The Kappa Effect in Pitch/Time Context Dissertation

THE KAPPA EFFECT IN PITCH/TIME CONTEXT

DISSERTATION

Presented in Partial Fulfillment of the Requirements for

the degree Doctor of Philosophy in the Graduate

School of The Ohio State University

Noah MacKenzie, M.A.

*****

The Ohio State University

2007

Dissertation Committee:

Professor Mari Jones, Adviser

Professor Mark Pitt Approved by

Professor James Todd

Adviser Psychology Graduate Program

ABSTRACT

The kappa effect, an effect of spatial extent on the perception of time, is, relatively speaking, poorly understood, especially in the auditory domain. Five experiments demonstrate the kappa effect in the auditory domain by instructing listeners to judge the timing of a tone (Tone X) in relation to a tone immediately preceding it

(Tone A) and immediately following it (Tone B). These three tones, together, are referred to as a kappa cell. Experiments 3, 4, and 5 illustrate how the serial context of kappa judgments can influence the strength of the effect. Experiment 1 served as a control experiment to demonstrate the effectiveness of the independent variables. Experiment 2 replicated Shigeno (1986), perhaps the clearest presentation to date of the auditory kappa effect, yet used pitch (frequency on a logarithmic scale) rather than frequency (on a linear scale) as an independent variable. Experiment 3 added a three-tone serial context to the kappa cell. Experiment 4 added a serial context to the kappa cell that strongly conflicted with its pitch trajectory. Experiment 5 examined kappa cells with larger pitch motion (or change in pitch per unit time). Results are discussed in terms of auditory motion and the assumption of constant velocity.

Dedicated to my wife.

iii

ACKNOWLEDGMENTS

I wish to thank my adviser, Mari Riess Jones, for her support and patience during my graduate school career. Thanks to Heather Moynihan Johnston, Ralph Barnes, and

Jennifer Puente for unwavering and tenacious belief. Thanks to Doug Reeder; without him there is no data analysis.

Thank you to my mother, who instilled in me a love of learning. Finally, thank you to my wife who has been a constant source of love, encouragement, and comfort throughout this experience.

VITA

May 2, 1975 ...... Born – Anchorage, AK

1997 ...... B.A. Psychology, Penn State University

2000 ...... M.A. Psychology, The Ohio State

University

2001 – 2005 ...... Graduate Teaching and Research Associate,

The Ohio State University

2005 – Present ...... Lecturer, University of Wisconsin

PUBLICATIONS

1. Jones, M.R., Moynihan, H., MacKenzie, N., & Puente, J.K. (2002). Stimulus- driven attending in dynamic arrays. Psychological Science, 13(4), 313-319.

2. Jones, M. R., Barnes, R., Brunetti, R., Ellis, R., Johnston, H., Large, E. et al.

(2006). News from the roar lab at the Ohio State University. Cognitive Processing, 7(1),

60-64.

FIELDS OF STUDY

Major Field: Psychology

TABLE OF CONTENTS

Page

Abstract ...... ii

Dedication ...... iii

Acknowledgments ...... iv

Vita ...... v

List of Tables ...... viii

List of Figures ...... ix

Chapters:

1 Time and (pitch) space revisited ...... 1

2 Baseline studies...... 25

3 Replication of kappa studies...... 38

4 Kappa in serial context...... 51

5 Kappa with opposing serial context...... 71

6 Kappa cells with greater pitch motion ...... 81

7 General discussion ...... 104

List of References ...... 115

vii

LIST OF TABLES

Table Page

1 Possible pitch values for Tone X in Experiment 1 by Pitch Direction

condition………………………………...... 42

2 Possible pitch values for Tone X in Experiment 5...... 85

viii

LIST OF FIGURES

Figure Page

1 Schematics of patterns used in Experiment 1a (panel a) and Experiment

1b (panel b) sequences...... 29

2 p(B) as a function of X Time in Experiment 1a...... 32

3 p(B) scores as a function of the X Time variable in Experiment 1b...... 34

4 Mean p(B) scores in Experiment 1, as a function of X Time and Context,

Present (Experiment 1b) or Absent (Experiment 1a)...... 36

5 Schematic of an Up sequence in Experiment 2...... 41

6 p(B) responses as a function of the pitch distance of Tone X from Tone

A for Experiment 2...... 45

7 PC scores as a function of the X Time variable in Experiment 2...... 46

8 PC as a function of the temporal distance (ms) and pitch distance (ST) of

Tone X from Tone A for Experiment 2...... 47

9 PSE scores as a function of X Pitch in Experiment 2...... 48

10 Schematic of a sequence with Serial Context = 0 in Experiment 3...... 53

11 p(B) responses as a function of X Pitch for Experiment 3...... 57

12 A significant interaction of X Pitch and Serial Context on p(B) in

Experiment 3...... 58

13 Interaction of X Time and X Pitch in Experiment 3...... 60

ix 14 PC scores as a function of the X Time variable in Experiment 3...... 61

15 PC as a function of X Pitch in Experiment 3...... 62

16 PC as a function of the temporal distance (ms) and pitch distance (ST) of

Tone X from Tone A for Experiment 3...... 63

17a PC as a function of the temporal distance (ms) and pitch distance (ST) of

Tone X from Tone A for Experiment 3 (where SC=0)...... 64

17b PC as a function of the temporal distance (ms) and pitch distance (ST) of

Tone X from Tone A for Experiment 3 (where SC=4)...... 65

17c PC as a function of the temporal distance (ms) and pitch distance (ST) of

Tone X from Tone A for Experiment 3 (where SC=8)...... 66

18 PSE scores as a function of X Pitch in Experiment 3...... 68

19 Schematic of a sequence in Experiment 4...... 72

20 Effect of X Time on p(B) judgments in Experiment 4...... 76

21 Null effect of X Pitch on p(B) judgments in Experiment 4. The SC 4

condition from Experiment 3 is plotted for comparison...... 77

22 p(B) scores as a function of the X Time variable in Experiment 1b...... 88

23 p(B) responses as a function of X Pitch for Experiment 5...... 89

24 p(B) responses as a function of Serial Context for Experiment 5...... 91

25 Interaction of X Time and X Pitch in Experiment 5...... 92

26 Effect (ns) of X Pitch and Serial Context on p(B) in Experiment 5...... 93

27 p(B) judgments as a function of X Pitch for the combined SC0 conditions

of Experiments 3 & 5. Larger values for X Pitch (x-axis) indicate greater

distances (in semitones) of Tone X from Tone A...... 96

x 28 p(B) judgments as a function of X Pitch and Kappa Cell conditions for

SC0 patterns. No kappa effect is present for the KC4 condition

(Experiment 3) while a kappa effect is present in the KC8 condition

(Experiment 5)...... 97

29 p(B) judgments as a function of X Time and Kappa Cell condition for

SC0 patterns...... 98

30 Significant effect of X Pitch on p(B) scores from the SC0 condition of

Experiment 5...... 100

31 Significant interaction of X Time and X Pitch for the SC0 condition of

Experiment 5...... 101

32 PSE scores as a function of X Pitch in Experiment 5...... 102

CHAPTER 1

TIME AND (PITCH) SPACE REVISTED

Introduction

Literature on the construct known as the space-time continuum has traditionally been the domain of modern physics, mainly in terms of the relativity theory of Albert

Einstein (1920). According to relativity theory, as the velocity of an object increases

(relative to a stationary observer), the object will appear to undergo transformations both in spatial extent and in temporal extent. Relativity theory has, of course, been borne out in an ever-increasing number of experiments throughout the last century of research in physics. Space and time are now mainly seen as inseparable aspects of one underlying dimension, space-time. (Following a distinction proposed by Garner (1970), they may also be conceived as integral, a point returned to later).

The phenomenon of motion is crucial to any description of relativity theory. As an object moves through space-time, its properties of motion may to some degree determine the way that the object is perceived. Although controversial, some have reported that the motion of an object itself gives rise to distortions in the perception of that object from the perspective of an observer occupying a different frame of reference (e.g., Caelli,

Flanagan, & Green, 1982).

The experiments detailed herein raise the issue of whether relativity theory could inform psychology in certain ways. There is a small but significant body of research

1 suggesting that something akin to psychological relativity exists. Psychological relativity can be thought of as the effect of space on temporal perception (or conversely, the effect of time on spatial perception). The goal of this dissertation is to describe how the auditory kappa effect, arguably a kind of manifestation of psychological relativity, could be modified by changing the motion-like properties of auditory events.

Psychological Relativity: Tau and Kappa

Perhaps the first to demonstrate psychological relativity was Benussi (1913).

Benussi showed that judgments of spatial distances could depend on the time scales in which those distances are presented. In this experiment, subjects were presented with three successive flashes of light that defined two spatial distances (and concomitantly two temporal intervals). Subjects were asked to judge which of the two spatial distances was larger. Benussi found that viewers’ judgments of the two spatial distances changed as a function of the temporal intervals formed by the lights.

Helson and King (1931) extended these findings into the tactile domain. Here, three points on a subject’s skin were stimulated in succession. If the time interval between the second and third points was longer than the time interval between the first and second points, the subject reliably reported that the spatial distance between the second and third points was greater than the spatial distance between the first and second points, although actually the reverse may have been true. Continuing the analogy with relativity theory, subjects appeared to respond to changes in spacetime, that is, to changes in the ratio of distance:time, or d:t. In other words, the temporal extent of stimuli reliably effected a change in the perception of spatial extent, suggesting a dependency such that

2 longer temporal intervals were perceived as taking place over “longer” spatial distances.

Helson and King dubbed this phenomenon, in which longer time intervals appear to take place over larger spatial distances, the tau effect.

Abe (1935) used stimuli similar to Benussi’s; three successive flashes of light demarcated two spatial and temporal intervals. Here, however, spatial extent was the independent variable, with viewers’ judgments of temporal extent functioning as the dependent variable. Viewers were instructed to judge which of the two spatial intervals appeared to happen “more quickly”, that is, appeared to take place over a smaller temporal interval. Abe found that a longer temporal interval could be made to appear shorter be decreasing the spatial distance between successive flashes, and vice versa; that is, a shorter temporal interval could be made to appear longer by increasing the spatial distance between successive flashes.

