These notes discuss Chapters III & IV.
In the arguments that follow, Meyer will rely on several concepts arising from Gestalt psychology. Gestalt psychology was formulated prior to the First World War in Germany by Max Wertheimer, Kurt Koffka and Wolfgang Kohler. The Gestalt psychologists argued that perceptions do not arise from assembling simple elements of perception into a larger whole. The most striking aspect of perception, they argued, is that the whole is perceived before one is aware of the parts. Overall patterns appear to have primacy in perception. Gestaltists identified a number of principles ("Gestalt laws") that are presumed to govern the formation of perceptual wholes.
In contrast to the behaviorists, the Gestaltists placed much less emphasis on the role of learning in perception. However, throughout Chapter II, Meyer has proposed that expectations are learned. On pages 83-84, Meyer endeavors to distance himself from those aspects of Gestalt psychology that down-play the importance of learning:
"For Gestalt theory in reacting against the sensationist concept of perception and the association theory of learning leaned too far in another direction. It attributed almost all grouping to the "spontaneous" organization of simple shapes" and tended to minimize or deny the role of learning in the perception and organization of figures. Since the present analysis of expectation has continually stressed the importance of learning in the selection and organization of sense data, it is necessary to emphasize that it is employing Gestalt terminology and utilizing the data supplied by its experiments but that it is not adopting its theoretical explanation of perception. ... Hebb examines the Gestalt theory of learning in some detail and advances convincing evidence of its shortcomings." [p.84]
Of the many Gestalt laws, Meyer makes use of the following:
""what has been called the law of return, the law that, other things being equal, it is better to return to the starting point whatsoever, than not to return."" "... the term "return" need not be taken literally; that is, the opening materials may indicate what the final tone of a piece is to be without explicitly presenting it in the opening moments." [p.151]
Music that conforms to the Gestalt principles may be considered better organized. But one should not assume that this makes the music better. It is the deviations from a sort of ideal Gestalt structure that allows expectations to be aroused and manipulated. As Meyer notes, "the better the psychological organization, the less likely is it that expectation will be aroused." [p.87]
"Although the psychological organization is always as good as possible, this does not stipulate that the organization is always as good as the mind would wish. It is this dissatisfaction with the psychological organization which gives rise to expectation and perception of deviation." [p.91]Continuing his cognitivist theme:
"Without thought and memory there could be no musical experience."At first, Peretz's patient "IR" might be regarded as a counter-example. A listener without any musical memory, who nevertheless enjoys music. But IR might continue to have moment-to-moment schematic expectations, without having any long-term veridical expectations.
"Problem solving and the aesthetic process are essentially one and the same thing except for this proviso: that in aesthetic thinking, the relationship between strucutral troubles and their resolutions are intelligible and resolvable. ... Alternatively a confused and doubtful situation resulting in a generalized expectation of clarification, will give rise to feelings of suspense and affective responses." [p.88]
Meyer spends a considerable part of Chapter III discussing the psychology of rhythm and meter. On pages 106-107, Meyer provides a useful description of Woodrow's early research:
"These conclusions were confirmed by the studies of Woodrow who found that when time intervals are equal and every second sound is accented, the rhythm will appear to be trochaic. If intervals are equal and every third sound is accented, the rhythm will appear as a dactyl. Thus the trochee and dactyl may be grouped together [p.106; continuing p. 107] in the sense that both are primarily products of intensity differences rather than durational differences.
"Just the opposite is the case with iambic and anapestic rhythms. they are basically products of duration differences. If we start with a trochaic rhythm and gradually increase the interval after the louder sound, we arrive at an imabic rhythm. similarly if we begin with a dactylic rhythm and gradually lengthen the interval after the louder sound, the rhythm tends to become an anapest. thus the greater the relative duration of one tone or beat of a group, the greater the tendency for it to complete the group; while the greater the relative intensity of a beat, the greater the tendency for it to begin the rhythmic group. In other words, durational differences tend to result in "end-accented rhythms," and intensity differences tend to result in "beginning-accented rhythms."
