Implicit assumptions of (prospective) music school teachers about musically gifted students

Abstract

Stereotypical assumptions associating high levels of giftedness and outstanding performance with maladaptive behavioral characteristics and personality traits (cf. disharmony stereotype) are rather prevalent in the school context as well as in the musical domain. Such preconceptions among teachers can influence student assessment and corresponding performance expectations, which might, in turn, impact future lesson planning. In an experiment using a controlled vignette approach, the current study, with N = 211 (prospective) German music school teachers, investigated how background information, combined with a manipulated music recording, affected (prospective) music school teachers’ assessment of a fictive student’s performance, behavioral characteristics, personality traits, and teachers'  consequential lesson planning. Experimental variations included the fictive student’s supposed level of giftedness, social interaction, age, and duration of instrumental lessons. Results indicated that music school teachers’ preconceptions of students assumed to be musically gifted were a high level of intellectual and musical abilities with behavioral characteristics and personality traits rated at least equivalent to those of students assumed to have average giftedness. Teachers’ lesson planning was not influenced by any of the manipulated background information. Taken together, the observed pattern of effects contradicts the disharmony stereotype but tends to align more with the harmony stereotype as music school teachers’ prevailing preconceptions about students supposed to be musically gifted.

1 Introduction

Highly gifted but maladjusted—these assumptions are widely assumed to be key attributes of musically gifted persons and are often promoted by their visibility in the media in addition to subjective experiences (Baudson, 2016; Gnas et al., 2020; la Motte-Haber, 1996). In our Western society, it is not uncommon that individuals with an attributed giftedness experience incorrect and partially negatively connoted assumptions, especially in highly competitive domains such as music (Bullerjahn, 2004; la Motte-Haber, 1996; cf. Gnas et al., 2020). Socially shared beliefs such as stereotypes regarding a certain group may evoke rapid top–down categorizations to facilitate cognitive processes due to generalizations and lead to simplified information processing through the retrieval of existing knowledge about this group (Fiske et al., 1999; Schindler & Bartsch, 2019; VandenBos, 2007).

1.1 Harmony versus disharmony hypothesis

Existing research literature distinguishes between two conflicting theories of stereotypical assumptions regarding giftedness, which could influence a person’s psychological well-being (e.g., Preckel & Vock, 2021). Whereas the harmony theory emphasizes a stereotypical view of giftedness as accompanied by high resilience, superior intellectual abilities, strong social skills, and adaptability (e.g., Baudson, 2016; Baudson & Preckel, 2013; Persson, 1998), the disharmony theory suggests a stereotype of giftedness as a combination of high intellectual abilities and maladaptive behavioral characteristics and personality traits; in brief, a vulnerability through giftedness (e.g., Baudson & Preckel, 2013; Gallagher, 1990; Neihart, 1999; Preckel & Baudson, 2013; Preckel & Vock, 2021; Preckel et al., 2015). The latter stereotype is also reflected in psychiatric genius research and within biographical analyses of famous writers, artists, or musicians, following the myth of the “mad genius”, even though the evidence that such a condition exists is low and mostly anecdotal (e.g., Baudson, 2016; Dietrich, 2014; Gallagher, 1990; Gnas et al., 2020; Gordon, 2015; Lombroso, 1891; Neihart, 1999; Preckel & Vock, 2021; Preckel et al., 2015; Simonton, 2014).

1.2 Behavioral characteristics and personality traits of musically gifted individuals

Numerous studies have investigated behavioral characteristics and personality traits in relation to exceptional musical giftedness (for an overview, see Costa-Giomi, 2015) with results tending to support the stereotype indicated by the harmony theory rather than the one implied by the disharmony theory as a suitable description of people with high giftedness. For example, Greenburg and MacGregor (1966) revealed some low positive correlations (.16 ≤ r ≤ .20) between factors of musical abilities and behavioral characteristics among elementary school children. Furthermore, Greenberg et al. (2015) were able to identify personality traits as predictors of musicality in their national study with N = 7870 participants, whereby openness acted as the best predictor. Similarly, Rose et al.’s (2019) findings indicate that musicians exhibit higher openness to experience than non-musicians. Kemp’s (1996) research compared musicians from different fields and with different levels of education with non-musicians in terms of personality and temperament and found that professional musicians described themselves as more introverted, sensitive, imaginative, and independent. In her study, Mund (2007) compared participants in the German “Jugend forscht” competition for young scientists and the German “Jugend musiziert” competition for non-professional instrumental students (in the age of 12 to 21 years) with a representative control group of peers (in the age of 15 to 17 years) who did not participate in either competition. Participants in both competitions showed better academic performance (see also Bullerjahn & Gembris, 2019; Gembris & Bullerjahn, 2019 for the domain of music), higher socioeconomic status, higher scores in creativity, conscientiousness, extraversion, and emotional stability, and higher self-satisfaction than the participants in the control group (Mund, 2007). Furthermore, participants in the “Jugend musiziert” competition were also found to be more sensitive and warm-hearted (Mund, 2007) and to have high (competition-related) motivation and self-regulatory skills (cf. Bullerjahn & Gembris, 2019; Gembris & Bullerjahn, 2019).

1.3 Teachers’ implicit assumptions about students with attributed (musical) giftedness

Teachers’ implicit theories about their supposedly highly gifted students appear to be particularly problematic (Baudson, 2016; Baudson & Preckel, 2016), due to their impact on both motivation and behavior in educational settings (Spinath & Freiberger, 2011). Thus, stereotyping can influence teachers’ grading of their students, lesson planning, and teaching activities, possibly resulting in reduced teaching quality or failure to support gifted students (Jussim & Haber, 2005; Kunter et al., 2013). According to the Pygmalion effect (Rosenthal & Jacobson, 1968), students who are attributed an above-average giftedness by their teachers will be more likely to show better learning results compared to their classmates due to the optimized support or improved individualized teaching quality they receive. In contrast, as a result of self-fulfilling prophecy (Merton, 1948), stereotyped attributes of teachers regarding negatively connoted behavioral characteristics and personality traits of their students can have a negative impact on students’ abilities and development (cf. e.g., Boser et al., 2014; Missett et al., 2014; Murphy et al., 1999; Pajares, 1992; Reis & Renzulli, 2004). Experiencing stereotype threat, students may perceive their giftedness as a social handicap and therefore try to minimize or eliminate its visibility (Baudson, 2016; Coleman & Cross, 1988; Cross, 2005; Gross, 1998; Spencer et al., 2016). In consequence, students’ learning progress might be affected, and their learning outcomes might not truly reflect their ability (cf. underachievement; Appel et al., 2015; Baudson, 2016; Baudson & Preckel, 2013; Gallagher, 1990; Holling et al., 1999; Preckel & Vock, 2021; Spencer et al., 1999, 2016; Steele, 1997; Steele & Aronson, 1995).

