Differences between scale steps and absolute interval sizes: A new test for intervallic awareness

Abstract

Musical scales can be described as either an organization of scale-step degrees or as a pattern of absolute interval sizes. Even though experimental data show that these two melodic features might have different perceptual implications, not every music education method or psychology experiment separately accounts for them. The present study undertakes an investigation of scale steps, absolute interval sizes, and their cognitive role on melodic perception. The development and partial validation of a new psychometric instrument are reported, and the results are discussed in regard to its experimental and educational implications.

Keywords

intervallic awareness scale steps intervals sight-singing melodic perception

Scale steps and absolute interval sizes

Every musical scale can be encoded according to a sequence of absolute interval sizes or scale steps. The distance between each tone of the C major scale, for instance, is quantified according to the following sequence (in cents): 200, 200, 100, 200, 200, 200, 100. Notice that between E and F (Figure 1), the number of cents is half the distance between C and D, for instance. In scale steps, however, every single scale step assumes the same value, since each note conforms to pre-established scalar framework. Figure 1 provides an example of how the same scale can be encoded according to scale steps and absolute interval sizes.

Figure 1.

Melodic encoding in terms of scale steps and cents.

The difference between scale steps and absolute interval sizes is not purely numerical, and there is a relatively large body of empirical research indicating that these two scalar aspects might be related to different cognitive processes. Dowling and Fujitani (1971) have shown that individuals with moderate musical training find it difficult to decode and recognize absolute interval sizes, and that for those individuals, melodies tended to be perceived and processed in terms of contour¹ and scale steps. According to Dowling & Bartlett (1981), “data indicates that the initial memory representation of a novel melody contains accurate information about contour and (probably key), but not intervals.”

In addition, Dowling (1978) has provided further evidence to demonstrate the possibility that individuals are sensitive to contour and scale-step information but are somewhat insensitive to absolute intervallic information. The author presented participants with a tonal stimulus, which had to be compared with either an exact transposition, a tonal answer (which altered the mode but maintained scale steps and contour), or a random atonal stimulus (Figure 3). Participants were asked to accept exact transpositions and to reject any other comparison stimuli.

Theoretically, individuals could distinguish between tonal answers and exact transpositions by analyzing the absolute intervallic pattern for each melody. For instance, the sequence A–B–C (Figure 1) is formed by the intervals of a major second and a minor second, while its tonal answer, C–D–E (Figure 1), is formed by two consecutive major seconds. The experimental results revealed, in this case, that absolute intervallic information was not perceptually salient and that individuals could not reliably tell the difference between a target and its tonal answer and/or transposition. The author concluded, therefore, that the “function of mode is not to fix a set of intervals in semitones as belonging to a melody,” and that instead of abstracting absolute interval sizes, individuals were sensitive to the placement assumed by each pitch within a scalar framework, as well as to their contour organization.

These findings grounded Dowling’s (1986) definitions of two types of mental representations for melodies. The first, which are called scale-step representations, allow relative frequencies to be perceived as “sets of scale steps in a tonal scale framework, in a way analogous to their representation in a movable do system” (Dowling, 1986). The second, called interval representations, allow an individual to “encode a melody as a set of logarithmic interval sizes between successive notes” (Dowling, 1986). Thus, Dowling presents the idea that scale-step representations enable the perception of each note as a member of a determined scale, while interval representations allow for the perception of each interval as an entity, independent of tonality or scale.

Another interesting example of separation between intervals and scale steps has been provided by Attneave and Olson’s (1971) study. The authors found that non-musicians could not transpose absolute interval sizes into different pitch ranges (e.g., C–D to Eb–F), even though they could easily do the same task with a previously known melody (NBC chimes). What is interesting is that individuals who were successful at transposing a familiar tonal melody were incapable of doing the same task with isolated intervals. While individuals could manipulate the tonal framework, which is structured by intervallic relationships, they could not do the same with intervals which were not surrounded by a scalar context.