Cohen, Hansel and Sylvester (1953) replicated Abe’s work and were the first to name this new phenomenon, calling it the kappa effect. The kappa effect refers to the effect of spatial extent on the perception of time. In Cohen et al.’s experiment, subjects sat in a darkened room and saw three successive flashes of light presented at horizontally displaced spatial locations. The subject was asked to adjust the timing of the middle light so that the time interval between the first and second lights appeared equal to the time interval between the second and third. In this research the independent variable of spatial distance was of special interest; the experimenters orthogonally varied the distance between the first and second lights and the distance between the second and third lights.

Cohen et al. found that subjects, when instructed to equalize the two time intervals, adjusted the timing of the middle light so that the time interval between two flashes that

3 were farther apart in space (than the other pair) was shorter than the time interval between the other two flashes. One may thus postulate that if three events separated in space occur successively, but separated by equal temporal intervals, that temporal interval bounded by events farther apart in space will seem longer. Thus, subjects adjusted the time interval between two flashes far apart in space to be shorter than necessary, in order to achieve perceived isochrony. In this task, the results imply that perceived displacements in space and time are positively correlated.

Cohen et al. (1954) examined tau and kappa in the auditory modality. In the tau experiments, subjects heard a sequence of three sine-tones of equal duration that delineated two temporal intervals. The first tone in a sequence was equally often 1, 2, 3, or 4 kHz, while the third (yoked) tone was 3, 4, 1, or 2 kHz, respectively. Subjects were required to adjust the frequency of the second tone so that it was “intermediate” in frequency between the first and the third tones. Cohen et al. found that a listener adjusted the frequency of the second tone such that tones closer together in time were made farther apart in frequency. In other words, listeners apparently heard the tones delineating the shorter of the two time intervals as closer together in frequency. Thus, to make the middle tone “intermediate” in frequency, they adjusted the frequency of the middle tone to be farther from the frequency of a tone that was temporally closer to it. (Importantly,

Christensen and Huang (1979) essentially replicated these data, confirming Cohen et al.’s findings 25 years later.)

In Cohen et al.’s kappa experiments, presented in the same (1954) paper, the procedure was essentially the same except that the observer adjusted the timing of the second tone so that the first time interval seemed equal to the second time interval. The

4 results suggested a slight tendency for time intervals to be influenced by the frequency separation of the events bounding them, although this effect was not statistically significant.

Shigeno (1986; 1993) has provided the clearest evidence, to date, for auditory kappa. In a series of experiments, Shigeno played listeners a series of patterns in AXB format. On every trial, tones A and B (that is, the first and third tones) were fixed in time and frequency; that is, both the length of time between A and B and the frequency separation between A and B were held constant over trials in a session. Tone A was fixed at 1000 Hz, while Tone B was fixed at 2500 Hz; in addition, these tones were separated from each other by an interstimulus interval (offset to onset) of 1 sec. The only element whose properties could vary from trial to trial was tone X.

The interstimulus intervals (ISIs) between the first and second and between the second and third tones were denoted as t1 and t2, respectively. The properties of tone X that varied from trial to trial involved its relative timing and its frequency. Thus, on any given trial, the time ratio t1/(t1+t2) was equally often .41, .44, .47, .50, .53, .56, or .59. In addition, tone X could vary in frequency, being equally often 1000, 1350, 1750, 2150, or

2500 Hz. Again the task required people to render a higher-order time judgment about the relationships among the three tone: Judge whether X is closer to tone A or to tone B.

Shigeno showed that tone X was significantly more often judged closer in time to tone A (or B) if it was closer in frequency to tone A (or B) (the kappa effect). In addition, tone X was more often judged closer in frequency to tone A (B) if it was closer in time to tone A (B) (the tau effect).

5 Crowder and Neath (1994) showed an analogous effect with three-tone melodies, where the notes in these melodies demarcated two temporal intervals. Subjects were asked to indicate whether the first or the second temporal interval was the longer of the two. Crowder and Neath found that tones were perceived as having greater separation in time if the pitch distance between them was large (6 semitones) than when it was small (1 semitone).

In effect, listeners more often judge that the auditory event X is closer in time to event A (B) if event X is closer in frequency to event A (B). This sort of finding has been termed a redundancy gain, a term proposed by Garner (1970). A redundancy gain is a facilitation in the performance of classification or identification tasks under certain stimulus conditions. For example, when a subject is instructed to judge the color saturation of a visual object, task-irrelevant variation of the brightness of that object influences performance on the saturation task (Garner & Felfoldy, 1970). When two perceptual dimensions interact with each other such that variations in one dimension affect judgments of the other, the dimensions are said to be integral. (Dimensions are separable if the dimensional structure of each is directly perceived, and variations in one dimension do not affect judgments of the other.) In situations like the ones described above, when the temporal interval between two tones was strongly, positively correlated with the frequency interval between those same tones, performance on this temporal task was increased. Thus, from this perspective space (vis a vis frequency distance) and time can be conceived as integral dimensions.

Melara and Marks (1990) have offered a slightly different perspective on multidimensional stimuli. They hypothesized that perceivers always have immediate

6 access to perceptual dimensions; that is, perceivers are always able to access individual attributes of the stimuli (e.g., an auditory sequence’s pitch or temporal structure). With integral dimensions, however, extraction of attributes along one dimension (e.g., temporal structure) must necessarily occur within the context of the other dimension

(e.g., pitch structure). With integral dimensions, context created by one dimension constrains the experience of attributes in the other dimension.

In a situation like the one described above, an auditory sequence’s pitch structure may contextually constrain the experience of its temporal structure. The attribute “timing of Tone X” has one perceptual meaning when paired with the attribute “closer to Tone A in pitch” but a different perceptual meaning when paired with a different attribute “closer to Tone B in pitch”. Context established by the pitch relationships between Tones A, X &

B “weights” the extraction of temporal information.

Melara and Marks (1990) refer to this as “stimulus-level processing”. Following this view, the kappa effect could result from the fact that listeners are unable to ignore the pitch attributes of Tone X when attempting to extract information about the temporal attributes of Tone X. This is because the pitch attributes of Tone X create perceptually different experiences of the timing of Tone X. Assuming the pitch and temporal attributes of Tone X are in fact integral, the listener is forced to consider Tone X as a unified stimulus whole, though they retain primary access to each dimension individually. This view is incomplete, however; context may interfere with or facilitate performance in a variety of ways, and there is no way in this view to specify why bigger pitch distances should be accompanied by perceptions of longer time spans.

7 Time Judgment

Broadly speaking, there exist two classes of psychological models that attempt to account for the results of temporal judgment tasks. The first of these, interval-timing models, attempt to explain an organism’s timing of isolated temporal intervals. A second category of models about time judgments includes dynamic attending models. This section reviews both within the context of understanding various influences on time judgments. Notably, however, neither class of model contains an explicit mechanism by which frequency (and/or pitch) information may influence temporal judgments.

Interval timing models, in general, focus upon the way people encode single isolated time intervals. One influential model in this category is given by Scalar

Expectancy Theory (SET) (Church, Meck, & Gibbon, 1984; Gibbon, 1977). SET has had some success in predicting an organism’s performance in duration discrimination tasks.

Of central concern in this modeling tradition are explanations about time discrimination in temporal judgment tasks and whether or not these conform to e.g., Weber’s Law. The origins of SET can be traced to Creelman (1962), who developed one of the first models to quantitatively predict performance in a duration discrimination task. In Creelman’s view, subjects will base their estimates of the length of a temporal interval on the number of “pulses” that accumulate during the interval. Both the mean number of pulses generated during a particular interval (of d ms) and the variance of the number of pulses is equal to λd, where λ represents the rate of pulse accumulation and d represents the length of the temporal interval.

Creelman’s model postulates a linear relationship between variance and interval duration (since variance is equal to interval duration multiplied by a constant, λ). This

8 implies that time judgments will not necessarily follow Weber’s Law. Getty (1975) challenged this view and hypothesized that the standard deviation of the psychometric density function obeys Weber’s law. In this view, both the mean number of pulses accumulated during an interval and the standard deviation of the number of pulses are proportional to stimulus duration.

Unlike Creelman’s approach, SET (Church, Meck, & Gibbon, 1984; Gibbon,

1977) is an interval timing model that can predict Weber’s Law for time judgments. That is, it predicts that the standard deviation of the number of pulses generated during an interval will be proportional to the interval duration. In its basic form (which was developed to account for timing behavior in animals), SET depends on reinforcement; an animal will “learn” the expected interval duration between food deliveries and store it in long-term memory. During any particular interval, the animal’s internal pacemaker generates pulses from the time of the last food delivery. These pulses accumulate in an

“accumulator”. At any moment, the number of pulses in the accumulator is compared (in a “comparator”) to the learned interval duration. If these two values are close enough, the animal makes a food response. Uniquely, however, SET claims that measures of behavior seem to adjust to proportions of temporal intervals rather than to their absolute values, a claim in line with the reliance on Weber’s law postulated by Getty (1975).

The notion of timing behavior as dependent on “pulses” is not limited to interval- timing models. The second class of models, dynamic attending models, conceive timing as linked to pulses, albeit in a considerably different fashion from interval-timing models.

Dynamic attending models address time judgments about isolated time intervals only as special cases of a larger, serial context. It postulates that graded pulses of attentional

9 energy become time-locked to this larger serial context, offered by some environmental situation or task.

Large and Jones (1999), in describing their dynamic attending model, claim that timing behavior is inherently oscillatory, in that timing involves an engagement (or

“entrainment”) of internal oscillatory periods with the time periods comprising an attended-to sequence. As distinct from the interval-timing view, in which “pulses” are ticks from some internal clock, the “pulses” of dynamic attending models correspond to foci of attentional energy at specific moments, where these pulses vary in location (i.e., timing) and width (i.e., specificity) as a function of temporal regularity; temporally regular sequences lead to the generation of more concentrated pulses of attentional energy at specific points in time.

