Sound Image of Time. Time widens the circle of the verses, and I myself know some verses that are, like music, all things to all men. J. L.

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1 Marina Korsakova-Kreyn, 2007 Sound Image of Time Time widens the circle of the verses, and I myself know some verses that are, like music, all things to all men. J. L. Borges It is said that music begins where words fail. Music s vague messages awaken cloud-like feeling idiosyncratic, and yet direct and precise in its animalistic power. The delicate beauty of the art of music would wither long time ago if not the mighty physiological element that the sound flow of music elicits from us, shaking, making shivers, affecting heartbeat, and giving pleasure that, though called aesthetic emotions, arrive from the dark pleasure-seeking quarters of the brain. In the visual arts images are either suggestive or simply depict familiar shapes, such as clouds, trees, a face, and so on. What exactly, then, do we recognize in music? In musical sounds we see no familiar images, discern no definitive symbols or sign. Music presents nothing to the touch, displays no 'things,' and contains no words to say 'this is a house and this is a hat.' Perfectly abstract, music grants limitless freedom to the imagination. It is the subjective phenomenon par excellence. By following its sound patterns, our subconscious mind analyzes the tonal and temporal relationships of music. Miraculously, we recognize ideas and imagery. We think in music. Musical compositions exist in a peculiar universe, where two main organizing principles rein: tonal force field and psychological time. These principles shape the `objects' and forms of music. Unlike visual images that are possible to embrace at a glance and from any point of observation, musical compositions unfold orderly through time to our mind. 1

2 Tonal Chronotope In musical experience we are confronted with time: not just events in time, but time itself, as it were, spread out for our contemplation as a space spread out before us in the visual field. R. Scruton Music is also called the Image of Time. By creating feeling of time, music recreates the feeling of life itself. While giving our attention to the sound stream of music, we entrust ourselves to the interpreter's will to molds the state of our soul. Chronotope literally means time-space. In music time and sound are tightly interwoven and unified, much like how time and space are inextricably bound in the material world. Listening to music, we perceive an orderly sound-stream unfolding along the Arrow of Time. A change in the order of tones or in rhythm can completely transform a musical thought Changing time-values in the Motif of Fate from the Fifth Symphony by Beethoven generates new entity. A special case exists in the organization of time in music: structured silence, or structured absence of sound. Mozart considered pauses to be the most beautiful aspect of music, when moments of structured silence are filled with psychological tension, rich in expressiveness. We can compare pauses in music with negative space in architecture and sculpture. Like an open window or a door leading out to the unknown, pauses can create a feeling of anticipation and tension. 2

3 2. View on Palazzo Vecchio from the opening in a wall of the Brunelleschi's cupola, Florence Musical thought is conveyed to our mind through sounds organized in time. In the visual arts images occupy space while in music images 'occupy' time. Time is the musical analog of visual space, the true space of music. 2. Old-New Synagogue, Prague 4. M. Kreyn, Face 5. Worms Cathedral Playing with time 3

4 Music is a playing with sound-time. The very secret of interpretation of a musical composition lies in the subtleties of this time-manipulating. Musical thought dictates tempo and its changes. Rubato, expressive stretching and compressing of whole measures, (from 'stealing' - when borrowing time, a performer should not forget to give it back), and agogic, slight changes in duration of individual tones, are what indeed enlivens musical performance. Music comes to our mind via sequences of sound events. We connect and weave them into a meaningful stream that gives the sensation of emotion and gesture. As Susanne Langer writes, music recreates the "logic of emotion." In our real life we feel the pace of time through our emotional states. Contented people "do not observe fleeting hours", but time seems at a standstill during misfortune and boredom. By shaping our feeling of time, music creates the feeling of psychological life. Where visual arts humanize space, music humanizes time. Among the fine arts, music displays the strongest dichotomy between order and expressive freedom. Fantastically free, subjective, and in the highest degree abstract, music is maintained by an order, efficient and elegant. While tonal organization is based on a hierarchy of tones, the arrangement of sounds in time begins with an elemental periodicity that resembles the regularity of breathing and heart beat. Atop this living, flexible periodicity there are woven intricate rhythmical patterns. Tonal and temporal organizations are inseparable in music: together they create the unity of a musical organism, from a simple tune up to the most complex musical forms. Aesthetic unification of artistic space Perceptual schemas, which have long been recognized to be important in visual perception and cognition, appear to be of equal importance in the perception of musical tones. Jordan D.S. & R. N. Shepard 4

5 There exists an idea that the entire history of European art is in fact a history of visual perspective of its theory and practice. We cannot imagine our perception of the world today without perspective. Our knowledge of perspective and our habituation to its rules practically dictate our way of seeing. In other words, familiarity with perspectival representation has 'tuned' our brain and to some extend conditioned our current perception of the visible world. In fact we find that perspective is, much like 'truth,' historically contingent. As a symbol it evolves in tandem with the evolution of the dominant symbolic order at large. Ervin Panofsky called perspective a "systematic abstraction from psychophysiological space" when psychophysiological space is transformed into mathematical space. Subjective, or curvilinear, perspective generates images more closely representative of the natural method of seeing than the image given by linear perspective. The reason is two-fold: retinal curvature and our two constantly moving eyes (saccades) produce a "spheroidal field of vision." Euclid's Eighth Theorem supports this natural way of seeing, stating that an evident difference in size between two equal objects located at different distances from an observer is better determined by a ratio of angles, not by a ratio of distances. From what we know, the ancients adhered faithfully to this principle, as evidenced for example in their architecture. The columns of ancient temples were slightly curved (entasis) precisely in order to create the illusion of a straight line. According to Panofsky, antique thought had not yet defined space as a "homogeneous and infinite system of dimensional relationships" that was eventually granted by central perspective. Antiquity had no feeling for the infinity that is implied by linear perspective. In ancient art, space and bodies within the space were united into the whole, with no particular distinction between the bodies and space, "body" and "non-body." The perceptual space in antique art was "visually symbolized," as compared to modern art, where, thanks to perspective, the same space appears in "logical form." 5

