Eighty pairs of stimuli (items E1–E80 described musically in Image 1 in Supplementary Material) were composed based on the two alternative forced choice paradigm, as in the majority of previously presented batteries, where the child decides if a pair or stimuli are equal or different. The 80 pairs were designed to evaluate seven MP subdomains: contour (13 items), timbre (12 items), meter (10 items), pitch (5 items), scale (15 items), duration (20 items), and loudness (5 items):

An important difference between the proposed battery and previous batteries is the inclusion of items beyond the paradigm of tonality. Most previous batteries, such as the MBEMA (Peretz et al., 2013) and The Primary Measure of Music Audiation (Gordon, 1986) consist exclusively of stimuli built around tonality; however, there is little a priori reason to restrict items to a single musical code. Moreover, increased variety will permit exploration of how each item and its respective parameters behave psychometrically within a multidimensional model. Although atonal stimuli are included in the PROMS (Law and Zentner (2012), these are restricted to the set of melody subtests, and are restricted to free chromaticism (i.e., using the 12 tones of the Western chromatic scale with no particular underlying structure), a likely consequence of the authors' choice of “basic,” “abstract,” and “stylistically neutral” stimuli. As seen in the description of the items in each domain above, we deliberately chose musical paradigms based on historical systems of Western music: tonal, atonal and modal, as well as sounds without defined pitch (i.e., percussion and electronic noise) to circumvent such restrictions in a systematic way. Moreover, while the MBEMA uses exclusively synthesized piano sounds, and the Primary Measure of Music Audiation uses sinusoidal waves, we adopted a wide range of timbres (i.e., different musical instruments, electronic sounds, filtered white noise, etc.) in order to be less restrictive.

Finally, by having a systematic set of musical paradigms as the basis of stimulus composition, we take into account the particularity of each domain in the manipulation of musical parameters. For example, while rhythmic changes in all three of the previously cited batteries have been associated with strong and weak beats in musical measures, we manipulated sound durations, and in the domain of meter, we changed types of meters (from binary to ternary and vice versa) including “unusual” meters, such as 5 and 7 beats. We also used different types of scales and continuous sounds (glissandi) in the domain of contour, to afford increased opportunity to assess musical discrimination. Details of the musical modes of the stimuli and their paradigms (i.e., equal or different) are shown in Table 2 (left side).

The proposed battery can be administered within 30 min, as suggested by teachers in a pilot study to avoid interference due to attention. Among adults, active listening tasks of even a few hours can lead to reorganization of certain cortical representations (Pantev et al., 1999), and although evidence is lacking for children, restricting the number of items may be advisable to avoid practice effects.

The following software were used: Rosegarden for midi tracks, Linux Sampler for sampling, Piano and instruments gig: Maestro Concert Grand V2 (piano), Philharmonia Orchestra (percussion, clarinet and guitar), Vienna Symphonic Orchestra Pro (Oboe, flute, violin), Pure Data for sound synthesis and filtering (Puckette, 2007), Lilypond for score engraving (Nienhuys and Nieuwenhuizen, 2003), and Snd to create wave and spectral graphs.

Fourteen evaluators (one per school) undertook training to ensure that equivalent instructions were given. Providing feedback to participants in the form of demonstrative facial signs or oral positive/negative cues was discouraged. To counter loss of attention or demotivation, the motivational phrases “you are almost finished,” “do not give up” and “it is almost complete” were used. Phrases, such as “you are doing well” were discouraged, as they could be perceived as feedback in relation to the answers given and thus interfere with performance.

This research was approved by the Ethical Committee from the Federal University of Sao Paulo (CAEE: 00751812.3.0000.5505). Written informed consent was given by parents or children's legal guardians.

All children were tested alone in a quiet setting at school using Philips headphones (model SHL 9560). Prior to beginning the test, a standardized set of instructions was read by the evaluator. Six pre-test stimuli were played to evaluate whether the child fully understood the instructions:

“You, [child's name], will hear two sound sequences separated by a short silence. You should decide if these sound sequences are the same or different. Then, press the different button if the two sequences are at all different, no matter how small. Press the equal button if you believe that the two sequences of sounds are exactly the same.”