The dynamic attending view predicts that a rhythmic sequence of events should allow listeners to “entrain” to this rhythm to the extent that judgments about the pitch and/or timing of an event will be affected by how close to the “beat” of the induction sequence the event occurs. Support for this prediction was found by Barnes and Jones

(2000), who showed that temporal intervals ending “on the beat”, given a prior induction sequence of tones, were more veridically judged.

In a task analogous, but not isomorphic, to those that are used in conjunction with tau research, Jones, Moynihan, MacKenzie, and Puente (2002) showed that the pitch of a tone was more veridically judged if that tone fell “on the beat”, given a prior, isochronous context sequence of tones, with decreasing accuracy the further “off the beat” the tone occurred. Thus, here, as in the classic tau literature, temporal relationships between

10 rhythmic events systematically influenced listener’s perception of the non-temporal (i.e., pitch) relationships between them.

Boundary Conditions: Time Scales and Populations

Difficulty of the Temporal Judgment

As noted previously, Cohen et al.’s (1953) experiment presented subjects with three successive flashes of light presented at horizontally displaced spatial locations.

They denoted, as T, the total time of the stimulus (i.e., the amount of time between the offset of the first flash and the onset of the third light flash). Cohen et al. found a kappa effect when T ranged from .6 s to 6.4 s. Within this window the kappa effect tended to decrease as T increased, though the kappa effect was present at all levels of T studied, a result in line with more contemporary examinations of visual kappa (e.g., Jones &

Huang, 1982). Shigeno (1986; 1993), perhaps unsurprisingly, found an auditory kappa effect using T values of 1200 ms.

However, to date, no systematic examination of the temporal boundary conditions of auditory kappa has been conducted. Huang and Jones (1982) evaluated the temporal boundary conditions for visual kappa. In one experiment, analogous to Cohen et al.’s

(1953) experiment, subjects were presented with three successive light flashes at different horizontally displaced locations. The first and third light flashes always subtended eight degrees of visual angle from a viewing distance of approximately one meter. The main variable of interest, T, or the amount of time between the first and third light flashes, functioned as a within-subjects variable, where T was equally often: 160, 320, 480, 640,

800, 1000, 1200, or 1500 ms. The ratio t1/T (where t1 denoted the time interval between

11 the first and second light flashes) was equally often: .3, .4, .5, .6, or .7 and functioned as an additional within-subjects variable. Finally, the ratio s1/S functioned as a third within- subjects variable, where s1 denoted the spatial separation between the first and second light flashes and S, which was fixed on every trial, denoted the spatial separation between the first and third light flashes, i.e., eight degrees of visual angle from a distance of one meter. The ratio s1/S was equally often: .3, .4, .5, .6, or .7.

Subjects judged whether the first or second temporal interval was shorter. At the smallest T values (160 and 320 ms) there was a large kappa effect for all values of t1/T; subjects apparently based their temporal judgments “almost entirely upon the spatial relationships” (p. 11). For intermediate values of T (480, 640, and 800 ms) subjects were more accurate in their judgments but still showed a kappa effect for all values of t1/T.

When T was 1000, 1200, or 1500 ms, however, subjects showed a kappa effect only for the most difficult judgments, that is, when t1/T equaled .4, .5, or .6). For the easiest temporal judgments, corresponding to the t1/T conditions of .3 and .7, the kappa effect was markedly decreased.

Huang and Jones conclude that the difficulty of the temporal judgment influenced the strength of the kappa effect. Specifically, as temporal judgments became more difficult, the kappa effect became more marked, i.e., viewers came to base their judgments more and more on only spatial information. In this study, temporal judgments could be made more difficult in one of two ways: by making the primary judgment more difficult (as with t1/T values of .4, .5, or .6) or by making T smaller. At the smallest T value, for example, there was virtually no effect of the t1/T variable, with subjects responding entirely on the basis of spatial information.

12 Converging evidence for the modulation of kappa by task difficulty is provided by

Parks (1968). In this experiment, subjects were again shown three light flashes displaced along the horizontal dimension. Half of all subjects saw the three light flashes presented successively (the successive condition), as in previous experiments (e.g., Cohen et al.,

1953; Huang & Jones, 1982). We may denote these flashes in order of presentation as flashes 1, 2, and 3. On a given trial, subjects were presented with flash 1, followed by flash 2, and finally with flash 3, which could assume one of three spatial distances from flash 2 (4, 8, or 16 in), and one of three temporal distances from flash 2 (290, 340, or 390 ms). Flash 1 and flash 2 were always separated by 10 in and 240 ms. These subjects were instructed to match the second temporal interval, 2-3 (the “test” interval) to the interval 1-

2 (the “standard” interval), which they did by using a control knob situated beneath the display (the control knob altered the timing of flash 3). These subjects displayed the classical kappa effect, making the test interval almost 93 ms longer than the standard, on average, in conditions where flash 3 was separated from flash 2 by 4 in, and making it 76 ms longer, on average, when they were separated by 8 in.

We may conclude from this and other studies (e.g., Huang & Jones, 1982) that the difficulty of the temporal judgment is a large factor in whether or not the kappa effect obtains. Jones and Huang (1982) claim that the strength of the kappa effect “depends in part on the salience of the context”. For the auditory kappa effect, this would mean that as temporal judgments are made more difficult, the context (frequency attributes of the to- be-judged events) becomes more salient. This equates to an effect of frequency information on judgments about time. For example, as the middle X tone comes closer in time to the midpoint of the temporal interval formed by the A and B tones in Shigeno’s

13 (1986) task, the frequency of the X tone becomes more salient. When it is difficult for subjects to judge to which of two tones (A or B) the X tone is closer in time, the frequency of the X tone strongly affects judgments about its timing, relative to situations in which this temporal judgment is easier.

Concerning the effect of “context” per se, this account of auditory kappa is similar to the one proposed by Melara and Marks (1990) who claim that extraction of attributes in one dimension (e.g., temporal information) must necessarily occur within the context created by the other dimension (e.g., pitch information). In this regard, the term context is taken to mean changes within a co-occuring context and it does not necessarily speak to the role of a larger serial context. With integral dimensions, context created by one dimension constrains the experience of attributes in the other dimension. Jones and

Huang (1982) propose additionally that the context created by pitch information becomes more salient as the difficulty of the temporal judgment increases.

Phenomenal Distance

The kappa effect appears to depend on phenomenal distance, rather than distance per se (Jones & Huang, 1982). Thus, Lebensfeld and Wapner (1968) examined the kappa effect with Müller-Lyer lines and found that the kappa effect increased for events connected with lines with outward fins (> <) relative to lines with inward fins (< >).

Although the objective length of the horizontal line segment remained unchanged, the phenomenal length did not; accordingly the phenomenal distance associated with the outward-fin lines appeared longer than phenomenal distance associated with the inward- fin lines. The greater this phenomenal distance, the greater the increase in the kappa

14 effect (i.e., more systematic distortion in temporal judgments due to greater perceived distance).

This raises an important issue for the kappa effect: is spatial extent as such necessary for the kappa effect, or might functional analogues (like auditory pitch distance) suffice? For auditory events, one can easily speak of “where” in a frequency continuum the event took place. We may use spatial descriptors to define a particular frequency (e.g., “high” or “low”). When making judgments of pitch, listeners have shown stimulus-response compatibility effects when using vertically arranged buttons (Walker

& Ehrenstein, 2000), indicating that pitch is at least to some degree treated as spatial.

Further, it has been argued in discussions of auditory “objecthood” that the role of auditory frequency for auditory stimuli is analogous to the role of visual space for visual stimuli (Belin & Zatorre, 2000; Jones, 1976; van Valkenburg & Kubovy, 2003; Woods et al. 2001). In this way, pitch distance may be conceived as a kind of phenomenal distance.

Absolute Pitch and Auditory Relativity

How robust is the auditory kappa effect? One may answer this question by examining a subset of listeners whose pitch perception is atypically precise, namely listeners with absolute pitch. Absolute pitch is defined as the ability to categorize musical pitches in the absence of an external reference. Listeners with absolute pitch often rely on this information to the exclusion of information about relative pitch, i.e., information about pitch relationships. It is unique in that there is no comparable phenomenon in the visual domain, and as such provides an opportunity to learn more about the strength of the auditory kappa effect; it might be that people with absolute pitch are relatively

15 insensitive to the kappa effect, since the auditory kappa effect depends on the ability of pitch to influence time judgments. Listeners perceiving pitch in this way (i.e., in a way different from the majority of listeners) may not be subject to the kappa effect; in other words, if kappa is usually seen in “normal” listeners, it might disappear for listeners with an atypical way of perceiving pitch.

Shigeno (1993) conducted the first evaluation of the auditory tau and kappa effects in people with absolute pitch. Shigeno, in a replication of the (1986) task described above, used the AXB paradigm and instructed subjects to judge whether the X tone was closer to the A or the B tone in pitch (tau experiment) or time (kappa experiment). The A tone was fixed at 880 Hz (A5), while the B tone was always 1760 Hz

(A6). In the octave condition, the X tone could equally often be: 990 Hz (B5), 1056 Hz

(C6), 1188 Hz (D6), 1254 Hz (D#6), 1320 Hz (E6), 1408 Hz (F6), or 1584 Hz (G6). In the whole-tone condition, the X tone varied from 1020 Hz to 1620 Hz in steps of 100 Hz; the X tones in this condition did not correspond to notes on Western musical scale. In all other respects, the stimuli and procedures were identical to those in the (1986) studies described previously.

The results were striking. Subjects with absolute pitch did not display the tau effect in the octave condition; that is, when people possessing absolute pitch judged the closeness of two stimuli in pitch, and when these stimuli corresponded to notes on a

Western musical scale, subjects were not influenced by the temporal proximity of the two stimuli. The tau effect reappeared in the whole-tone condition; when the stimulus continuum consisted of tones that did not correspond to Western musical notes, possessors of absolute pitch were influenced by the temporal proximity of the two tones.

16 However, possessors of absolute pitch displayed the kappa effect in both conditions. The frequency of the X tone reliably effected a change in subjects’ responses such that the X tone was more often judged closer to A (B) in time if it was closer to A

(B) in frequency. As the author points out, although kappa and tau are sometimes described as converse phenomena, this cannot be strictly true given this pattern of results.