6 From the "visual symbolization" of antiquity to the "logical form" of systematic space of the Renaissance, the evolution of our perception of aesthetic space evolved in tandem with the changing view of the nature of space at large. The homogeneous and dimensionless space of Neo-Platonists was gradually replaced by the infinite space of true central perspective with one all-powerful vanishing point to which all lines converge. This new system grants the modern observer a clear understanding of sizes and distances. For example, a highly popular checkerboard floor pattern became an "index for spatial values" so that individual bodies, the distances between them, and their movement were visually captured as if by numerical values based on the count of floor tiles. With this method in place, the stage was set for the future appearance of Cartesian coordinates. From the 14th century, artists and architects of the Renaissance such as Giotto, Brunelleschi, Alberti, Piero della Francesca and others used algebraic and geometric methods in working with perspective. Their work marked the mathematical rationalization of a unified aesthetic space. These shifts in perception merely reify epochal changes, and thus the changes in human rationality, asserting the latter's locality and historical contingency. To apply, for instance, our modern distinction between positive and negative space is, with respect to the ancients, an incoherent concept. The point is that our spatial logic is quite fluid, evolving through history. *** It is believed that the optical foundation of perspective was laid down by Al-Hazen in 1000, who was first to explain conical projection of light to the eye, centuries before unified orientation in space was consciously and stylistically realized as perspective. (Zahoor A., 1998, e-book on Islamic Civilization: < ***Panofsky in some ways anthropomorphized space, yet this is sensible since he talks about artistic, that is, humanized space. Central perspective, with its infinite space and one arbitrary chosen vanishing point, acts as the aesthetic manifestation of the departure from the absolute center and absolute limits of the ancient world view. It illustrates the transition from the geocentric Universe of Aristotle to the infinite Universe of Giordano Bruno. Mathematical rationalization created a type of space where sizes and distances were presented with systematic consistency to perception. The elegance and simplicity of this intellectual schema entered 6

7 into a union with the magic of aesthetic creativity. At the same time, this new rationalization "involved extensive abstraction from the psychophysiological structure of space." It bound us to see in a monocular way, as though with one single and immobile eye or the virtual eye. The most intersecting recent addition to the story of seeing comes from current research in stereovision that says about fusion of two monocular visions into Cyclopean view, which gives our perception an image of the world that is never recorded directly by any sensory array, but constructed by our neural hardware, in Henkel s words. With the advent of linear perspective, the subjective perception of the visible aesthetic world was rationalized, thus subjecting artistic phenomenon to mathematically precise rules. But like all technical discoveries in the handcraft underlying the visual arts, this new perspective created a model that, precisely through its systematic rigors, allotted the painter greater creative freedom. By developing a rationalized method for the unification of visible space, the painter, rather than stifling himself creatively by such a bounded system, actually opened the door to a higher level of representation. In the same way that he overcame the technical problems of paint by mastering the medium, he overcame the problems of spatial depth by applying perspective. Paradoxically, the world of music also possesses perspective tonal perspective. The evolution of harmonic language in the classical European tradition presents us with the musical analogue to the story of development of central perspective in the visual arts. Like the history of linear perspective, the history of functional harmony in music illustrates and reifies changes in perception and understanding of the world. Our discussion here is not about the expressiveness of musical forms per se, but about the transformation of the very medium of music, its building material that was demanded by creative thirst for expressiveness. The subtle changes in organization of the tonal field of music and its mathematization occurred chronologically in parallel with the rationalization of visual space via central perspective. When Christopher Wood wrote that the history of Western (European) art 7

8 was presented by Panofsky as the history of perspective, he meant this only with respect to visual art and in no measure included the art of music. But the space of music did experience comparable changes in a course of cultural history. How impressive are the signs of the historical development of tonal perspective in music! As linear perspective tuned our eyes to a tempered visual space, the evolving tonal perspective gradually tuned our ears to the tempered tonal space of music. Bringing space to its logical form both in music and in the visual arts was necessary in order to achieve the aesthetic unification of artistic space, three-dimensional in visible art and time-tonal in music. Linear perspective awarded 3-D space the accurate proportionality of sizes and distances and became a powerful compositional device easily available to learning. Similarly, in music, the aesthetic unification of tonal space by means of tempering the tonal schema revealed the possibility of creating highly complex musical forms. But in this process of tempering, the natural tonal field suffered inevitable distortions abstraction of psychophysiological space in the Acousmatic domain of music. Today, while listening to music, we generally hear a mistuned tonal schema in which only one melodic interval, the octave, remains true to the natural psychophysiological tonal space. In the visual arts, the reinterpretation and unification of space through convergent perspective was accompanied by a deviation from visible psychophysiological space that is, from the natural, neuro- and psychophysiologically determined ways of perception. From the binocularity of seeing and mobility of gaze, and from spheroidal nature of the visual field. We find the reflection of this natural way of seeing in ancient architecture, ancient vases and murals, Byzantine mosaics, and Russian icons. The difference in spatial perception between the modern artist and creators of ancient art cannot be explained by a different neurophysiology of seeing. According to Panofsky, the difference reflects a changing worldview, namely, that this "perspectival achievement is nothing other than a concrete expression of a contemporary advance in epistemology or natural philosophy." It is a common thread running through the fabric of cultural evolution. 8

9 Tonal perspective Objects of musical and visual space inhabit their respective systems of coordinates. In the visible world the locations of images are defined by the Cartesian coordinates - width, height, and depth - and an intuitively perceived gravitational force. Consider M. C. Escher's "Another World." A bird and a horn in a window represent a module, or a building block, on which the whole drawing is constructed. The lower and upper modules are also rotated 180 degrees so that the window with a horn appears on alternate side of the bird. At first glance the contour of the lower and upper bird seems reshaped, and our natural sense of gravity and direction is challenged and distorted. As soon as we realize that this is the same image shown from three different vantage points, the feeling of distortion weakens. The center bird and a left window make a visual module that appears in front, from above and from below. 6. M. C. Escher, Another World (Wikipedia, fair use) In the visual world, our intuitive understanding of the force of Gravity gives us a sense of direction. In this paradoxical work, a visual module consisting of a bird and a horn in a window appears from three different perspectives. Before we adjust our sight to different perspective, the bird seems reshaped. 9

10 Atop Auguste Rodin's "Gates of Hell" there are three male figures - the "Shades." In reality, the same male figure, Adam, serves as a module of the entire composition. The contour of each figure looks different from different perspective. 7. A. Rodin, Gates of Hell (Wikipedia, fair use) A. Rodin, Shades (Art Gallery of South Australia media centre, fair use) We encounter a similar phenomenon in musical structure. Escher himself wrote in one of his letters about the similarities between divisions of a plane in the visual arts and divisions of time in music. Like a module-based image, a module-based composition can exist in music. A melodic theme can behave as a module, or building block. A melodic module can incur various transformations: it can be inverted (mirrored), augmented, diminished, or broken into fragments that each may start living their independent lives. 9. J. S. Bach, Two-Part Invention in C, fragment 10