During the six pre-test stimuli, the evaluator was permitted to help the child, explaining why and when the stimulus pairs were the same or different. The six pre-test stimuli and instructions were repeated until the child understood; for these six pre-tests, the program gives feedback for the evaluator and child, informing them if the response was correct or not.

The 80 items from the battery were then played, and responses were recorded by the software as 1 if the question was correctly answered and 0 if answered incorrectly. The child and evaluator did not receive any feedback about how many items were marked correctly or incorrectly. There was no limit to the amount of time allowed for the child to press the button. Items were presented only once during testing. The test duration was on average 30 min. The children were not allowed to take a break since the test was automatized such that the subsequent stimulus began immediately after the previous answer was given. In contrast to other batteries, stimuli were presented in a random order (described in Supplementary Material) to avoid local independence (i.e., contingencies in responses) and artifacts due to fatigue.

A common issue recurrent in the psychometric literature but which has yet to be resolved in MP data relates to population heterogeneity and exploration of the stability of the items under different background variables (e.g., sex and age). Invariance testing is a fundamental psychometric procedure to determine if the measurement properties of the items, and of the model, are comparable across important demographic features (e.g., sex, age, race). Invariance testing is pertinent in the context of MP since cultural aspects of MP have been explored using the MBEA, and parts of the original version were shown not to be suitable for evaluating musical abilities across populations with different musical traditions (Paraskevopoulos et al., 2010). In other words, if the researcher or clinician seeks to compare MP across cultures, the items and their underlying factors need to be comparable (invariant). There are different procedures to study the invariance of a given model including multiple indicators, multiple causes (also known as MIMIC also called CFA with covariates Jöreskog and Goldberger, 1975; Muthén, 1989), multi-group CFA, and a more recent method called alignment (Muthén and Asparouhov, 2014). For a review of these procedures and other modern invariance testing techniques see Van De Schoot et al. (2015).

We used MIMIC model to explore the effects of sociodemographic variables (i.e., age, sex, and school type [private vs. public]) on the general MP factor and separate items. This procedure clarifies aspects of measurement invariance and heterogeneity. The former results from inspection of direct relationships between the sociodemographic variables and items that are not mediated by the general MP factor. If significant, this indicates measurement non-invariance due to differential item functioning (DIF). Because we have no a priori hypothesis about which items might exhibit differential functioning, we used the approach described by Brown (2015) where direct relationships between the sociodemographic variables and the items were fixed at zero; then, upon inspection of modification indices, we freed the effect of sociodemographic variables on the items with the highest modification indices (superior to 4.00) and determined whether this enhanced the model.

Population heterogeneity was explored via relationships between the sociodemographic variables and the general MP factor. If significant, this indicates that the factor means are different for different levels of the sociodemographic variables. For two dichotomous covariates (school type and sex), the heterogeneity effect on the m-factor is given as Cohen's d (standardized effect size) where 0.2 to 0.3 is considered a “small” effect, 0.5 a “medium” effect and anything higher than 0.8 a “large” effect (Cohen, 1977). For age, the effect is expressed in terms of a standardized regression coefficient.

The following indices were used to better understand the viability of subscales: (a) coefficient omega (ω; Revelle and Zinbarg, 2009; Mcdonald, 1999), a factor analytical model-based reliability estimate, originating from the work of Jöreskog (1971) estimating the proportion of variance in the observed total scores attributable to all modeled sources of common variance; (b) a coefficient omega hierarchical (ω_h; Mcdonald, 1999; Zinbarg et al., 2005), model-based reliability index, which judges the degree to which composite scale scores are interpretable as a measure of a single common factor. ω_{h is} was computed by dividing the squared sum of the factor loadings on the general factor by the model estimated variances of total scores; (c) omega subscale (ω_s), a reliability estimate for a residualized subscale controlling for that part of the reliability due to the general factor (Reise, 2012); and (d) the explained common variance (ECV) defined as the ratio of variance explained by the general factor divided by the variance explained by the general and group factors. Key details about each index, its calculation, and interpretation are described in Rodriguez et al. (2016b).

