Linear tension in tonal music with correlations in fine art

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Linear tension in tonal music with correlations in fine art
Brever, Carol Ann
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vii, 117 leaves : illustrations (some color), music ; 29 cm

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Master's ( Master of Humanities)
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University of Colorado Denver
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Department of Humanities and Social Sciences, CU Denver
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Tonality ( lcsh )
Art and music ( lcsh )
Art and music ( fast )
Tonality ( fast )
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )


Includes bibliographical references (leaves 111-117).
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Submitted in partial fulfillment of the requirements for the degree, Master of Humanities.
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by Carol Ann Brever.

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University of Colorado Denver
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Auraria Library
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38325331 ( OCLC )
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Carol Ann Brever B.A. University of Idaho, 1958
A thesis submitted to the University of Colorado at Denver in partial fulfillment of the requirements for the degree of Master of Humanities

This thesis for the Master of Humanities degree by Carol Ann Brever has been approved

Linear Tension in Tonal Music with Correlations in Fine Art Brever, Carol Ann (Master of Humanities)
The mind seeks stability and consistency, and it has a strong need to organize what it perceives in sight and sound into some semblance of order. This need for order is one of many psychological principles which affect the manner in which fine art and music are perceived. These principles may include the desire for simplicity, change, continuation, and balance as well as centric attraction and gravitational pull. These psychological principles affect the development of expectations which, in turn, affect human response.
This study will examine some of these principles which may create linear tension in tonal music. Correlates in fine art will be presented for the purpose of explication and clarification of these principles. Chapter one describes the purpose and limitations of this study. Chapter two examines the historical innovations which have taken place in music, such as the development of tonal relationships, rules of harmony and the use of ornamentation. In

fine art, the development of perspective, line and ornamentation are examined.
A number of psychological studies have been done which relate to the manner in which the mind processes auditory and visual stimuli. Chapter three relates the results of these studies, and it examines the psychological principles which may affect music and art. Chapter four describes the various devices which create tension in music, with correlations, wherever possible, to fine art. Some of these devices include gravity, linear direction, centricity, obstructions, gaps, deviations, and ornamentation. Chapter five summarizes the study and concludes that, through one's orientation to the world, through deviations or distortions from what is expected, through a sense of motion, and through increased complexity, that tension is created in both music and fine art.
This abstract accurately represents the content of the candidate's thesis. I recommend its publication.

1. INTRODUCTION......................................1
Limitations ....................................2
FINE ART........................................ 6
Developments in Music...........................7
The Development of Tonal Relationships.....7
Changes in the Expression of Harmonic
Theories Relating to Tonal Relationships
and Perception............................11
The Development of Ornamentation in
Linear Developments in Fine Art................15
The Development of Perspective............17
Distortion and Contrapposto...............19
The Use of Linear Shapes..................20
Framing................................. 21
The Development of Ornamentation in Art__22

Theories of Psychological Affect.................25
Psychological Principles Applied to Music
and Fine Art.................................... 37
The Desire for Simplicity........................41
Balance, Equilibrium and Symmetry................42
Tonal Center.....................................43
Attraction of the Center in Art..................44
Expectation.................................... 45
Repetition, Change and Monotony..................48
CORRELATIONS IN ART.................................55
Gravity and Linear Direction.....................56
Tonal Center.....................................68
Center in Art................................... 74

Circles and Ellipses............................76
Obstructions................................. .79
Perspective................................... 101
5. CONCLUSION.......................................109
WORKS CITED,..............................................Ill

In the fields of education and humanities, the manner in which the brain processes information is of particular significance. Several important studies have been done in the past few decades which relate the perception of aural and visual stimuli to music and fine art. These studies have been referred to here in order to answer such questions as: What general psychological tendencies affecting human nature also affect musical expression? What role does expectation play in the development of tension in music? What is dissonance? In what sense does gravity affect musical tension? Do psychological tendencies affecting music also impact other arts? What specific devices have been used to develop tension in music and fine art?
The purpose of this paper is to answer questions such as these. Specifically, this study will describe the psychological tendencies which create tension in human nature and identify several correlations between these tendencies and the expressive devices used in music and those used in fine art.

The term 'tension' is used as either a state of imbalance, a straining toward resolution, or as possessing the power to evoke an emotional response. There has been no attempt to ascribe any further connotation to this term. To impute a specific emotional quality, such as joy, sorrow, playfulness or anger, would be highly subjective. The study focuses only on the existence of affect and not its description.
This study assumes the viewpoint that there are inherent in music or fine art itself, devices capable of producing tension, and it is these devices which have been investigated. This is not to deny that other factors such as culture have impacted perception. Certainly, the manner in which music and fine art have been perceived has changed over the centuries. Factors which may have been affective in the past, for instance, may no longer be affective. The purpose here, however, is to investigate only the inherent tension-creating devices relating to line in melody and art
A problem arises in defining tension in terms of line alone, as other elements, such as dynamics, harmony, and rhythm in music, and color and light in art, may be involved in any given

example. As much as possible, this study focuses on linear factors, while allowing sufficient freedom to reference other factors.
Because a musical work in a non-Western idiom may create
a different effect from one in a Western idiom, this study is
limited to music in Western culture during the Common Practice Period encompassing the Baroque, Classical, and Romantic eras. While it is generally understood that tension may build in music within motifs, phrases, periods, or even movements, this study is limited to consideration of tension on a smaller unit scale.
Chapter 2 is a discussion of the most salient innovations which have occurred in music in terms of linear development. In addition, a discussion of some theories relating to expectations and perceptions are included. Wherever linear innovations have been noted in art, these are also discussed.
In order to understand the cause of tension in music,
Chapter 3 presents some of the general psychological principles which relate to the perception of music and the specific musical devices used. As appropriate, these will be correlated to devices used in art. A discussion of Gestalt principles includes the results of a number of studies which have been done in the area of

auditory and visual perception. Some of these principles refer to the need for order, simplicity and balance, and the effect of gravity and motion.
Chapter 4 concerns the specific devices used in developing tension in music, and explores some correlations to devices used in fine art. Some of these devices are gaps, obstructions and ornamentation, which apply to both fields. (Some of the devices apply only to one field, such as chromaticism in music and deformation in art.) Because the principles involved are most easily understood through the use of specific examples, the study includes numerous examples from a variety of eras, composers, and artists to illustrate a specific device. Although some of the examples may contain several tension-creating devices, for the purpose of clarity only one device is focused upon at a time.
After a very brief overview of the most important linear innovations in music and fine art, Chapter 5 discusses the results of a number of psychological studies relating to the processing of auditory and visual stimuli. The study then reiterates a description of the general psychological tendencies inherent in human nature and the manner in which they impact the perception of music and art. Some of these tendencies were

toward simplicity, order, balance, and continuity. This study then describes how these tendencies have led to specific devices which create tension in music, with some correlations to devices in fine art.

In order to understand how psychological tendencies affect music, it is first necessary to understand the history of linear innovations, as well as what was considered normative historically. The forces which create affect in music have been analyzed in many different ways throughout history. In this chapter, these developments will be discussed, as well as some theories regarding what has been considered by some as a 'natural' basis of music.
Linear innovations in fine art are described in an attempt to find affective devices in art which correlate to those in music.
This necessarily eliminates from discussion many important innovations in both music and art, such as rhythm and color, and it limits the discussion to those innovations which relate to devices which are inherently affective rather than those which rely solely on perceptions within a particular era. It must be pointed out, however, that a device may be inherently affective, although society's perception of the device may change from era

to era. The principle that dissonance causes affect, for instance, may be valid in spite of the fact that people's perception of what constitutes dissonance may change.
Even the untrained person in today's society has been inundated with traditional harmony and, therefore, perceives music through the veil of that harmony. This study can only attempt to relate to studies which indicate that there are psychological rules which dictate perception, while allowing that the stimuli are processed through 20th century eyes and ears.
Developments in Music
TiieDevelopment of,Tonal Relationships
The perception of dissonance and the development of expectations have changed over the centuries. Since expectations which are unmet or are denied create tension, the concept of tension has also changed. Tonality, for instance, was not firmly established until the 17th century, and it was codified by Bach and Rameau in the 18th century. In the 16th century, certain tonal progressions were commonly used which would be

considered unusual today, and therefore, affective. For instance, the major and minor scales, which are based on the Ionian and Aolian modes, were the expected scalar patterns during the Common Practice Period. Although other modes are utilized in contemporary music, they may sound strange to any ear unaccustomed to them, and they would therefore be affective. Conversely, the 3rd scalar tone was considered dissonant in the 9th century and is considered consonant today. The manner in which these tension-creating devices have been perceived through the ages has altered their affective power.
By the end of the Renaissance, the use of the early church modes was replaced by a bi-modal system of Ionian and Aeolian modes. The Aeolian mode, which contains minor triads based on the first, fourth, and fifth tones, necessitated an alteration to a major triad on the fifth tone in order to provide a leading tone to the tonic, or tonal center. This raising of the 7th tone of the scale resulted in our present harmonic minor scale.
All tones consist not only of the fundamental tone, but also of the softer overtones. These overtones (Ex. 1) occur on the octave, fifth, fourth, major third and minor third, etc., above the fundamental, and their frequencies are multiples of the frequency of the fundamental tone.