Shigeno appeals to a stage-of-processing description; though the kappa effect (i.e., the effect of space on temporal perception) may take place at either the precategorical or a categorical level, the tau effect (i.e., the effect of time on spatial perception) may take place only at the precategorical level. Thus possessors of absolute pitch, presumably using categorical judgments in the tau task, when the task requires a focus of attention on pitch (i.e., a pitch judgment task), do not show an effect of temporal factors on pitch perception.

However, when the task requires a time judgment the auditory kappa effect is quite robust, occurring even in listeners with absolute pitch. As mentioned previously, listeners with absolute pitch tend to rely on categorical information about pitch to the exclusion of information about the pitch relationships within a sequence. Auditory kappa results from situations in which the pitch relationships within a sequence influence judgments about the temporal characteristics within a sequence. For example, when Tone

X, in Shigeno’s (1986) task, is closer in frequency to Tone A than it is to Tone B, it is more often judged closer in time to Tone A than it is to Tone B. As auditory kappa depends on pitch relationships, rather than on putative pitch identification, a listener with absolute pitch is unable to use this skill to help them perform the task, and is just as susceptible to auditory kappa as a listener who does not possess this ability.

17 Pitch Expectancies and Time Perception

Other literature (e.g., Boltz, 1989; 1998; Hirsh, Monahan, Grant, & Singh, 1990;

Mondor & Bregman, 1994; Pitt & Monahan, 1987) has examined the effect of pitch on time perception. For example, in what might be the closest musical analogue to the above studies, Boltz (1998) played listeners a standard and a comparison melody and asked them to judge the tempo of the comparison relative to the standard. She found that comparison melodies containing many large pitch intervals (relative to pitch intervals of preceding standards) were judged to unfold significantly slower than the standards, i.e., they seemed longer. Comparison melodies containing smaller pitch intervals were judged to unfold significantly faster; the time intervals comprising these melodies seemed shorter. This finding is in line with previous research on the kappa effect showing that time intervals bounded by events farther apart in pitch space are perceived as longer (here equating to a response of “slower”).

Hirsh et al. (1990) asked listeners to determine which of two monotonic, isochronous sequences of 1000 Hz tones contained a delayed onset (that is, which pattern deviated from isochrony). Of interest is the fact that the tone instantiating the delayed onset could be shifted up or down (“skip”) either two or nine semitones. In a psychophysical task, Hirsh et al. found that subjects were poorer at discriminating a time pattern that deviated from isochrony when the tone instantiating that deviation followed a large pitch skip (nine semitones), compared to a pitch skip of only two semitones. This task reveals that pitch can influence time discrimination thresholds but because the task requires only detection of deviation from isochrony, it does not provide us with any

18 information about systematically distorting effects of pitch on time perception, namely those which figure into kappa.

Boundary conditions and time scales for the kappa effect thus appear remarkably similar across different experimental approaches. First, it seems clear that there is converging evidence that the more difficult the temporal judgment, the stronger the kappa effect (e.g., Huang & Jones, 1982). That is, as the temporal task becomes more difficult, subjects rely increasingly on (irrelevant) spatial information to make temporal judgments.

Second, the kappa effect seems to depend on phenomenal distance, rather than on distance per se (Jones & Huang, 1982; Lebensfeld & Wapner, 1968). This may be why the kappa effect can appear in modalities other than vision (e.g., audition). Third, the kappa effect is robust enough that even people with very acute pitch perception (i.e., possessors of absolute pitch) display it. Finally, converging evidence for the auditory kappa effect comes from other areas of the auditory perception literature. For example, both Boltz (1998) and Crowder and Neath (1994) have found evidence for something like an auditory kappa effect within the domain of music perception.

Theoretical Approaches to Kappa

Why does the auditory kappa effect exist? One explanation of the kappa phenomenon appeals to the physical characteristics of the stimuli. The wavelength hypothesis (Yoblick & Salvendy, 1970) rests upon an earlier finding of Cohen et al.’s

(1954) work, namely that tones of lower pitch seem to sound longer to listeners. When listeners are instructed to adjust the duration of a high-pitched tone to make it equal in duration to a low-pitched tone, they reliably make pitch these high-pitched tones longer

19 than they need to be. Yoblick and Salvendy (1970) argue that wavelengths of individual sounds, rather than differences between tones in, e.g., pitch space, are the crucial components by which kappa manifests. Wavelength, defined as a literal physical distance, may be perceived as being intrinsically spatial. Essentially, lower tones are perceived as longer because their wavelengths are longer. Cohen et al. (1954) showed a kappa effect with stimuli that had both frequency and wavelength components (i.e., pure tones), but no kappa effect with stimuli that have frequency but no wavelength component (visual flicker or tactile vibrations). This explanation may not be the whole story, though, for as Hass & Hass (1984) have pointed out, as a sound wave (or any other kind of wave) passes from one medium into another, only frequency information is preserved; that is, wavelength information may be lost in the transition from a medium like air, to one such as the tympanic membrane.

Another hypothesis addressing the kappa phenomenon hinges on the apparent

“movement” of a stimulus through time and space. Cohen and other authors (Cohen,

Hansel, & Sylvester, 1955; Hass & Hass, 1984; Newman & Lee, 1972; Price-Williams,

1954) postulate that the mechanism by which the kappa phenomenon manifests is contingent upon a predisposition of an observer (or listener). In sequences like the ones used in Cohen et al. (1953), the authors argue that a subject is biased to perceive a single object moving through time, rather than to perceive a series of different objects that each turn on and off in succession (Cohen, Hansel, & Sylvester, 1955). This is an argument in line with Wertheimer’s classic ideas on apparent movement (1912). In fact, according to the authors, in Cohen et al.’s original (1953) experiment, subjects often described perceiving the stimulus as one light, moving horizontally, that was obscured at several

20 points. Here, a subject is assumed to perceive a perceptual “object” traveling at a constant velocity. In other words, subjects perceive events that are widely separated in space (real spatial extent or pitch space) as widely separated in time because subjects assume a persistent perceptual object traveling along an implied trajectory at a constant velocity. Given this constant velocity bias, it would therefore take longer to move between two points that are farther apart in space than to move between two points that are closer together.

Perhaps a more parsimonious formulation of Cohen et al.’s (1953) original hypothesis was put forth by Jones and Huang (1982). These authors have followed others

(e.g., Price-Williams, 1954) in claiming that subjects impute uniform motion to discontinuous displays (auditory or visual) that delineate temporal and spatial intervals.

However, they disagree with one specific claim made by Cohen et al. (1953). Jones and

Huang noted that subjects need not actually experience a display as moving. Rather, they proposed a model of tau and kappa effects where “spatial, or temporal, judgments . . . are a weighted average of the given interval, temporal or spatial, and the expected time or distance that would be traversed at a given velocity”. In other words, although the familiar relations between distance, duration, and velocity provide a framework for judgments of this type, it is not necessary to perceive “movement”, as such, in the display. We may refer to this as the imputed motion hypothesis.

Given highly complex auditory signals (e.g., music or speech) with which humans are confronted on a daily basis, it seems prudent to note that another definition of

“context” could refer to the sonic environment in which an auditory event occurs.

Obviously, stimuli of the type used by Shigeno (1986; 1993), that is, patterns in AXB

21 format, possess a very simple frequency/time structure. Only three tones are presented to the listener, and only the middle tone can vary from trial to trial. However, it is interesting to speculate what the auditory kappa phenomenon might look like if it is instantiated within a longer, more complex frequency/time serial context.

Recent research on the kappa phenomenon has focused primarily on vision (e.g.,

Sarrazin, Giraudo, Pailhous, & Bootsma, 2004), with the result that the auditory kappa effect is still poorly understood. More importantly, to date, all of the research specifically designed to study the auditory kappa effect has used discrete stimuli presented in isolation. That is, no studies exist that present any serial context for the events instantiating the kappa phenomenon. Shigeno (1986), as previously noted, used the AXB paradigm, where the subject’s task was to make judgments about the middle tone in a group of three successively presented tones. Crowder & Neath (1994) used three-tone melodies.

The main issue to be addressed in the present research is this: To what extent might auditory kappa be influenced by serial context? In this endeavor, five experiments will use the AXB paradigm established by Shigeno (1986) for studying auditory kappa, but with one important change: three of the experiments will utilize patterns possessing added serial context.

The idea of studying serial context effects with respect to the kappa phenomenon takes this line of research into the domain of music and other more complex auditory sequences. It may be argued that stimuli such as those used in prior kappa studies (e.g.,

Shigeno, 1986) do not possess a high degree of ecological validity; studying kappa in longer auditory sequences might provide a better framework for understanding how this

22 phenomenon might be operating on a “real-world” level. However, a systematic examination of the kappa phenomenon has not been conducted using these longer sequences.

Jones (1976; Jones and Yee, 1993) has noted that, in longer auditory sequences, when changes in pitch are both small and unfold relatively quickly, a consequent

“motion-like” property of the melody has the potential for influencing listeners’ perception. Jones (1976), for instance, proposed that auditory patterns can be conceived in terms of pitch-time trajectories, or pitch velocities. At certain rates, such trajectories can guide one’s attending along paths of implied pitch motion, generating expectancies for certain pitches at certain times. Motion-like properties refer to the relational or integral aspect of a stimulus’ structure, in much the same language in which the kappa effect is usually discussed.

What implications would motion-like properties hold for the kappa effect in context? One hypothesis, stemming from the imputed motion hypothesis described earlier, can be summed up as follows: To the degree that the kappa effect is a result of the imputed movement of the stimulus, a serial context that preserves certain pitch velocities could also preserve the kappa effect. Specifically, a serial context that maintains or reinforces the velocity-like properties of the stimulus will preserve, or possibly enhance, the kappa effect relative to sequences in which no (or different) context is present. In short: Adding motion-like “context” to the AXB patterns of Shigeno (1986; 1993) would

(minimally) produce no change in subjects’ responses relative to sequences that consist only of the AXB tones (i.e., kappa would obtain), while adding context that disrupts the

23 motion-like properties of the sequence would diminish, comparatively, the strength of the kappa effect. This can be referred to as the Auditory Motion (AM) Hypothesis.