Moreover, stereotyping can have an impact on teachers’ assessments of a student’s musical performance due to cognitive biases such as expectancy errors or the halo effect, which over-illuminates characteristics and qualities due to one particularly salient characteristic (cf. Kahneman, 2011). According to Cohrdes and Kopiez (2015) as well as Cohrdes et al. (2012), background information about the performer can have an influence on musical assessments. Furthermore, musical (e.g., playing technique, interpretation, musical expression), extra-musical (e.g., room acoustics, visual impression of the musicians), and non-musical (e.g., stereotypes or preconceptions of the assessing persons) factors play a significant role in musical assessments (McPherson & Schubert, 2022). Thus, misconceptions regarding musical giftedness or the failed recognition of musically gifted students can also prevent target group-oriented and appropriate support for music students.

In the field of educational research, studies focusing on the relationship between students’ (exceptional) levels of giftedness and their stereotyped attributed behavioral characteristics and personality traits reveal ambivalent results; evidence yields mainly positive assumptions (e.g., Galloway & Porath, 1997; Rizza & Morrison, 2003), predominantly negative attitudes (e.g., Cramond & Martin, 1987; Lee et al., 2004), or mixed findings (e.g., Geake & Gross, 2008; McCoach & Siegle, 2007; Morris, 1987; Needham, 2012). This ambivalence may be explained by the fact that previous studies have often investigated attitudes toward gifted students explicitly, evoking both socially desirable response behavior and response bias (De Houwer, 2006; Kahneman, 2011; Preckel et al., 2015). In contrast, implicit measures assess attitudes indirectly by examining their effects on spontaneous behaviors and thus reveal automatic and unconscious attitudes (De Houwer, 2006; Deutsch & Strack, 2006).

To date, the results of more recent and better controlled experimental studies with active control groups have revealed the prevalence of the disharmony stereotype as a mental representation of both practicing and prospective teachers (e.g., Baudson & Preckel, 2013, 2016; Matheis et al., 2017, 2020; Preckel et al., 2015). Baudson and Preckel (2013, 2016) used a short vignette approach for their investigations with N = 321 preservice and practicing (Baudson & Preckel, 2013) or N = 246 practicing teachers (Baudson & Preckel, 2016), examining teachers’ implicit personality theories about students described along three dimensions including students’ ability (gifted vs. average), gender (female vs. male), and age (eight vs. 15 years). The results of their multivariate analysis of variance (MANOVA) and of the repeated-measures analysis of variance (ANOVA) with post-hoc univariate tests respectively were in line with the disharmony stereotype. In Baudson and Preckel (2013), the level of giftedness had the strongest effect on teachers’ judgments (η²_p = .60). Here, highly gifted students were rated as more open to new experiences (η²_p = .42) but less extraverted (η²_p = .09), less emotionally stable (η²_p = .04), and less agreeable (η²_p = .14). Furthermore, teachers rated highly gifted students as more intellectually capable (η²_p = .64), more motivated (η²_p = .03), less prosocial (η²_p = .14), and more maladjusted (η²_p = .28) in Baudson and Preckel (2016).

In another study, level of giftedness, adjustment difficulties, and gender were used as predictors for triggering stereotypes among N = 182 preservice teachers, controlling for effects within a single-target implicit association test (ST-IAT) as well as an affective priming task (Preckel et al., 2015). Automatic associations between giftedness and maladjustment, analyzed through a between-subjects ANOVA, were stronger for male than for female students (d = 0.29). This finding was confirmed by the affective priming task, when this assessment was made after the ST-IAT that had already assessed associations of giftedness with adjustment difficulties: Teachers’ evaluations then were significantly more positive for gifted female than for gifted male students (d = 1.07). Thus, implicit associations, which are in line with the disharmony stereotype, seem to have been made only for male students within this investigation.

The first study, which provided data on conceptions of gifted individuals with a representative sample of N = 1029 German adults, revealed two conceptions of giftedness within the latent class analysis (LCA): Twice as many participants were rated as being in line with the disharmony than with the harmony stereotype (Baudson, 2016).

Matheis et al. (2017, 2020) used a longer version of the vignette approach for their samples with N = 690 German and Australian (Matheis et al., 2017) and N = 315 Australian preservice teachers (Matheis et al., 2020). In both studies, the fictive situation included a social interaction between the central fictive student and others. Since there was no variation of the social interaction and since the other students were described as uninterested in communicating with the central fictive student, their experimental setup led to a negatively connoted communication situation, which could support stereotypical assumptions. While the fictive student’s level of giftedness and gender acted as independent variables, intellectual ability, lack of social–emotional ability, maladjustment, teachers’ self-efficacy, and enthusiasm served as dependent variables (cf. Hachfeld et al., 2012; Matheis et al., 2017,  2020). Repeated-measures ANOVAs with follow-up univariate tests (Matheis et al., 2017, 2020) as well as structural equation modeling (Matheis et al., 2017) were used to analyze the data. Participants in Matheis et al.’s study (2017) associated giftedness with high intellectual abilities (η²_p = .12) and maladjustment (η²_p = .12) and showed lower self-efficacy for teaching the gifted (η²_p = .05). No significant main effect was found for lack of social–emotional ability or teachers’ enthusiasm. Matheis et al. (2020) examined both the influence of giftedness and gender on teachers’ stereotyping. In total, participants associated students’ high giftedness with high intellectual abilities (η²_p = .12) and maladjustment (η²_p = .16; controlled for social desirability). Moreover, regarding teachers’ ratings on students’ maladjustment, they found a significant interaction effect (giftedness × gender: η²_p = .04; including social desirability as covariate). Whereas averagely gifted female students were assessed as less maladjusted than averagely gifted male students, highly gifted students were assessed as equally maladjusted (regardless of their gender) and more maladjusted than averagely gifted.