In total, 1006 children were tested, 69.9% of whom were enrolled in public schools, 45% male, with approximately 200 children from each grade 1 through 5. The mean ages and standard deviations (SD) by grade were: first grade (mean = 6.44, SD = 0.83), second grade (mean = 7.25, SD = 0.63), third grade (mean = 8.37, SD = 0.80), fourth grade (mean = 9.35, SD = 0.8), and fifth grade (mean = 10.29, SD = 0.7). Five out of 14 schools were private schools, representing the non-proportional enrolled students in São Paulo State. Table 1 shows the number of boys and girls across the grades, by type of school (private/public).

The goodness of fit for the bifactor model's seven specific factors and general m-factor returned a satisfactory adjusted model: χ(3000)2 = 3415.408, p < 0.001; RMSEA = 0.012 (90% confidence interval [CI] = 0.010 to 0.014), Cfit = 1.000; CFI = 0.931 and TLI = 0.927.

The standardized factor loadings for each item on the m-factor and on specific factors are shown in Table 2, where the items are grouped by the specific factor. Details about the music mode (i.e., tonal, atonal, electronic noise, and others) and paradigm (i.e., same or different) are also identified. Details of the bifactor model, standard errors for each factor loading, and their respective p-values are available from the corresponding author. The corresponding musical stimuli descriptions are presented in Supplementary Material.

Standardized factor loadings represent the degree to which each item is associated with its underlying factor; values closer to 1 represent stronger correlations with the underlying factor. A negative correlation indicates that the item is inversely correlated with the underlying factor. The “same” items (i.e., two identical sequences of sounds) loaded onto the m-factor with negative factor loadings. The factor loadings onto the m-factor are higher than those onto the specific factors.

The following indices were derived from the bifactor model: ω = 0.977, ω_H = 0.938, and EVC = 0.754. From ω_H, we found that 93.80% the variance in the unit-weighted total scores could be attributed to the differences between participants in the general MP factor. The square root of ω_H (0.968) indicates an excellent correlation between the general factor and the observed total scores. The reliabilities of the five specific factors [calculated as ω_(s)] were very low when controlling for reliability of the general MP factor: ω_(s)Contour = 0.088, ω_(s)Duration = 0.142, ω_(s)Meter = 0.112, ω_(s)Timbre = 0.367, and ω_(s)Loudness = 0.309, ω_(s)Scale = 0.097, ω_(s)Pitch = 0.205.

None of the 80 items showed DIF. It can be concluded that girls and boys with the same level of the m-factor do not differ in their likelihood to respond to any given stimulus correctly. Similarly, no DIF was observed for children enrolled at public vs. private schools, or based on age. Children of different ages, or in different types of schools, who have the same amount of m-factor do not have a higher likelihood of responding correctly to any given item.

Boys showed a higher mean for the m-factor as compared to girls, but this difference was very small in terms of magnitude (d = 0.122, p = 0.033). Children from public schools had moderately lower values of m-factor as compared to those enrolled in private schools (d = −0.416, p < 0.001). No effect of age (β = 0.052, p = 0.099) was observed; therefore, there is no evidence to suggest that age is associated with MP achievement.

Information curve for all items and latent trait distribution for the general factor.

The distribution of the m-factor (histogram) is shown in Figure 4, demonstrating a normal-like distribution (skewness = −0.062 and kurtosis = 0.970), and the total information curve for the m-factor is presented in Figure 5. The total information curve shows a peak around zero (the mean in the z-score scale), indicating that the 80 items have optimal precision in children with an average amount of MP skill, and less precision in assessing very skilled or very impaired children (greater than 2 standard deviations from the norm). In this figure, the y-axis shows information (precision) of the m-factor (not a probability function to infer normality).