Ex. 1 Overtone series




The Pythagorean scale related all tones of the diatonic scale to intervals of perfect fifths, which have a 2:3 ratio of string lengths. Successive ascending fifths, however, sounded more and more dissonant within the harmony. In mean temperament, developed in the sixteenth century, the perfect fifth was slightly tempered, which resulted in a pure third within the harmony. Mean temperament produced a very satisfactory sound within the simpler keys, but sounded out of tune in the more complex keys. This system, therefore, was adequate for the limited number of keys which were used at that time. During the Baroque period, however, the expansion of the number of keys using chromatic tones necessitated a further adjustment. Bach developed a system of equal temperament which divided the scale into twelve equal tones. This was a compromise which made it possible for instruments to sound "in tune" in all keys, both major and minor.
Changes in the Expression of Harmonic Rules
By the end of the 17th century, the concept of tonality was firmly established and was codified in the treatises of Bach and Rameau. The basic rules of harmony continued with little change throughout the Common Practice Period, though there were changes in the manner of expressing harmony. By the beginning

of the 18th century, increasing importance was placed on harmonic structure, and polyphony began to give way to homophony. During the 18th century musical forms such as the Baroque dance suites were abandoned in favor of the Classical styles, such as the sonata-allegro form. As a result of the refinement of equally tempered tuning, particularly as it relates to the building of musical instruments, modulations from one key to another increased, as did the use of non-chord tones. (It must be noted that what was perceived as non-chord tones is largely based on culture, but that whatever was perceived as non-chordal was inherently affective.) The increasing use of chromaticism and modulation lessened the sense of tonality and increased ambiguity, eventually leading to new musical relationships such as quartal harmony. By the beginning of the 20th century, twelve-tone serialism totally abandoned tonality. In atonal music, every tone is equal, so no tone can be sensed as being more important than any other, and expectations in terms of harmonic relationships cease to exist.
Theories Relating to Tonal Relationships and Perception
The manner in which scales are perceived has led to differing theories of tonal relationships. Although perception may

be altered through cultural factors, the following theorists assume that there is some inherent meaning in music. Oswald Jonas, in his Introduction to the Theory of Heinrich Schenker, calls the overtone series "Natures only source for music to draw upon" (Jonas, 15). Since the seventh tone of the diatonic scale differs from the seventh partial, Jonas does not consider the seventh scale tone as based on Nature. He believes that:
[the interval of] the fourth appears only as a relation between the third and fourth partials. it does not occur as an interval above the fundamental... because of the ear's tendency to prefer simpler relationships, where available, to more complicated ones, the ninth partial, for example, will manifest itself rather as the third partial of the third partial. This characteristic tendency of tones to appear as closer-and therefore stronger-overtones also has important consequences... the perceptibility of overtones decreases as their distance from the fundamental and the complexity of their relationship increase (Jonas 16; emphasis added).
Since the first five partials are the strongest, as well as the simplest, and since they constitute the triad (Ex. 2), Jonas considers the triad as the most natural basis in music, noting that "The triad is the simultaneity given by Nature, and the intervals that it comprises are the consonances given by Nature" (Jonas, 16). He refutes the term, 'dissonance', believing instead that all tones are, to some degree, overtones. He does, however, concede

Ex. 2
that overtones closer to the fundamental are more usable in music. He also refutes the idea that habituation makes tones acceptable (Jonas, 18). The basis for his theory is that the overtone series and the resulting polyphony are basic to nature. He uses the overtone series as his frame of reference in analyzing tonal relationships (Jonas, 15). Jonas sees chromatic alterations as temporary attempts to change the harmony, rather than as tones having validity in their own right (Jonas.31). He also refutes functional harmonic theory, "which grants independence only to degrees I, IV and V" (Jonas,.35). He sees thirds only as a path to the fifth, and he perceives dissonance as determined by voice leading, which compels tones to move in a particular manner.
Victor Zuckerkandl agrees with Jonas on the importance of a triad, but he focuses more on how tones function within their context, rather than on any absolute theory on harmonics. He

points out the discrepancy between ratios derived from string length and those derived from frequency rates (Zuckerkandl, Sense, 67-75).
A very important facet of Zuckerkandl's theory is that the interval of a melodic fifth does not have the same meaning as that of the harmonic fifth-that it is not simply a folding out of the partial chord. The melodic fifth has a sense of yearning absent in the harmonic fifth (Zuckerkandl, Man. 121). He writes that, "It is utterly misleading to distinguish between melody as the horizontal and harmony as the vertical dimension of music. Music knows only the horizontal. Just as melody is tonal progression, tonal motion, so harmony is chordal progression, chordal motion" (Zuckerkandl, Man. 123). According to Zuckerkandl's theory,
The normal way for melody to move is by steps, from tone to neighboring tone on the scale; on the other hand, no two neighboring tones, with the sole exception of the root and the 7th of the 7th chord, belong to the same chord. Thus the very norm of
melodic motion means conflict with the chord_____
Every time the melody moves out of the chord a small disturbance is created, there is friction, disagreement between tone and chord .... Thus the progress of the melody from tone to tone is at the same time an alternation, an oscillation between opposite states of order disturbed-order restored (Zuckerkandl, Sense. 235-36).

In addition to their placement in a melodic or harmonic context, the rhythmic location of non-chord tones also affects their non-harmonic perception. When they appear on weak beats they have considerably less effect
The Development of Ornamentation in Music
The Baroque use of ornamental devices such as turns and trills was not integral to the music; they were seen as added to rather than a part of the music. During the Classical and Romantic periods ornamentation became more integrated into the musical line. Unlike the ornamentation found in Baroque works for keyboard, Chopin's chromatic runs could never be eliminated from a piece without destroying the music.
Linear Developments in Fine Art
In the 13 th century, Italian art was still highly influenced by the static Byzantine style, which was flat and two-dimensional, with striated drapery. Figures were generally faced frontally with little sense of motion or expression. By the early 14th century,

the striated drapery began to be replaced with more natural folds. Movement was now indicated through the arrangement of figures. Some degree of depth appeared using foreground, middleground and an occasional background, though it was far from the level of perspective later developed by Brunelleschi and Alberti. The trend toward natural facial expression and modeling continued through the 15 th century when figures began to be integrated three-dimensionally into space.
Alberti's treatises on painting, architecture and sculpture reflected the importance of mathematical proportion during the 15th century, and this emphasis on math, in turn, affected fine art of this period. The 15th century mind was deeply influenced by mathematics and proportion. According to Michael Baxandall, "Exchange problems were of an extraordinary complexity because each substantial city had not only its own currency but its own weights and measures" (Baxandall, 96). It was therefore extremely important for anyone in commerce to be able to instantly calculate the contents and value of various containers such as barrels and sacks. Baxandall translates the mathematical skills required in commerce to those same skills applied to art, and that, "Piero della Francesca had the same equipment for a barter deal as for the subtle play of intervals in his pictures"

(Baxandall, 97). Because of the influence of mathematical ratios, it was very natural that such advances in perspective were made during the 15 th century.
TheJP_evelopment of Perspective
In 15 th century linear perspective, lines appear to recede into the distance toward a single vanishing point, while horizontal lines remained parallel. Alberti codified the organization of space, as well as the methods to be used in composition in his treatise, De Pictura. According to his theory, the base line of a field should be divided into segments of one-third the height of a foreground figure. The vanishing point was established at the height of the figure, and orthogonal lines were drawn from this vanishing point to the base line. (Hartt, 230) Paintings frequently incorporated a variety of geometric shapes into views of complex structures and pavillions, which required great perspective skill.
In the last half of the 15th century, artists experimented with different versions of perspective. Instead of a single vanishing point, for instance, each structure might have its own perfect perspective, and there might be multiple foci and panoramic views. In addition, perspective was expanded even further with severe foreshortening and unusual viewpoints, such

as the bird's eye and worm's eye views, but without converging vertical lines. Baxandall defines scorci as, "a local application of perspective" and explains that scorci can appear in a painting devoid of systematic perspective (Baxandall, 143). During the early 15 th century gilt, as well as expensive ultramarine blue, which was made from lapis lazuli, had been lavishly used to emphasize important figures. By the middle of the century, as the use of these expensive materials became more restrained, artistic skill became increasingly more important. Artists displayed that skill through the use of techniques such as scorci (Baxandall, 143).
In order to induce religious feeling during the Baroque period, the new forms of perspective and unusual viewpoints were common. The eye frequently moved rapidly toward the background in art, and architectural components were incorporated into ceiling art to lead the eye upward.
During the 19th century, perspective was re-examined, and many techniques were developed to draw a viewer into the picture, such as tilting a floor, thereby drawing the eye into the depth. During the Post-Impressionist period, artists began to experiment with distorted figures and geometrical shapes such as breaking up planes into various shapes. This led to the

development of cubism. The 19th century break with traditional perspective was dramatic, like the atonal break from traditional harmony in music.
Distortion and Contrapposto
Whereas High Rennaissance artists, such as Michelangelo, used musculature to depict power and motion, Mannerism, which Hartt defines as "standardization, artificiality, and elaboration", retained the sense of motion with a generally more delicate form in order to "glorify court society and a highly formalized version of religion" (Hartt, 639). This dramatic sense of motion continued during the 17th century, when Baroque art was used by the Catholic Church to counteract some of the effects of the Reformation. The art of this time was meant to evoke the strongest religious feelings. Many other devices were used to amaze and evoke an emotional response. For instance, artists frequently used optical illusion, distorted forms, unbalanced composition, and extremely twisted contrapposto figures which turned the action away from the mass.