11 Legend: White arrow: theme-module Black arrow: inverted (mirrored) theme-module Striped arrows: fragment of the theme-module Shaping the invisible Visual pattern recognition finds direct analogues in auditory pattern recognition. W. J. Dowling Any melody can be presented as a melodic contour, as a combination of ups and downs in pitch. In the tonal field, a melody can sound as if 'bent' by the tonal forces, or as if appearing to the ear from 'different points of view' in a given tonality J. S. Bach, Two-Part Invention in C (theme) 11. M. C. Escher, Another World (Wikipedia, fair use) The Invention's theme appears in varied forms within same tonality. The theme sounds as if 'bent' by the tonal force field or as if 'shown from a different perspective' within a given reference system. Escher's bird is presented in Cartesian coordinates, while a melody is presented in the tonal system of reference. In both spaces visual and acousmatic a switch in perspective makes the image appear as though 'reshaped.' 11

12 Arrow of time Time prevents everything from being given at once H. Bergson The fundamental differences between objects of music and visual art come from the nature of their respective space, namely from time-constrain of tonal chronotope as compared to 3-D space of arts. We easily recognize mirrored and rotated objects as 'the same' in the visible world. But in music we encounter more subtlety in such permutations. Melodic intervals, unlike visual objects, change their character depending on direction. For example, the melodic interval of Fourth sounds more active when it goes up than when it goes down. The most important characteristics of music are the orderly arrangement of tones along the arrow of time, and that the images of music appear gradually. In a single glance we may appreciate a physical object, but it takes time to perceive a melodic object. We cannot play a melody 'at once' (all of its tones simultaneously), without drastically changing the musical image Mirrored visual image 13. Mirrored (inverted) Mary Had a Little Lamb A musical composition, like a living organism, begins at a point in time and develops along the arrow of time. 14. J. S. Bach, Two-Part Invention in C, theme 12

13 When the tones of the Invention's theme are played at once, the theme becomes unrecognizable: 15. Sound cluster: Tonal field The sound space of music is based on gravitational properties of tonal relationships. The field of attraction shapes and holds together melodic objects. O, since everything in music happens in time, melodic objects of music are generated by tonal tensions distributed along the Arrow of Time. While listening to music we perceive tonal relationships as alternating sensations of tonal stability and instability. The tonal force field resembles the familiar force field of gravity. Tonal attraction is perceived by the ear as a force that pulls sounds towards some center of stability. The following two short harmonic progressions give clear illustration to the concept of the tonal force field Workings of tonal force filed: a). the resolution into stability; b) the suspension The resolution into a tonally stable tonic triad produces a peaceful mood (1), while moving into a tonally dissonant chord creates the feeling of tension and instability (2). This sensation is a result of tonal forces. Speaking figuratively in terms of Newtonian physics, unstable tones possess greater potential energy than stable tones. T S D T 17. Basic tonal frame-formula of the functional harmony. Academic names of the chords are Tonic, Subdominant, Dominant, and Tonic. The formula sounds so pure and simple! Yet it has sired an astonishing variety of tonal compounds and relationships. 13

14 A simple scale offers a straightforward explanation to how and why the tonal field works. The scale is a tonal system of coordinates, or tonal schema. The dominating tonal schema of the modern world is the Diatonic scale. In the Diatonic scale, the first tone (tonic) is a center of stability, or 'potential well,' to which all other tones are attracted with varying intensity. 18. C-major scale For example, in the C-major scale the "C" is the center of stability, while the tone "B" is highly unstable and leans towards the "C." This means that the "B" has a lot of tonal potential energy. B C 19. Tonal gradient Each tone of the scale differs in degree of attraction towards the tonal center, and this tonal gradient of attraction, this difference in tonal status, makes possible musical patterns that constitute musical compositions, beginning with a simple tune and up to highly complex structures such as Fugue and Sonata form. Tonal hierarchy, and not merely differences in pitch, is the true source of the tonal field. As soon as sounds reveal their tonal relationships, tonality springs up. An isolated sound does not produce tonality. For tonal tension to appear and form a tonal space we need the company of musical sounds, just like the appearance of societal structures requires a group of individuals. When a musical sound is followed by different sounds, it creates tonal relationships that generate tonal schema, or tonal hierarchy. - The system of reference. 14

15 In the tonal hierarchy each sound has its status and meaning. When we listen to a melody, we intuitively evaluate tonal interrelationships. Perhaps this is why Leibniz described music as "an unconscious calculation." We intuitively calculate the tonal weight of each tone by comparing it with other tones. This process of mental comparison connects separate sounds into a tonal surface: our mind weaves tonal events into a continuum. To poet Joseph Brodsky, music was "water's twin." Configuration of tonal energy levels While listening to music we perceive tonal relationships as alternating sensations of tonal stability and instability. In other words, we subconsciously calculate relative energy levels determined by the tonal gradient. Our brain compares energy costs needed for processing melodic elements of the musical stream. The differences in cost and thus in tension make flow of music a psychological wave that both builds and provokes emotional state by mimicking inner tensions that life generates in our body. In terms of the tonal gradient, a musical composition is indeed a configuration of energy levels, or levels of tonal attraction, distributed along the arrow of time. In total, our mind evaluates tonal relationships, while from the flow of tonal-energy proportions organized in time, there emerges a cue to emotion a suggestive, vague contour of thought that opens wide to the imagination. Like any pattern recognition, music perception operates within a system of reference. In music, this system is called the tonal schema, or more broadly, tonality. We define tonality as a system of tonal relationships akin to the gravitational field. The tonal field shapes musical objects like melodies, for example and maintains their unity, similarly to how forces of gravitational attraction form and maintain the unity of physical objects in the material world. Everything is relational in music (akin to physical space, which acquires meaning through the relationships of the objects inhabiting it or through their absence). The magic begins when different tones unite into musical thought. A single musical sound, on its 15