"This analysis explains why trochaic rhythms do not easily arise in triple meter. for the two-unit trochaic rhythm ( _ u) can arise in a three-beat meter meter only if one of the rhythmic units is two beats long (2,4). And the difficulty with this pattern lies in the fact that such temporally differentiated groups tend to become end-accented. The only way in which such a normally end-accented pattern cann become trochaic (beginning accented) is to place a strong stress upon the accent so that intensity differences outweigh, as it were, durational ones." [pp.106-107]
"Meter is a product of the division of a given time span into parts of equal duration but unequal accentuation. ... The same metric unit may be the basis for various different rhythms. In other words, although the relationship of unaccented to accented beat is not fixed, there must be accent and release if there is to be meter at all. what is fixed about metric organization is the number of beats, not their disposition." [p.115]In my view, the reason why meter differs from rhythm is that they have different cognitive origins.
"The rise of tonal harmony, necessitating a coincidence in the vertical organization of texture, the emergence of the homophonic style, and the icnreasing importance of dance style music with its emphasis on motor patterns, all made for the predominance of what we have called the primary metric level." [p.117]Meyer discusses hemiola:
The disturbance of the metric organization not only acts as an intensification it also acts to recondition the metric scheme present throughout the movement. It makes the meter seem fresh and new when it once again moves with its usual regularity. This process of reconditioning [like dishabituation?] is particularly common where triple meter is used because, since triple meter does not generally admit of secondary [p.118; continuing p.119] accents, it tends to become more tiresome and singsongy than meters which are or can be easily compounded." [pp.118-119]
By the end of this chapter, I am left wondering how all of Meyer's observations relate to the Gestalt law of good continuation.
Chapter IV introduces some of Meyer's most important concepts, including the idea of gap fill. The chapter is entitled Principles of Pattern Perception: Completion and Closure and this highlights Meyer's emphasis on how patterns become completed. Completenss, for Meyer, is a basic psychological need:
"... incompleteness gives rise to expectations of completeness"
"Our opinion or feeling as to the completeness of a given stimulus is a product of the natural modes of mental organization." [p.128]
Meyer distinguishes two types of incompletion:
"Two types of incompleteness can be distinguished: (1) those which arise in the course of the pattern because something was left out or skipped over; and (2) those in which the figure, complete so far as it goes, simply is not felt to have reached a satisfactory conclusion, is not finished. The first type of incompleteness may be said to be a product of a "structural gap," the second type, a product of a delay in the need and desire for "closure." [p.130]Meyer likes abstraction:
"it would appear reasonable to consider the law of completion of a corollary of the law of continuation, since all incompleteness is, in some sense, a lack of good continuation" [p.129]
"For completion is not simply cessation -- silence. It involves conclusion .." [p.129]
"A structural gap occurs were something is felt to be left out."
"... the term "gap" implies the possibility of subsequent completion." [p.130]
"It should be noted that though this is not properly speaking an instance of a structural gap, it is an example of a lack of closure." [p.131]
Closure is culturally defined:
"In the music of a culture the tonal materials given in the style system establish a norm of melodic completeness. ... When the practiced or cultivated listener becomes aware that one of these steps has been passed over (left out) he expects, albeit unconsciously, that the missing tone will be forthcoming later in the series. He expects, in short, that the structural gaps created by such a skip will eventually be filled in." [p.131]
Meyer quotes Henry Watt:
""To pass over a note immediately creates a desire for it, and it then becomes a fit note to bear the climax." ... Watt found that the larger the interval (the larger the skip), the more likely that it will be followed by contrary motion (motion which will fill in the tones passed over). He also notes that [p. 131; continuing p. 132] the studies of Turkish music made by Hornbostel and Abraham and the study of Swedish folk tunes made by Fox Strangways reveal similar tendencies. In their article on "Muhammedan Music" in .I "Groves Dictionary," Lachmann and Strangway note that "after a third, return is usually made to one of the notes which have been leapt over."* In our own culture the rule of counterpoint which states that after a skip the melody should move by stepwise motion in the opposite direction is imply an application of the law of completion to a particular practice.*[cites Jeppesen]" [p.132]
Skip size is contextual:
"an intervallic distance which would constitute a skip or gap in one system might not be one in another system." [p.132]
Meyer implies that closure arises from filling-in the gap:
"... in the direction of closure, toward the elimination of gaps in their structure." [p.132]
Meyer quotes Winthrop Sargeant from "Types of Quechua melody," .I "Musical Quarterly," Vol. 20 (1934) p.239:
""It has no doubt been noted ... that the Quechua musician often fills up one of the minor triads of his pentatonic scale with an extra tone which he uses in an ornamented capacity -- usually as a passing tone between two or more important melodic notes. . . . Often a kena-player will take a well-known pure pentatonic melody and ornament it .I "ad libitum" with these extra tones."" [p.133]
Meyer also suggests that the development of scales in different cultures moves toward equidistant intervals. This is also explained by the filling-in of structural gaps:
"Thus the tendency toward equal temperament and the propensity to add new tones to a scale with unequal distances both seem, from this point of view, to be products of a more general psychological need for structural completeness -- for the elimination of structural gaps not only in the melodic line of the individual piece but also in the tonal system itself." [p.134]
Here is a summary statement of the aesthetic/affective claims:
"A structural gap, then, creates a tendency toward "fillin in." And if this tendency is delayed, if the completion of the pattern is blocked, affect or the objectification of meaning will probably follow." [p.134]
Meyer introduces the idea of "saturation:"
"The principal of saturation ... A figure which is repeated over and over again arouses a strong expectation of change both because continuation is inhibited and because the figure is not allowed to reach completion."
"... the arousal of expectation through saturation" [p.135]
"Koffka observes that there is an intimate relationship between saturation and emotion" [p.136]
"It is necessary once again to emphasize the importance of context upon these processes. A repeated pattern at the end of a work need not give rise to saturation, since at this point the listener understands, or thinks he understands, the significance of the repetition: that is, because this is the end of the piece, lack of forward motion, a composed fermata, is expected and desirable." [p.136]
Meyer links these conceptions with tonality. In effect, the gap-fill concept is essential to articulate a scale, and establish the tonality of a work, which Meyer claims is the most important facet of style:
"One of the most powerful and persuasive forces conditioning and controlling the sense of completeness which a melody pattern gives is the tonal organization or the scale of the culture." [p.138]
"Tonality is probably the most important facet of style, the .I "sine qua non" of even the most primitive musical organization." [p.138]
"The listener's sense of closure and finality can, as Farnsworth has shown, be altered through training.* W.V. Bingham* has shown that opinions as to the finality of a series of tones can be influenced by information stipulating the number of tones to be heard in the series. If, for instance, listeners were told that the fifth tone in a series was to be the last, it appeared to possess a finality which it did not as a rule have otherwise. This furnishes experimental evidence, if any was needed, for the statement that what we know, either becuase we have been told or have learned through practice and experience, influences our judgment of what we perceive and hence our feeling of completeness and our expectation based upon that feeling." [p.138]
Arthur Bissell (1921) had already proposed that pitch height within the melodic range influences direction of the subsequent pitch.
""The direction of expectation, whether to a tone below the first tone of a melody or above it, depends largely on the absolute pitch of the latter. In general, the lower this is the less will the melody be expected to descend on the next following tone; while correspondingly the higher it is the less will the melody be expected to rise on the next tone."* [Arthur D. Bissell, .I "The Role of Expectation in Music." New Haven: Yale University Press, 1921; p. 19] Actually, the situation is somewhat more complicated than this. For our expectations depend on our awareness of potential range as well. That is, a tone which would be "high" for one voice or instrument, and would consequently be expected to descend, might be low for another voice or instrument and would consequently be expected to rise." [p.139]
"Melodicaly speaking, relaxation is associated with the decline in tension which is effected when pitches are lower -- when a progression descends at its close.* Curiously enough, however, the lowering of the dynamic level, which is also a normal concomitant of relaxation, does not necessarily accompany closure." [p.139]
Some testable hypotheses:
"fast tempi, loud dynamics, and high ranges (but not necessarily ascending melodic lines) are usually together, while slow tempi, soft dynamics, and low ranges are also usually together." [p.139]
Given Meyer's theoretical claims, my question is: Why doesn't rhythm have gap fill? That is, why wouldn't (8 16 16) imply (16 16 16 16)?
"A feeling of harmonic completeness arises when the music returns to the harmonic base from which it began or moves to one which in some way was implicit in the opening materials." [p.150]