The Use of iineaiiSJiap.e&
From the late Renaissance into Mannerism, the use of affective devices increased, such as the increased use of diagonals, the vortex, and interlocking figures. In addition, innovations with space and composition, and the conflict between mass and line were used to develop affect. Curves, ovals, arabesques, crossing diagonals, contrapposto figures, and oblique recessions were used to develop movement.
In Flanders, the Italian influence continued with the use of foreshortening, counterforces and contorted figures moving diagonally into depth. In 17th-century Holland, however, Calvinistic Protestantism took a puritanical view toward art. As a result, the Dutch style had little of the fervor of the Catholic Counter Reformation, relying primarily on portraits and scenery for subject matter. Its style relied more on new light techniques and used glances, poses and gestures, as well as a sense of motion to develop expression.
In France, during the reign of Louis XIV, art remained restrained with classical influence and with little sense of motion. The use of new light techniques increased, and tension decreased with simpler poses. The use of cool classic scenes, which

emphasize the static horizontal line further diminished tension. The Roccoco style developed during the 18th century, but its influence was more evident in architecture and interior design than in painting. Straight lines were bent into curves as the result of growing preference for lighter, more delicate portrayals of scenes in the fetes galante style. The fetes galante style incorporated diagonal and curvilinear lines, but used them without the drama of the Baroque, gently receding into depth with little sense of motion.
The late 18th century saw many changes in painting styles. Classical themes, heroic themes, and portraits were common. The turbulent times of the French Revolution brought about dramatic use of diagonals, sharp angles, and obstructed lines to indicate strong motion and affect.
Although the diagonal line in perspective has the potential for moving deep into space, and therefore creating tension, it has the opposite effect when used in a triangle, which encloses and soothes the composition. A similar effect is achieved by the tondo, or round form, which forces any action in upon itself. Both forms were common during the Renaissance. The opposite effect was

achieved by cutting off figures at the edge of a painting, which will tend to draw a viewer into the picture and therefore increase tension. This technique was frequently used both in the Renaissance and during the Impressionist period.
The Development of Ornamentation inArt
Although gilding played a prominent part in decorative painting during the middle ages and in the Renaissance through the middle of the 15 th century, line was also used decoratively. This was evident in the rich detail, decorative patterns and refinement of surfaces in the 14th and 15th centuries. Ornate detail remained popular in the 15 th century with artists such as Botticelli, who created rich surface detail. From the latter part of the 17th century, decoration became lighter and more delicate with the development of the Rococo style.
To summarize, both music and fine art have over the past 400 years undergone many changes, both in the manner of their
organization ahd the means by which they project affect. Among the many changes in music are the development of tonality, the concept of dissonance, mean and equal temperament, the change

from polyphony to harmony, the use of ornamentation and chromaticism, and the development of atonality. Historically, changes comparable to those in music have taken place in the area of fine art.
In terms of fine art, this chapter has discussed the development of perspective, the use of the different linear styles, contrapposto poses, distortion, and framing. It has been explained how the Renaissance emphasis on mathematics and proportion greatly influenced the development of perspective. In all of this, it has been necessary to omit many non-linear and cultural innovations, such as the 15th century importance of gestures and the use of color and light.

In order to understand how psychological tendencies affect music and fine art, it is necessary to understand the nature of psychological tendencies in general, how auditory stimuli are processed, and how expectations are generated. This chapter will address these matters in the context of the arts.
In order to maintain interest, the mind desires a tolerable level of tension in music and art, as well as in life. Tension increases on a continuum between boredom and chaos, evidencing a constant ebb and flow of tension and release, a waxing and waning within certain parameters. The point of equilibrium at which interest is maintained may have great variance. A musical stimulus may create great affect at one time but not at another or in one context and not another. Additionally, a predisposition to remain open to an experience has a strong effect on the resulting emotion, as anticipation can greatly enhance the effect of an experience. Since fundamental psychological principles may affect

perception in music and fine art, this chapter will reference a number of psychological studies on the subject of auditory perception and the development of expectations.
Theories of Psychological Affect
The tendency of the mind to perceive all stimuli in the simplest manner will cause it to organize tones into logical groupings. These are called Gestalts. Victor Zuckerkandl argues that Gestalt principles are exhibited in music more than anywhere else (Zuckerkandl, Man. 103). He explains that, "I hear a transposed melody and recognize it as the same I heard in another key, although not a single note was left unchanged. This fact demonstrates clearly that I hear the whole before the parts, that the Gestalt is prior to its constituents (Zuckerkandl, Man. 103). A problem arises in applying Gestalt theory to music, however. It is easy to understand that we can see an entire painting at one time. In music we hear only one tone of a melody at a time. Most of the research into Gestalt has been on linguistic and visual patterns, and Zuckerkandl questions whether or not the exact same principles can be applied to auditory stimuli. For Zuckerkandl, the acoustical Gestalt derives its meaning from dynamic qualities. For instance, when a melody is transposed the dynamic quality must be changed

as well as the notes if the Gestalt is to change (Zuckerkandl, Man. 111). To illustrate, if the five-tone C scale is followed by a five-tone G scale, the two scales will have the same meaning only if the G scale is perceived as being in the G tonality.
In example 3 a, the G scale is perceived as belonging to the dominant chord of the key of C, so the tones are heard as 1 2 3 4 5, 5 6 7 8 9 in the key of C. In example 3 b, the tonality, which begins in C and moves to G, results in the tones being heard as 1 2 3 4 5 in C, followed by 1 2 3 4 5 in G. The perception has changed because
the tonal center has changed. The dynamic field is therefore what determines perception of these tones. By and large, Zuckerkandl accepts the traditional Gestalt view of music, as does E. H. Gombrich in art.

Gombrich explains the visual process in which, "our visual impressions do not fade immediately but stay with us for sufficiently long to enable us to turn the mosaic of small snapshots into a coherent and continuous image" (Gombrich, 96). Rather than a smooth tracking of the lines in a painting, Gombrich points out that studies of eye movement show that the eyes "dart around in 'saccadic' movements, during which they transmit no information to the brain. Only when they come to relative rest do they resume their function" (Gombrich, 122). The mind, which gravitates toward logic, then, attempts to organize events into a comprehensible whole.
One important study in musical perception involves the Implication-Realization model of Eugene Narmour, which is based on the work of Leonard Meyer. Narmour examines melodies on the micro level, that is, from tone to tone, to determine the implicative quality of each step or leap. For the purpose of his study, he rejects the influence of style or rules of tonality and examines the expectations developed by each interval (Narmour, ix). Contrary to Schenkerian theory, which examines music on the larger structural levels, Narmour believes that the relationship is motivated by "scaled parametric noncongruence" (Narmour, xi).
That is to say, Narmour bases his theory of the perception of music on the realization or denial of two universal hypotheses that "When form (A + A), intervallic patterns (A + A), or pitch

elements (a + a) of a given melody are similar (A, A, or a), the listener subconsciously or consciously infers some kind of repetition of pattern, element, or form and that, "When form, intervallic patterns, or pitch elements are different (A + B, A + B, a + b), the listener subconsciously or consciously perceives some implied change in form, pattern, or element (C C, or c)" (Narmour, 3). He therefore claims that, "such forms exhibit one of two universal functions, either closure or nonclosure (in some degree)" (Narmour, 3).
E. G. Schellenberg defines 'closure' as rest, or release from tension and that closure occurs "when three successive tones create a large interval followed by a smaller interval, or when they change pitch contour (up-to-down, up-to-lateral, down-to-up, down-to-lateral, lateral-to-up, and lateral-to-down; 'lateral' being a repeated tone)" (Schellenberg, 76). This is quite different from the structural sense of closure as an authentic cadence. Narmour calls the initial interval the 'unclosed' or 'implicative' interval. The following note then completes the 'realized' interval. Narmour bases his theory of expectancy on the five bottom-up, Gestalt-based principles of continuation: registral direction, intervallic difference, registral return, proximity, and closure (Cuddy, 452). Schellenberg further explains that, "the Gestalt

principles of proximity, similarity, and symmetry are said to contribute to these implications" and that "violations of implications produce particular affective and aesthetic effects (Schellenberg, 77).
Narmour considers the size of an interval and whether or not the direction is reversed in determining the degree of closure. He states that closure occurs when:
1. a rest, an onset of another structure, or a repetition interrupts an implied patterning
2. metric emphasis is strong
3. consonance resolves dissonance
4. duration moves cumulatively (short note to long note)
5. intervallic motion moves from large interval to small interval
6. registral direction changes (up to down, down to up, lateral to up, lateral to down, up to lateral, or down to lateral) (Narmour, 11-12).
Small intervals, according to Narmour, imply both continuation of registral direction and intervallic similarity, and leaps imply a reversal of direction and a smaller interval (Narmour, 8). These formulations are clearly codified in the 16th and 18th century theories of counterpoint (see, for example, Fux, Gradus ad Parnassus). His bottom-up principles of melodic expectancy are:

Registral direction Small intervals imply a
continuation in the same direction
Large intervals imply a continuation in the opposite direction
Intervallic difference Small intervals imply a realized
interval of a similar size
Large intervals imply a realized interval of a smaller size
Registral return Implies a return to the pitch
region of first note of the implicative interval for both small and large intervals.
Proximity A general implication for small
Closure Closure is realized when (1)
pitch contour changes direction, and/or (2) a large interval is followed by a smaller one (Cuddy, 453).
There could thus be varying degrees of closure. In a pattern of C-G-F, for instance, there is reversal with a small realized interval, satisfying the expectancies of direction, difference, and closure. In a pattern of C-G-A, there is no reversal with a small

realized interval, satisfying the expectancies of difference, and closure. In C-G-D, there is reversal with a large realized interval satisfying the expectancies of direction, return, and closure.
Narmour distinguishes the "top-down" process of cognition from the "bottom-up" process. The top-down process considers the context, such as harmony and structure, as well as cultural influences in the processing of stimuli, whereas the bottom-up process considers only the note-to-note motion and direction. He recognizes that both types of processing occur with a stimulus, but his theory relies on the bottom-up Gestalt rules of pattern perception in determining the implications (Narmour, 9 ).
In addition, Narmour points out a problem he sees with some traditional Gestalt principles which state that parts are perceived only as part of a unified whole. Narmour agrees with Leonard Meyer on the importance of bottom-up Gestalt principles in defining the meaning of music, but there is disagreement on top-down processing. Whereas Meyer credits both the top-down and bottom-up process, Narmour rejects the concept of an innate, pre-determined whole and believes instead that individual parts have meaning and implications. He therefore believes that the bottom-up Gestalt principles of proximity, similarity, and common direction determine implication and realization (Narmour, 62-65).

Lola Cuddy and Carole Lunney further tested Narmour's implication-realization model in an experiment to rate how well a third tone continued a melody. According to Cuddy and Lunney:
There are three main predictions that can be made if Narmour's bottom-up principles are influencing melodic expectancies on a tone-to-tone level. The first is that the pattern of expectancies should depend on the size of the preceding implicative interval. Second, any given implicative interval should generate expectancies for a set of continuations (rather than one specific continuation), since different expectancies are generated by each principle. Finally, since these principles are assumed to be independent of style and musical experience, there should be no differences in their operation as a function of music training or exposure (Cuddy, 454).
The results of the Cuddy and Lunney research indicated three main findings:
First, there was support for three of Narmour's five principles of tone-to-tone melodic expectancy-intervallic difference, registral return, and proximity-and support for a modified version of a fourth principle-registral direction. Second, there was support for Narmour's (1990) assertion that the operation of the bottom-up principles of expectancy is independent of experience, at least for the range of experience tested here. Third, there was evidence that, in addition to the principles proposed by the implication-realization model, there was a strong influence of perceived tonality on continuation judgments (Cuddy, 458).