At least one set of competing hypotheses can be generated for the present experiments. These stem from different approaches to time perception in serial contexts.

Specifically the experimental findings of Hirsh et al. (1990) have addressed the way in which the pitch and rhythm of a melodic context affect a listener’s perception of embedded time intervals. As described above, Hirsh et al. found poorer discrimination for temporal intervals when the tone instantiating a deviation followed a large pitch skip

(nine semitones), compared to a small pitch skip of (two semitones). This predicts an effect of pitch on time perception different than that predicted by the kappa phenomenon.

Summary

Research from both the tau and kappa literature and related literature regarding how pitch expectancies may influence time perception has been reviewed. To date, the literature on the kappa effect has not studied how the addition of serial context may influence the shape of the kappa effect. Research from the pitch expectancy literature (in which a temporal context is provided for time judgments) has traditionally focused on concepts such as attention (e.g., Mondor & Bregman, 1994), pitch (vis a vis time) independence (e.g., Pitt & Monahan, 1987), or music-theoretic relationships (e.g., Boltz,

1989), while eschewing discussions of the kappa phenomenon. The following five experiments will test interpretations of the Auditory Motion Hypothesis.

CHAPTER 2

BASELINE STUDIES

Experiments 1a and 1b may be conceived as “baseline” experiments for the studies to follow. In subsequent experiments, the pitch of a to-be-judged event will be manipulated, however in Experiments 1a and 1b, pitch is unchanging on any given trial.

It is also intended to examine the effect of the addition of serial context, as such, on performance.

Experiment 1a presents subjects with three-tone monotonic sequences, while

Experiment 1b presents subjects with six-tone sequences. These sequences are the same as those used in Experiment 1a but for the addition of an isochronous three-tone “serial context” added to the beginning of each sequence (see Figure 1). In both experiments, the task is the same; on each of a series of trials, subjects judge whether the second-to-last tone in a sequence (Tone “X”) is closer in time to the tone preceding it (Tone “A”) or to the tone following it (Tone “B”). We predict a main effect of timing for both experiments such that subjects will be best at discriminating the largest temporal displacements. That is, listeners will perform better at this task the closer Tone X is to either Tone A or Tone

B in time.

Another issue in Experiment 1 involves the role of serial context: do listeners perform better at this task when given a longer serial context for their judgments? At least two current approaches to time discrimination predict a role for serial context effects in

25 these kinds of sequences. Drake and Botte (1993) claim that just-noticeable differences

(JNDs) for time discrimination in these kinds of tasks vary as a function of both the IOI

(Inter-Onset Interval) variability of the sequence and the number of IOIs in that sequence.

Specifically, a listener’s JND should decrease as function of the standard error of the mean IOI in a sequence (SE). Here, the sequences used in Experiment 1a will contain only two unequal IOIs. Sequences in Experiment 1b, in contrast, will contain five IOIs, with three of them held constant at 700 ms. Because SE is thus lower on average for the sequences in Experiment 1b (12.65) than for sequences in Experiment 1a (40), this account predicts better performance on a time discrimination task in Experiment 1b than in Experiment 1a.

Large & Jones (1999) also emphasize a role for serial context. This model predicts the same outcome as Drake and Botte (1993), but for different theoretical reasons. They propose a model of dynamic attending in which attentional oscillators

(defined by their phase and period) synchronize with, or entrain to, rhythms in the external environment. These oscillators allow for the generation of expectancies about

“when” an event will occur. Regular sequence rhythms allow for the generation of strong expectancies. The addition of rhythmic context in the sequences of Experiment 1b would thus provide a more efficient framework in which to make temporal judgments of the second-to-last tone, by enhancing the contrast (a phase difference) between the time a listener expects an event to occur and when that event actually occurs.

26 Method

Participants

A total of 39 participants were recruited from an undergraduate psychology course at OSU and participated in return for course credit. Ten participants were assigned to Experiment 1a, while 29 participants were assigned to Experiment 1b. All subjects were required to have good hearing in both years and less than ten years of formal musical training.

Apparatus

Stimuli were programmed on a PC-compatible 200 MHz Pentium computer using version 6.0 of the MIDILAB program (Todd, Boltz, & Jones, 1989). This interfaced with a Roland MPU-401 MIDI processing unit. This in turn controlled a Yamaha TX81Z FM tone generator set to the “sine wave” voice. (A sine wave is defined as a pure tone with one spectral frequency component.) Stimuli were amplified by a Crown D-75A amplifier and sent to subjects through AKG K-270 headphones.

Stimuli

All tones were sine-wave (pure) tones with a duration (i.e., ontime) of 200 ms. In

Experiment 1a, listeners heard three-tone sequences, while in Experiment 1b, 29 listeners heard six-tone sequences. In Experiment 1a, all sequences were monotonic; all tones in the sequence had the same pitch. Equally often, this pitch was C#5, D#5, E5, F5, or G5.

The first and third tones (here denoted Tone A and Tone B, respectively) were always be separated by an ISI (Inter-Stimulus Interval) of 1200 ms. The second, to-be-judged, tone

27 (here denoted Tone X) equally often assumed one of eight timing values. Expressed in terms of ISI between Tone A and Tone X, these were: 430, 450, 470, 490, 510, 530, 550, or 570 ms.

For Experiment 1b sequences, the only change to the patterns was the addition of a three-tone serial context to the beginning of each trial, where the first three ISIs were also held constant at 500 ms. Tone X (now in the fifth serial position) assumed one of the eight ISIs possible in Experiment 1a sequences. Experiment 1b also contained an additional between-subjects variable, Serial Context; three different serial contexts were employed, distinguished by the pitch change (in semitones) between successive tones of the serial context. Listeners in the SC0 (Serial Context 0) condition heard truly monotonic sequences; that is, there was no pitch change present in the serial context, so that the pitch of the serial context took on one of the five pitch values possible for sequences in Experiment 1a. Listeners in the SC4 (Serial Context 4) condition heard a four semitone change between successive tones of the serial context (i.e., the three tones of the serial context were C4, E4, and G#4, respectively), while subjects in the SC8

(Serial Context 8) condition heard an eight semitone change between successive tones in the serial context (i.e., tones in the serial context were C3, G#3, and E4, respectively).

Schematics of patterns in Experiments 1a and the SC0 condition of Experiment 1b are shown in Figure 1.

28 (a)

To-be-judged tone (b)

{ Serial Context }

Time

Figure 1. Schematics of patterns used in Experiment 1a (panel a) and Experiment

1b (panel b) sequences. (Only Serial Context = 0 is presented, for clarity).

Design

In Experiment 1a, X Pitch (i.e., the pitch value of Tone X) served as one within- subjects variable. The variable of X Time (i.e., the ISI between Tone A and Tone X) served as another, with the eight levels described above. The primary design of

Experiment 1a was thus a 5 x 8 repeated-measures design, with five within-subjects levels of X Pitch (C#5, D#5, E5, F5, or G5) and eight within-subjects levels of X Time.

This resulted in 40 patterns unique to each subject.

In Experiment 1b, the design was essentially the same as that of Experiment 1a, exception for the addition of a between-subjects variable, Serial Context, which had three levels: 0, 4, and 8, with the designations reflecting the pitch change (in semitones)

29 between successive tones of the serial context. The primary design of Experiment 1b was thus a 3 x (5 x 8) mixed-factor design, with three between-subjects levels of Serial

Context (0, 4, or 8), five within-subjects levels of X Pitch, and eight within-subjects levels of X Time.

Procedure

Participants heard tape-recorded instructions outlining the task while attending to a diagram that illustrated it. All listeners were asked to make a judgment concerning the timing of the second-to-last tone. They were told that their task was to indicate on a

Midilab response box whether the second-to-last tone was closer in time to Tone A or to

Tone B.

Following the instructions, a block of 10 practice trials with corrective feedback was played to subjects. The practice trials consisted of trials randomly chosen from the experimental set of trials. Subjects then received 5 experimental blocks with no feedback.

The 40 possible patterns in each experiment were be played twice per block, leading to a total of 400 trials. Trials were presented in quasi-random fashion with constraints on order; no more than 3 trials with identical values of X Pitch or X Time occurred in a row, and no more than 5 trials with identical correct answers occurred in a row. Two different counterbalance orders were constructed, with approximately half of all subjects receiving one counterbalance order, and half the other. At the conclusion of the experimental blocks, subjects completed a questionnaire on their musical background and training.

30 Results & Discussion

For the present experiments, three main dependent measures were calculated.

One, p(B), reflects the probability that a listener responds “B”, that is, responds that Tone

X is closer to Tone B in time. Data analysis will also make use of a statistical bootstrap algorithm devised by Foster & Bischof (1991). In this procedure, a large number of samples (1000) is drawn with replacement, from the original data set. Each of these samples is then fitted by the psychometric function and two estimates, a point-of- subjective equality (PSE) estimate and a JND estimate, are calculated. Here, the PSE estimate corresponds to that level of X Time at which a subject “switches” from responding “closer to A in time” to “closer to B in time”. However, it is important to realize that the values obtained for PSE correspond to points along the (theoretical) psychometric function, and may not correspond to the actual levels of X Time that were used in the experiment.

Experiment 1a. A 2 x (5 x 8) ANOVA was conducted on p(B) scores from

Experiment 1a, with 2 between-subjects levels of Counterbalance Order crossed with 5 levels of X Pitch and 8 levels of X Time. The ensuing F ratio displayed only a main effect of X Time, F(7, 56) = 52.27, Mse = .068, p < .0001, indicating that subjects were more likely to respond “B” (that is, that Tone X was closer to Tone B in time) the closer in time Tone X was to Tone B. This is shown in Figure 2. No other effects or their interactions were significant. The effect of Counterbalance Order was not significant

(F<1), and as such the data were reanalyzed, collapsing over the Counterbalance Order variable. The results from the subsequent ANOVA indicated that the X Time variable was again the only variable to exert a significant effect, F(7, 63) = 55.56, Mse = .065, p <

31 .0001. (Note: In all subsequent experiments and analyses, though two different counterbalance orders were always used, a significant effect of Counterbalance Order was never found, and so for the remainder of the experiments presented, ANOVAs will collapse over this variable.)

