Bach, Escher, and Mental Rotation: An Empirical Study in the Perception of Visual and Melodic Congruency

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1 1 Bach, Escher, and Mental Rotation: An Empirical Study in the Perception of Visual and Melodic Congruency Marina Korsakova-Kreyn Touro College, Lander College for Women, 227 West 60th Street New York, NY Abstract Among the most fascinating aspects of music are the quasispatial properties of tonal space and structures. For instance, any conventional melody can be visualized as a contour as a combination of ups and downs. A melodic contour can be bent by tonal forces, and all its melodic intervals can be mirrored. In addition, a contour can be augmented and diminished in duration, which is conceptually similar to a proportional enlargement and diminution of a visual object. Certain musical compositions, specifically Baroque fugues, resemble divisions of the plane, such as in M. C. Escher tessellations and M. K. Čiurlionis paintings. When the tonal space of music is visualized as phenomenal gravity (Scruton, 1997), tonal melodies can be explained as melodic objects shaped by the tonal force field. We hypothesized that the cognitive processing of these transformations may draw on spatial abilities developed for visuospatial reasoning and that the perception of melodic transforms involves the same neural substrate in the parietal cortex (specifically BA 7), which is engaged in visuospatial processing. We conducted a behavioral study that compared the perception of congruency of 3D geometrical figures and congruency of tonal melodies. The visuospatial task used a set of stimuli from a study in mental rotation (Shepard and Metzler, 1971), whereas the melodic rotation task used a set of melodies selected from the clavier compositions of J. S. Bach. The same melodies were used for a control task on timbre judgment. Performance was positively correlated for visual and melodic spatial tasks (r =.40), but the pattern of correlations overall differed between sexes. Males performed better than females on all three tasks. The obtained results converge with previous investigations that found gender effect in the visuospatial mental rotation task, and offer new information about gender effect in music perception. The discovery of a positive correlation between melodic and visual spatial tasks provides supporting evidence for the hypothesis of supramodal processing in music perception and inspires new directions for discussing the aesthetic experience. Keywords: music perception, supramodal processing, mental rotation, melodic transformation, gender effects A musical scale is a system of reference for our mind to read tonal patterns. In a scale, the tones are organized hierarchically: the first note of a scale (tonic or tonal center) is a depression of potential tonal energy and all other tones differ in the intensity of their attraction to the tonal center. The difference in degree of attraction (not just difference in pitch) is the source of melodic patterns the source of music, as we know it today. Explaining music in terms of phenomenal gravity (Scruton, 1997) leads to thinking about melodies as objects shaped by the power lines of a force field of tonal attraction. For the ear, transformation of a melody is akin to transformation of a material object for the eye. In polyphonic music, and sometimes in thematic development of sonata allegro form, a melody serves as a constructing unit (module) that can be augmented, diminished, bent, or mirrored (Fig. 1). A catalog of visuospatial transformations (Shepard and Cooper, 1982) can be compared point by point to a catalog of melodic transformations used in polyphonic technique.. Figure 1. Melodic transformation: Two-Part Invention in C, J. S. Bach. Melodic theme and its translation (white arrows), mirroring (black arrows), and augmentation of the theme s beginning fragment (striped arrows) Introduction Music is essentially intuitive and sensual. Yet one of the most interesting subjects of advanced music training is analysis of musical form, the purpose of which is to teach musicians how to recognize and examine musical architectonics. Analysis of musical form uses extensively spatial concepts. Music a subjective and abstract art has a high degree of structural order. Music compositions are made of tones arranged in time, and music s two main dimensions are tonal space and structured time. The tonal and temporal dimensions are inseparable and together they create the unity of a musical structure the tonal chronotope. The easiest way to explain the tonal dimension is by comparing the tonal space of music to the gravitational field. Figure 2: Another World, M. C. Escher. Image of two windows, with a bird and a horn, serves as a constructing unit for the overall composition (Wikipedia, fair use )