16 own, is rather an acoustical signal, but when a stream of musical sounds unfolds a musical thought to our mind, we transcend acoustics and find ourselves in the acousmatic world the world of hearing, of an active and attentive process. ***("Pythagoras is reputed to have lectured to his disciples from behind a screen, while they sat in silence attending to his words alone, and without a thought for the man who uttered them. The Pythagoreans were therefore known, Iambilicus tells us, as akousmatikoi-those willing to hear," from The Aesthetics of Music by R. Scruton.) In some mysterious way, the intuitive analysis of tonal relationships, determined by the tonal gradient, evokes not just emotions, but ideas. Music, as an intellectual construct is able to deliver profound philosophical ideas, and the architectonics of music can be amazing in its complexity and elegance. But when discussion turns to the question of basics in music perception, one aspect seems to be beyond doubt namely, that tonal hierarchy is not the design of an inventive human mind, but a discovery of natural phenomenon that allows psychological patterning a gift of nature. The tonal schema of reference (the scale) was formed when the physics of sounding strings and pipes met the neuro- and psychophysiology of hearing, and when these were joined by the sensitive human soul that has been bringing meaning into the sound material. Mental Rotation in Visual and Acousmatic Space Our experiment on mental rotation in 3-D space and in music was intended to test a rather radical hypothesis that the brain same mechanism for processing the hierarchically organized information whether it is music or visual patterns. In other words, I suggested that our higher mental functioning is less tied to a modality of patterns than it is commonly accepted. In terms of cognitive neuroscience, I hypothesized that perhaps the brain reads both music and spatial information as a signal-distribution within system of reference and uses same neural substrate, even if the nature of signal-distribution is different. 16

17 The participants in this experiment had two tasks: on congruency of visual images and on recognition of melodic transformation. The idea of a melodic contour and its transform implicitly supposes existence of a certain space where the very transformation can happen. A list of types of visual transformation suggested by Shepard & Cooper includes a translation, a rotation, as dilation (i.e., a uniform expansion or contraction), or some combination of these (as well, under some circumstances, as a reflection). Each of these properties of the visual objects transformations has an analogue in polyphonic music, where a musical theme can be transposed (translated), bent by the tonal forces (as if presented under different angle), reflected, augmented and diminished (dilated) through change of time-values, or have some combination of these types of transformation. When wee think of music as organization of some space that is governed by two unifying principles tonal attraction and temporal structuring then a melodies can be though as a melodic object shaped by the tonal forces, the same way that things in the material world are shaped by gravity. Movement of such object through the tonal space will change its tonal appearance. Playing or listening to polyphonic compositions by J. S. Bach always makes me marvel actually awe - at the beauty and intricacy of his polyphonic thinking. Just reading his text could be entertaining to the informed eye. One can find in his art the great inventiveness, and kindness, and courage, and nobility of spirit. Imagining how his musical theme is discussed between parts and moves through the tonal space, interacts, and becomes transformed in a quasi-visual manner, I come up with the idea that perhaps music does employ neural mechanisms that was intended to provide visuo-spatial orientation. By selecting the study s main experimental tasks the auditory on mental rotation of a melodic contour and a visuo-spatial on congruency of 3-D objects I reasoned that in both of them the brain is involved in pattern-recognition within certain system of reference. In the visual task it is the Cartesian system coordinates within the gravitational field. In the acousmatic realm of music, structured time provides the discipline of tonesequencing while tonal attraction serves as analogue of the field of gravity. In the auditory part of the study, the participants listened to a series of 27 melodies and their 17

18 transforms, all of which were selected from keyboard compositions by J.S. Bach. The melodic transforms were Mirrored, Composite, and Bent versions of a given melody. Melodic contour of the Minuet Mirrored contour Composite contour Bent contour 20: Types of transformation of a melodic contour In the visual task, we used a simplified replica of the classic Shepard & Meltzer experiment on mental rotation, composed of 122 pairs of images of three-dimensional geometric objects. The Shepard & Meltzer s collection of images provides excellent visual analogies to melodic contour transforms. The three-dimensionality of the images is calibrated by cubes from which they are constructed. If the system of tonal reference (tonal schemata) can be compared to a quasi-cartesian system of coordinates (linear perspective), then a Bent melodic contour would be like an object observed from a different angle within given tonality that defines tonal perspective. 21: Mental rotation of 3-D object: task on congruency (Shepard & Meltzer, 1971). 18

19 To recognize a melodic object means transcending the temporal aspect of a musical form and perceiving it in a quasi-spatial manner, as if embracing at once. This is a process that allows us to recognize a familiar melody after listening to just a few initial tones. Pylyshin writes that in music the word hear need not to entail anything about the duration of that experience. Depending on pitch composition, moving a melody along a given scale might generate a relatively mild synergetic impression of changing color of a melodic contour. For example, playing a theme (1) from the Two-Part Invention in C by J. S. Bach from the A (2) instead of the C (1) converts the melody from bright major to darker minor mode. Playing the melody from the G (3) leaves it in major mode. But when the same melody is played from the E (4), the contour s transformation goes beyond changing the mode and gives an impression of bending Figure 22: J. S. Bach, Two-Part Invention in C: the invention theme in C major when played from C (1), in major when played from G (2), in a minor when played from A (3), a bent theme when played from E (4). The Composite version of melodic contour combines bending and incomplete mirroring. The Bent transform is the easiest to recognize since the bent contour preserves its most important characteristic direction of pitches. And the Mirrored transform stands between the easy Bent and very difficult Composite version. It is useful to think about recognition of melodic transforms as a task on congruency: when an object is turned moderately, it is easy to recognize as the same. When the angle is large and in 19

20 Mirrored transform all melodic intervals that comprise the contour change their direction the task becomes more difficult, particularly because the stimuli can actually be incompletely inverted, as it happens in the Composite version. The participants were forced to imagine the original contour and then use this as template when listening to the transforms. The important thing is that a template needs to be remembered as a complete object when it is compared with a transform. The experimental data showed a moderate correlation between the success rates in processing visuo-spatial information and music perception task, as well as gender effect, which was in agreement with other studies that demonstrate that males in average perform better on visuo-spatial task than females (Voyer et al, 1995). 100% 80% 60% 40% 20% 0% y = x R 2 = % 20% 40% 60% 80% 100% Melody recognition 23: Correlation between scores on the visuo-spatial and music perception task % 9 0 % 8 0 % 7 0 % 6 0 % 5 0 % 4 0 % 3 0 % 2 0 % 10 % 0 % V M T 24: Gender effect: average solid, males - vertical stripes, females horizontal stripes. V-Visual task: M- Melodic task; T- Timbral task 20