On a theoretical level, Goldemberg (2011, 2015) also proposed a differentiation between scale steps and absolute interval sizes. Based on analogous concepts of phonological awareness, the author drew a parallel between verbal and musical reading, in which the concepts of bottom-up and top-down processing served as a framework for speculations about sight-singing abilities. According to Goldemberg (2015), bottom-up processing is a strategy in which individuals are oriented by melodic intervals, while top-down strategies are those in which the individual makes inferences about melodic patterns derived from familiarity with tonal environments.

This briefly reported literature serves as an example of the distinction which might exist between melodic intervals and scalar features, especially from a psychological point of view. Within experimental environments, however, it may be fairly difficult to separately assess the perception of scale steps and absolute interval sizes, since scale-step manipulations often entail a change in cents. The next section of this article will report literature which relates to this issue and will additionally discuss educational implications regarding this distinction.

Scale steps and absolute interval sizes: an epistemological issue

In a seminal study, Dowling (1986) drew the conclusion that some individuals may be sensitive to absolute intervallic organization. His experiment assessed how well participants could recognize a given tonal melody, considering that this melody could be presented as an exact transposition or imitation. Exact transpositions were created by changing the tonality of the stimuli. Imitations were also transpositions, but they presented an alteration in one musical note by a whole diatonic scale step. Those two melodic transformations could be accompanied by the same or by a different harmonic context, which determined the excerpt’s scale-step organizations.

However, this study did not manipulate interval sizes and scale steps separately. Imitation melodies, which presented a different note in relation to the acquisition melody, were, in fact, transformed in terms of absolute interval sizes. However, these transformations resulted in scale-step changes. For instance, if, the target melody was C G C D G D, it could be represented according to its scale steps plus contour: 1 –5 +1 +2 –5 +1, and its imitation would be D A D F# A D, or 1 -5 +1 +3 -5 +1. Note that, besides a change in absolute interval sizes, there was also a change in scalar steps, since the fourth note went from a third to a second degree. Since this experiment did not separate scale-step manipulations from intervallic manipulations, it is unknown if absolute interval sizes were critical to perform the task.

Welker (1982), aimed to assess schema formation for melodic themes and variations, has assessed the perceived similarity ratings between a prototype (initial theme) and its transformations. Those transformations could alter intervallic information by inverting contour, while maintaining number of skipped scale steps (the melody C3–E3–G3 would become C3–A4–F4) or by reducing the absolute size of every interval within the melody (major thirds, minor thirds, and perfect fourths became major seconds, and fourths and fifths became minor thirds).

Based on the perceived similarity ratings, the authors concluded that individuals were, in fact, capable of abstracting thematic information from the melodic excerpts, and overall recognition of transformed melodies was above chance. Such an experiment, however, is another example of failure to isolate specific intervallic perception. Besides the fact that Welker (1982) did not provide an analysis for each type of transformation (the authors only provided similarity ratings in function of the number of transformations employed), the very nature of intervallic inversions and reductions does not allow for direct assessment of absolute intervallic perception, which, in fairness, was not the direct goal of the study. Still, it is impossible to know, from the experimental outcomes, which aspect was perceptually salient.

Another example is provided by Eiting (1984), which indicated that participants were able to use absolute interval sizes to compare two tonally structured melodies. The author conducted a forced-choice task experiment, in which individuals had to indicate, between three comparison stimuli, the one which best resembled a model stimulus. Comparison and model stimuli could differ in regard to absolute interval size (exact number of cents between two tones), relative interval size (proportions of distance between two tones), and absolute pitch (frequency). The author did not provide comparisons between two melodic sequences which pertained to the same diatonic context, and therefore the comparison stimuli were always transposed in relation with the model stimuli.