0.8

0.6

p(B) 0.4

0.2

0 430 450 470 490 510 530 550 570 X Time

Figure 2. p(B) as a function of X Time in Experiment 1a.

Mean PSE for Experiment 1a was 495.64 ms, indicating that listeners are performing reasonably well at this task. Since PSE can be considered the point at which a subject “switches” from responding “A” to “B”, perfect performance would be denoted by a subject “switching” at 500 ms, corresponding to the exact temporal midpoint of the interval formed by Tone A and Tone B. Mean JND in Experiment 1a was 76.64 ms; this is a puzzling finding, since the most Tone X could deviate from the midpoint of the

32 temporal interval formed by Tones A and B was 70 ms; a finding like this would seem to suggest that no listener was able to perform the task, yet as Figure 2 indicates, most listeners performed adequately. The variability in JND, however, was extremely large

(standard deviation of JND scores = 44.48). Also, upon further examination there was one subject in Experiment 1a who might be considered an outlier; his or her JND was 177 ms. With this outlier removed, the mean JND in Experiment 1a came down to 66.60 ms.

The variability, however, was still fairly large (31.09).

Experiment 1b. A 3 x (5 x 8) mixed-factor ANOVA was conducted on p(B) scores from Experiment 1b, contrasting 3 between-subjects levels of Serial Context (0, 4, or 8), 5 within-subjects levels of X Pitch, and 8 within-subjects levels of X Time. A significant effect of X Time was obtained, F(7, 182) = 176.50, Mse = .068, p < .0001, indicating, as in Experiment 1a, that listeners were more likely to respond “B” if Tone X was closer to Tone B in time. This is illustrated in Figure 3. No other effects or their interactions were significant.

33 Figure 3. p(B) scores as a function of the X Time variable in Experiment 1b.

Mean PSE for Experiment 1b was 502.71 ms. This indicates, as in Experiment 1a, that listeners performed well at this task, since perfect performance equates to a PSE of

500 ms. Mean JND in Experiment 1b was 58.39 ms with a standard deviation of 28.80.

As in Experiment 1a, however, there was one subject who had a JND that was extremely large (176 ms); with this subject removed, the mean JND for Experiment 1b was 51.96 ms (standard deviation = 17.05)

According to recent theories of time perception (Drake & Botte, 1993; Large &

Jones, 1999) listeners may do better at detecting deviations from isochrony when these deviations occur as part of a longer isochronous context. To test this hypothesis, the data from Experiments 1a and 1b were combined and a new between-subjects variable,

Context Presence, was created to reflect whether a sequence contained serial context (as

34 in Experiment 1b) or did not (Experiment 1a). A 2 x (5 x 8) ANOVA was performed on this combined data set, with two between-subjects levels of Context (Present or Absent), and the five levels of X Pitch and eight levels of X Time used in the previous analyses.

Unsurprisingly, a significant effect of X Time was obtained, F(7, 259) = 177.34,

Mse = .066, p < .0001, indicating that listeners were more likely to respond “B” the closer Tone X was to Tone B in time. However, this main effect was qualified by a significant interaction of X Time with Context, F(7, 259) = 2.42, Mse = .066, p < .05.

This interaction is shown in Figure 4. Subsequent analyses, however, confirmed that the effect was a relatively weak one. A series of unequal N Tukey post-hoc analyses failed to find any significant pairwise differences across levels of the Context variable.

Additionally, though a significant linear trend to the data was found for the X Time variable, F(1, 37) = 304.22, Mse = .266, p < .0001, further analysis revealed that the shape of this linear trend did not differ between levels of the Context variable. However, in terms of Proportion Correct (PC) scores, listeners still averaged slightly better performance for Context Present sequences (mean PC = .745) than for Context Absent sequences (mean PC = .723).

35 Context

Present Absent

0.8

0.6 p(B) 0.4

0.2

0 430 450 470 490 510 530 550 570 X Time

Figure 4. Mean p(B) scores in Experiment 1, as a function of X Time and

Context, Present (Experiment 1b) or Absent (Experiment 1a).

An independent-groups t-test was then performed on this combined data to

examine the effect of the independent variable Context Presence on JND scores. Both of

the outlying subjects referred to previously were removed from the analysis. The results

were “marginally” significant, t(35) = 1.83, p = .07. However, the overall trend in the

data suggests that people performed slightly better with sequences containing serial

36 context (mean JND = 51.96 ms) compared to sequences not containing serial context

(mean JND = 66.60 ms).

These data thus provide some support for the hypotheses put forth by Large and

Jones (1999), who claim that regular sequence rhythms allow for the generation of stronger expectancies. One way this could be achieved is that isochronous serial context may enhance the phase discrepancy between the time a listener expected Tone X to occur

(here equated to the midpoint of the temporal interval formed by Tone A and Tone B) and when that event actually occurred.

Summary

Two experiments were conducted. In Experiment 1a, listeners were presented with three tones and asked to judge whether the second tone (Tone X) was closer to the first tone (Tone A) or the third tone (Tone B) in time. Tone X could assume one of eight timing values with respect to Tone A, while Tones A & B remained separated from each other by a fixed temporal amount. Results indicated that this was an effective manipulation of Tone X timing.

In Experiment 1b, the task and procedure were the same. The only change from

Experiment 1a involved the addition of a three-tone isochronous serial context added to the beginning of the patterns. Results paralleled Experiment 1a.

Combining the data from Experiments 1a and 1b resulted in the creation of a new variable, Context Presence. When combined in this fashion, the data seem to indicate that the presence of an isochronous serial context is helpful in time discrimination tasks. This finding is in line with previous research.

CHAPTER 3

REPLICATION OF KAPPA STUDIES

The main goal of Experiment 2 was to replicate the (1986) kappa experiment of

Shigeno, yet using logarithmic frequency, rather than linear frequency, as an independent variable; that is, to see whether the kappa effect obtains with pitch. Recall that Shigeno

(1986) played listeners a series of patterns in AXB format. On every trial, tones A and B

(that is, the first and third tones) were fixed in time and frequency; that is, both the length of time between A and B and the frequency separation between A and B were held constant over trials in a session. Tone A was fixed at 1000 Hz, while Tone B was fixed at

2500 Hz; in addition, these tones were separated from each other by an interstimulus interval (offset to onset) of 1 sec. The only element whose properties could vary from trial to trial was tone X.

2500 Hz.

38 Stimuli and conditions in Experiment 2 are similar to those reported by Shigeno, with the timing and frequency characteristics of Tone X being the primary independent variables. The major change of Experiment 2 with respect to Shigeno (1986) is the usage of pitch, i.e., frequency on a logarithmic scale, as an independent variable, rather than frequency on a linear scale. On each of a series of trials, a listener heard three tones that either ascended or descended in pitch, and was instructed to judge whether the middle tone was closer to the first or the third tone in time. Here, given the results of Shigeno

(1986), we might expect that subjects will be more likely to report that the middle tone is closer in time to the tone that is more similar to it in pitch, where this may be either the tone immediately preceding it (Tone A) or following it (Tone B). (An additional variable,

Pitch Direction, was also created to examine what effects, if any, the direction of pitch motion has on the kappa effect.)

Here, unlike Experiment 1, the to-be-judged events will possess implied pitch motion, in the sense that there will be a pitch change between successive events (i.e., pitch velocity will assume a non-zero quantity). The Auditory Motion (AM) hypothesis predicts a main effect of pitch for these sequences, since it is related closely to the imputed motion hypothesis put forth by Jones and Huang (1982), which claims that the relations between the distance, duration, and velocity of successive elements provide a natural framework for judgments of this type. In other words, if kappa is dependent on the expectancies induced by the motion-like properties of to-be-judged events, kappa should be present in the results of Experiment 2. More direct tests of the central tenet of the AM hypothesis (namely that the presence or absence, as well as the type, of serial

39 context will influence the strength of the kappa effect) are present in the following chapters.

A different outcome of Experiment 2 may be predicted. Hirsh et al. (1990) showed larger relative difference limens (DLs) for events instantiating larger pitch skips compared with smaller ones. They found poorer discrimination for temporal intervals when the tone instantiating a deviation followed a nine-semitone pitch skip, compared to a two-semitone pitch skip. This predicts an overall worsening in time discrimination performance with increasing pitch separation between events, an effect of pitch on time perception quite different from the kappa effect.

Method

Participants

Twenty-one participants were recruited from an undergraduate psychology course at OSU and participated in return for course credit. As in Experiment 1, all subjects were required to have good hearing in both years and less than ten years of formal musical training.

Apparatus

The apparatus was the same as in Experiment 1.

Stimuli

All tones were sine-wave (pure) tones with an ontime of 200 ms. On each trial, listeners heard three-tone sequences (where, following Shigeno, the

40 sequence is now represented as AXB) that either ascended or descended in pitch; which ones listeners heard depended on the between-subjects condition of Pitch

Direction to which they had been assigned (Up or Down). Both Tones A and B remained fixed in pitch and time on every trial. For Up sequences, Tones A & B were C5 (523 Hz) & G#5 (831 Hz), respectively, while for Down sequences,

Tones A & B were G#5 and C5, respectively. Tones A & B were always separated by an ISI (Inter-Stimulus Interval) of 1200 ms. A schematic of an Up Pitch

Direction sequence is given in Figure 5.

B Higher X Frequency A

Lower

1 2 3 Serial position

Figure 5. Schematic of an Up sequence in Experiment 2.

Tone X assumed one of 5 pitch values. These correspond to the possible pitch values used in the sequences from Experiment 1 as shown in Table 1. Also shown in Table 1 is the distance in semitones (st) of each possible value of Tone

X from Tone A. The same pitch values were used for Up and Down sequences.

41 Tone X Tone X Distance in semitones (st) from Tone A (Up) (Down) 1 C#5 G5

3 D#5 F5

4 E5 E5

5 F5 D#5

7 G5 C#5

Table 1. Possible pitch values for Tone X in Experiment 1 by Pitch

Direction condition.

As in Experiment 1, Tone X also assumed one of eight timing values.