21 By analyzing the data, we also found an interesting phenomenon of octave equivalence, when a Composite transform is often perceived as a Bent if one of the melodic intervals within a melody gives compensation to the octave. A possible interpretation to this phenomenon is that a drastic change within melodic contour can go unnoticed if an inversion of a musical interval is perceived as a shift forced by limitation of a voicerange. In recent years, researchers in the brain imaging field have suggested that professional musicians process visuo-spatial information differently than non-musicians (Schmithorst &. Wilke, 2002; Gazer &. Schlaug, 2003). Bhattacharya et al (2001) EEG study on the visual rotation found that the musicians have different pattern of brain activation during mental rotation task as compared to non-musicians. There has been no research yet on mental auditory rotation in music perception. It would be extremely interesting to learn how we are able to process polyphonic music and how musicians can think of a complex musical composition as an architectonically balanced form. However, it is also possible that our experiment was in reality a test on fluid intelligence, which simply said us that some people are just smarter than others in their reaction to the patterned information that the world offers us continuously. Hidden dimension of overtones The history of music is the history of the gradual discovery of possibilities within the tonal field. And as any other cultural development, the history of exploration into the tonal field reflects the evolution of human thought itself. Keeping in mind the extreme abstractness of music, one feels awe when detecting the signs of historical layers within the subtle changes of the natural that is the overtones based tonal schema changes that were demanded, and achieved, by search of the expressiveness of music. After centuries of experimentation with the tonal system of reference the subtle changes entered the tonal space: while the precious tonal hierarchy was preserved, each of the member-tones of the tempered tonal schema gained the potential to become an independent tonal center in its own right. In other words, different tones can become 21

22 centers of a tonal 'solar system' in a course of a single musical composition. This democratization was crucial to the language of harmony, because it allows the freedom of tonal modulation when any tone can become a tonal center within same musical composition. This freedom of reorientation within tonal field of a given musical composition, the freedom of movement from one tonal center to another within same musical composition is precisely the freedom of tonal modulation. The history of musical development demanded, and finally received, the flexibility in changing the tonal status of an individual tone, which led to the wider exploration of the tonal field. The tonal system of reference - the hierarchical structure of the tonal field - originates in the physics of sounding strings and pipes. When we hear a musical sound produced by a violin or guitar we perceive the sound as a musical 'particle.' A melody is thence a line constructed of these musical particles. In reality, any musical sound that is naturally produced by strings and pipes (vocal production included) is a chord. When we touch a string, we literally can see how that chord appears: the sounding string looks fuzzy because it vibrates, and vibration indicates a swift subdividing of the string on 2, 3, 4, 5, 6, and so on. With each division the string produces a softly sounding overtone, or harmonic. Thus a sounding string generates a swift unrolling of the overtone series a trail of overtones. 25. Melodic intervals of (Octave, Fifth, Fourth, and Third) Overtone series for the tone of "C:" When a plucked string begins vibrating it looks fuzzy because it begins spontaneous subdividing. Each subdivision produces a very soft and quickly diminishing sound. The sequence of the swiftly unrolling overtones is called the harmonic, or overtones series. The first overtone of the series creates the interval of the Octave with the fundamental ton. In all known cultures the melodic interval of the Octave is perceived as 'the same sound.' When people of different age and gender sing together in unison, they most likely 22

23 sing in octave. The next overtone makes the Fifth; some 1000 years ago, the melodic interval of the fifth was felt as somewhat perceptually equivalent to the octave, and monks sang Gregorian chant in parallel fifths (órganum). The next overtone is makes another Octave upward, and above it is an overtone that makes the major Third. The accumulation of overtones continues, but we stop here to observe what happens when these four overtones in the beginning of the series are brought close to each other. We find that these overtones make a major triad. In other words, a melodic particle a tone is actually a chord, or a rolled up collection of waveforms. The trail of overtones is 'curled' within the tone like the hidden dimension of the String Theory. We can visualize a musical sound as a wave-particle formed by rolled together sound waves that appear to our mind as a single sound. 26. Overtones series (beginning) of the middle "C": 27. Fundamental tone and its strongest overtones make major triad (over octave): Perhaps our brain is able to perceive and analyze this trail of overtones. The strongest proof of this is our predilection for the Pythagorean intervals. An ancient legend says that Pythagoras was first who gave mathematical expression to consonant, pleasing to the ear, melodic intervals of the Octave (1:2), Fifth (2:3), and Fourth (3:4). When a string is divided in half, a plucked segment produces the Octave; when is divided by three, it produces the interval of the Fifth; when is divided into four parts, a plucked small segment of the string produces the Fourth. The melodic intervals of the Octave, Fourth, and Fifth are called consonants for their pleasing sonic qualities. 23

24 But why are these combinations of sounds pleasant to the ear? The answer should be sought in the overtone series. Those overtones that belong to a beginning of a series make consonant intervals both with the fundamental tone and between themselves. The first overtone makes the Octave with the fundamental tone. The next overtone plus the first overtone makes the Fifth; and the next two overtones make the perfect melodic interval of the Third. The evidence and our conclusion are clear: when the tones of a melodic interval belong to the beginning of same harmonic series, they make a nice and simple auditory sensation. Perhaps, the brain needs less energy to process information presented by the consonant intervals since these intervals share basic essential information the same harmonic series, where the consonants correspond to the strongest overtones located in the very beginning of the series. If this is true, then the tonal gradient the level of attraction to tonal center is indeed a gradient of perceptual comfort. To say it differently, that which is easiest to analyze and demands less processing cost may constitute a pleasant cognitive event, at least on a very basic level (which I would hazard to term the general rule of laziness Precisely in consonants do we find a beautiful unity between pleasing sounds, the simplicity of mathematical proportions expressed in small integers, and the communality of the strongest overtones. For the ancients, the harmonious union of simplicity and of the elegance of mathematics and the pleasantness of the consonants was a sign of a divine order permeating and defining the Universe. To them, the Universe consisted of Scale and Number. Musical, or mathematized, harmony, even if not perceptible to the ear, was visible to the eye in the disposition of heavenly bodies. As for the concrete sounds of the "music of spheres," it was believed that the ears of mortals habituated to the music of the spheres at infancy, and therefore no longer were equipped to recognize it in older age. Scientific evidence supports the idea of different processing cots: an fmri (functional magneto-resonance research imaging) in neuropsychology showed that the perception of consonants evokes lesser cortical activation than the perception of dissonant compounds (Tillman et al, 2003). The feeling for consonant and dissonant combinations of tones is wired into the human brain quite early. In fact, six-month-old babies prefer consonant to 24