2 2 The best visual illustrations for module-based musical structures can be found in the works of M. C. Escher. (In one of his letters, Escher mentioned the paradoxical similarity between the division of the plane in visual art and division of time in music). For instance, the woodcut print Another World is built on a visual module made of two windows: one window with a bird and another window with a horn (Fig. 2). The module is seen from three different perspectives: from below, opposite, and from above. Our perception is played with by the appearance of the images from different angles of view. People s ability to recognize the same object when it is shown from different angles of view was explored in a famous study in mental rotation by Shepard and Metzler (1971). The researchers used a large set of drawings of 3D geometrical figures arranged by pairs; in each pair, one of the objects was rotated in relation to another (Fig. 3). The results of the study confirmed the author s main hypothesis that the greater the angle of rotation, the longer it takes to make a judgment on whether the two 3D objects are congruent or not. Figure 3: Samples of stimuli for two trials from a study in mental rotation (after Shepard and Metzler, 1971; Wikimedia Commons, by Jennifer Oneske) Empirical research shows that melodies are remembered in terms of their shape, or melodic contour, and that by using the standard melody as a template, people are able to recognize the transformation of a contour (Dowling, 1972, 1978). For example, a melodic contour seems bent when some of a melody s constituent intervals change in size, and the melodic contour becomes mirrored when all the intervals change direction (Fig. 4). Theme of Invention Bent theme Mirrored theme Figure 4: Transformation of a melodic contour from Twopart Invention in C major by I. S. Bach Musicians liberally apply spatial terminology in musicology and in teaching music to students at all levels. For a highly trained performer contemplating a complex musical composition, music is often sensed as a balance between the tonal shapes that comprise the main melodic themes, and melodic arches (connecting material). At some point, the performer can sense the whole composition at once, in all its architectural clarity and as if beyond the constraint of the temporal dimension. It is possible that musicians may differ from non-musicians in visuospatial reasoning. For example, musicians perform better on tests of spatial perception than non-musicians (Hassler, 1992), and musicians differ from non-musicians in the pattern of brain activation when performing Shepard & Metzler s mental rotation task (Bhattacharya et al, 2001). Listening to melodic transformations involving transposition and retrograde presentation generates activation in those parietal areas that are involved in visuospatial processing, including mental rotation (Jordan et al, 2001; Harris & Miniussi, 2003; Zatorre et al, 2009; Foster & Zatorre, 2010). In comparison with non-musicians, the brains of professional male keyboard players show increased gray matter volume in several areas of the cortex, including the superior parietal lobe that is important for visuospatial reasoning (Gaser & Schlaug, 2003). Brain imaging studies also point to the possibility of sex differences in the performance of melodic transformation and visuospatial tasks. Males generally perform better on mental rotation tasks than females (Voyer et al, 1995; Maeda & Yoon, 2014), and this advantage has been explained by the involvement of sex hormones (Hassler & Nieschlag, 1989; Peters et al, 2007) and by regional morphological differences between male and female brains (Koscik et al, 2009; Ardekani et al, 2013). These previous studies suggest the possibility of a relationship between performance on a mental rotation task and melodic transformation task, although an attempt at comparing the performance on mental rotation of 3D objects with performance on transformation of random sequences of tones (Cupchik et al, 2001) produced a rather puzzling pattern of results, which was due, most likely, to the absence of conventional melodic shapes. We hypothesized that the melodic transformation task and visuospatial mental rotation task should be positively correlated and that the musical experience should be positively correlated with both of these tasks. To test our hypotheses, we conducted a behavioral study that compared performance on the perception of congruency of 3D geometrical figures and tonal melodies. Method Two-hundred-thirty-one undergraduates of the University of Texas at Dallas, 163 females (ages with a mean of 24.64, SD = 6.44) and 68 males (ages with a mean 25.99, SD = 8.34) participated in the experiment in partial fulfillment their course requirements in psychology. All 231 participants performed the melodic contour transformation and visuospatial tests, whereas 114 of them (82 females and 32 males, ages with a mean of 24.75, SD = 5.74) in addition performed the control task on timbre change recognition. Participants who had 4 or more years of musical experience were characterized as musically experienced.