As an extension of the aforementioned vignette approach, Weyns et al. (2021) examined the effect of contextual information that contrasts with stereotypical assumptions about gifted students. In their study, involving N = 522 preservice teachers for elementary or middle school, they used a 2 × 2 × 2 between-subjects design where participants received one of eight different vignettes. In addition to the varied level of students’ giftedness and gender, they included the variation of social background information (having friends vs. neutral). However, this variation had no moderating effect on teachers’ stereotypical attitudes.

The first study regarding teachers’ stereotyping of highly gifted students in the domain of music was conducted by Gnas et al. (2020). Based on a sample of N = 169 practicing music school teachers, they revealed results similar to previous studies. Following the methodological vignette approach of the aforementioned studies within the school context, the authors tried to find effects on personality traits (using the “Five Factor Questionnaire for Children”; Asendorpf, 1998) and behavioral characteristics (using the questionnaire regarding “assumptions about gifted persons”; Preckel & Matheis, 2017) by means of MANOVAs and discriminant analyses. Level of giftedness (musically gifted vs. average) and gender (female vs. male) served as independent variables within the vignettes, resulting in a 2 × 2 between-subjects design. Similarly to Matheis et al. (2017, 2020), the researchers included a social interaction situation without variation in the fictitious description, which could support stereotypical assessments. While fictive students’ gender had a medium effect on the assumed behavioral characteristics and personality traits (.08 ≤ η²_p ≤ .10), the level of giftedness showed a large effect (.29 ≤ η²_p ≤ .44). No significant interaction effect of the two independent variables could be observed. Participants rated musically gifted students as more intellectually and musically capable, conscientious, motivated, and open to new experiences. In contrast to the findings of Baudson and Preckel (2013), participants rated gifted students as emotionally more stable (which is not in line with the disharmony stereotype) but also as more behaviorally challenging (in terms of externalizing problem behavior and disruptive behavior), less agreeable, and more socially incompetent. No differences were found in the areas of internalizing problem behavior and extraversion. Taken together, there are considerable differences between the assumptions of music school teachers about musically highly gifted students and musically averagely gifted ones, which partially support the existence of the disharmony stereotype in the musical domain.

In contrast to prevalent findings, which are predominantly in line with the disharmony stereotype, implicit assumptions that giftedness is necessarily connected with social–emotional deficits have been refuted by numerous empirical and epidemiological studies, countering the media’s common portrayal of an intellectually outstanding but emotionally unstable and socially incompetent individual (see, e.g., DeYoung et al., 2014; Freund–Braier, 2009; Limont et al., 2014; Martin et al., 2010; Neihart, 1999; Preckel & Vock, 2021; Preckel et al., 2015; Reis & Renzulli, 2004; Richards et al., 2003; Rost, 1993, 2009a; Wirthwein & Rost, 2011; Wirthwein et al., 2019; Zeidner & Shani-Zinovich, 2011). Results illustrate that highly and averagely gifted students do not essentially differ with respect to their social and emotional characteristics or personality traits; discrepancies are generally observed to be in favor of individuals with attributed giftedness. Hence, highly gifted individuals face advantages and problems comparable to those of averagely gifted individuals (Rost, 2009b). Divergent teachers’ assumptions about (musically) highly gifted students’ behavioral characteristics and personality traits may indicate the influence of stereotyped assumptions (cf. Gnas et al., 2020). Dealing with an unsuitable school environment, a lack of support services, and an unfavorable social or home environment can be risk factors for the social–emotional development of above-average gifted individuals (Preckel & Vock, 2021; Reis & Renzulli, 2004). Accordingly, it is not giftedness per se that is problematic but inappropriate reactions, unfavorable social interactions, or even misperceptions of the social environment, which can be fostered by teachers or social groups of peers, for example, and ultimately lead to error-laden implicit theories (Fiedler, 1999; Preckel & Vock, 2021; Preckel et al., 2015).

1.4 Aims and hypotheses

As the current state of research shows, teachers’ assumptions about (musically) gifted students might follow the disharmony stereotype. Within the present study, assessments of (prospective) music school teachers regarding musically gifted students are of particular relevance, since few results are yet available for this domain (cf. Gnas et al., 2020). The recording of such assumptions can draw attention to existing stereotypes and, by means of corresponding practical implications, contribute to raising awareness among teachers.

The present study extends and refines the method reported in Gnas et al. (2020) to trigger participants’ stereotyping of musically gifted students by adding more (reinforcing) variables into the vignette approach and by using additional audio recordings to investigate the impact of stereotyping on (implicit) musical performance assessments and further planning of instrumental instruction. Hence, the present study seeks to identify which kind of implicit assumptions—regarding behavior-, personality-, and performance-related dimensions—(prospective) music school teachers hold about allegedly musically gifted students. A confirmation of the existence of the disharmony stereotype in the musical context is expected, which should at least align with participants’ prototypical response patterns as presented in Gnas et al. (2020): Higher scores in the subscales of intellectual and musical abilities, performance and motivation, externalizing problem behavior, disruptive behavior, conscientiousness, and openness, as well as lower scores in social skills and agreeableness. To represent the disharmony stereotype in its entirety, additionally higher scores in internalizing problem behavior, and lower scores in extraversion and emotional stability (as measured by neuroticism) should be obvious for highly gifted students compared to averagely gifted ones (cf. Gnas et al., 2020).

Hypothesis 1

Students with an attributed musically high giftedness will be assessed more positively by music school teachers in terms of performance (e.g., more intellectually and musically capable, more motivated) and predominantly more negatively in terms of other behavioral characteristics and personality traits (e.g., maladjusted, socially incompetent, less agreeable) than students with an attributed musically average giftedness.

While Gnas et al. (2020) and Matheis et al. (2017, 2020) only used negatively connoted social interaction between fictive students in their vignettes, the current study extends this approach by varying between positive and negative connoted social interactions to balance information related to both kinds of stereotypes (harmony and disharmony stereotype; cf. the approach of Weyns et al., 2021). Since attitudes of other students (friendly vs. dismissive) toward musically highly gifted ones may trigger (prospective) music school teachers’ assumptions, this variable should be controlled.

Hypothesis 2

A positively connoted social interaction moderates teachers’ stereotypical assessment of behavioral characteristics and personality traits of students with an attributed musically high giftedness. Accordingly, negative attitudes regarding behavioral characteristics and personality traits, which are in line with the disharmony stereotype (cf. Hypothesis 1), are expected to be attenuated; therefore, adding counter-stereotyping information has a buffering effect.

In addition, the present study examines whether differences can be observed in terms of implicit performance assessment and subsequent decisions on lesson planning between highly gifted and averagely gifted students (in combination with other reinforcing variables) when musical performance is held constant.

