idiom. And although we have shown that Western listeners, who have been exposed to a vast range of musical styles and idioms, can distinguish the behavioral contexts of songs from non-Western societies, we do not know whether non-Western listeners can do the same. To reinforce the hypothesis of universal associations between musical form and context, similar methods should be tested with non-Western listeners.

Signatures of tonality appear in all societies studied

A basic feature of many styles of music is tonality, in which a melody is composed of a fixed set of discrete tones [perceived pitches as opposed to actual pitches, a distinction dating to Aristoxenus’s Elementa Harmonica (98)], and some tones are psychologically dependent on others, with one tone felt to be central or stable (99–101). This tone (more accurately, perceived pitch class, embracing all the tones one or more octaves apart) is called the tonal center or tonic, and listeners characterize it as a reference point, point of stability, basis tone, “home,” or tone that the melody “is built around” and where it “should end.” For example, the tonal center of “Row Your Boat” is found in each of the “row”s, the last “merrily,” and the song’s last note, “dream.”

Although tonality has been studied in a few non-Western societies (102, 103), its cross-cultural distribution is unknown. Indeed, the ethnomusicologists who responded to our survey (Text S1.4.1) were split over whether the music of all societies should be expected to have a tonal center: 48% responded “probably not universal” or “definitely not universal.” The issue is important because a tonal system is a likely prerequisite for analyzing music, in all its diversity, as the product of an abstract musical grammar (73). Tonality also motivates the hypothesis that melody is rooted in the brain’s analysis of harmonically complex tones (104). In this theory, a melody can be considered a set of “serialized overtones,” the harmonically related frequencies ordinarily superimposed in the rich tone produced by an elongated resonator such as the human vocal tract. In tonal melodies, the tonic corresponds to the fundamental frequency of the disassembled complex tone, and listeners tend to favor tones in the same pitch class as harmonics of the fundamental (105).

To explore tonality in the NHS Discography, we analyzed the expert listener annotations and the transcriptions (Text S2.4.1). Each of the 30 expert listeners was asked, for each song, whether or not they heard at least one tonal center, defined subjectively as above. The results were unambiguous: 97.8% of ratings were in the affirmative. More than two-thirds of songs were rated as “tonal” by all 30 expert listeners, and 113 of the 118 were rated as tonal by more than 90% of them. The song with the most ambiguous tonality (the Kwakwaka’wakw healing song) still had a majority of raters respond in the affirmative (60%).

If listeners heard a tonal center, they were asked to name its pitch class. Here too, listeners were highly consistent: Either there was widespread agreement on a single tonal center or the responses fell into two or three tonal centers (Fig. 6A; the distributions of tonality ratings for all 118 songs are in fig. S10). We used Hartigan’s dip test (106) to measure the multimodality of the ratings. In the 73 songs that the test classified as unimodal, 85.3% of ratings were in agreement with the modal pitch class. In the remaining 45 songs, 81.7% of ratings were in agreement with the two most popular pitch classes, and 90.4% were in agreement with the three most popular. The expert listeners included six Ph.D. ethnomusicologists and six Ph.D. music theorists; when restricting the ratings to this group alone, the levels of consistency were comparable.

In songs where the ratings were multimodally distributed, the modal tones were often hierarchically related; for instance, ratings for the Ojibwa healing song were evenly split between B (pitch class 11) and E (pitch class 4), which are a perfect fourth (five semitones) apart. The most common intervals between the two modal tones were the perfect fourth (in 15 songs), a half-step (one semitone, in nine songs), a whole step (two semitones, in eight songs), a major third (four semitones, in seven songs), and a minor third (three semitones, in six songs).

We cannot know which features of a given recording our listeners were responding to in attributing a tonal center to it, nor whether their attributions depended on expertise that ordinary listeners lack. We thus sought converging, objective evidence for the prevalence of tonality in the world’s music by submitting NHS Discography transcriptions to the Krumhansl-Schmuckler key-finding algorithm (107). This algorithm sums the durations of the tones in a piece of music and correlates this vector with each of a family of candidate vectors, one for each key, consisting of the relative centralities of those pitch classes in that key. The algorithm’s first guess (i.e., the key corresponding to the most highly correlated vector) matched the expert listeners’ ratings of the tonal center 85.6% of the time (measured via a weighted average of its hit rate for the most common expert rating when the ratings were unimodal and either of the two most common ratings when they were multimodal). When we relaxed the criterion for a match to the algorithm’s first- and second-ranked guesses, it matched the listeners’ ratings on 94.1% of songs; adding its third-ranked estimate resulted in matches 97.5% of the time, and adding the fourth resulted in matches with 98.3% [all Ps < 0.0001 above the chance level of 9.1%, using a permutation test (Text S2.4.1)]. These results provide convergent evidence for the presence of tonality in the NHS Discography songs (Fig. 6B).

These conclusions are limited in several ways. First, they are based on songs from only four behavioral contexts, omitting others such as mourning, storytelling, play, war, and celebration. Second, the transcriptions were created manually and could have been influenced by the musical ears and knowledge of the expert transcribers. (Current music information retrieval algorithms are not robust enough to transcribe melodies accurately, especially from noisy field recordings, but improved ones could address this issue.) The same limitation may apply to the ratings of our expert listeners. Finally, the findings do not show how the people from the societies in which NHS Discography songs were recorded hear the tonality in their own music. To test the universality of tonality perception, one would need to conduct field experiments in diverse populations.