25 dissonant intervals, which is not surprising since the human cochlea is already formed at the end of the second trimester and so becomes available to music (in filtered form). (Schellenberg & Trehub, 1996) In the diatonic scale, which is a common tonal schema of today, the major triad on a first tone makes a tonal triad. The tonal triad includes most stable tones of a given scale; this is also true for the minor scale, which is a version of the major scale. The tones of the tonic triad are close 'blood relatives,' belonging to the beginning of the same overtone series. The sound stream of music consists of tonal tensions and resolutions, which our brain analyzes and evaluates based upon 'family connection.' The overtone series, or overtone trails, create the hidden dimension of overtones that gives direction to the lines of attraction of the tonal field. In the same way that the hidden dimensions of the String Theory are not available to direct perception yet are at the heart of the material world, the hidden dimension of overtones is concealed behind pitch recognition. Yet it is precisely these concealed trails of overtones that define the property of music's medium. Rationalization of tonal space: the triumph of architectonics over psychophysiology The tonal system of coordinate, or tonal schema, defines a tonal space in which objects of music are formed and transformed. We are distanced by the thickness of time from an evolutionary period when the first signal system bifurcated into spoken language and music. On one end, vocal production (via phonemes) has been grounded in and disciplined by the determinism of words and syntax. On the other end, the abstract system of tonal tensions and resolutions has been utilized to communicate psychological states the feeling of times of life. The primordial 'paleontological' tonal schema had been most likely determined by the hidden dimension of overtones and by the range of the human voice. Modern Diatonic scale, constructed in agreement with the hidden dimension of overtones is known as the Just intonation scale, or Natural or Harmonic scale, since melodic intervals that built on tones of the scale are members of the same harmonic series. 25

26 In the seven-tone Just Intonation scale all melodic intervals are presented by simple fractions, and all consonants appear in their ideal form, related through the overtone series. Similar to how natural that is subjective or curvilinear perspective is pleasing to the eye, for example, in the space of ancient art, the natural tuning of the tonal schema creates pleasing auditory sensations: The perfect Fifths and Fourths of the natural scale sound sweet to the ear. The problem with Just Intonation tuning is that sizes of its melodic intervals are not invariant when shifted along the tonal schema, which means that this scale functions exclusively for a single tonality. Such construction precludes the freedom of modulation, the transition from one tonal center to another within the same composition. The beautiful sonorities of Just Intonation tuning give audible illustration of the ancient worldview: wholesome, harmonious, and united in spirit with the timeless Gregorian chant. With the development of polyphony, and particularly with appearance and popularity of keyboard instruments, music found itself constrained by the limitations of natural (Just Intonation) tuning. The beginning of polyphonic music belongs roughly to the end of the first millennium when the melodies of Gregorian chants were performed in a novel way in parallel melodic intervals of the perfect Fifth and Fourth. Both are Pythagorean consonants. Eventually the melodies became accompanied not just by a melodic 'identical twin,' but by different melodies. Thus was born polyphony, or many-voiced music. In developed polyphonic forms several melodic lines (voices) discuss a musical theme (J. S. Bach said about the Fugue, which is a highest form of polyphony, the "conversation between selected friends") (A. Schweitzer, J. S. Bach.) Each melodic line is interesting on its own and develops independently, to some degree, from other melodic lines. At their vertical intersection the voices create harmonies (chords) that are like musical knots or columns, which move along the arrow of time while obeying the logic of the language of functional harmony. This logic evolved within music gradually aided in large part by polyphony and its source is the same hidden dimension of overtones, the 'degree of separation' within the overtone relationships that gives us a sensation of tonal tension and 26

27 stability. In short, this is the same principle of energy levels, though now manifesting itself within the enriched form of functional harmony. The history of tuning, which is the history of tempering the Diatonic scale, is also a chronicle of the search for a compromise between sonic beauty and practicality. The goal was to protect as much as possible the natural purity of melodic intervals of the tonal schema while at the same time allowing for a range of several octaves, in which the maximum number of melodic intervals would satisfy the demand for melodic purity. In the visual arts, linear perspective had been emerging and becoming familiar to the eye in a gradual process of unification of aesthetic space, though at the expense of small distortions in the natural way of seeing. Similarly, the creation of the logical form of tonal space demanded that the ear accepted the tempered tonal schema. And any tempered scale, with respect to our natural way of hearing, is a distorted scale. The search for the logical form of tonal space began in antiquity. The diatonic scale, built on ascending perfect fifths, does not produce completion in the sense of octave equivalence: The concluding tone does not correspond to the beginning tone, and cannot fit mathematically in that system of construction. Turn between yearning for open tonal space and for sonic purity of melodic intervals that make that space, musicians tried to temper the tonal schema in such a way that the main melodic intervals would be more or less pure in the tonalities that are closely related, but distant keys would incur mistuned melodic intervals. In other words, the attempts to unite natural and logical tuning opened way to some tonal modulation but forced limits upon the real freedom of modulation. And while the Gothic period cared for the purity of the Pythagorean melodic intervals of Fifths and Fourths, the Renaissance was more interested in maintaining the sonic beauty of Thirds and Sixths, which at that time became accepted as consonant intervals. 27

28 28. Duccio di Buoninsegna, Last Supper, Museo dell'opera del Duomo, Siena (Web Gallery of Art) These attempts to find a satisfactory tuning system, and the compromises that were made between natural tuning and its tempered variants resemble the search for central perspective in the visual arts, when central and local perspective could coexist in a same painting. The new spatial schema of linear or central perspective united visible artistic space by 'homogenizing' it and giving it a system of simplified and equalized units of distance, that was so conspicuous in the popularity of checkered floors. In Pavel Florensy's words, linear perspective made space "feeling-less" by removing the subjectivity of perception of relations between the parts and objects of visual space. The search for the logical form of tonal space was in essence the search for the universality of the 12 semi-tones of the Diatonic scale so that each tone could potentially become a center of a certain tonal scheme. On a piano, a semitone is the distance between two adjacent keys on the keyboard. The incremental approach toward the mathematical limit of tempering led to the averaged space of Equal Temperament, whose distorted 28