Hypothesis 3

Variation in the background information of a performing student (level of giftedness, age, training duration) will influence teachers’ implicit performance judgments and consequently have an impact on their further lesson planning and goal setting. Accordingly, musically highly gifted students will be implicitly assessed more positively in terms of their musical performance and will therefore receive music pieces with a more difficult level for further lessons. A young age as well as a short duration of education will reinforce these effects (cf. assumptions about child prodigies; e.g., Feldman, 1986; Feldman & Goldsmith, 1990; Feldman & Morelock, 2010).

2 Method

2.1 Participants

Participants were invited to take part in the study via the mailing list of the Association of German Music Schools (Verband deutscher Musikschulen e. V.), via the universities of music, with the help of the general students’ committee or students’ council, or by means of advertising on social media. All participants had the opportunity to take part in a lottery at the end of the study and win one of ten 20 € vouchers from a music shop. The study was approved by the ethics committee of the University of Stuttgart (approval number 22-010). An a priori power analysis conducted with G*Power (version 3.1.9.7; Faul et al., 2007, 2009) revealed a minimum sample size of N = 153 participants required to detect effects of medium size within a MANOVA $(\alpha =.05\text{, }1- \beta =.80, {f}^{2}=.06)$.

In total, N = 230 participants took part in the study. However, n = 19 (8%) of the participants were excluded from subsequent analyses due to their answers when the manipulation check was carried out (see below), resulting in a final sample of N = 211 (prospective) music school teachers as participants. n = 133 (63%) participants of our sample identified themselves as female, n = 70 (33%) as male, and n = 2 (1%) as diverse, whereas n = 6 (3%) participants did not give any information about their gender identification. The sample reported an average age of M = 45.00 years (SD = 14.23, min = 19, max = 70) along with a working experience of M = 20.89 years (SD = 13.59, min = 0, max = 47). Most of the participants were teaching instrumental or singing lessons at the time of the research (n = 198; 94%) or had previously taught but no longer gave lessons (n = 8; 4%). N = 189 (92%) reported an (ongoing) teaching activity at a music school, mainly in the field of classical music (n = 152; 72%). Whereas n = 130 (63%) participants indicated having experience of teaching children assumed to be musically gifted, only n = 26 (13%) took part as a teacher in an education program with a special focus on musically highly gifted children. Finally, n = 47 (22%) participants indicated woodwind, n = 45 (21%) keyboard instruments, n = 39 (18%) bowed strings, n = 26 (12%) plucked strings, n = 24 (11%) vocals, n = 19 (9%) brass, and n = 7 (3%) percussion as their main instrument.

2.2 Design

Followed Gnas et al. (2020), the present design was extended by including more independent variables. The four dichotomous independent variables were (1) students’ level of giftedness (musically gifted vs. average), (2) students’ age (eight vs. 15 years; ages are based on Baudson & Preckel, 2013, 2016), (3) students’ expertise in terms of duration of education (two vs. four years of instrumental lessons), and (4) social interaction (positive vs. negative; cf. the approach of Weyns et al., 2021). Therefore, an experimental 2 × 2 × 2 × 2 factorial between-subjects design was conducted resulting in 16 conditions which were realized by a vignette approach (see below). Participants were randomly assigned to one of 16 vignette types. The central variable here is the level of giftedness, as stereotypes of musically highly gifted students are of interest; the expression of average giftedness was considered as a control group. The other background information served to possibly strengthen or weaken the stereotyping process. Behavioral characteristics, personality traits, and further lesson planning served as dependent variables. In addition, participants’ professional experience was recorded as a potentially confounding variable.

2.3 Measures

In accordance with Gnas et al. (2020), a survey-based approach to measuring assumptions about the behavioral characteristics of gifted people (Preckel & Matheis, 2017; cf. the extension by Gnas et al., 2020) with seven subscales and a standardized measure for children’s personality traits (Asendorpf, 1998) with five subscales was used. Lesson planning was prompted by three piano pieces of increasing difficulty, one of which had to be chosen by the participants. If none of the proposed piano pieces would suit their expectation, participants had the opportunity to suggest an alternative choice. The selection of pieces was based on expert judgments of German teachers at music schools or universities of music.

2.4 Materials

2.4.1 Vignettes

The vignette approach has been used in previous studies of the stereotyping of students with assumed giftedness (Baudson & Preckel, 2013, 2016; Matheis et al., 2017, 2020) and has already been adapted to the musical context (cf. Gnas et al., 2020). Here, the fictive situation description simulates real-life experiences and is particularly suitable due to its systematic variation of the concepts under investigation (Schoenberg & Ravdal, 2000). Hence, it enabled socially desirable response behavior to be controlled, as this seems to be problematic in research on assumptions about giftedness (Mõttus et al., 2008).

The vignettes were kept brief so that participants would rely on their own subjective, implicit beliefs when answering the questionnaires (cf. Weyns et al., 2021). Since the results in Gnas et al. (2020) were found to be independent of gender, only the female gender is represented in the vignettes. The variety in the description of the fictive female student “Siri” was composed of the four dichotomous variables, that is, her giftedness, age, duration of instrumental lessons, and type of social interaction with other students. The variety in social interactions provides information about whether contextual information has a reinforcing effect, no effect, or a moderating effect in terms of stereotyping. Figure 1 illustrates the English version of the vignette approach used in this study. Text in boldface indicates one of the different options of the independent variables that were experimentally varied within the vignettes. The second expression of each independent variable is displayed in the respective bracket. The remaining narrative parts were kept constant.

Fig. 1

Sample vignette for musically highly gifted, eight-year-old student Siri with two years of training duration and positive social interaction 

An example of a fictive music performance was added to the narrative part of the vignette in order to provide further information about the proficiency level of the fictive student “Siri.” In detail, a music performance of Johann Sebastian Bach’s Invention No. 8, F major (BWV 779) was recorded on a Midi-Keyboard. Subsequently, musical parameters (pitch, tempo, dynamics, and articulation), which are responsible for the appreciation of music performance (McPherson & Schubert, 2022; cf. also Associated Board of the Royal Schools of Music, 2017), were manipulated in a controlled manner (see App., Tab. 6 and Fig. 2). For the manipulation, Melodyne 5 editor (version 5.1.1.003; Celemony, 2020) was integrated as a plug-in in Cubase Pro 11 (version 11.0.0; Steinberg Media Technologies GmbH, 2020). The music example was kept constant across all conditions.