Expressed in terms of inter-stimulus interval, or ISI, between Tone A and Tone X, these were: 430, 450, 470, 490, 510, 530, 550, or 570 ms. All subjects experienced all levels of Tone X timing.

Design

The primary design of Experiment 2 was a 2 x (5 x 8) mixed-factor design, with two between-subjects levels of Pitch Direction, five within-subjects levels of X Pitch

Distance, and eight within-subjects levels of X Time Distance. Pitch Direction (Up or

Down) served as a between-subjects variable. The variable of X Pitch (expressed as the distance in semitones between Tones A & X, i.e., 1, 3, 4, 5, or 7) served as one within- subjects variable. The variable of X Time served as another, with the eight levels described above. This resulted in 40 patterns unique to each subject. 42 Procedure

Participants were randomly assigned to one of two Pitch Direction conditions.

They heard tape-recorded instructions outlining the task, while attending to a diagram that illustrated the task. They were told that their task was to indicate on a Midilab response box whether the middle tone in a sequence of three (Tone X) was closer in time to the first tone (Tone A) or to the third tone (Tone B). Participants performed this task by pressing the appropriate button on the response box (i.e., the button labeled “A” if

Tone X was closer to Tone A in time, and “B” if Tone X was closer to Tone B in time).

They were also instructed to ignore the pitch of the middle tone.

Following the instructions, the subjects were given a chance to have any part of the instructions clarified, should they wish. After these concerns, if any, were addressed, a block of 10 practice trials with corrective feedback was played to subjects. The first 5 trials of the practice block were very easy trials with comparatively large time changes, while the remainder of the practice trials were randomly chosen from the set of experimental trials. Following the practice block, the subjects had the opportunity to ask any clarification questions about the task.

Subjects then received 5 experimental blocks with no feedback. The 40 possible patterns were played twice per block, leading to a total of 400. Trials were presented in quasi-random fashion with constraints on order; no more than 3 trials with identical values of X Pitch Distance or X Time Distance could occur in a row, and no more than 5 trials with identical correct answers could occur in a row.

43 Following the experimental trials, the subjects filled out a brief questionnaire on their musical background and training. They were debriefed in an appropriate manner and excused.

Results & Discussion

A 2 x (5 x 8) mixed-factor ANOVA was calculated on p(B) scores from

Experiment 2. This resulted in a significant main effect of the timing of Tone X, F(7, 33)

= 26.701, Mse = .107, p < .0001. This indicates that, as in Experiment 1, subjects were more likely to respond “B” if Tone X was closer to Tone B in time. Overall the pattern of results is quite similar to Experiment 1, and indicates that the manipulation of X Time, as such, was strong enough to produce an effect.

In contrast to Experiment 1, however, the ANOVA also displayed a main effect of the pitch of Tone X, F(4, 76) = 20.726, Mse = .131, p < .0001. This illustrates the classical kappa effect, and indicates that listeners were increasingly more likely to respond “B” the closer in pitch Tone X was to Tone B. These data are illustrated in

Figure 6. No other effects or their interactions were significant.

Figure 6. p(B) responses as a function of the pitch distance of Tone X from Tone

A for Experiment 2.

To more closely examine the effect of the X Pitch variable on p(B) responses, the data were reanalyzed in terms of Proportion Correct (PC). A 5 x 8 repeated-measures

ANOVA was conducted on PC scores from Experiment 2. This resulted in a significant main effect of X Time, F(7, 140) = 15.830, Mse = .052, p < .0001, indicating that listeners performed significantly poorer on the task as the temporal location of Tone X fell toward the temporal midpoint of the AXB sequence (i.e., the more difficult the temporal judgment). This is shown in Figure 7.

Figure 7. PC scores as a function of the X Time variable in Experiment 2.

However, the ANOVA also indicated a significant interaction of the X Time variable with the X Pitch variable, F(28, 560) = 11.12, Mse = .035, p < .0001. This more subtle aspect of the kappa effect is illustrated in Figure 8. The effect of the X Time variable appears to be modulated by the effect of the X Pitch variable; listeners perform best on the task when Tone X is close to Tone A (B) in both pitch and time, and worst when Tone X is close to Tone A (B) in time but is far away from Tone A (B) in pitch.

Distance (ST) of Tone X from Tone A

Figure 8. PC as a function of the temporal distance (ms) and pitch distance (ST)

of Tone X from Tone A for Experiment 2.

The p(B) data was also reanalyzed in terms of PSE and JND for the 21 participants in Experiment 2. Data from 7 participants could not be included in this analysis due to inadequate probit fits. An inadequate probit fit could obtain if, for example, a listener responded only on the basis of X Pitch (though they were instructed not to). It might also obtain if the task was too difficult for them or (although unlikely) too easy for them. The data of the 14 participants in Experiment 1 for whom

47 psychometric functions could be obtained are shown in figure 9. These PSE scores were subjected to a repeated-measures ANOVA with one factor, X Pitch. A significant effect of X Pitch on PSE was obtained, F (4, 52) = 4.90, Mse = 12.22, p < .005. As the Tone X moves further from Tone A in pitch, the PSE for timing decreases. This is consistent with the kappa effect, considering that, in the absence of any effect of pitch on time perception, PSEs should hover around 500 ms, that level of X Time Distance that would exactly subdivide the ISI between Tones A and B. However, when Tone X is 7 st away from Tone A (X Pitch Distance = 7), it only needs to be 475 ms away from Tone A, on average, for a listener to “switch” from saying “closer to A in time” to “closer to B in time”.

Figure 9. PSE scores as a function of X Pitch in Experiment 2.

JND scores of these same 14 participants were also subjected to a repeated- measures ANOVA with five levels of X Pitch. No significant effect of X Pitch on JND was observed. In this experiment, subjects did not show any appreciable changes in difference limen as a function of the X Pitch Distance variable.

Summary

Using three tone AXB ascending and descending sequences, the pitch of the middle (X) tone was varied as was its timing. The pitch of Tone X appeared to significantly affect listeners’ responses to its timing. Subjects were more likely to say that

Tone X was closer to Tone A (B) in time if it was also close to Tone A (B) in pitch. This finding appears to replicate that of Shigeno (1986) who found that Tone X was significantly more often judged closer in time to tone A (or B) if it was closer in frequency to tone A (or B). This is the kappa effect. In addition, these results extend

Shigeno’s (1986) work in the sense that the Kappa Effect appears to occur in the context of pitch relationships, rather than only in linear frequency relationships per se. Subjects also appeared to “switch” earlier to saying “closer to B in time” with large values of the

X Pitch variable; that is, X Pitch significantly affected listeners’ PSEs.

No changes in difference limen as a function of X Pitch Distance were found, a result that conflicts somewhat with Hirsh et al. (1990), who found that difference limen were significantly larger for temporal intervals bounded by large pitch skips (9 semitones) than for intervals bounded by smaller ones (2 semitones). The failure to find a significant main effect of X Pitch on PC scores illustrates this conflict as well.

49 The Auditory Motion hypothesis, however, would argue that a listener in this experiment perceives events (in this case, sine tones) that are widely separated in space

(vis-à-vis pitch) as widely separated in time because events in the sequence follow an

(implied) motion-like trajectory, here either ascending or descending in pitch. If the listener assumes a constant velocity, it would take longer to move between two points on the trajectory that are farther apart in space than to move between two points that are closer together. These motion-like trajectories thus generate expectancies for certain pitches at certain times.

These expectancies appear to be so strong in some cases that when they are violated (as happens, for example, when Tone X is far away from Tone A in pitch but close to it in time) the listener’s perception of time is distorted. The perceived onset of

Tone X is “shifted” by some amount that makes Tone X more in line temporally with where it “should” have been, given the pitch relationships in the sequence.

CHAPTER 4

KAPPA IN SERIAL CONTEXT

Experiment 2 data indicates that kappa is a valid phenomenon. However, it remains an open question as to whether or not providing a serial context for temporal judgments would affect kappa. Experiment 3 addresses this question. For this study, on each trial a serial context cell, comprising a three-tone sequence, is added to the beginning of the three AXB tones (now referred to as a kappa cell). A schematic of an example pattern is illustrated in Figure 10.

The Auditory Motion hypothesis claims that it is the implied, motion-like properties of a sequence that give rise to the kappa effect. Therefore, disrupting the motion-like properties of a sequence may disrupt or abolish the kappa effect. In

Experiment 3, a serial context is provided for each kappa cell. Crucially, however, some serial contexts imply no pitch motion relative to the rest of the sequence.

51 An alternative to the predictions of the Auditory Motion hypothesis can be formulated with respect to Bregman’s (1990) discussion of Auditory Scene Analysis.

Specifically, these predictions are related to the phenomenon of auditory grouping.

Auditory grouping is one mechanism by which an organism is theorized to parse the disparate sound sources in the environment. One way an auditory group can be created is if the distance in pitch space between successive sounds is relatively small. This is known as the principle of “pitch proximity”. Auditory grouping thus makes the prediction that the patterns of Experiment 3 with monotonic serial context cells (i.e., where pitch is unchanging in the serial context) will segregate into two groups, the first group consisting of the first four tones (which all have the same pitch), and the second group consisting of the final two tones (which each have a different pitch).

Grouping principles lead to an interesting prediction regarding the kappa cell effects. Specifically, they imply that the greater the difference, in pitch, between the final tone of the first group (tone A) and the initial tone of the second group (tone X), the more these “groups” will segregate on the basis of pitch proximity. A key assumption made by

Bregman (1990), however, is that it is more difficult to compare “across” perceptual groups than “within” them. The task in the current set of experiments is to judge time, but in order to do this task, listeners must judge the middle tone’s temporal position in relation to two other tones, one of which is in a (theoretically) different perceptual group.

Because it should be harder to compare across groups than within groups, and since these groups will segregate more with increasing pitch distance between tone A and tone X, then it follows from this hypothesis that it should be harder to judge the timing of tone X

52 relative to tone A, the greater its distance in pitch from tone A. In effect, auditory grouping predicts a main effect of X pitch on accuracy of time judgments.

B __ Higher

Kappa Cell

Frequency __

| Serial | Context Cell

Lower 1 2 3 4 5 6 Serial position

Figure 10. Schematic of a sequence with Serial Context = 0 in

Experiment 3.