29 fifths, fourths and thirds used to upset (and continue to upset) the exquisite auditory perception of connoisseurs of tuning. In compensation for this irregularity, Equal Temperament liberated the language of harmony and allowed latently existing possibilities of harmony to emerge. Through 'democratizing' the tonal schema and equalizing the potential of all keys, Equal Temperament offered maximum practicality and convenience. As for the sonic beauty of Equal Temperament, the discussion continues. *** J. James, The Music of the Spheres, 1995, Springer-Verlag *** (Cho G. J., Discovery of Musical Equal Temperament in China and Europe in the Sixteenth Century, 2003, Edwin Mellen Press ***Duffin R.W., How Equal Temperament Ruined Harmony (and Why You Should Care, 2006, W. W. Norton The mathematical expression for Equal Temperament was first presented in the 16th century. The relationship between frequencies of two adjacent keys (i.e. a semitone) is equal to the 12th root of 2. In a system of polar coordinates this relationship makes a logarithmic spiral. Equal Temperament Diatonic Scale expressed in the logarithmic curve. The diatonic scale presents an example of gnomonic (homothetic) growth, a principle often encountered in nature, in which change of size does not change shape. For example, segments of sea shells grow 29

30 similarly in shape but vary in size. The homothetic principle is important to living growth. Tempering allowed musical 'objects' to both move freely within the tonal space and appear from different 'vantage points', and in different 'lighting.' (These synaesthetic descriptors reflect the difficulties that enter any discussion on the subtleties of musical experience.) Thanks to the given by Equal Temperament unification of artistic space of music, the tonal field acquired thickness and depth of functional harmony. Our ears adapted to the small distortions of melodic intervals of the tonal schema. Moreover, people eventually developed an intuitive sense of the language of harmony: while listening to a melody we subconsciously dress it with harmonies. The minor distortions of the melodic intervals that were so unpleasant, if not psychoacoustically painful, to the ear of musicians several centuries ago, during the search for the logical form of tonal space, eventually became the norm for the modern ear. The necessity of such logical order (for the sake of aesthetics of musical form) led to a new and more tolerant way of hearing in music, analogous to how omnipresent linear perspective 'retuned' the eye in perceiving visual art. Equal Temperament entered into practice in the middle of the 16th century. In visual art, the vanishing point of linear perspective united the visual field, though bringing along some slight distortions to the natural perception of visible space. Similarly, while sonically harming the subtle relationships of the ancestral dimension of overtones, Equal Temperament transformed and united the tonal field for the sake of the freedom of tonal modulation. Despite the auditory distortions of the tonal schema, the tonal hierarchy stays strong and the tonal gradient retains its place as music's most important morphological principle. The tonal hierarchy that had emerged millennia ago remains the working schema even when its elements are presented in approximation. Schema and creativity 30

31 Plainsong is timeless, like Christian eternity; humanistic music is time-ridden, like human life. D. Cooke Medieval paintings illustrate the process of gradual familiarization with and acceptance of linear perspective. In music though real but much less noticeable than advent of linear perspective in art the changes in tonal schema and perception of tonal space were happening smoothly through time, like flowing water. Sensitivity to tonal harmony had developed in general consciousness some half a millennium ago. But the feeling of tonal gravitation has been ever present from the time the humans acquired a sense of a melodic line. Scholars in medieval music define this perceptual ability for tonal relationship before the crystallization of the functional harmony that was completed in the 18 th century as sensitivity for modality. And yet, the feeling for functional harmony did not spring overnight: it had been gradually, and seemingly intuitively, developing in time by generations of musicians and listeners. The development of harmonically controlled tonality occurred much earlier than 1600, writes Caldwell. It was the polyphony s greatest gift to the European musical tradition that the tapestry of voices gradually revealed tonal relationships on a level of clusters of tones, these musical knots that are formed on meeting tones of separate melodic lines. If tonal schema defines tonal hierarchy and gives meaning to each tone of diatonic scale, the functional harmony defines tonal relationships and gives meaning to musical chords. These chordal tonal relationships create potential lines of direction to musical development and give rich support to a melodic line. The oldest surviving document on polyphony came from 10 th century AD. The polyphony is believed to originate in enhancement of the plainchant: from a parallel twovoice movement of a melody in the fifths and fourths in organum that was practiced at the end of the first millennium A. D. to the many-voiced polyphonic compositions of the 13 th century and the philosophy in voices of The Art of Fugue by Bach. Towards 16 th century, the development of polyphony created inescapable problems of tuning that were 31

32 related to tonal re-orientation within same musical composition when a composer tried to look at a musical theme-object from different tonal perspective. Artists living in the pre-linear perspective time created great expressive works; they brought meaning and unity to the representational scene with available to them artistic means. In the absence of the linear perspective, a plane of a painting was fragmented into sections with local organization of space. We can see it in the old Byzantine works and in the Russian icons, which were inspired by the Byzantine art. The absence of linear perspective never meant the absence of artistic expressiveness but a particular way of seeing at a given time in history. The medieval art, both visual and musical, was filled with humanness expressed in the familiar to that time manner. Characteristically, the very word mode can be interpreted as manner. * * It is perhaps ultimately from metior 'I measure'. Ovid says 'modum dare remis', 'to give the time to the oars'. From Caldwell, , pg. 2, footnote. Similar to how medieval artists depict objects within fragmented perspective-wise space, in a manner that they felt was right, the medieval musicians had their way of organizing musical material along the church modes, which in course of time became integrated into two main modern modes: major and minor. The church modes can be explained as musical analogues to the local perspective in medieval art. Like local application of linear perspective led to understanding the vanishing point and integration of local spaces into rationalized and unified artistic space, composing in church modes were the pre-condition to harmonic tonality, that is, to the language of functional harmony. The church modes were derived from the ancient Greek scales; in basic terms, they are variants of domineering today diatonic scale. We can visualize the modes as a family of scales, each built on one of the steps of a C major scale, with equally rightful b flat and b natural. The church modes came to musical practice with the Gregorian chant: a chant s melody was formed within a given mode and placed in tenor, or cantus firmis, and obeyed that mode s character and structure. In Caldwell s words, the church modes are not simply scales but rather a series of conventional groupings of standardized material which have grown up in the course of time. Already in these modes, the choice of a final 32