2.4.2 Measures of teachers’ assumptions about gifted students

Behavioral characteristics. Preckel and Matheis’ (2017) questionnaire, originally developed for the school context, was used to measure teachers’ “assumptions about gifted persons” (cf. Gnas et al., 2020). In their study, Gnas et al. (2020) added seven items to the original measurement with a special focus on musical abilities (.66 ≤ α ≤ .91). This extended version was also used in the present study. Included items refer to the dimensions of performance with the subscales intellectual abilities (six items, e.g., “This student is intelligent”), performance/motivation (six items, e.g., “This student gets good grades”), and musical abilities (seven items, e.g., “This student can play expressively musically”); socio-emotional abilities with the subscales internalizing problem behavior (five items, e.g., “This student is withdrawn”) and social skills (seven items, e.g., “This student is considerate”); and behavioral problems with the subscales externalizing problem behavior (five items, e.g., “This student is intolerant”) and disruptive behavior (five items, e.g., “This student disrupts class”). All items were assessed on a unipolar 6-point Likert scale (where 1 = “strongly disagree” and 6 = “strongly agree”).

Personality traits. For the external assessment of the assumed personality traits of the fictive student “Siri”, the “Five Factor Questionnaire for Children” by Asendorpf (1998) was used. This questionnaire is based on the Big Five of personality (see, e.g., Costa & McCrae, 1992a, 1992b; McCrae & Costa, 1987), whereby each of the following dimensions is represented by eight items: extraversion (e.g., “sociable—withdrawn”), agreeableness (e.g., “peaceful—belligerent”), conscientiousness (e.g., “careless—conscientious”), openness (e.g., “little interested—many-sided interested”), and neuroticism (e.g., “nervous—calm”). Accordingly, the questionnaire includes 40 pairs of opposite descriptions of a child’s personality traits based on a 5-point bipolar scale. For external raitings by parents, Asendorpf (1998) reported a median Cronbach’s α of .86 (.83 ≤ α ≤ .91).

Lesson planning. Lesson planning was measured as a dependent variable by a list of three music pieces from the same era but with different difficulty levels, suggested as the basis for future instrumental lessons. Participants were asked to choose one of the three listed music pieces for further lesson planning. In detail, they had the opportunity to choose between (1) the Minuet in G major, BWV App. 114 (from The Music Book for Anna Magdalena Bach), (2) the Invention No. 1, BWV 772, and (3) the English Suite No. 3, Prelude, BWV 808. The difficulty level of the suggested music was rated by experts in the field of instrumental pedagogy or teaching piano, resulting in an ascending order where the difficulty level of (1) was rated as lowest. The difficulty level of (2) was intended to be similar to that of the recording (i.e., Invention No. 8, F major, BWV 779), whereas the difficulty level of (3) was rated higher than that of the recording. In addition to the three choice options, participants had the opportunity to suggest an alternative or explain why they would not choose one of the three music pieces.

2.5 Procedure

An online questionnaire was created using SoSci Survey (version 3.2.40; Leiner, 2021), which took an average duration of M = 23.38 min (SD = 6.45, min = 10.02, max = 38.38) for the participants to complete. First, participants were welcomed. After giving their informed consent to take part in the study, participants were informed about the (technical) requirements and procedure of the study and were asked to reply spontaneously, intuitively, and completely. After the presentation of the vignette to which they were randomly assigned, a manipulation check was carried out to ensure that participants had carefully read the vignette and to determine whether their subsequent responses were actually related to the vignette they had been shown to counteract manipulation or bias. In detail, participants had to remember and indicate the introduced information about the fictive student described in the vignette; thus, they were asked the student’s name (i.e., Siri), level of giftedness, age, and training duration. To pass the manipulation check, at least 75% of the answers had to be correct. An additional condition was the correct reproduction of the level of giftedness, regardless of what else was correctly or incorrectly remembered, since implicit theories concerning students with an attributed giftedness were ultimately under investigation.

After the manipulation check, participants were asked to assess the behavioral characteristics and personality traits of the fictive student introduced by the vignette. Next, they listened to the music recording as the second part of the vignette and were requested to either select one of the three music pieces or to write a reason that another (specific) piece could be more suitable for future teaching than those suggested.

Finally, participants’ background information was gathered. Here, items selected from the Goldsmith’s Musical Sophistication Index (Gold-MSI; Müllensiefen et al., 2014; Schaal et al., 2014) were used as well as items eliciting demographic details. After creating an individual code which gave them the option to revoke their participation and thus their response data in the future, participants had the opportunity to take part in a lottery. Lastly, they were fully debriefed, as information about the purpose of the study was not fully disclosed at the outset to avoid response biases and socially desirable reactions.

2.6 Data analysis

Data were analyzed with R (version 4.2.3; R Core Team, 2022) using RStudio (version 4.2.3; RStudio Team, 2020). First, participants’ responses were checked for quality, cleaned, and aggregated to prepare them for subsequent analyses. Participants who did not pass the manipulation check were excluded from subsequent analyses, resulting in a final sample of N = 211. After that, five to seven items for the assumed behavioral characteristics (cf. Preckel & Matheis, 2017) and eight items for each of the assumed personality traits (cf. Asendorpf, 1998) were combined into subscale scores. Descriptive analyses were followed by multivariate analyses of covariance (MANCOVAs, using type II sums of squares). To test the initially derived hypotheses, students' level of giftedness and social interaction were used as independent variables, seven subscales for behavioral characteristics and five subscales for personality traits as dependent variables. Participants’ teaching experience was added as covariate, since Gnas et al. (2020) were able to demonstrate its significant impact on the results. When there were significant main effects, follow-up univariate post-hoc tests (ANCOVAs, using type II sums of squares) were conducted to inspect them more closely. The Benjamini–Hochberg procedure was used to correct false discovery rate (Benjamini & Hochberg, 1995; see Haynes, 2013). If the requirements for a MANCOVA were not satisfied, Chi²-tests for possible main effects and log-linear analyses for possible interaction effects were performed. Open text fields (e.g., giving space for alternative piece suggestions for further lesson planning) were analyzed in a qualitative manner via MAXQDA 2022 (VERBI Software, 2021). To sort participants’ answers thematically, categories were created and reviewed by a second rater; interrater reliability indicated substantial agreement between the two raters with κ = .66 (Landis & Koch, 1977).