It was assumed that, since individuals were able to judge the exact transpositions as similar to the initial stimuli, they were sensitive to absolute intervallic information. It could be questioned, however, if the ability to differentiate between exact transpositions, in Eiting’s (1984) experiment, served as a good measure of exact interval size perception. When the same melody was replicated 200 cents higher (condition S1/T12, Eiting, 1984, p. 85), individuals could have used a strategy which was sensitive to the scale steps of the new-established tonality, just as reported by Dowling (1978) and not to the absolute interval sizes. It seems likely that the author reported perception for absolute interval sizes because he only accounted for the changes that transposition could have on absolute interval sizes. If we consider that individuals could have judged the two melodies in relation to its scale-step dispositions (which remained invariable), perhaps the absolute intervallic perception was still not salient.

More recently, neuropsychological studies have come across the same issue of separating interval sizes and scale steps. Trainor, McDonald, and Alain (2002) used an oddball paradigm to evaluate the pattern of neural activity associated with the processing of what they called “intervallic information.” Figure 2 provides an example of the stimuli used to test brain responses for each oddball terminal. The authors indicated that when the last note of a melodic sequence was altered from a G to an A (Figure 2), this evoked a right frontal positivity peaking around 50 ms and a central parietal P3b peaking around 580 ms.

Figure 2.

Stimuli used for an EEG experiment with intervallic oddballs (Trainor et al., 2002).

Such Event-Related Potentials cannot, however, be uniquely associated with intervallic oddballs, since the manipulations exerted an effect on both interval sizes and scale-step dispositions (as exemplified in Figure 2). The effect of scale steps should be specially considered, in this case, since the standard stimuli consisted of highly structured scalar features (ascending major scales). With that considered, we could question the conclusion that “the auditory cortex [. . . ] encodes the exact pitch distances between tones in the absence of absolute pitch information” (Trainor et al., 2002), since brain responses could be related to disruption on diatonicity and/or scale-step organizations, and, most importantly, since Dowling’s studies have shown that individuals tend to perceive melodic information in terms of scale degrees.

The reported literature, which indicates an iterant confusion between scale steps and absolute interval sizes, is what motivates the present research. Besides raising this theoretical issue, this article will discuss the educational and scientific implications that such a differentiation might have. The next section of this text reports some experimental outcomes, as well as some theoretical concepts which indicate that scale steps and absolute interval sizes should be separately addressed with educational purposes.

Scale steps and absolute interval sizes: an educational issue

In his article from 1986, Dowling concluded that individuals who were able to combine scale step with interval representations reached success in certain melodic perception tasks. In a similar manner, Goldemberg (2015) suggests that the integration of bottom-up and top-down strategies may result in some cognitive and educational advantages for performing sight-singing tasks. The present section of this article will review some of the educational implications which might arise from the epistemological differentiation between scale steps and absolute interval sizes.

Dowling’s (1986) experiment indicates that individuals with high levels of musical training were able to combine the perception of absolute interval sizes with the perception of scale-step features. Individuals with moderate musical training were less capable of differentiating exact transpositions from imitations. According to the author, this outcome suggests that listeners with moderate musical training could only represent melodies in terms of diatonic scale steps. In contrast, experienced musicians were able to rely on interval representations when the harmonic context was presented as a difficulty factor for the discrimination between exact transpositions and imitations. In Dowling’s (1986) words, “professionals presumably had scale step representations at their disposal, but were able to use other recognition strategies when the task demanded it.”