Music varies along two dimensions of complexity

To examine patterns of variation among the songs in the NHS Discography, we applied the same kind of Bayesian principal components analysis used for the NHS Ethnography to the combination of expert annotations and transcription features (i.e., the representations that focus most on the singing, excluding context). The results yielded two dimensions, which together explain 23.9% of the variability in musical features. The first, which we call Melodic Complexity, accounts for 13.1% of the variance (including error noise); heavily loading variables included the number of common intervals, pitch range, and ornamentation (all positively) and the predominance of the most common pitch class, the predominance of the most common interval, and the distance between the most common intervals (all negatively; see table S25). The second, which we call Rhythmic Complexity, accounts for 10.8% of the variance; heavily loading variables included tempo, note density, syncopation, accent, and consistency of macrometer (all positively) and the average note duration and duration of melodic arcs (all negatively; see table S26). The interpretation of the dimensions is further supported in Fig. 7, which shows excerpts of transcriptions at the extremes of each dimension; an interactive version is at http://themusiclab.org/nhsplots.

In contrast to the NHS Ethnography, the principal components space for the NHS Discography does not distinguish the four behavioral contexts of songs in the corpus. We found that only 39.8% of songs matched their nearest centroid (overall P = 0.063 from a permutation test; dance: 56.7%, P = 0.12; healing: 7.14%, P > 0.99; love: 43.3%, P = 0.62; lullaby: 50.0%, P = 0.37; a confusion matrix is in table S27). Similarly, k-means clustering on the principal components space, asserting k = 4 (because there are four known clusters), failed to reliably capture any of the behavioral contexts. Finally, given the lack of predictive accuracy of songs’ location in the two-dimensional space, we explored each dimension’s predictive accuracy individually, using t tests of each context against the other three, adjusted for multiple comparisons (88). Melodic complexity did not predict context (dance, P = 0.79; healing, P = 0.96; love, P = 0.13; lullaby, P = 0.35). However, rhythmic complexity did distinguish dance songs (which were more rhythmically complex, P = 0.01) and lullabies (which were less rhythmically complex, P = 0.03) from other songs; it did not distinguish healing or love songs (Ps > 0.99). When we adjusted these analyses to account for across-region variability, the results were comparable (Text S2.4.2). Thus, although musical content systematically varies in two ways across cultures, this variation is mostly unrelated to the behavioral contexts of the songs, perhaps because complexity captures distinctions that are salient to music analysts but not strongly evocative of particular moods or themes among the singers and listeners themselves.

Melodic and rhythmic bigrams are distributed according to power laws

Many phenomena in the social and biological sciences are characterized by Zipf’s law (108), in which the probability of an event is inversely proportional to its rank in frequency, an example of a power-law distribution (in the Zipfian case, the exponent is 1). Power-law distributions (as opposed to, say, the geometric distribution) have two key properties: A small number of highly frequent events account for the majority of observations, and there are a large number of individually improbable events whose probability falls off slowly in a thick tail (109).

In language, for example, a few words appear with very high frequency, such as pronouns, while a great many are rare, such as the names of species of trees, but any sample will nonetheless tend to contain several rare words (110). A similar pattern is found in the distribution of colors among paintings in a given period of art history (111). In music, Zipf’s law has been observed in the melodic intervals of Bach, Chopin, Debussy, Mendelssohn, Mozart, and Schoenberg (112–116); in the loudness and pitch fluctuations in Scott Joplin piano rags (117); in the harmonies (118–120) and rhythms of classical music (121); and, as Zipf himself noted, in melodies composed by Mozart, Chopin, Irving Berlin, and Jerome Kern (108).

We tested whether the presence of power-law distributions is a property of music worldwide by tallying relative melodic bigrams (the number of semitones separating each pair of successive notes) and relative rhythmic bigrams (the ratio of the durations of each pair of successive notes) for all NHS Discography transcriptions (Text S2.4.3). The bigrams overlapped, with the second note of one bigram also serving as the first note of the next.

We found that both the melodic and rhythmic bigram distributions followed power laws (Fig. 8), and this finding held worldwide: The fit between the observed bigrams and the best-fitting power function was high within each region (melodic bigrams: median R² = 0.97, range 0.92 to 0.99; rhythmic bigrams: median R² = 0.98, range 0.88 to 0.99). The most prevalent bigrams were the simplest. Among the melodic bigrams (Fig. 8A), three small intervals (unison, major second, and minor third) accounted for 73% of the bigrams; the tritone (six semitones) was the rarest, accounting for only 0.2%. The prevalence of these bigrams is significant: Using only unisons, major seconds, and minor thirds, one can construct any melody in a pentatonic scale, a scale found in many cultures (122). Among the rhythmic bigrams (Fig. 8B), three patterns with simple integer ratios (1:1, 2:1, and 3:1) accounted for 86% of observed bigrams, whereas a large and eclectic group of ratios (e.g., 7:3, 11:2) accounted for fewer than 1%. The distribution is thus consistent with earlier findings that rhythmic patterns with simple integer ratios appear to be universal (123). The full lists of bigrams, with their cumulative frequencies, are in tables S28 and S29.

These results suggest that power-law distributions in music are a human universal (at least in the four genres studied here), with songs dominated by small melodic intervals and simple rhythmic ratios and enriched with many rare but larger and more complex ones. Because the specification of a power law is sensitive to sampling error in the tail of the distribution (124), and because many generative processes can give rise to a power-law distribution (125), we cannot identify a single explanation. Among the possibilities are that control of the vocal tract is biased toward small jumps in pitch that minimize effort, that auditory analysis is biased toward tracking similar sounds that are likely to be emitted by a single sound-maker, that composers tend to add notes to a melody that are similar to ones already contained in it, and that human aesthetic reactions are engaged by stimuli that are power law–distributed, which makes them neither too monotonous nor too chaotic (116, 126, 127)—“inevitable and yet surprising,” as the music of Bach has been described (128).