3 Results

Means (M) and standard deviations (SD) of the total final sample size (N = 211) for the behavioral characteristics and personality traits are provided in Table 1. For all statistical analyses, α < .05 was used. Scale reliability was estimated by computing Cronbach’s alpha (Cronbach, 1951), which is also listed in Table 1. Here, values ranged between .68 ≤ α ≤ .93, indicating mainly acceptable to excellent reliability (Streiner, 2003; Tavakol & Dennick, 2011). Overall, these values are mostly similar to or higher than those of Gnas et al. (2020). An inter-scale correlation indicated significant associations between most of the scales with values ranging from −.79 ≤ r ≤ .83 (see Table 1). Table 2 shows means (M) and standard deviations (SD) of teachers’ assessments with regard to the dependent variables (seven subscales for behavioral characteristics and five subscales for personality traits). Following hypotheses 1 and 2, the analyses considered only the level of giftedness and the social interaction as independent variables. On a descriptive level, group differences can already be identified on various scales.

Table 1 Means (M), standard deviations (SD), scale reliabilities, and intercorrelations of subscales related to behavioral characteristics and personality traits of gifted students assumed by (prospective) music school teachers

Table 2 Means (M) and standard deviations (SD) of dependent variables as a function of level of giftedness and social interaction

3.1 Testing of hypotheses 1 and 2: teachers’ assumptions about musically highly gifted students’ behavioral characteristics and personality traits

Following hypotheses 1 and 2, only the level of giftedness and social interaction as independent variables were considered in the MANCOVAs. However, to acknowledge the full scope of the present experimental design, analyses of students’ age and duration of education were also conducted. Since neither students’ age nor training duration displayed significant main effects, the reporting of our results focuses on the 2 × 2 design corresponding to the hypotheses; the results of the MANCOVAs are listed in Table 3. To interpret the results, Cohen’s (1988) guidelines for effect sizes were used (cf. Ellis, 2010).

Table 3 Results of MANCOVAs including the covariate professional experience

Significant main effects were found for both independent variables and for the covariate in both, the behavioral characteristics and the personality traits. To test hypothesis 1, the statistically significant main effects were further explored in post-hoc tests; teachers’ professional experience continued to be included as a covariate due to its significant impact on the results. However, the interaction effect of level of giftedness and social interaction was non-significant in both cases. Thus, hypothesis 2 cannot be confirmed, since the social interaction did not exhibit a moderating effect.

Based on the results of the MANCOVAs, follow-up ANCOVAs—including the covariate professional experience—were calculated only for the two significant main effects (level of giftedness, social interaction), since the interaction effects did not reach statistical significance. Overall, both the level of giftedness and the social interaction had a significant influence on teachers’ assessment of the fictive student with regard to several scales of behavioral characteristics and personality traits (see Table 4): For the level of giftedness, significant values were found for intellectual abilities, performance and motivation, musical abilities, conscientiousness, and openness. For the social interaction, significant values resulted for all scales of behavioral characteristics except musical abilities and for all scales of personality traits except conscientiousness. Furthermore, depending on their professional experience, teachers significantly differentiated between differently described students in the areas of internalizing problem behavior, social skills, extraversion, and neuroticism.

Table 4 Results of follow-up univariate tests (ANCOVAs)

Taking these results together, hypothesis 1 can be partially confirmed, since students with an attributed high giftedness were assessed more positively in terms of performance (intellectual und musical abilities, performance, and motivation) but—contrary to expectations—similarly (internalizing and externalizing problem behavior, social skills, disruptive behavior, extraversion, agreeableness, and neuroticism) or more positively (conscientiousness and openness) in other behavioral characteristics or personality traits than students with an attributed average giftedness.

3.2 Testing of hypothesis 3: teachers’ lesson planning

To test hypothesis 3, participants’ answers were sorted by the dichotomous levels of independent variables (students' level of giftedness, age, and training duration) to identify potential group differences regarding their lesson planning and goal setting for further instruction (see Table 5). A considerable number of respondents also decided not to select any of the music pieces mentioned (= answer 4) and to leave a comment within an open text field. Most participants’ comments indicated the desire to provide music pieces with more variety regarding style, composer, or era (k = 34; 51%). In addition, a fundamentally different level was desired (k = 14; 21%), since the proposed pieces were too easy (Minuet in G Major, BWV App. 114), too similar (Invention No. 1, BWV 772), or too difficult (English Suite No. 3, Prelude, BWV 808) for the upcoming lessons.

Table 5 Relative frequencies of piece suggestions for further instruction as a function of level of giftedness, age, and training duration (cf. hypothesis 3)

To test whether piece selection was influenced by any of the independent variables (cf. hypothesis 3), a Chi²-test was used. Only answer options 1 to 3 were considered for the calculations, since these include the music pieces proposed for selection (N = 169). No significant association between piece selection and level of giftedness (χ² = 5.03, df = 2, p = .08, V = 0.17), students’ age (χ² = 3.81, df = 2, p = .15, V = 0.15), or students’ training duration in instrumental lessons (χ² = 0.15, df = 2, p = .93, V = 0.03) could be observed. This finding was confirmed by log-linear analyses, which were conducted to test for a potential dependency between teachers’ lesson planning and the interaction of two independent variables (level of giftedness × age: χ² = 23.16, df = 165, p = 1; level of giftedness × years of instrumental education: χ² = 23.11, df = 165, p = 1; obtained values according to Pearson). Thus, hypothesis 3 cannot be confirmed within the current sample.

4 Discussion

The present study investigated how (prospective) music school teachers’ stereotypes of students’ musical giftedness could be triggered by means of their assumptions concerning students’ performance, behavioral characteristics, and personality traits. Further, the study investigated how teachers’ views on giftedness might impact their subsequent lesson planning. Thereby, the examination of the so-called (dis)harmony stereotype played a central role; this stereotype states that a key characteristic of highly gifted people is the association of an exceptional achievement level and (mal)adaptive behavioral characteristics and personality traits. Similar findings to those of previous studies in the school context and especially in the musical domain were expected.

However, the results of the present study are only partially consistent with the findings of Gnas et al. (2020). In line with Gnas et al. (2020), music school teachers differentiated between individuals with an attributed high level of giftedness and those with an attributed average giftedness. In detail, highly gifted students were rated as being more intellectually and musically capable and motivated, as well as more conscientious and open to new experiences, without differing in terms of internalizing problem behavior and extraversion from students assumed to be musically averagely gifted.