The idea that experienced individuals are able to work with both scale steps and intervals is in agreement with some of the theoretical findings stressed by Goldemberg (2011, 2015). According to his research, the increased level of musical experience might be related to the capacity to work with a melody in terms of microstructures, such as intervals, and of macrostructures, such as scales and melodic patterns. Dowling and Goldemberg both agree that cognitive strategies of integration between scales steps and absolute interval sizes might be related to success in certain musical activities:

a fluent sight-singing, in which bottom-up and top-down strategies are integrated [. . . ] enables the reader to reinforce the process by having two strategies or to compensate difficulties they might have in one strategy with the other, in which may possess more fluency or knowledge. (Goldemberg, 2015)

Professional musicians had not only the capacity for scale-step representation but also explicit control over when and how to use it, with the result that they were able to perform accurately in transposition recognition even when tonal context shifted (Dowling, 1986)

In conclusion, the differentiation between scale steps and absolute interval sizes appears to be psychologically robust, and acknowledging this possibility could allow for significant improvements in experimental and education paradigms. The concepts of scale-step representations, interval representation, bottom-up sight-singing, and top-down sight-singing constitute the theoretical framework which served as the basis for the development of three musical tasks. Those tasks, which together form the Intervallic Awareness Test (IAT), are described and partially validated in the next section of this article.

Intervallic awareness: development of a new psychometric instrument

Three different paradigms have been developed to investigate intervallic perception within different musical contexts. The basic idea underlying these tasks is that the production of certain absolute interval sizes might be affected by different melodic contexts. The final form of the IAT encompassed a set of production tasks, and therefore this instrument can only be administrated to individuals with musical training. At the end of this article, future versions of the test will be discussed, and a possible application for musically naive individuals is proposed.

Besides these three novel musical tasks, the final form of the IAT incorporated a close version of Dowling’s (1978) discrimination paradigm. Individuals were presented with two short melodic excerpts and were asked to indicate if they were exact transpositions of each other. Melodies could either be exact transpositions or tonal answers (Figure 3). The first melodies were always in C major and the second ones were either in E minor/major or A minor/major (Dowling, 1978). The complete form of the IAT is available in Supplemental Appendix I.

Figure 3.

Initial melody, exact transpositions, and imitations exemplified by Dowling (1986). According to the author, if the initial melody was the one indicated by the letter A, “listeners were supposed to respond positively to 1B and 1D and to reject 1C and 1E.”

Paradigm 1: Intervallic addition task

The first paradigm, called the Intervallic Addition Task, presented individuals with a short tonal melody and asked them to sing a specific interval from the last note of that melody. The specific assumption behind this task is that, if individuals are able to sing the exact interval required, they are able to represent absolute interval sizes regardless of the tonal context. If, for instance, the item asks individuals to sing a major third from the third degree of a C major scale, they should sing the note G# (Figure 4b). However, if scale-step representations are cognitively salient, individuals would probably sing a G, which fits within the diatonic framework of the C major scale (Figure 4).

Figure 4.

After hearing the stimulus (a), individuals were asked to sing a major second from the last note of the excerpt: (a) stimulus, (b) response indicating interval representations, and (c) response indicating scale-step representations.

Paradigm 2: Intervallic inversion task

In this task, individuals heard a short melodic excerpt (Figure 5a), and then they were asked to sing the exact inversion of each intervallic pattern (Figure 5b). This task was designed to test the ability to produce a specific interval within a melodic excerpt. The accuracy on this task depends on the ability to ignore the first intervals, and to sing their inverted order. Individuals heard a perfect fifth, and instead of singing it, were required to sing a major second (Figure 5b).

Figure 5.

After hearing the stimulus (a), individuals were asked to sing the exact inversion of absolute interval sizes (b) from the same note of the stimulus.

Paradigm 3: Intervallic substitution task

Individuals listened to a short melodic excerpt (Figure 6(a)) and then they were asked to substitute the first interval with a different one. The specific assumption behind this task is equal to the previous one. The only difference, in this case, is that the second interval remained the same. In Figure 6, for instance, individuals were asked to substitute the major third with a major second, and this resulted in two changes regarding absolute pitch dispositions (Figure 6(b)).

Figure 6.

After hearing stimulus (a), individuals would be asked to substitute the major third with a major second (b).

Method

Instruments

A pilot test was carried out with three music undergraduate students from the University of Campinas (Unicamp). A pilot study was performed to verify the adequacy of materials and protocols. The test assumed its final version with 48 items, of which 24 of comparison, eight of adding, 10 of inversion, and six of substitution.