Narmour believed that both top-down and bottom-up processes might be operative at times, and either one might predominate in any given situation. "In ambiguous situations, such as at the beginning of melodies, he proposed that bottom-up processes would dominate" (Cuddy, 454). Further experiments by E. Glenn Schellenberg, using a simplified version of Narmour's model, not only strongly supported Narmour's findings, but also applied his principles to atonal music. His results indicated a definite correlation between tonal and atonal results, but that Narmour's principles had less influence in atonal music than in tonal style.
Narmour makes the argument that "Musical laws never escape the fundamental laws of psychology" (Narmour, xi) and that, "cognitive universals that control all manner of human behavior, including certain significant aspects of the perception, cognition, and learning of all styles of music, must exist (Narmour, 66). His belief that "Recognition of implication per se is, of course, a primary cognitive means by which human beings simply survive" (Narmour, 13) coincides with Leonard Meyer's belief that "the same basic psychological processes underlie all affective responses, including those to music" (Cuddy, 452). "[Narmour's] principles," according to Schellenberg, "particularly those from his

revised model, can be seen as closely related to, and possibly derived from principles of perceptual organization that function in audition as well as vision" (Schellenberg, 118).
Most of the studies testing Gestalt principles were applied to visual stimuli prior to being applied to auditory stimuli. In relating to visual affect, Gilbert Rose states that "Tension and release, built into the work of art, corresponds to a sensitivity to tension and release, which is a primary attribute of perception (Rose, 502). He sees tension and release as "both the inner dynamic of emotion and the structure of aesthetic form" (Rose, 503). He sees artistic perception, however, within its context, in the light of personal experience and knowledge, much of which might be tacit. He claims that*
This vital function-sensitivity to expressiveness-is rooted in a biological necessity: an organism must make an on-the-spot appraisal of the outside world's perceived hostility or friendliness in order to know whether to advance, withdraw, or wait and see. In other words, affect is the first and most basic response to the dynamic aspects of reality, that is, its perceived qualities of tension and release, and the interpretation placed on these qualities in the light of knowledge and imagination. (Rose, 503)

Research by Ray Jackendoff also supports Rose's belief in the importance of context, and he compares the perception of music to the acquisition of language. He lists three possible methods of parsing, which would apply to either language or music. In the first method, which he terms the single serial choice parser, each tone is perceived as the most logical outgrowth of the preceding tone. As the melody continues, when an incorrect analysis occurs, the mind must backtrack to select another alternative tone at some point. The second method, which he calls the serial indeterministic model, when confronted with indeterminacy, collects evidence and makes the analysis only at the end. The third method, the parallel m ultiple-analysis model, separates into multiple branches, eliminating any which become implausible (Jackendoff, 210-13). Jackendoff attributes the concept of musical expectation, or what he terms prospective hearing, to the theory of musical parsing. Taking the position of the parallel model he relates this method of parsing to music when he says:
each fragment of music, as it is heard, builds in the listener expectations of what is to come. Either these expectations are fulfilled by the succeeding music, with an accompanying positive affect or satisfaction in the listener, or else they are not fulfilled, with an accompanying negative affect such as surprise or disappointment (Jackendoff, 221).

In addition to prospective hearing, the parallel model also allows for retrospective hearing, which considers backtracking to any point of indeterminacy, thus allowing for satisfaction or surprise in listening to music (Jackendoff, 222). Although Jackendoff agrees in the validity of the expectation theory of affect, he recognizes that there are many other factors which can influence affect, such as tempo, volume, structure and the attack and release envelopes of notes. (Jackendoff, 226).
Through his associative network model, Emery Schubert has proposed an explanation of how negative emotion can be enjoyed in music. According to Schubert:
... incoming information, such as music, can be processed in one of three ways: (1) the information can match a schema exactly, meaning that the information is familiar, (2) the incoming stimulus may partially match an existing schema and this partial match is enough to activate the schema (and therefore the information is assimilated by that schema), or (3) no schema matches the incoming signal-the signal is novel and a new schema may need to be formed (this process is referred to as accommodation). According to Mandler (1984) a consequence of the mismatch of information and schema is the generation of emotional arousal (Schubert, 20).

Schubert has proposed that it is the violation of an expectation which is the cause of pleasure. In his associative network model, he has shown that an activated negative emotion node which he defines as a single negative concept, will disable the displeasure centre whenever the context is aesthetic (Schubert, 25). He states that, "The mere activation of negative emotion nodes in an aesthetic context is pleasant" (Schubert, 26).
Psychological Principles Applied to Music and Fine Art
There are a number of psychological principles which help us to understand how both music and fine art are perceived, such as the need for order and simplicity, the need for balance and equilibrium, integration into a Gestalt, the development of expectations, gravitational pull, centric attraction, and the effect of motion. There are also a number of similarities between music and fine art in the application of these principles and the use of specific tension-creating devices. Among the devices used in both fields are gaps, ambiguity, obstructions, changes in line, convergence, contraction or compression, and ornamentation. In

addition to the above, it is necessary to investigate other factors where a direct correlation between music and art is lacking, e.g., chromaticism and dissonance in music, and perspective and contrapposto in art.
The mind has a strong need to organize what it perceives in sight and sound into some semblance of order. It must have at least some sense of where it is going and how it will get there. When rules constantly change, the mind is thrown into a state of chaos, and it struggles to find some logical pattern on which to base predictions about the future.
When the way is predictable, there is little tension; on the other hand, when there is incompleteness, ambiguity or obstructions, then tension rises. The mind seeks to develop hierarchies of order and to arrange perceptions into some logical sequence. As long as the mind can easily grasp this order, it remains relatively unchallenged and the familiar is typically more comfortable and easier to assimilate than the novel.

One method which the mind utilizes is "chunking" which is the perceptual accumulation of bits into larger chunks which are more easily perceived. Children's chants, for example, are easily remembered because of the rhythmic grouping. Phone numbers are grouped in 3 plus 4 digits for ease in perception, and ballet enchainments are more easily memorized when the steps are grouped. Likewise, when an arpeggio is perceived as a chord, or ascending notes as a scale, rather than as individual notes, the patterns are read or memorized very easily. Thus, we see that the mind tends to arrange discrete stimuli into more easily perceived patterns.
The mind seeks stability and consistency, in a word, patterns. Meyer's Law of Good Continuation is based precisely on this principle. It states that "A shape or pattern will, other things being equal, tend to be continued in its initial mode of operation" (Meyer, 92). Narmour's implication-realization model hypothesizes that the appearance of similarity, proximity, and common direction causes the listener's input system subconsciously to perceive an implication of continuation" (Narmour, 75). For example, if a pitch is repeated, another

identical pitch would be expected, absent rhythmic factors. According to Narmour's theory, small intervals up to a major third would imply continuation, and intervals larger than a minor sixth (other than the octave) would imply a reversal of direction.
Perfect fourths and fifths are more ambiguous and could imply either continuation or reversal. He does point out, however, that other cultures which hear microtones, might conceive of thirds as being wide intervals (Narmour, 77).
In order for a satisfying realization to occur, a large interval (a minor sixth or larger), which implies a reversal, should be followed by a smaller interval, though that interval should be at least a minor third (Narmour, 153). Furthermore, the larger the initial interval, the stronger is the implication, or expectation. He considers reversal as an, "inborn cognitive mechanism commensurate with the bottom-up Gestalt laws-constantly operative in our input systems not only in the processing of melodic implication but also in the perception of other syntactic phenomena" (Narmour, 150).

The Desire For Simplicity
In Gestalt psychology, the Law of Pragnanz states that the mind tries to perceive patterns of any type in the simplest way possible. Leonard Meyer explains that:
The mind is constantly striving toward completeness and stability of shapes ... the mind, when left to operate on its own, will improve those figures which are not as 'good' as they might be ... and that good organization, stable shapes, will resist change and will tend to remain constant even in changes of the stimulus conditions (Meyer, 87).
In Sense of Order. Gombrich applies the principles of Pragnanz to art when he states that, "There is an observable bias in our perception for simple configurations, straight lines, circles and other simple orders and we will tend to see such regularities rather than random shapes in our encounter with the chaotic world outside" (Gombrich, 4). He continues, "Melodies are subject to the same laws as are the visual ones, except only that the ear is able to follow and to resolve a much more complex order than the eye, which has to take in the whole simultaneously in one moment" (Gombrich, 287). He points out that we are deluged with constant stimuli and would remain in total confusion were it not for the fact that we try to organize these stimuli into simpler

patterns (a type of chunking) by making guesses, then making corrections (Gombrich, 4). Thus, simple patterns are the easiest to remember; complexity demands more of the listener.
ManssJ^Uikrim andLSymmetty
According to Jackendoff, "One of the principles of grouping creates a preference for symmentricai organization" (Jackendoff, 222). There is a natural preference for symmetry, which, according to Gombrich, is related to our sense of balance and movement (Gombrich, 129). Balance and symmetry, however, are not mutually exclusive terms. Symmetry is merely one aspect of balance, which simply means the attraction of opposing forces. With few exceptions, music is essentially asymmetrical due to the element of time. In music, the occasional retrograde pattern, the rondo form, and the sonata-allegro form most nearly approach symmetry. There were, however, rare instances of complete symmetry in cancrizans in Renaissance music, such as, "The End Is My Beginning And The Beginning Is My End" and in Baroque music, such as portions of Bach's "Musical Offering," which were identical both forward and backward. As Rudolf Arnheim observes, symmetry, repetition, and simplicity, which