In contrast to the results of Gnas et al. (2020), the present findings revealed no significant differences between students whose level of giftedness was attributed differently with respect to externalizing problem behavior, disruptive behavior, socially competence and compatibility, and emotional stability. Overall, students with attributed high giftedness were rated more positively within the performance domain and—contrary to expectations—either equally to or better than averagely gifted students regarding other behavioral characteristics and personality traits within the present study. Thus, hypothesis 1 can only be partially supported; the existence of the disharmony stereotype in the musical context cannot be confirmed by the present study, since the negative component of the stereotype is not reflected in the results (i.e., higher scores in internalizing and externalizing problem behavior, disruptive behavior, as well as lower scores in social skills, extraversion, agreeableness, and emotional stability (as measured by neuroticism) for highly gifted students compared to averagely gifted ones). These results are in line with empirical and epidemiological findings of earlier studies, in which the disharmony stereotype was also disproved (cf. Martin et al., 2010; Neihart, 1999; Reis & Renzulli, 2004; Rost, 1993, 2009a; Zeidner & Shani-Zinovich, 2011). Rather, the obtained evidence points more in the direction of the harmony stereotype, whereby high abilities are associated with positive behavioral characteristics and personality traits. One reason for the difference between the results of Gnas et al. (2020) and the present study could be related to differences in sample characteristics. However, against the background of self-selection bias (see, e.g., Heckman, 1990, 2010), most of the participating teachers were interested in this topic anyway (cf. Gnas et al., 2020) and might therefore have already been informed and sensitized about teaching musically gifted students by further programs and training. Furthermore, in terms of prognostic validity, it is only possible for a small number of individuals to enroll in programs of universities of music after passing an entrance examination; thus, these seem to be mainly musicians who have reached a high level of musical expertise due to their own above-average musical giftedness (besides practicing). Consequently, teachers could have less disharmonical assumptions about musically gifted students due to their own experience with high musical abilities.

In addition, context effects may be responsible for the difference between the results of the present study and those from studies in the school context (Schwarz & Sudman, 2012). Even though teachers are generally able to correctly assess the performance of their students within the school context, there is evidence that teachers’ assessments are less successful with regard to motivational–affective student characteristics (Spinath, 2005; Urhahne et al., 2010, 2011). However, since music lessons are mostly held on an individual basis or in small groups, there is a closer relationship between students and teachers, which could lead to a more accurate teacher assessment of students’ characteristics within the musical domain (cf. Gnas et al., 2020). For example, Baudson and Preckel (2013, 2016) and Matheis et al. (2017, 2020) reported results that are consistent with the disharmony stereotype due to participants’ association between high intellectual abilities and maladaptive behavioral characteristics and personality traits. Similar results were only found in the school context and the present study in relation to the participants’ assumptions about highly gifted students regarding higher intellectual abilities, openness, and motivation than the reference group.

The participants’ judgments revealed in the present study are consistent with most results of previous studies in the musical domain, according to which musically gifted individuals are more conscientious, opener to new experiences, and more motivated and perform better than musically averagely gifted ones (Bullerjahn & Gembris, 2019; Gemrbis & Bullerjahn, 2019; Mund, 2007; Rose et al., 2019). In contrast, musicians described themselves in Kemp’s research (1996) as reserved or introverted, which cannot be confirmed by the present study. However, these former studies focused on explicit investigations or self-assessments of musicians, whereas the present study captured implicit theories regarding highly gifted individuals by means of external assessments.

Moreover, no evidence of a moderating effect of social interaction was revealed in the present study, since there were no significant interaction effects between the level of giftedness and social interaction. Thus, hypothesis 2 cannot be confirmed. These findings are in line with the results of Weyns et al. (2021), who also found no moderating effect through adding counter-stereotyping information. Nevertheless, the variation of social interaction revealed up to large effects regarding students’ assumed behavioral characteristics and personality traits within the present study, emphasizing the relevance of this independent variable. Thus, participants receiving a vignette that described a successful social interaction between Siri and the other orchestra members assessed the fictive student as intellectually more capable as well as more motivated. Furthermore, the fictive student was rated more positively in the areas of internalizing and externalizing problem behavior, disruptive behavior, social skills, extraversion, aggreeableness, openness, and neuroticism.

Finally, based on the results of the Chi²-test and the log-linear analyses, hypothesis 3, stating that background information regarding a student’s characteristics will influence teachers’ implicit performance judgments and consequently have an impact on their further lesson planning and goal setting, cannot be supported by the present data. Contrary to expectations, no correlation between the choice of music piece for educational purposes and the level of giftedness (in combination with background information about the students’ age or duration of education) could be observed in the present study. A possible explanation for the unexpected results could relate to participants’ response biases, for example, responses due to a tendency toward the middle to avoid anxiety about making extreme judgments on the basis of only a short auditory stimulus (McPherson & Schubert, 2022).

4.1 Practical implications

Musically highly gifted students may suffer from both the harmony and disharmony stereotypes: Exerting the dynamics of self-fulfilling prophecies (Merton, 1948; see also, e.g., Jussim & Harber, 2005), teachers’ expectations and stereotypical attitudes—particularly those which are in line with the disharmony stereotype—can significantly influence students’ behavior, performance, and development, especially in early learning phases when support is crucial (Davidson et al., 1998; Gagné, 2009; Gagné & McPherson, 2016; Kemp, 1996). Furthermore, stereotypical assumptions can evoke a negative (musical) self-concept (Gnas et al., 2020), which is related to musical performance (Austin & Vispoel, 1998; Fiedler & Spychiger, 2017) and taking up and continuing music lessons (Demorest et al., 2017). Missing lessons or even dropping out of lessons ultimately hinders students from fully realizing their potential. In order to provide appropriate support, teachers should be able to adapt to changing learner demands in order for students to achieve musical excellence (Davidson et al., 1998; Hallam, 2018).

However, the existence of the harmony stereotype can also produce negative consequences: For example, teachers’ attitudes and expectations might put students under pressure and make them feel that they cannot live up to expectations (cf. Baudson & Preckel, 2016). Furthermore, according to the stigma of giftedness theory (Coleman & Cross, 1988; Cross, 2005), there may be a worry among students about being excluded because of their giftedness. In consequence, gifted people try to hide or even deny their own giftedness, resulting in dysfunctional behaviors. Training programs in initial and continuing teacher education can make a targeted contribution to raising awareness and, ultimately, counteracting stereotypical assumptions in the long term (cf. Gnas et al., 2020).