Procedures

Music undergraduates from the University of Campinas (N = 21, 14 male, and 7 female, mean age = 21.28, SD = 2.93) volunteered to take the IAT. The instrument was administered with approval from the university’s ethics committee, and the administration of the test took place throughout 2 weeks on the campus. Every task was explained and exemplified to the participants prior to the beginning of each section. If the tasks remained unclear, participants were encouraged to stop the test and ask for further explanation. The auditory stimuli were presented with a grand piano timbre synthesized from Finale’s library and were heard through loudspeakers (Samsung MX-F630). Answers were recorded (mono) with the software Voice Record Pro 3.1.9, which was installed in an iPad 4. The completion of the test took an average of approximately 32 min.

Scoring system

A preliminary analysis of the audio indicated a consistent pattern of mistakes that participants would make in the task. The mistakes which were most frequently noted were in regard to interval accuracy, maintenance of pulse, and number of trials taken to respond to each item. Therefore, the scoring system was based upon those criteria. A 4-point Likert-type scale was adopted to rate the participant’s performance as follows:

4—Correct interval, steady pulse, first trial

3—Correct interval, steady pulse OR first trial

2—Correct interval, unstable pulse AND more than one trial

1—Incorrect interval

Failure to maintain the pulse was considered as a partial mistake since we were interested in finding out whether participants were able to represent absolute interval sizes within a musical context. For instance, should a short break be added before each musical note, participants could give enough time for the tonal context to fade away in their memory, as demonstrated by Bartlett and Dowling (1980) as well as by Dowling (1991). Besides, with free timing, participants would be able to consciously calculate intervallic distances based on their previous knowledge about music theory, and therefore we would not be strictly measuring reflexive aural skills.

Comparison items were rated according to Dowling’s (1978) criteria, and individuals indicated on a sheet of paper whether standard and comparison melodies were exact transpositions. There were four categories of answers: “Sure Different,” “Different,” “Same,” and “Sure Same” (Dowling, 1978). Those four categories corresponded to a 4-point Likert-type scale, indicating degrees of certitude for each answer.

Data analysis and discussion

To evaluate whether the scoring system served as a good indicator of performance at the test, an expert professor from the Music Department at the University of Campinas scored the performance of five participants according to his own criteria. Pearson’s r was estimated at .983, p < .001, between the scores given by the professor and by the author of this study, thus indicating a fairly high correlation between the professor’s criteria and the criteria previously adopted. This statistical measurement evaluates the strength of a linear correlation between two variables, and it is often used as an indicator of the percentage of agreement between two raters or rating systems (e.g., Etterson, Shanteau, & Krogstad, 1987; Holmes, 2009; Hung, 2012).

Cronbach’s alpha was used as an internal consistency measure, and its value was estimated at .864. This number indicates, from 0 to 1, “the extent to which all the items in a test measure the same concept or construct” (Tavakol & Dennick, 2011). Cronbach’s alpha is also used as an indicator of how susceptible the data are to measurement errors and inaccuracies. The instrument is considered more reliable the closer the Cronbach’s alpha is to 1. The IAT was designed to be used in the first semester of Ear Training. Thus, a strong correlation between these variables would indicate that the instrument truly measures the aspects that it was built to measure. Spearman’s ρ was estimated at .744, p < .01, between the scores of 166 individuals. Comparison items were also used to check for criterion validity. The average scores obtained on those items correlated .79 with the average scores obtained on the addition, inversion, and substitution items.