predominate in Classicism, reduce tension, while the irregular, the asymmetrical, and the complex, which predominate in the expressionism of the Romantic period, heighten tension (Amheim, Art. 67).
Tonal Center
For a tone to have dynamic meaning, it must exist in a musical context, for it is not the tones which dictate meaning, but the tonal relationships (Zuckerkandl, Sense. 116). Once a second tone is played, a tonal center is suggested which creates a dynamic pull. This dynamic pull is fluid, however, and may change with successive notes, confirming the dynamic center, creating a new one, or creating ambiguity. Once the center is established, however momentarily, other tones of the scale possess certain tendencies in relation to the center. The first tone of the scale is the most static, not having any tendency to move. Tones 3 and 5 are relatively stable, and the resolution of the remaining tones is more or less ambiguous.
Toward the end of the nineteenth century, tonal centers became more and more obscure with increasing chromaticism and various scale forms, eventually leading to twelve-tone serialism

and complete atonality. Without a tonal center, it is not possible for any interval to relate to a tonic. As a result, there is no longer any sense of expectation that a tone will move in any given direction. That is not to say that there is no sense of direction. Other factors, such as rhythm, pitch, and harmony assume the role of developing a logical pattern.
ALtmcHomolthe Center, in Art
Just as tones of the scale are attracted to the tonic in music, the eye is attracted to a dynamic center in painting. As this study has already noted, various tones of the scale have a tendency to resolve to other specific tones. There is some correlation between this musical attraction and the attraction of the eye towards specific centers in painting.
Rudolf Amheim speaks of centricity as based on an infant's tendency to see himself as the center of his world, with motion directed toward himself. He explains:
The eccentric stands for any action of the primary center directed toward the outer goal or several such goals or targets. The primary center attracts or repels these outer centers, and the outer centers, In turn,

affect the primary one____The tension between the
two antagonistic tendencies trying to achieve equilibrium is the very spice of human experience, and any artistic statement failing to meet the challenge will strike us as insufficient. (Amheim, Power. 2-3)
He further explains that "Any state of equilibrium in which the vectors of a field compensate one another implies the establishment of a center" (Amheim, Power. 13). The dynamic center, however, can be any location on a plane, not necessarily in the vectorial center, and any deviation from that dynamic center creates tension (Arnheim, Power. 17). To Arnheim, visual experience is dynamic; a field contains tensions pointing in various directions.
Zuckerkandl speaks of a single tone as having a sensation of beginning, a state of expectation (Zuckerkandl, Man. 129). Meyer speaks of the expectations which derive from the "possibilities and probabilities inherent in the materials" (Meyer, 44). Meyer uses the excited atmosphere of the concert hall as an example of the "tension of expectancy" (Meyer, 75). Expectations are largely influenced by our experiences and training. A person knows

much more than he is aware of knowing. The myriad decisions we make each day are, for the most part, unconscious.
Consciously reasoning through every decision would be exhausting. We extrapolate from our experiences and develop expectations about what is to come. If our expectations are met, we feel satisfied. On the other hand, if our expectations are not met, we experience surprise or anxiety-in a word, tensions. Katz questions why violating expectations is an important source of musical affect, and explains one possibility by observing that "jokes work by fooling the brain into maintaining two competing, incongruous concepts at once," and dual activation of his network model increases the affect (Katz, 106).
Through hearing a word used in context numerous times, a person may understand the meaning without ever having read the definition. This process of extrapolation enables one to draw inferences from a limited amount of data, allowing decisions to be made without any apparent conscious effort. Using the tacit knowledge gained through one's life experiences, a person is able to project that knowledge into music and fine art. Objects are perceived as having directional force, for instance, because we have seen those objects move. A picture of a man walking does

not specifically portray motion, and yet we know that he is much more likely to be walking forward than backward. This tacit knowledge aids in organizing and synthesizing stimuli into the Gestalt.
Forward matching, a type of extrapolation in which a person can predict the next event, occurs in both music and fine art.
Every instrument, including the voice, has a specific range of comfort, and scales expect to descend eventually. As a scalar passage approaches the upper limit of that range the expectation of change is greatest, and the tension the keenest. Man appears to have an innate sense of what will 'fit' in music. A person, without ever having heard a song before, will have a good idea of the alternative notes which might come next. Some pieces seem quite predictable, while others appear to surprise us. These surprises can create tension or interest.
We are no doubt aided in this feat by what has been called the iconic or 'echo memory', the continued presence of a sensation in our consciousness before it fades and is filed in the long-term memory store.... Listening to a familiar piece of music we may feel or sense the next phrase appearing over the horizon as it were; we anticipate its shape and perhaps also its mood while still listening to the notes which strike our ears (Gombrich, 288).

Delay in the resolution of expectations can have either of two different effects. If the delay is for a short duration, tension rises, with satisfaction at the resolution. If the resolution is delayed for a long duration, or if the resolution never arrives, the tension rises and then deflates. If a person begins Christmas preparations in August, he loses interest by December. The excitement of anticipation peaks and can then be sustained only so long before it wanes.
RepetitionJChange and Monotony
There must be a balance between boredom and chaos. Just as too many stimuli can cause sensory overload leading to inattention, too much simplicity or regularity requires too little of the mind, and the mind again ceases to pay attention. Katz explains that "objects or stimuli that exhibit unity in variety will be thought beautiful" and that both order and complexity are necessary for artistic merit (Katz, 80). "When the expected happens in our field of vision," explains Gombrich, "we cease to attend and the arrangement sinks below the threshold of our awareness" (Gombrich, 151). He notes, for example, that

repetition leads to a degrading of sound patterns. "If a word is repeated long enough it appears to be drained of meaning and becomes a mere puzzling noise" (Gombrich, 151).
Repetition, however, can be a very effective means of heightening tension. We know that a pattern is not likely to go on forever, yet we do not know when or how it will change. The very ambiguity caused by the delay in continuation creates suspense. Oswald Jonas explains this urge for completeness when he says that, "Just as the original, most primitive impulse toward artistic creativity finds its expression in imitation, so the first response on the part of the recipient is the joy or recognition" (Jonas, 1). The mind resists change, and yet, paradoxically, it invites it. People have a certain comfort zone in which they normally operate, but they still need to stretch outside that zone in order to avert boredom. Change attracts the eye and ear. It is what arrests our attention and creates interest, or tension.
It is not only recurrence we expect of music, but change. So deeply is this expectation implanted in us that there is no more effective device for the creation of suspense in classical music than the cessation of change and the repetition of a single sequence of tones or chords. We feel that such a preparation must herald a profound revelation and we are rarely disappointed. What is too expected, too redundant, lacks interest (Gombrich, 300).

Groups of similar objects may be perceived as repetitions of the same object in both music and art. When a stimulus is repeated too many times, the mind ceases to attend, and saturation may occur. Neurons bombarded with a strong stimulus, "rapidly fatigue and are less sensitive to further stimulation.... After a period of intense sensory stimulation the visual system only gradually recovers its sensitivity for the kind of pattern to which it has been exposed" (Gregory, 30-31). According to what Gombrich calls 'the etc. principle', "Looking at a crowd or a troop of horses we will be less aware of the exact loss of detail because we will tend to expect that the members of this mass will be identical and read them accordingly" (Gombrich, 99).
The eye is attracted to any change, but only if the change is substantial enough to overcome this 'etc. principle'. If any visual or auditory stimulus is buried within a multiple-repeated pattern, the change most likely will be ignored. The straight line is the simplest visual form and any variance will be noted. Since the mind expects simplicity, it therefore also expects continuity. Any break in continuity will be noticed. Thus, the longer a pattern continues in either music or art, the more apparent will be any change.

In both music and art, the psychological energy required to ascend creates tension. According to Gombrich, "We associate height with effort and with dominance and we tend to think of this dimension in different terms from the way we think of length and breadth" fGombrich. Sense. 169). Schapiro attributes the qualities of upper and lower to our posture and relation to gravity, and "perhaps reinforced by our visual experience of earth and sky" (Schapiro, 214). Because of man's sense of gavity in lifting any object and because of the limitations of the range of both voice and musical instruments, there is a perception of effort in approaching that limit. The placement of the highest point in a musical phrase is commonly the climax of the phrase, although the lowest point, less commonly, may be the pitch focus, as other factors such as the rhythmic placement and dynamics may impact its effect (Kennan, 7). According to William Christ, "ascending contour, combined with progressive cadence, results in anticipation of continuation" (Christ, 72). He continues, "As a phrase unfolds, the pattern of motion to the highest pitch directs our attention to that pitch" (Christ, 74). Meyer affirms the effect of gravity on melodic tension when he says, "Melodically speaking, relaxation is associated with the decline in tension which is effected when pitches are lower..." (Meyer, 139). In terms of

visual perception, "any initiative toward movement must overcome the inertia inherent in weight" (Amheim, Power. 16). Narmour states that, "gravity does not explain architecture, but architecture is subject to its law" (Narmour, 4). Thus, it can be seen that gravity may have an effect on music and art, although that effect can be mitigated by other factors.
Can a single letter of the alphabet, a single tone, or a single dot on canvas have meaning by itself? Or can they acquire dynamic properties only in relation to other letters, tones or dots? According to Jan LaRue, "The vibrations of a single sustained note, the shock waves of a clipped staccato, induce motion even in isolation" (LaRue, 1). Wassily Kandinsky would argue, on the other hand, that "[The point] maintains itself firmly in place and reveals not the slightest tendency to movement in any direction whatsoever, either horizontal or vertical. Furthermore, it neither advances nor recedes" (Kandinsky, 32). Whether one agrees with LaRue or Kandinsky, there is no question that once the second note or dot appears, there is a sense of motion. "Directed tension", according to Arnheim, "is as genuine a property of visual objects as size, shape, and color (Amheim, Art. 423). The dynamic quality