3 3 The visuospatial task was a shortened replica of the classic Shepard and Metzler experiment in mental rotation, and was composed of 122 pairs of images of 3D geometric objects (Fig. 3). The images were presented to the participants as a PowerPoint slide presentation. Duration of each stimulus was 3 seconds; the stimuli were divided by a 3-second gap, during which the participants made the judgment on congruency. The auditory tasks included the main task on melodic contour transformation and the control task on timbre change. The main task of melodic rotation was designed as a musical counterpart of the visuospatial mental rotation task and consisted of a set of 27 melodies in their standard and altered form that presented melodically congruent and noncongruent transforms. The melodies and their transforms (one transform for each melody) were selected from the clavier compositions of J. S. Bach and recorded on CD with a grand piano. The melodies were 7 to 16 notes long, relatively balanced in mode (major-minor), balanced in meter (duple versus triple), and differed in tempo and character. On each trial, a melody was followed, after a pause of 2 seconds, by its transformed version. Melodic contour transformations included three categories: Mirrored, Bent, and Composite (Fig. 5). Melody of Minuet Mirrored (inversion) Bent (tonal answer) Composite (incomplete inversion) Figure 5: Transformation of melodic contour: Minuet from Notebook of Anna-Magdalena Bach In Mirrored transforms all melodic intervals of a contour reversed their direction. In Bent transforms, some melodic intervals of a contour changed in size, but because the relative pitch-direction of the intervals was preserved, this made Bent transforms congruent with the original form. Altering the size of the melodic intervals made the melodic contour bent, which was conceptually similar to the visual effect observed in mental rotation when the sides of the cubes of a geometric object appeared shortened or lengthened in size due to a change in the viewing angle (Fig. 3). Composite transforms had only some of their melodic intervals reversed in direction; because of non-systematic changes, Composite transforms represented melodic noncongruency. For all melodic stimuli, the temporal organization of a melody and of its corresponding transform was identical. The same 27 original melodies were used in the control task where participants made judgment on how many tones in a sequence were different in timbre from the other tones: 1, 2, or 3. Cakewalk software was used to control the change of timbre from piano to harpsichord. The acoustically oriented (non-spatial) perception of individual tones did not involve an integrated perception of melodies as compared to the quasispatial perception of the melodic objects in the main musical task. Results For all 231 participants, the visuospatial and melodic transformation tasks were correlated, r =.40, p <.001. Musical experience was correlated with the melodic transformation task, r =.40, p <.001, but not with the visualspatial task. A similar pattern of correlations was obtained for men and women independently (see Table 1). Table 1: Correlations among the visual and melodic tasks and musical experience for all 231 participants All participants Visual Melody Experience *** Visual 0.40*** Male participants Visual Melody Experience ** Visual 0.28** Female participants Visual Melody Experience *** Visual 0.39*** *** p <.001; ** p <.01; * p <.05 For those 114 participants who performed all three tasks (including control task on timbre recognition) the visuospatial and melodic transformation tasks were correlated, r =.37, p <.001, as were the visuospatial and timbral tasks, r =.33, p <.001, and the melodic transformation and timbral tasks, r =.27, p <.001 (Table 2). Performance on the melodic transformation task correlated with musical experience, r =.41, p <.001, but neither the visuospatial task nor timbral task correlated with musical experience. A repeated measures ANOVA for the 114 participants revealed that both for the melodic and visual tasks, there were main effects of experience and gender, whereas for the timbral task, there was a main effect of gender only. There was no significant interaction experience X gender for either of the tasks. Separate analyses for males and females in the group of 114 participants (Table 2) revealed a significant correlation between the visuospatial and melodic transformation tasks for both males, r =.46, p <.01, and females, r =.28, p <.01. However, for males this was the only significant correlation (though for males the correlation of musical experience and the visual task approached significance, r =.34, p <.06.) The results for females included correlations between the visual and timbral

4 4 tasks, r =.30, p <.01; between the melodic transformation task and the timbral task, r =.24, p <.05; and between the melodic transformation task and experience, r =.48, p <.001. Therefore there was a very a specific correlation of the visual and melodic transformation tasks for males, and a more general pattern of correlations among the various tasks for females. A repeated measures ANOVA for males showed a main effect of experience for the melodic and visual tasks, but not for the timbral task. In comparison, a repeated measures ANOVA for females revealed a main effect of experience for the melodic and timbral task but not for the visual task. The results of MANOVA showed a significant effect of music experience for females only (p <.001). Table 2: Correlations among the visual and melodic tasks and musical experience for the 114 participants who did all three tasks including the timbral task. All participants Visual Melody Timbre Experience *** 0.17 Visual 0.37*** 0.33*** Melody 0.27*** Male participants Visual Melody Timbre Experience Visual 0.46** 0.04 Melody 0.19 Female participants Visual Melody Timbre Experience *** 0.20 Visual 0.28** 0.30** Melody 0.24* *** p <.001; ** p <.01; * p <.05 Discussion The results of our study confirmed the predicted positive correlation between the melodic rotation task and visuospatial task, though the study did not find that music experience was important for visuospatial reasoning (see Tables 1 & 2). The positive correlation between the two modality-different tasks, visual and