An independent-samples t-test was carried out to see if individuals were more accurate when trying to identify tonal answers or exact transpositions, t(11) = 0.57, p = .57, but no difference was found. A one-sample t-test looked for mean scores above hypothetical chance level (2.66). Only Participants 5 and 15 showed an above chance performance, p < .05. Participant 14, on the contrary, showed a performance which was consistently below chance, p < .01, indicating that he might have inverted his answer patterns. Such a possibility is highlighted, still, considering that this participant presented a high performance at the IAT. Overall results indicate that individuals could not reliably tell the difference between exact transpositions and imitations (with the exception of Participants 5, 14, and 15). This result is consistent with Dowling’s (1978) findings.

Data indicate that the IAT has satisfactory levels of psychometric quality. Criterion validity indicated a moderate to high correlation with Dowling’s (1978) comparison task, which is a good indicator of absolute intervallic perception within tonal contexts. The second measure of criterion validity indicated that the test requires aural and sight-singing abilities similar to those required in a college level ear training course. Even though the estimates of criterion validity, internal consistency, and interrater reliability are somewhat satisfactory, it is wise to consider that this investigation could profit from the engagement of larger sample sizes. The three tasks hereby presented could be, in this case, included in a factor analysis, which usually requires a larger number of participants to be reliable (Curran, West, & Finch, 1996).

Conclusion

The literature reported in this study brings to evidence an iterant confusion between scale steps and absolute interval sizes. The tenuous distinction between those two melodic features motivated the development of the IAT, and perhaps the possibility of separating absolute interval sizes from scale steps may incite a fair amount of educational and experimental discussions.

According to Fournier, Moreno Sala, Dubé, and O’Neill (2019) cognitive strategies based on scale-step features are widely used by music students and teachers. In fact, many ear training and sight-singing methods are based on top-down strategies (Goldemberg, 2011, 2015), and musical exercises usually come from melodic patterns, tonal cadences, and arpeggios (e.g., Kodaly’s method). Bottom-up strategies, on the contrary, were strongly proposed by Lars Edlund (1963), who developed a widely known method for sight-singing absolute interval sizes (Figure 7). Even though many educational strategies have been based on either scale steps (Kodaly, as described in More, 1985) or absolute interval sizes (Edlund, 1963), there is not an educational approach which mutually encompasses those two melodic features.

Figure 7.

Example of sight-singing exercise proposed by Edlund (1963), where students are required to sing a pattern of intervals which do not conform to any standard musical scale.

With that considered, the IAT could serve as groundwork for the development of new sight-singing and aural training methods. Addition tasks, for instance, require the ability to represent and produce specific intervals within a tonal context, and based on the distinction between scale steps and absolute interval sizes, this task might be different from asking individuals to sing a perfect fifth (e.g., C and G) within the context of C major. Methods combining intervals and scales should focus on the production and the perception of specific intervals within diatonic contexts, rather than associating intervals with diatonic leaps between scale degrees (e.g., major second from E to F# within the context of C major, as represented in Figure 2).

The IAT might also encourage new investigations into the field of melodic perception and cognition. As previously reported, there is a considerable amount of experimental data indicating that scale-step organizations might affect the way absolute interval sizes are perceived (e.g., Attneave & Olson, 1971; Dowling, 1978, 1986; Dowling & Bartlett, 1981). In the reported literature, as well as in the present investigation, intervallic distances are not processed in terms of cents, and individuals tend to recognize leaps measured in terms of scale steps rather than in terms of absolute interval sizes. The IAT could provide, in this context, an excellent tool for further investigating perceptual processes related to scale-step perception.

The IAT might also encourage new investigations into the field of melodic perception and cognition. According to the reported literature (Attneave & Olson, 1971; Dowling, 1978, 1986; Dowling & Bartlett, 1981) as well as to the results hereby presented, intervallic distances are not fully processed in terms of cents, and individuals tend to recognize leaps measured in terms of scale steps rather than in terms of absolute interval sizes. The IAT could provide, in this context, an excellent tool for further investigating perceptual processes related to scale-step perception.