We find strong evidence that the items within each of the seven specific factors converge to inform a general (MP) factor, the m-factor. Statistically, the set of 80 items encompassing eight domains (seven specific factors + one general factor) returned excellent fit indices. Musically, the compositional hybrid model used herein extends the content of available scales, balancing items based on the tonal paradigm of the so-called common-practice period with two others present in Western music: the modal paradigm and post-tonality. The latter is not a paradigm per se, but rather a way to organize musical parameters (i.e., pitch, duration/rhythm, intensity, timbre) in a way that contradicts tonality. These elements of musical language beyond tonality (Boucourechliev, 1993) originate from the musical avant-garde (Griffiths, 2011). Hence, the m-factor offers a more flexible exploration of musical possibilities that does not rely on the assumption that the tonal system is musically universal, allowing assessment of musical understanding beyond a narrowly defined conception of Western tonal music. Although the idea of a general music factor had been described in Law and Zentner (2012) alluding to Charles Spearman's g-factor for intelligence, formal procedures (i.e., bifactor modeling) to evaluate if the data fit to such model had not previously been conducted. Moreover, as in the case of the g-factor, the distribution of the m-factor across a random sample of children was normal.

Through the bifactor model, we observed that the viabilities and reliabilities of MP subscales were poor. Moreover, when ω_H (0.938) is compared with ω (0.977), almost all of the reliable variance in total scores (0.938/0.977 = 0.96) can be attributed to the general factor, which reflects individual differences in MP taken as a whole. Only 3.9% (the difference between 0.977 and 0.938) of the reliable variance in total scores can be attributed to the dimensionality associated with the specific domains. Only 2.3% (i.e., the difference between 1.000 and 0.977) of the estimated variance is due to random error. It is important to stress that although the data advocate for parceling analytically (to recreate the m-factor at a latent level), they do not support reporting at the level of the subscales, because the subscales are not reliable; instead, it is advisable to report only the general m-factor. Summing the number of 80 items answered correctly can be interpreted as an essentially unidimensional reflection of MP, regardless of the multidimensionality evident in the data. In other words, the m-factor is robustly reliable even though it is a multidimensional construct, and the specific subdomains displayed weak viability beyond the general MP factor.

This lack of subscale viability is consistent with the findings from bifactor models applied to other areas of child evaluation (Jovanović, 2015; Wagner et al., 2016), and applied to 50 other different scales assessing various aspects of psychopathology and personality (Rodriguez et al., 2016a). From those studies, two main results have arisen: (1) although all measures had been assumed to be multidimensional, unit-weighted total scores overwhelmingly reflected variance due to a single latent variable; and (2) unit-weighted subscale scores mostly reflected the general trait, not specific dimensions (Rodriguez et al. (2016a).

In common practice, findings of multidimensionality are often considered to be a sufficient justification for reporting subscale scores. There are several important concerns, however, with this practice (Reise et al., 2013). Moreover, even in the presence of multidimensionality, the use of total scale scores can be justified (Gustafsson and Åberg-Bengtsson, 2010), whereas findings of multidimensionality do not guarantee that subscales can provide meaningful and reliable information about subdomains that is unique from the general construct.

Despite our lack of evidence supporting subscale viability and reliability, MP subscales have been useful in several different contexts. For instance, the MBEA melodic discrimination ability subscale provided a way of finding out treatment development and cognitive remediation in schizophrenia (Kantrowitz et al., 2014) and the domain of rhythm perception is clearly associated with prosody perception (Hausen et al., 2013). Evaluating the subscale viability of these instruments may help to determine if those correlations are truly subscale-specific.

Given the large sample size, modeling at the item-level was viable in this study. Tools measuring MP and its components tend to use parcels to represent the domains, where the achievement in a given domain is a composite (normally a sum) of the correctly endorsed items. In this procedure, each parcel is treated as the observed indicator rather than evaluating the items individually. When properly modeled, item-level analyses and parcel-level analyses should generally converge on the same centroid (Little et al., 1999). For our battery, we offer evidence in favor of parceling. Researchers interested in using our model for MP at a latent level (i.e., distinguishing common from residual variances) can use a facet–representative parceling procedure for the seven specific factors, even with small sample sizes (Little et al., 2002). By taking the average of the correct items that were assigned to each parcel, the researcher can model a unidimensional trait via confirmatory factor analysis, having seven parcels as the items. We recommend using the average of correct answers per parceling due to the unbalanced number of items per parcel. This procedure will reduce the complexity of the model making the analysis more viable than a full item-level decomposition.