of music, which creates a sense of tension, arises out of the relationship between tones. Tones which cause tension are those which have a strong impulse to move. The stronger the urge to move in a specific manner, with the strongest sense of progression and desire for completion, the greater will be the affect. Zuckerkandl believes, however, that tones are heard within their musical context. What precedes and follows a specific interval or coexists with it at any point in time, determines the level of expectation. Zuckerkandl explains that:
It appears that every interval has a kind of preference for one particular meaning ... every interval seems to place itself by its own weight, as it were, into a definite position in the dynamic field. This might be called its natural position, and the corresponding dynamic meaning its natural or normal meaning. In relation to it the other possible meanings of the interval assume the character of deviations, significant deviations, from a norm.. .(Zuckerkandl, Sense. 79).
Zuckerkandl further explains that the mind desires a sense of movement-a sense of drive toward a goal or resolution, and our expectations are influenced by our experiences and our knowledge of style. When we see a painting of a ballerina executing a grande jete, we know precisely where she will land. We also sense when she will land and this perception may help to increase the sense of motion. This mental image, although it may

help, is not sufficient to produce the movement. Additional factors, such as location, size, line, and surroundings must be present to create movement. On the other hand, Arnheim disagrees with the traditional psychological view that expectation based on previous knowledge will produce a sense of motion. He believes that movement is a property which is inherent in the formal criteria, such as line, shape, and color (Arnheim, Art. 416). If the formal characteristics are not present, no amount of imagination can supply the motion.
To summarize, there are a number of psychological principles in nature which affect our perception of music and art. Among these are the need for order, stability, simplicity and balance. The mind tends to perceive stimuli as a whole and to gravitate toward a tonal center in music and visual center in art. From these tendencies, the mind develops expectations, which have the power to increase or decrease tension. Repetitions, gravity and motion are means by which tension is affected. A number of studies on auditory and visual perception have supported the principle of inherent expectations in tonal and spatial movement.

In the previous chapter, psychological principles and the manner in which they relate to music and art were discussed.
Now, the discussion turns to the specific devices which demonstrate those principles as they develop tension in music, with some correlations to fine art. As will be seen, these devices include the effect of gravity, attraction of the center, obstruction, ambiguity, deviation, chromaticism, polyphony, and ornamentation. Numerous examples have been used to demonstrate these devices. However, only one device is discussed in each example for the purpose of clarity. This presentation of examples will slight some very important innovations, for example, rhythm, harmony, light and color, in an attempt to limit the discussion to linear effects such as direction, movement perspective, and linear style.

Gravity and Linear Direction
It has been shown that gravity exerts a psychological force on our expectations. Rudolf Arnheim says that the psychological energy needed to ascend creates tension (Arnheim, Power. 16). Although Arnheim was referring to art, this rule apparently also applies to music. The feeling, of effort in an ascending scale creates tension. In the Beethoven Sonata Op. 57 (Ex. 4) the ascending arpeggio creates a sense of drive to the high F, with immediate release of tension on the F an octave lower.
Ex. 4 Sonata Op.57, Beethoven
In any phrase the point of greatest tension is likely to be the highest tone; the degree of tension generated is likely to be affected by the location of the highest tone. Placement on a downbeat increases the tension. However, as Kennan points out, "Placement of it in the last half [of the phrase] is the most usual arrangement, since that allows for a greater sense of buildup to the high point and sustains interest more effectively" (Kennan, 5).

He adds that it is sometimes possible for the lowest pitch to have a feeling of climax, if it has a sense of arrival (Kennan, 7). The following examples demonstrate increasing tension according to placement of the high point of the phrase. In Schumann's "About Strange Lands and Places" (Ex. 5), the highest note falls in the first half of the phrase, lessening its effect. Furthermore, it falls on the weaker second beat in 2/4 time, which also diminishes its affective power.
In Chopin's "Nocturne in B" (Ex. 6), the highest pitch is B, which falls in the second half of the phrase. Its affect is diluted because it does not fall on a beat and because the sixteenth-note pattern acts as an ornament or embellishment, leading to the following strong beat on F. This pitch, F, is actually the highest point of the melody. The Nocturne in Db (Ex. 7) takes its time in building up to the high Bb, which is on the strong downbeat, thereby creating greater tension.
The psychological force exerted by gravity on music also affects the dynamic force in art. Whereas the effect of gravity in music is limited to the concept of high and low tones, the effect of gravity in art is considerably more diverse. It can affect vertical, horizontal, oblique, as well as curved and wavy lines.

Ex. 5, About Strange Lands and Places, Schumann
Ex. 6 Nocturne in B, Chopin
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ttrrrrTv 'ww\\ ji w wmw r tt i
Ex. 7 Nocturne L Db, Chopin
r^3t: £; J~ lAJ*-*, ffft |
-vL->Jr 1 _ r/Ti i h r tph i a
-fth 7 *_ c ra -ar t jr -fazr.
-W l Q_ L gZHIZIZ f ' 11

In a painting, if two objects of equal size are placed one on top of the other, the painting will look unbalanced and will appear as if there is a directional force pointing downward. If the painting is to look balanced, the top object must appear smaller, either through size, shape or color (Amheim, Art. 30). The top portion of a painting therefore carries more weight than the bottom portion. Arnheim explains how two factors affect visual balance: weight and direction. Weight can be affected by location, depth, size, intrinsic interest, isolation, shape and compactness (Arnheim, Art. 23-25). He further explains:
Weight is influenced by location. A "strong" position on the structural framework... can support more weight than one lying off-center or away from the central vertical or horizontal. This means, e.g., that a pictorial object in the center can be counter-balanced by smaller ones placed off-center ... the weight of an element increases in relation to its distance from the center ... the greater the depth an area of the visual field reaches, the greater the weight it carries ... (Arnheim, Art. 23-24).
The most obvious way in which gravity impacts line is through the vertical/horizontal axis. Objects high on the axis tend to exert a downward force. The greater their mass, the greater the thrust. The effort associated with upward movement is considerably more than the effort needed to move sideways. The speed and ease of sideways movement creates the effect of

widening, whereas the vertical line tends to slenderize. The psychological effect is that "The lean vertical shaft may make us tense and stretch our muscles, the spreading horizontal shape will make us feel relaxed and calm" (Gombrich, 201). A good example of the lack of tension on the horizontal plane is Edward Hopper's Early Sunday Morning (fig. 1). In spite of the vertical windows and barber's pole, the impression is almost totally horizontal and static.
The direction of a line is also affected by a sense of gravity. One of the most dynamic lines available to the artist to indicate directional force is the diagonal. Gombrich has noted that "any diagonal configuration is perceptually less easy to grasp than the horizontal or vertical connection" (Gombrich, Sense. 184). It is as if the oblique line which wants to lie flat horizontally (gravity), struggles to rise and find its proper place. The diagonal line is seen by Amheim as "straining toward or away from the basic spatial framework of the vertical and horizontal" (Amheim, Art. 424-25). Obliqueness, he notes, "is always perceived as deviation, hence its strongly dynamic character. It introduces into the visual medium the vital difference between static and dynamic shapes" (Arnheim, Art. 187). An example Arnheim uses is that of the static effect of windmills in the horizontal/vertical axis (fig. 2a). The sense of motion is greater when the arms are in a balanced

Fig. 1 Edward Hopper, Early Sunday Morning. The Whitney Museum of American Art, New York.
Fig. 2

diagonal position, (fig. 2b), but the effect is greatest when the arms are in an, unbalanced asymmetrical position (fig. 2c) (Amheim,
Art. 425).
A comparison of two equestrian statues will show that the source of the dynamics lies not in the anticipation of a horse's movements so much as in the diagonal lines. Donatello's Equestrian Monument of Gattamelata (fig. 3) is almost totally on the vertical/horizontal plane, creating very little sense of motion. The static quality is enhanced by the curved lines of the leg and tail which enclose the composition. The figure Is completely vertical, with the smallest horizontal elements. In David's Napoleon (fig. 4), on the other hand, the dynamic quality is created by the almost completely oblique painting. The horse, the mountains, the arm and leg are oblique, and the torso is leaning back. Here only the smallest elements are on the horizontal/vertical axis.
An interesting comparison exists in Piero della Francesca's Resurrection (fig. 5). A static sense of rest is created by the vertical and horizontal elements in the upper portion and the triangular composition. The tension exists in the figures of the three soldiers, who are leaning their bodies or heads obliquely.
An interesting paradox exists here: Christ is awake, but in a

Fig. 3 Donatello, Equestrian Monument of Gatlamelata,
Fig. 4 Jacques-Louis David. Napolean at St. Bernard. Musee National du Chateau de Versailles.

Fig. 6 Rembrandt van Riin. The Storm on the Sea of Galilee. The Isabella Stuart Gardner Museum, Bos-

position of repose, while the soldiers, who are in a dynamic configuration, are asleep. It is easy to see the powerful effect of the oblique line when Rembrandt's The Storm on the Sea of Galilee (fig. 6) is viewed at an oblique angle. When the painting is tilted so that the ship is upright, much of the tension disappears.
According to the Law of Pragnanz, stimuli are perceived in the simplest possible manner. Since a straight line is simpler than a curved line, there is an expectation that a line will continue in a straight manner. The straight line, therefore contains less tension. Preference for Curved lines over straight lines, however, is no indication of tension. At various times, different preferences have held sway, as in the straight lines of Aft Deco and the curved lines of Art Nouveau. It is not preference which dictates tension, but the intrinsic quality of curves (Gombrich, 117). The intrinsic quality, however, is influenced by the expected norms of the time.
The curved line indicates movement more clearly than the straight line (Gombrich, 137). It suggests directional flow. While the straight line is a direct statement, the curved line carries more ambiguity. It can easily lead in any direction and can sharpen or loosen its turns, or even turn back on itself. When a curved line depicts a mass, it can form a concave curve, which has even more force than a convex curve (Arnheim, Art. 231). The degree of the

concavity determines the degree of force generated. The force of the curve is more emphatic when used in the strongly linear style of Matisse or Munch, since the painterly style makes the line less obvious. In addition, the strong outline emphasizes the difference between the figure and ground, making the line even more important. The tension of the line can be further increased by changing the thickness of the line, which increases the complexity and interferes with continuity. Van Gogh used this technique to create great affect. In Starry Night (fig. 7) his swirling brushstrokes of varying widths and lengths form a vortex, creating tremendous dynamic energy in the sky. This contrasts with the repose of the village. The strong, curved outlines of the hills add to the dynamic impression.
Irwin Edman speaks of the, "easy fluency of a curved line, the decision of a straight one," and that "specific types of lines, jagged and broken ones, smooth or wavy ones, circles and ellipses, all, like the high and low notes of music, the intense and dull tinges and values of color, have unique nervous correlations" (Edman, 92). In speaking of the effect of line, he says that "A broken rhythm on the canvas breaks the flow of our perception and our impulsive motor response. A fluent and wavy line releases tension and makes both our perception and our half-realized reaction easy and pleasurable. (Edman, 93)

Fig. 7 Vincent van Gogh, Starry Night. Museum of Modern Art, New York.