The addition items proposed in this study, for instance, could be turned into a perception rather than a production task. In this case, individuals would hear a C major scale as the prime (e.g., Bharucha & Stoeckig, 1986; Krumhansl, 1979, 1990) followed by a diatonic interval, and then they would be asked to estimate the distance between those two tones (e.g., Russo & Thompson, 2005). If scale steps play a role in intervallic perception, the distance between C and E (Figure 1) would be perceived as similar to the distance between A and C (Figure 1), even though these intervals are different in terms of cents. Addition and inversion items could also be turned into perception tasks. In this case, individuals could be asked to rate how similar two melodies are (e.g., Schmuckler, 1999) and those melodies could either present an inverted or a random melodic pattern. If absolute interval sizes are salient, inverted melodies would be rated as more similar than random ones.

Those versions of the IAT could allow its administration to musically naive participants, and a series of theoretical issues could then be addressed. For instance, we could investigate how the perception of scale steps modulates the perception of absolute interval sizes or how the acquisition of tonal schemes (Krumhansl, 1979, 1990) affects the perception of intervals. Absolute intervallic perception could also be used to investigate the acquisition of statistical knowledge for novel musical systems, and to evaluate how such knowledge could affect the categorical and continuous perception of distance between two consecutive tones.

We should acknowledge, however, the fact that the IAT is oblivious to some recent findings about music perception and embodied cognition. Embodiment, according to an increasingly large body of studies (see Leman & Maes, 2014, for a review), is a fairly useful tool for understanding the way that human beings interact with music. In regard to melodic intervals, there is one piece of evidence suggesting that individuals are generally able to estimate the distance between two notes based on visual cues (Thompson, Russo, & Livingstone, 2010). The authors found that even head movements and/or facial expressions could carry out information about the size of a sung melodic interval.

The fact that body movement might modulate intervallic perception is arguably an important aspect to be investigated in the future. The relationship between scale steps and absolute interval sizes is likely to be moderated by aspects such as facial expression, for instance, and maybe embodied strategies could be integrated into IAT training drills, either in educational or experimental contexts.

Finally, we cannot say that the IAT has entirely fulfilled the purpose of separating scale steps from absolute interval sizes. There are numerous cognitive strategies that might have influenced participants’ performances on the IAT, and individuals could sing accurate intervals based on somatosensory feedback (see Zarate, 2013, for a review), or even on memory for musical tokens, such as the starting interval of a familiar folk tune (Smith, Nelson, Grohskpof, & Appleton, 1994).

We can say, however, that the IAT was conceptualized after Dowling’s (1978) experiment, in which individuals were required to perceive specific intervals within a tonal context. A good way to check if our study fulfills the purpose of isolating intervals from scale steps is by evaluating if an aural training strategy based on the IAT would result in a performance improvement on Dowling’s task. For instance, we could train individuals to sing specific interval sizes within tonal contexts (i.e., Paradigm 1) and see if this training would improve performance on Dowling’s task. If our paradigms in fact require cognitive control over scale-step representations and interval representations, we would expect participants to become more accurate when differentiating tonal answers from exact transpositions.

Supplemental Material

POM-18-1319.R3_supplementary_materials – Supplemental material for Differences between scale steps and absolute interval sizes: A new test for intervallic awareness

Supplemental material, POM-18-1319.R3_supplementary_materials for Differences between scale steps and absolute interval sizes: A new test for intervallic awareness by Pedro de Alcântara Senra de Oliveira Neto and Guilherme Alves Delmolin de Oliveira in Psychology of Music

Footnotes

Authors’ note

Pedro de Alcântara Senra de Oliveira Neto is now affiliated with Center of Mathematics, Computing and Cognition (CMCC), Federal University of ABC, Bangú, Santo André, Brazil.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Institutional Program for Scientific and Technological Initiation, which is funded by the Brazilian agency FAPESP.

ORCID iD

Pedro de Alcântara Senra de Oliveira Neto

Supplemental material

Supplemental material for this article is available online.

Notes

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