4.2 Limitations

Gnas et al. (2020) have already discussed several aspects of the vignette approach with respect to the possibility of its biasing impact. From their point of view, there might be limitations in terms of ecological validity in the narrative context, such as the mention of the fictive orchestra and its members, as the size of the orchestra in music schools might be a function of its number of students in total as well as the distribution of instruments among them. For instance, smaller music schools may not be able to offer orchestra rehearsals and performances as they have too few students (Gnas et al., 2020). Nevertheless, trained music school teachers should have sufficient experience to be aware of such scenarios and able to assess them accordingly. Due to the sample size and the variety of instruments taught by the participants, it is reasonable to assume that the variation in the sizes of music schools might be large enough to avoid such a bias within the present study. Furthermore, the vignette approach offers the possibility of investigating the desired variables experimentally with a high level of external validity by manipulating everyday situations in narrative fashion. The findings of the present study—especially the observed effects of the social interaction manipulated within the vignettes—should stimulate researchers to critically reflect on, validate, and experimentally vary scenarios, terminologies, and conceptualizations.

It may seem trivial at first that Siri, who was allegedly musically highly gifted, was rated by teachers as both intellectually and musically capable. However, the vignettes present only dichotomously categorized variables (e.g., musically highly gifted vs. averagely gifted), while the efficacy of the independent variables is plotted on a multilevel continuum (e.g., a 6-point Likert scale), which provides a much more differentiated insight into teachers’ assessment. Furthermore, intellectual and musical giftedness do not necessarily have to be mutually dependent (Thalmann-Hereth, 2009); clear evidence regarding the long-term effects of music lessons on intelligence is still lacking, although Costa-Giomi (2015) was able to determine in her review the short-term general cognitive benefits as well as neurological changes associated with music instruction (cf. Hallam, 2010; Schellenberg, 2006).

The present study is the first to present a musical performance that had previously been manipulated in a technically controlled manner using various parameters (pitch, tempo, dynamics, and articulation) without losing external validity. It was linked to narrative aspects of the vignette approach to record the impact of the independent variables on music school teachers’ further lesson planning and to gain insights into teachers’ goal setting. For this, the varied level of giftedness was reinforced by combinations with other variables, namely students’ age and training duration. Thereby, the recording was kept constant for reasons of controllability and due to the underlying design to check whether the evaluation of the teachers differed on the basis of the different combinations of variables.

4.3 Future perspectives

Due to the heterogeneity of results available in the musical context, it is necessary to re-examine the results of the present study in future research. Musical performance could be included in the design as another independent variable, and thus another possible influencing factor, to investigate the interaction of students’ biographical characteristics and performative performance characteristics for stereotype formation.

However, studies should not be repeated only within the musical context. Cross-domain comparisons are equally valuable to gain a general picture of implicit assumptions about individuals with a special (domain-specific) giftedness. Synergies within these findings could be used to achieve cross-disciplinary knowledge on this topic as well as education and sensitization, for example at schools or clubs by means of training programs. Various event formats within education and training programs are suitable for this purpose, as such training can significantly contribute to improving teachers’ attitudes toward gifted students (Geake & Gross, 2008). Furthermore, studies would benefit from considering additional target groups. The implicit response behavior of parents and fellow students could be compared with teachers’ response behavior, for instance (cf. Gnas et al., 2020). Such comparisons should examine whether different target group-related assumptions are in line with previous empirical and epidemiological findings to prove if special training programs are needed to raise awareness of and ensure adequate support for highly gifted individuals.

Furthermore, it might be of interest to record teachers’ achievement level or expertise in order to include this as a further covariate in the analyses (cf. Gnas et al., 2020). It can be assumed that (prospective) music school teachers have reached a high achievement level; nevertheless, it would be interesting to determine whether music school teachers with attributed high musical abilities systematically assess their students differently than teachers with lower musical abilities, since experiences due to one’s own abilities could well influence assessments.

For future research, it seems useful to first capture teachers’ (implicit) assessments of students’ musical performance. This can be done by means of an appropriate set of criteria. In this way, influencing factors could be determined on the basis of the experimentally varied vignettes, and possible biases could be recorded more systematically. It would be interesting to further vary the manipulation in terms of selection, intensity, frequency, and possible combinations of diverse parameters. A change of perspective also seems exciting: While in this approach a manipulated version with errors was presented, a very good performance could equally be presented and linked to the different levels of giftedness. Based on the participants’ comments, the selection of the presented pieces should be refined and expanded in the future for the subsequent recording of teachers’ further lesson planning and goal setting. For example, other pieces from different eras could be provided for selection. Nevertheless, both technically and musically comparable pieces from the same era were deliberately chosen to enable better control by excluding, as far as possible, further challenges and confounding features such as the use of pedal, attention to rubato passages, or subjective preferences. A possible solution for further research projects is to provide a broader selection of pieces. On the one hand, it would be conceivable to present more than three levels. On the other hand, different levels could be represented by several pieces from different eras, assuming that a clear classification can be achieved. Orientation may be provided by music lists, such as those of the competition “Jugend musiziert” (DEUTSCHER MUSIKRAT gGmbH, n. d.), which were created in cooperation with the Association of German Music Schools, the Federal Academy for Musical Youth Education Trossingen, and other professional associations. However, these are not explicit recommendations, but merely suggestions and ideas. Accordingly, a critical attitude remains even after careful examination of the mentioned lists, since the classification of musical works to different levels seems to be intricate. To date, abstract metrics for evaluating the complexity of music pieces have not been devised.

4.4 Conclusion

Contrary to most findings of prior studies in both the school and the musical context, the disharmony stereotype could not be confirmed in its a priori assumed strength by the present study. Rather, there are indications that point to the harmony stereotype. The present study underlines the ambivalence, complexity, and relevance of this research field and suggests further investigation of implicit theories (in the musical domain) to educate and sensitize teachers regarding existing assumptions about (musically) gifted students and to fully exploit available potential in the future.

Appendix

See Table 6

Table 6 Overview of types (parameters) and places (bars) of technical manipulation

and Fig. 2.

Fig. 2

Note. Manipulations are drawn in (cf. Table 6). Transcribed by the first author

Music score of Johann Sebastian Bach’s Invention No. 8 (F major, BWV 779) indicating the types (parameters) and places (bars) of the technical manipulations.