The wavy line is a curved line with more or less regular undulations. It has the same quality of tension as the curved line, but to a greater degree, due to the compression. It can be stretched or contracted, or it can have varied undulations. The greater the irregularity, the more difficult is the perception and the greater the tension. "Perceptually the wavy line is far from simple because of the fluctuating interactions between figure and ground which arise as we look from bulge to bulge or from hollow to hollow" (Gombrich, 184).
Tonal Center
If the triad is the basis of music, as Oswald Jonas proposes (Jonas, 18), then tones 1, 3 and 5 are the most stable, and other tones of the scale will tend to gravitate toward them, tone 1 (the tonic or tonal center) having the strongest attraction. Subsequent tones will affirm, or create ambiguity about the tonal center. Compare the two examples beginning with a partial C scale (Ex. 8a and 8b). In Example 8a, the second measure somewhat affirms the C tonality, but the V7 chord in the third measure makes it certain. In Example 8b there is some degree of ambiguity. The F chord in the second measure could be either a IV chord in the key of C or a I chord in the key of F. Since it outlines a root position F

Ex. 8-a
chord, it can be perceived more as a I chord in F, which is confirmed by V7 chord in measure 3, which resolves to F.
As we listen to music, we are constantly adjusting our perceptions in light of subsequent events. This commonly happens in modulations from one tonal center to another. Even in modulations, however, the change of key may not be immediately discemable. The appearance of accidentals may be a clue, but only if the new tonality uses tones which it does not have in common with the old tonality. As Zuckerkandl says, "we intuitively distinguish between the main road of the movement and the side roads and detours that take us from one station on the main road to the next, elaborating, expanding, enriching the movement" (Zuckerkandl, Sense. 43). It is necessary to ask if the subsequent tones affirm or contradict the initial assumption.

Repetitions or frequent returns to the tonic, for instance, reaffirm tonality while a pause on a tone other than a tonal center might contradict it. In the Haydn Variation in C (Ex. 9), the C is repeatedly affirmed in the first two measures, solidifying the tonality.
Ex. 9 Variations, Haydn
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Lb^ss£ % *
-^-0 F=
*8 !- 0 0- f" -Lr 4 11
In reviewing further examples (Ex. 10a through Ex.l0e), it is evident that the half step between scale degrees 7 and 8 creates the strongest tendency to resolve upward into the tonic, whereas the 2nd scale degree generally wants to resolve down to the tonic.
10-b Natural minor
-g ; | U U f
M I 1 I
10-c Harmonic minor

l- * u i
10-d Melodic minor
w H r l i
J \-U m 1 =F= '1 1 1 j j 11
10-e Lydian mode

J 4 4* ? { t *

Similarly, the 4th scale degree has a general tendency to resolve down to the 3rd scale degree. The 6th scale degree, however, is the least stable. In certain patterns it can have an urge to continue on its way through tone 7 to 8. In the natural minor there is a whole step between tones 7 and 8 of the scale and a half step between tones 5 and 6, eliminating the tendency for 7 to move upward and removing the ambiguity of tone 6. The raised 7 th tone of the harmonic minor retains its urge to move upward to tone 8, but the 6th tone, being only a half step from the 5th tone, loses some of its ambiguity and has a definite tendency to resolve downward to tone 5. There is an expectation for the scale to move stepwise in a direct manner (Zuckerkandl, Sense. 235) and, as Meyer explains, "to pass over a note immediately creates a desire for it (Meyer, 131). The one and a half step gap, an augmented 2nd, between tones 6 and 7 then creates some degree of tension in the harmonic minor.
In the ascending melodic minor, the raised 6th and 7 th tones create a strong drive towards 8. In the descending pattern, the lowered tones create a lesser drive to tone 5. It appears that the half step creates a desire for resolution to the closest stable tone. By illustration (Ex. 10a and lOe), it is easy to see that the F# of the Lydian mode has a greater drive to G than does the F natural of the major scale.

It can be seen that there is much greater ambiguity in the minor scale than in major. Once the minor third is heard, there are more possibilities for tonal progression than there are in the major. The question immediately arises as to which form of the minor scale will be used, or even if the tones represent 1-2-3 of a minor scale, or tones 6-7-8 of the relative major scale. Again, greater ambiguity produces greater tension. According to Gombrich, there is inherent anxiety and unease in the minor which does not exist in the major. (Gombrich, 299).
Melody, however, does not operate independently.
Harmony reinforces or creates melodic expectations. For instance, tone 7 normally has a strong tendency to resolve to tone 8, with an accompanying V-I authentic cadence. If a deceptive cadence, V-vi, is used instead, as Zuckerkandl illustrates (Ex. 11), "harmony nullifies the concluding effect of the 7-8 step and transforms release into tension" (Zudkerkandl, Sense. 224).
Ex. 11 Zuckerkandl, Sense p.225
m 5 *f 9 T* E m 1

I I IV V7 vi
vi ii in vi

While Western society has been habituated to the complete cadence and with certain tonal progressions since Baroque times, Zuckerkandl strongly takes issue with the theory that habit plays a part in expectation. He makes clear that, "the dynamic qualities cannot arise from our getting habituated to music" (Zuckerkandl, Sense. 223). Even though dynamic quality may be inherent in the affective devices used in music, expectations and the resulting degree of affect experienced have changed over time. In Thomas Morley's "Goe From My Window" (Ex. 12), for instance, the
Ex. 12 Goe From My Window, Morley
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e j- L_ F ITT^-^ ^ nr-p-

ambiguity in tonality sounds unusual, and therefore affective to the present-day ears. In the 16th century, however, this scalar pattern may have been quite ordinary, and therefore less affective.
Just as the tonic attracts other tones of the scale, so the visual center attracts other points on a plane. This attraction, however, is not absolute. There are other points which exert pressure. Arnheim has demonstrated with disks placed in various locations, to show the tensions pulling the disk. He explains the slightly off center disk (fig. 8a) that, "There is something restless about it. It looks as though it had been at the center and wished to return, or as though it wants to move away even farther" (Arnheim, Art. 11). In Fig. 8b, the disk is even farther off center, and:
may be seen as drawn toward the contour to the right
____We can find a distance at which the disk looks
"too close", possessed by the urge to withdraw from the boundary. For any spatial relation between objects there is a "correct" distance, established by the eye intuitively" (Arnheim, Art. 12).

Fig. 9 Michelangelo, Creation of Adam. Sistine Ceiling, Vatican, Rome.

The boundaries, center, and vertical, horizontal and diagonal vectors all influence the disk; any point on these lines creates varying degrees of stability, the center carrying the greatest pull, and therefore the greatest stability. The corners, however, contain somewhat less stability than the center. "No pull in any one direction is felt when pulls from all directions balance one another" (Arnheim, Art. 16). Although the center is the most balanced position, other points of lesser balance occur along diagonals. "The point of balance seems to lie somewhat closer to the comer of the square than to the center," says Arnheim, but balance is achieved when opposite forces are equal (Arnheim, Alt, 14).
Stability in a painting is greatest in the center. In The Creation of Adam, (fig. 9), Michaelangelo has used oblique lines in the figures of both God and Adam. As powerful as the figures are, however, the placement of the hands in the center tend to focus the meaning on the act of the creation.
How much of the perception of circles and squares is inborn and how much is due to training, is questioned by Gregory and Gombrich. They relate the problems Malawi girls had in setting a

rectangular table. They were raised in round homes and were unfamiliar with straight lines (Gregory, 180-81). There are, nevertheless, centric and eccentric forces which determine the dynamics of the circle. All lines projecting outward from the center create a strong centric force. The sunburst pattern, which is a completely centric system, projects force outward equally in all directions, but a frame enclosing it will counteract that force (fig. 10a and fig. 10b).
The tondo, or oval, form emphasizes the center so strongly that anything placed in the center appears important, overpowering any other factors. Framing a tondo form makes the center even more dominant. Gombrich states that, "The richer the elements of
the frame, the more the centre will gain in dignity___The frame,
or the border, delimits the field of force, with its gradients of meaning increasing towards the centre" (Gombrich, 156-57). Even without an ornate frame, however, the edge of a painting still produces eccentric force by enclosing it, as illustrated in Michelangelo's Qoni Madonna (fig. 11).
The center of a tondo is the most stable, restful location.
When the figures are placed off center, "they gain in dramatic timeliness" (Arnheim, Power. 85). In the Doni Madonna, however, the heads are placed at the top of the painting. Arnheim observes

Fig. 11 Michelangelo. Doni Madonna. Uffizi Gallery, Florence.