auditory, could be interpreted as a manifestation of supramodal processing, meaning that the perception of coherent melodic images and their transforms transcends modality of sensory information. In broader reading, this hypothesis implies that gestalt might be supramodal generally. The hypothesis of supramodality is in accord with Alexander Luria s (1973) model of functional hierarchy of the brain, in which the secondary and tertiary cortical zones of the brain perform an integrative role which is necessary for more complex gnostic processes (Luria, 1973, p. 77). Therefore, Luria s model proposes that with an increase in complexity of the gnostic processes and with ascent in functional hierarchy cognitive mechanisms become less modality specific. Considering that music is not essential for survival of the species, it is reasonable to suggest that music engages cognitive mechanisms that were finessed by evolution for survival-oriented purposes. The available data (and philosophic discourse on the aesthetic of music) lead to the conjecture that visuospatial processing and the perception of melodic transforms engage common cognitive mechanism and share the same neural substrate in the parietal lobe (specifically BA7). The neurobiological aspect of the hypothesis of supramodality relies on neuroimaging studies in musicianship-related plasticity (Gaser & Schlaug, 2003; Wan & Schlaug, 2010) and on research in mental rotation (Bhattacharya et al, 2001) and melodic contour transformation (Dowling, 1972), whereas the philosophical foundation of the hypothesis relies on the works of Florensky (1925), Scruton (1997), and Prigogine (1997). The crucial musical aspect of the hypothesis of supramodality is the resemblance of tonal space to the gravitational field. Listeners perceive tonal space as a hierarchy of perceived tonal tension (Krumhansl & Kessler, 1982; Fredrickson, 1995). Perceived tension is intimately related to the perception of consonant and dissonant compounds, which, in turn, might be related to the cost of neuronal auditory processing. For example, the consonant Pythagorean intervals and major triad differ from the dissonant intervals and triads by the amount of shared spectral information: the greater overlap of the beginning overtones in the harmonic series of tones, the more consonant the combination of the tones and the simpler the ratio of frequencies of the tones Where the real gravitational field is an absolute physical phenomenon, a tonal force field is a mental construct that springs as a mental system of reference as soon as the human mind detects homogeneous perceptual elements (tones) and attempts to construct a coherent melodic entity. Artfully arranged tonal interactions within the force field of phenomenal tonal gravity generate melodic topology that is perceived as music: for instance, as a melody. When a melody changes its position along a scale, this can produce changes in melody s shape, which are reminiscent of the transformation of living forms as illustrated by D Arcy Thompson (1917). In the presented study we found a significant positive correlation between the quasispatial melodic task and the visuospatial task, which suggests that both tasks might be relying on the same processing resources in the brain, even if the tasks belong to different domains: tonal time-space, twodimensional and cyclical, versus 3-dimensional visual space. The results indicate that men possess a specific cortical network dedicated to processing mental rotation, whereas women engage additional, more general, cognitive resources (Ecker et al, 2006). The gender effects in performing mental rotation tasks have been explained in terms of a neurobiological basis that involves sex hormones (Hassler & Nieschlag, 1989; Hausmann et al, 2000; Hooven et al, 2004; Peters et al, 2007), and as a result of specific adaption for

5 5 mental rotation in the parietal lobe of men as compared to women (Koscik et al, 2009). Overall, the evidence suggests that visuospatial reasoning and melodic processing might engage different strategies and even different cognitive mechanisms in females as compared to males (Good et al, 2001; Tcheang et al, 2013). We also found that some participants with no formal musical training showed excellent performance both on the visuospatial task and quasispatial melodic task, as if the difference in modality of the two systems of reference visual and tonal did not matter for these participants. Therefore, it is quite possible that our study tested fluid intelligence inborn abilities for pattern recognition and inductive and deductive reasoning (Choi et al, 2005). The presented behavioral study could not answer the question of whether there is actual involvement of a shared neural substrate in processing visuospatial mental rotations and melodic transformations, but recent neuroimaging studies offer evidences suggesting that this is the case (Foster & Zatorre, 2010). However, we cannot exclude the competing explanation: that the activation of the parietal cortices is related rather to maintaining cognitive control (Coull & Frith, 1998; Cusack, 2005; Husain & Nachev, 2007) than to spatial processing proper, regardless of whether the stimuli are auditory or visual. Conclusion The main concept of the presented study reflects on the performing experience of a classical pianist. This experience is saturated with an awareness of the quasispatial nature of complex musical structures. The Weimar poets famous definition of architecture as frozen music has been universally accepted as a metaphor, yet it is not implausible that, for the human mind, music is indeed sonic architecture in motion or proportions in motion. The hypothesis of the gradient of neuronal cost of auditory processing (which is still in want of direct empirical conformation) suggests that the psychophysics of melodic compounds depends on the amount of important shared information in the harmonic series of tones that make the compounds. This approach gives specific rationale for Leibniz motto that music is unconscious calculation. Thinking about the foundations of music perception as an intuitive reaction to artful sequences of sonic proportions in the phenomenal tonal field inspires new kinds of studies in aesthetic emotion. 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