We observed that items under an equal paradigm (pairs of stimuli exhibiting no difference) were negatively related to the m-factor while different items (pair of stimuli where there are differences) were positively related to the m-factor. This indicates a methodological effect on the way the different types of items capture MP skills. Because the other available MP batteries did not investigate features at item-level, inverse factor loading patterns have not yet been described, partially due to noise introduced by parceling procedures adopted in the interpretation of the available MP batteries. Future psychometric investigations might incorporate this new source of variance (the paradigm) into a specific type of confirmatory model called “multitrait-multimethod,” where variance due to paradigm (the multimethod part of the model) and variance due to the seven domains (the multitrait part) are modeled. Thus, CFA offers multiple possibilities for evaluating the psychometric features of MP models and their fit to empirical data. Our decision regarding how to group and test the items was based on the traditional organization of MP batteries (e.g., pitch, scale, meter and so on); however, many other factor structures could be tested. For instance, given 80 stimuli, many of which extend beyond the diatonic paradigm, completely novel specific factors beyond those traditionally conceptualized could be constructed by grouping items based on musical modes (tonal, atonal, modal, electronic noise). These alternative models, if found to fit the data, might allow exploration of novel MP features, particularly if novel subscales are found to be reliable under a bifactor model.

To our knowledge, invariance testing has not been described in the MP literature. In the present study, we found that none of the items showed differential item functioning regarding age, sex, or type of school. In other words, none of the 80 items have a different probability of being answered correctly by children of different ages, sexes, and school type. Thus, the items are stable indicators of MP. Previously, different hypotheses have been raised in terms of comparing cultures on their MP skills (Zatorre, 2016) and language background (Peretz et al., 2013). However, without precise information regarding batteries designed to measure MP and their invariance features in those target groups, results may be biased due to differential item functioning. In that case, a given musical task might be answered differently between groups (i.e., two groups perceive a given musical paradigm differently given the same amount of MP trait).

The present study reports that children enrolled in public schools exhibited a lower amount of m-factor (with a moderate effect size). In contrast, only a very small effect of sex on m-factor was observed–one that would require a similarly large sample size to replicate. Even in this very large sample size including a range of ages, there was no evidence that the m-factor was correlated with age. This contrasts with Peretz et al. (2013), who found a small correlation between the Montreal Battery of Evaluation of Musical Abilities (MBEMA) with age (Pearson's r varying from 0.29 for untrained children to 0.31 for musically trained children) in a population from 6 to 8 years old). Regarding our lack of correlation with age, it is important to emphasize that this is a cross-sectional study. Therefore, inferences regarding the development of MP across childhood are not possible. Moreover, because this is the first study to evaluate invariance across different ages, the finding cannot be compared reliably with studies using other batteries which may be susceptible to differential item functioning based on age. Ideally, longitudinal studies would be necessary to first evaluate the stability of MP across age and then to establish growth trajectories of MP development.

A total information curve for the m-factor showed that the 80 items measure MP most accurately among children with average skills (peak of information at zero on the Z-scale). Therefore, the m-factor can be considered optimal for use with averagely skilled children, and consequently our battery may not optimally measure MP among children with amusia or with exceptional musical skills. Children with congenital amusia are “…unable to recognize well-known tunes in the absence of lyrics, and they have difficulty differentiating melodies on the basis of pitch cues alone, despite having normal hearing, speech, and intellectual ability, and ample opportunity for musical exposure” (Peretz et al., 2013). To optimize assessment of such a poorly skilled population, it would be necessary to know two parameters obtained via confirmatory factor analysis: each item's factor loading and threshold. To identify children with amusia, items exhibiting very low thresholds and with high factor loadings would be needed. Previously, the available batteries to evaluate MP have not reported these data at item-level, and therefore how the constituent items might behave psychometrically in extreme populations remains to be formally tested.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The reviewer KI and handling Editor declared their shared affiliation, and the handling Editor states that the process nevertheless met the standards of a fair and objective review.