that, "The central base is the mother's womb, from which the story arose," intensifying the image of family (Arnheim, Power. 85). The tension is also enhanced by the diagonal arms, one of which cuts across the Virgin's neck, as well as by the crowding together of the heads.
The elliptical form has the same centric and eccentric forces as the tondo, but to a lesser degree. Arnheim claims that "the oval pays with a loss of centric symmetry for an increase in tension," and that there is ambiguity between roundness and extension (Arnheim, Power. 89). The ellipse can be seen as two overlapping circles and, as such, can have two focal centers. Arnheim warns, however, that two centers appear clearly only when the circles are in the horizontal configuration. "In the vertical, the symmetry is overlaid by the hierarchic difference between above and below" (Arnheim, Power. 92).
Since the mind gravitates to the simplest, most direct line in order to maintain the continuity, anything which obstructs flow will create tension. According to Meyer's definition of the law of affect, "Emotion is evoked when a tendency to respond is

inhibited" (Meyer, 22). On the other hand, "In any medium," according to Gombrich, "change can become so frequent and abrupt that it leads to an overloading of the system, an impression of confusion or at least of restlessness, while the right dosage of continuity and change makes for ease of perception experienced as clarity" (Gombrich, 296).
A melodic line can be obstructed by a sudden change of register, volume, or style. In Beethoven's Appassionata Sonata (Ex.13) and in Chopin's Scherzo in Bb minor (Ex. 14), all three
Ex. 13 Sonata Op. 57. Beethoven
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Ex. 14 Scherzo in Bb minor, Chopin

types of changes are used by the composers. By proceeding from the descending pianissimo pattern to the fortissimo F major inversions in the Beethoven and from the middle sotto voce pattern to the low-high fortissimo in the Chopin, both composers generate considerable tension.
In art, obstructions can take the form of an abrupt change or interruptions of a line, or amputation. Degas made frequent use of amputation in his ballet paintings by slicing off figures at the edges, giving the impression that the action was continuing outside the frames. One example of this technique is utilized in the painting, The Rehearsal (fig. 12).
"Occlusion," says Amheim, "always creates visual tension. We sense the occluded figure's striving to free itself from the interference with its integrity. When tension is undesirable, occlusions are avoided" (Amheim, Art. 252). A very pronounced example of occlusion, as well as changes of direction is in Henri Gaudier-Brzeska's Crouching Figure (fig. 13). The contorted lines are interrupted and bisected, creating tension at every twist and turn.

Fig. 12 Edgar Degas, The Rehearsal. The Frick Collection, New York.
Fig. 13 Henri Gaudier-Brzeska, Crouchine Figure. Walker Arts Center, Minneapolis.

The psychological need for order and simplicity implies a desire for clarity. Anything which gives rise to uncertainty, therefore, will create tension. A number of different devices are used to develop anxiety, which can be either momentary or of longer duration. As previously pointed out, tones of the scale have a strong tendency to resolve in a specific manner. In the following three versions of "Mary Had A Little Lamb" (Ex. 15a, b and c), it becomes very apparent that ambiguity can have a strong effect on tension.
Ex. 15-a

Ex. 15-b

Ex. 15-c


In example 15a, there is an almost total absence of tension. The piece begins strongly centered on the tonic, with repeated notes on C, which reaffirms the tonality of C. In addition, the melodic line moves only stepwise and does not escape beyond the first three tones of the C scale.
In 15b, the original version creates a small amount of ambiguity by starting on the third tone, which is not as stable as the tonic, but it immediately descends to the tonic. The leap of a third creates only the smallest amount of tension.
In 15c, there is considerably more ambiguity. After the first two notes, this could be in any of a number of keys. We suspect it is in the key of Eb or C, but this is not borne out when we hear the E natural. We also know that it is not A minor, as the 7th tone, G, resolves downward instead of upward into A. Likewise, D minor and F major and harmonic minor are eliminated because the melody would turn on tone two of the D minor scale, and it places F on a weak beat. Therefore, excluding the possibility of modes, only when we hear the C do we know for certain that the key is C. This uncertainty is clearly what creates the tension in the tune.

Expressive melodies frequently begin on tones other than the tonic. This technique can be further enhanced by avoiding the tonic as long as possible, creating uncertainty as to the identity of the tonic tone. The second theme of the first movement of Chopin's Piano Concerto #1 in E minor (Ex. 16) begins on G#, the 3rd scale tone, which is not as stable as the tonic tone. The melody progresses up the scale and, changing to faster eighth notes, passes through the tonic and continues to the G# before reversing itself. Even on the descent, with occasional changing
Ex. 16 Concerto No. 1 in E minor, Chopin
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A H V ^ 1 m P 9
9 r , J r
mj -J-* o
0 Uh T- 1 -1- - rir -=- 1
A 1 Ppm ~ i 9 p j 1
m r m 1
m-ji -W J- i-S LI

directions, it again quickly overshoots the tonic E and stops on D#, the most unstable 7 th tone. The effect of the ambiguity is further enhanced by the fact that the melody consistently avoids the root of every chord.
In the Scriabin Prelude, Op. 13 No3 (Ex. 17), the melody creates affect when it avoids the tonic G, electing instead to descend from the D down to the A, the 2nd tone of the scale. The melody then ascends stepwise to the B. The 2nd tone of the scale has a natural tendency to resolve down to tone 1. A leap, however, is normally expected to resolve stepwise in the opposite direction. By following the latter rule, Scriabin again avoids the tonic G. The only appearance of the tonic G appears on the weak second beat, which reduces its effect.
Ex. 17 Prelude, Op. 13, No. 3, Scriabin
9 j 0 1 f r f Ir J 1 p-'-f r
SN rr ' J =M= | +=?=-? , -p 1
[-T-p= d -1 J

Ambiguity creates tension in fine art just as it does in music. The most obvious example of ambiguity in art is in the contrapposto pose, in which the head and body are turned in different directions. This device was commonly used during the High Renaissance and Baroque periods to develop tension. Michelangelo's The Prophet Isaiah (fig. 14), utilizes this technique of opposing directional forces by turning the arms in the opposite direction from the head and legs. The sense of tension derives from the direction of the action pulling away from the mass.
The extrapolation from past experiences and interpolation, which is the filling-in of what is missing, allows a person to maintain continuity. According to Gombrich, "Discontinuity may arouse us and give us a jolt when it clashes with our forward
matching_____But it may also cause us to fill in from our
imagination what we have come to expect" (Gombrich, 108). For example, the mind fills in the missing note (Ex. 18a) and continues the ascending scale. The Law of Simplicity, which states that, "any stimulus pattern tends to be seen in such a way that the resulting structure is as simple as the given conditions permit", dictates that the straight line is the simplest, and therefore the expected form

Fig. 14 Michelangelo, Prophet Isaiah. Sistine Ceiling, Vatican, Rome.
Ex. 18-a

(Arnheim, Art. 63). Any gap appears as a deviation. This would be true, however, only if the notes or objects are sufficiently close together so that they can be perceived as a whole. It can be seen (Ex. 18b) that if there is too much separation, they are perceived as separate entities and no fill-in occurs.
The direction and shape a melody forms can also affect the degree of tension. The octave scale (Ex. 19a) is the most direct path, with the least possible tension. The only tension produced is from the ascending line. In the next example (Ex. 19b), the additional tension is caused by the rhythmic variation. The ambiguity is caused by the uncertainty as to when the melody will recommence. In the third example (Ex. 19c), the leaps create a slight disturbance, which creates tension. Zuckerkandl explains that "In a way, stepwise motion can be considered normal motion, in the sense that it involves the least effort in the move from tone to tone; while every skip goes beyond the norm in that it expresses a greater effort by taking us to a more distant tone more rapidly than the normal succession of intervening steps would permit" (Zuckerkandl, Sense. 65). Finally, in the pattern in Ex. 19d, uncertainty relates to a sense of musical direction.
Ex. 19-a Ex. 19-b Ex. 19-c Ex. 19-d

When contrasting patterns are separated by more than one or two notes, the urge to fill in is diminished. The jolt felt in disjunct motion increases with the degree of the contrast.
Compare the Chopin Mazurka (Ex. 20) with the Brahms Intermezzo (Ex. 21). In the Chopin, the only tension in the first two measures
Ex. 20 Mazurka 5 in Bb major, Chopin
11 -f P =~T -} jfp-z-p 1
ta- i~. m tr
Ex. 21 Intermezzo Op. 118 No. 2, Brahms
4 FT 4- -U-l -FT,
=*F|^=i ZM m 0 iEM=, t|H *t_= Hrr-t r r *

is caused by the ascent of the scale and by the leap of a sixth in the fourth measure. Consider how much more affect is created by the leap of a seventh in the second measure of the Brahms Intermezzo (Ex. 21). The expectation here would be for the B, the 2nd scale degree, to resolve downward to the tonic A. The movement upward of a 7th to the A is unexpected, and the wide gap itself is affective.
A continuing disjunct pattern, such as in Beethoven's Sonata No. 5 in C minor (Ex. 22), creates a reaction similar to that of a zigzag line in art. The complexity of the series requires constant readjustment of the sense of direction, increasing the tension dramatically. In art (fig. 15a, b, and c), the greater the compression of zigzags, the greater will be the affect.
Again, there is a significant correlation between music and art in the effect of gaps, or disjunct lines. Since a straight line is simpler than one with gaps, a gap will create tension in art. "It is the break in visual continuities," according to Gombrich, "which is noticed most easily" (Gombrich, 100). According to Amheim, "If movement is absent, the work is dead; none of the other virtues it may possess will make it speak to the beholder" (Arnheim, ArL. 434). It is the gap which stops the flow of motion and continuity.

Ex. 22 Sonata No. 5 in C minor, Beethoven
f>=! 1 i J J . t. L * r- ? ~n
=£=5= =2=91- d|r^=r^ ,i
Fig. 15

Whenever we see a gap, there is an urge to fill in what is missing in order to maintain the continuity. The urge to fill in is greatest in a strongly linear style.
Deviations which create tension in music include any device which diverges from the simplest, most expected course. One form of such deviation in music is diminution and augmentation as in the Bach's Canon I (Ex. 23) from The Art of the Fugue. The inverted augmentation at measure 5 and the diminution at measure 7 increase the complexity of the music, demanding greater attention and, therefore, increasing the tension.
Deviations from the scale may also create tension. Accidentals, which may appear foreign to the general line are in this category. The use of accidentals may occur in many ways. They can be used as a temporary dissonance, to modulate to another key, to ornament a passage, or to introduce a more exotic chord. In Chopin's Nocturne in Ab (Ex. 24) the Ab tonality is clearly established in the first two measures. The B natural in measure three, which is a is a member of an Ab diminished chord, then appears especially affective.

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