33 tone (from two different tones) the finalis became a cue to the birth of tonal modulation. The feeling of tonal closure is a feeling of tonal attraction. While in modern terminology modulation means moving from one tonal center to another within same musical composition, the old meaning of word modulatio actually referred to a melody, and thus tonal modulation classifies an ending, a conclusion of a melody. One of the most interesting and important procedures in early music was application of musica ficta, the false music. Such unpleasant name was given to a musical practice that helped creating the modern tonal force field. Musica ficta were accidentals or the chromatically altered pitches that went beyond the diatonic scale: performers used musica ficta to avoid unpleasant intervals like triton and make certain melodic compounds more beautiful. From today, this practice seems as a beginning of the 12-tone thinking, as going beyond the seven steps of the diatonic scale. Thus sonic necessities and preferences of live performance were prevailing over strict rules of the standardized material of Church modes. Thus the performers had a choice to emphasize their selection of tonal perspective. 28: The a) presents a modulation to the church mode 4 (the 'phrygian' mode), while the b) is a modulation to a-moll. Depending on a choice of accidentals, a performer could interpret the modulation in one of two ways (after Caldwell, ). Caldwell comments that consonant harmonization of a concluding melodic tone (finalis) was more important than tonal logic of that ending. In other words, here loyalty to local tonal perspective overweighs the case for tonal unity on a grater scale. In the absence of tonal unity, musical composition is like a series of areas of local perspective that Schulenberg describes as interlocking local events. To the modern ear, endings in medieval music may sound as if left in a suspension. But this was not so to the medieval ear that was accustomed to the musical logic of the age. 33

34 The development of polyphonic, or many-voiced, music caused emergence of the ear s sensitivity for tonal relationship between clusters of sounds which are formed on meeting points of several melodic lines. It was polyphony that gave a melody the depth of harmony, which has a power to lead the melodic line and infuse it with meaning that is not obvious in melody on its own. Similar to how linear perspective brought simple concept of vanishing point into artistic consciousness, the gradual emergence of tonal unity led to simplification of tonal organization in music. In time, the church modes were integrated into two main modes, the major and minor. Tonal compounds and their relationships gradually evolved into triadic functional harmony. With recognition of strong tonal certainty, music acquired expressive elements of potent deviation from the certainty like the interrupted cadence or unexpected modulation. The all-supporting tonal formula of functional harmony with its well defined chord of stability tonic triad allowed the musicians to explore a wide range of weak tonal relationships. Unlike clear mental registering of linear perspective and it s consciously perceived arrival to the world of visual arts, tonal unification in music culminated in a frequencywise equalization of relationships between neighboring tones of the 12-step tonal schema was deeply intuitive, mostly subconscious process. Toward the 16 th century, musical practice owns a set of harmonic formulas that show a developed sense of harmonic tonality. The old plainchant technique was still in use by composers of 17 th and 18 th centuries. Yet, the modern ear, conditioned to tonal certitudes, perceives modal music and its sensibilities differently than the medieval ear. We listen to music of John Dunstaple and Guillaume de Machaut through the thickness of time that accumulated and transformed musical devices into the tonal system that we live with today. And this implicit knowledge of tonal conventions, which we effortlessly acquire via passive listening at a very early age, transforms and tints the perception of the modal, pre-tonally unified music. De-unification of Artistic Space 34

35 In the visual arts, icon-painting, which preserved seeing in pre-linear perspective manner well into modern age, met in time with the newly developed perspectival techniques like, for instance, cubism, where Cezanne turned lovingly to the idea of binocular vision. Others cubists, Braque and Marcel Duchamp, employed multitude of viewpoints. In Russia, adepts of suprematism attempted to seize the fourth dimension (Malevich) and to create irrational space, with its infinite extensibility into the background and foreground (Lissitzky). Perspective-wise, fragmentation of visual space in modern art has its analogue in music, namely in the set or twelve-tone music. Schulenberg writes that like pretonal polyphony, the music composed in such spaces will not necessarily move from one space - or from one prolonged sonority - to another in a goal directed manner. Such processes may simply represent the passage from one static (non-implicative) pitch field to the next. In other words, the localization of artistic space has been re-invented by novel means, in this case by way of weakening tonal polarity. When we listen to music, tonal hierarchy arrives to our consciousness on an intuitive level. That is, our evolved ability to differentiate sounds not just on the basis of their pitch but through expressive relationships between tones is purely intuitive. The tonal schema is not a mental construct, that is, the tonal filed is not a human invention, but rather a gift of nature. This is why it makes sense to look for a source of the tonal field in the physical and neuro-physiological processes. Through history, the morphological demands of aesthetic space overpowered any loyalty to the psychophysiology of natural perception, both in music and in the visual arts. Linear perspective 'subjugated' artistic phenomenon to mathematically exact rules, but this systematization and unification of the outside world's image aided mightily the expansion and liberation of the personal, inner world. Panofsky writes that "Perspective opens art to the realm of the psychological, in the highest sense, where the miraculous finds its last refuge in the soul of the human being represented in the work of art." Analogously, the systematization of tonal space within the realm of music was the requisite logical tool that helped open the door to greater artistic expressiveness. 35

36 So we see that the changing mentality (subconscious) and new ideas (logical formalism) demand new forms both in music and in the visual arts changes that affect the very medium of the arts. True fine art always represents a sort of condensed humanness unveils humanity's essential, universal, and eternal features despite its creation at a given moment or epoch. Thus in reality there are very few main themes in the arts, but innumerable ways realize them as the evolution of thought, of scientific and philosophic development is inescapably reflected in the fine arts. We hear in the music of Mozart and Haydn the spirit of the Age of Enlightenment. We recognize it in the clarity and conciseness of their musical thoughts and in the certainty of the tonal centers within the cyclical (thanks to octave equivalence) schema of tonal gravity. The music of the First Viennese School as if reflects an image of the Newtonian Universe itself its certainty and perfection. In the music of the 18th century, polyphonic style deferred to the homophonic style, but not before giving to the homophonic style the precious gift of functional harmony. The logic of functional harmony had been gradually formed in polyphonic music on the intersections of melodic lines, in sequences of musical knots and columns. Thus within the stream of linear development of voices in polyphonic music, there occurred a process of crystallization of harmonic progressions. Eventually, elements of these progressions, the chords, became autonomous entities. In general, the modern ear does not even try to follow middle voices in harmonic progressions that regularly accompany melodies of the First Viennese School. In other words, the modern listener, unlike say a medieval one, interprets chords as single units and not as compounds created at the meeting points of melodic lines. Musical scores of that period look like minimalist art, and they have very few authors' remarks. 29. W. A. Mozart, Sonata in C (fragment) 36