Method

Participants

Thirty participants were recruited from an undergraduate psychology course at

OSU and participated in return for course credit. As in Experiments 1 & 2, all subjects were required to have good hearing in both years and less than ten years of formal musical training.

53 Apparatus

The apparatus was the same as in Experiments 1 & 2.

Stimuli

All tones were again sine-wave (pure) tones with a duration of 200 ms. On each trial, listeners heard six-tone sequences; which ones listeners heard depended on the between-subjects condition of Serial Context (0, 4, or 8) to which they had been assigned. (The variable of Pitch Direction was disregarded for this and all following experiments; pilot experiments, which included both Up and Down conditions, indicated that no systematic differences accrued to this variable). Tone

A and Tone B again remained fixed in pitch and time on every trial. For all sequences, Tones A & B were C5 (523 Hz) & G#5 (831 Hz), respectively. Tones

A & B were always separated by an ISI (Inter-Stimulus Interval) of 1200 ms.

Tone X again assumed one of 5 pitch values, corresponding to the same pitch values it could take on in Experiment 2. As in Experiments 1 & 2, Tone X also assumed one of eight timing values. Expressed in terms of inter-stimulus interval, or ISI, between Tone A and Tone X, these were again: 430, 450, 470,

490, 510, 530, 550, or 570 ms. All subjects experienced all levels of Tone X timing.

The crucial difference in Experiment 3, compared to Experiments 1 & 2, is the addition of a serial context cell to the beginning of each of the patterns. Serial context cells consisted of the addition of three tones to the beginning of all patterns used in Experiment 2; with the exception of serial context, the patterns

54 used in Experiments 2 & 3 are identical, i.e., the kappa cells remain the same in both of these experiments. The three tones comprising a serial context cell were all pure tones with an ontime of 200 ms. Each tone was followed by a silent ISI of

500 ms.

Timing characteristics of each level of Serial Context were identical.

Differences in implied pitch motion were conveyed through the pitch distances between successive tones in the serial context cell. Three levels of the Serial

Context variable were used in Experiment 3 (SC0, SC4, SC8). These differed in terms of the amount of pitch motion implied in each. Level SC0 (Serial Context

0) of the Serial Context variable corresponded to a pitch distance of 0 ST between successive tones of the serial context cell; effectively, this meant that all tones in the serial context cell were at the same pitch as Tone A of the kappa cell, namely

C5. This serial context implied no pitch motion. Level SC4 of the Serial Context variable corresponded to a pitch distance of 4 ST between successive tones in the serial context cell. For all sequences, the serial context cell was thus C4 – E4 –

G#4. This serial context implied a moderate amount of pitch motion. Finally, level

SC8 of the Serial Context Variable corresponded to a pitch distance of 8 ST between successive tones in the serial context cell; the serial context cell was thus

C3 - GS3 - E4. This serial context implied a (relatively) large amount of pitch motion.

55 Design

The primary design of Experiment 3 was a 3 x (5 x 8) mixed factor design. Serial

Context (with the three levels of SC0, SC4, or SC8) served as the lone between-subjects variable. The variable of X Pitch (again expressed as the distance in semitones between

Tones A & X, i.e., 1, 3, 4, 5, or 7) served as a within-subjects variable. The variable of X

Time served as another within-subjects variable, with the eight levels described above.

This again resulted in 40 patterns unique to each subject.

Procedure

The procedure for Experiment 3 was virtually identical to Experiment 2.

Participants were randomly assigned to one of three Serial Context conditions. They heard tape-recorded instructions outlining the task and were told that their task was to indicate on a Midilab response box whether the fifth tone in a sequence (Tone X) was closer in time to the fourth tone (Tone A) or to the sixth tone (Tone B) in a series of six.

Participants performed this task by pressing the appropriate button on the response box

(i.e., the button labeled “A” if Tone X was closer to Tone A in time, and “B” if Tone X was closer to Tone B in time). They were also instructed to ignore the pitch of the middle tone. All other aspects of the procedure were the same as those of Experiment 2.

Results & Discussion

A 3 x (5 x 8) mixed-factor ANOVA was calculated on p(B) scores from

Experiment 3. This again resulted in a significant main effect of X Time, F(7, 189) =

84.127, Mse = .080, p < .0001, indicating, as in Experiments 1 & 2, that subjects were

56 more likely to respond “B” if Tone X was closer to Tone B in time. Overall the pattern of results is quite similar to Experiment 1, and indicates that the temporal manipulation of the X Tone was effective in influencing listeners’ responses.

Data from Experiment 3 also displayed an overall effect of X Pitch, F(4, 108) =

10.956, Mse = .098, p < .0001. This again illustrates the classical kappa effect, and indicates that listeners were more likely to respond “B” (i.e., Tone X is closer to Tone B in time) the closer in pitch Tone X was to Tone B. These data are illustrated in Figure 11.

Figure 11. p(B) responses as a function of X Pitch for Experiment 3.

This main effect was qualified, however, by a significant interaction of X Pitch with Serial Context, F(8, 108) = 2.201, Mse = .098, p < .05. This effect is illustrated in

57 Figure 12. Plotting X Pitch vs p(B) in this way affords us an opportunity to examine a visual benchmark of the strength of the kappa effect in each Serial Context condition, namely, the slope of the line corresponding to each level of the Serial Context variable.

As shown in Figure 12, the line corresponding to SC0 (diamond shapes) is virtually flat, indicating that temporal judgments did not change very much as a function of X Pitch.

Serial Context

Figure 12. A significant interaction of X Pitch and Serial Context on p(B) in

Experiment 3.

58 The lines corresponding to SC4 and SC8, however, show a positive slope. Trend analyses confirm that the SC0 condition displays no linear trend, F(1,27) = .023, Mse =

.243, p > .5, while the SC4 condition displays a significant linear trend, F(1,27) = 9.01,

Mse = .243, p < .01, as does the SC8 condition, F(1,27) = 11.690, Mse = .243, p < .005.

(As the levels of the X Pitch variable are not equally spaced in these designs, these trend analyses take into account those that are, namely the X Pitch levels of 1, 4, & 7; linear fits to these trends yielded slopes of .006, .112, and .133 for SC0, SC4, and SC8, respectively.)

A significant interaction of X Time with X Pitch was also obtained, F(28, 756) =

1.786, Mse = .019, p < .01. This is shown in Figure 13. Trend analysis of the X Time variable (collapsed over levels of the X Pitch variable) confirm the presence of an overall linear trend, F(1,27) – 120.91, Mse = .388, p < .001. However, pairwise comparisons of the linear trends for each level of the X Pitch variable indicate that the shape of the linear trend for X Pitch level 3 differs significantly from the shapes of the linear trend for X

Pitch level 5, F(1,27) = 8.05, Mse = .021, p < .01, and the linear trend for X Pitch level 7,

F(1,27) = 7.02, Mse = .017, p < .05; listeners appear to be increasingly likely to respond

“closer to Tone B in time” the greater the temporal distance of Tone X from Tone A; however this trend appears weaker with X tones that are 3 st from Tone A at levels of the

X Time variable corresponding to 510 and 530 ms. No other pairwise linear trend comparisons were significant.

59 Distance (ST) of Tone X from Tone A

Figure 13. Interaction of X Time and X Pitch in Experiment 3.

The data of Experiment 3 were also analyzed in terms of Proportion Correct (PC) scores. PC scores from Experiment 3 were subjected to a 3 x (5 x 8) mixed-factor

ANOVA (with 3 levels of Serial Context, 5 levels of X Pitch, and 8 levels of X Time).

The data displayed a significant effect of X Time, F(7, 189) = 31.190, Mse = .056, p

<.001. Listeners performed significantly poorer on the task as the temporal location of

Tone X fell toward the temporal midpoint of the AXB sequence (i.e., the more difficult the temporal judgment). This is shown in Figure 14.

60 Figure 14. PC scores as a function of the X Time variable in Experiment 3.

The data also displayed a significant effect of X Pitch, F(4, 108) = 4.415, Mse =

.024, p < .005. A series of Tukey HSD post-hoc tests were performed to determine the source of this effect. As can be seen in Figure 15, listeners performed slightly, though significantly, better on the task when Tone X was 3 st away from Tone A (compared to when it was 5 st or 7 st away. That is, listeners performed slightly better for X Pitch values of 5 & 7, as compared to values of 1 & 3.

61 Figure 15. PC as a function of X Pitch in Experiment 3.

However, the significant effect of X Pitch on PC qualified by a significant interaction of the X Time variable with the X Pitch variable, F(28, 756) = 5.724, Mse -

.029, p < .001. This is shown in Figure 16. Averaged across levels of the Serial Context variable, listeners again displayed the classical kappa effect; in fact this result is similar to that found in Experiment 2; listeners perform best on the task when Tone X is close to

Tone A (B) in both pitch and time, and worst when Tone X is close to Tone A (B) in time but is far away from Tone A (B) in pitch.

Distance (ST) of Tone X from Tone A

Figure 16. PC as a function of the temporal distance (ms) and pitch distance (ST)

of Tone X from Tone A for Experiment 3.

This significant 2-way interaction, finally, was qualified by a significant 3-way interaction of X Serial Context, X Pitch and X Time, F = 1.418, Mse = .029, p < .05. As can be seen in Figure 17, the significant interaction between X Pitch and X Time virtually disappears in the SC0 condition (Figure 17a); this provides another indication that the

63 kappa effect is substantially diminished in the SC0 condition compared to the SC4

(Figure 17b) or the SC8 condition (Figure 17c) (cf. Figure 12).

Distance (ST) of Tone X from Tone A

Figure 17a. PC as a function of the temporal distance (ms) and pitch distance (ST)

of Tone X from Tone A for Experiment 3 (where SC=0).

Distance (ST) of Tone X from Tone A

Figure 17b. PC as a function of the temporal distance (ms) and pitch distance (ST) of Tone X from Tone A for Experiment 3 (where SC=4).

Distance (ST) of Tone X from Tone A

Figure 17c. PC as a function of the temporal distance (ms) and pitch distance (ST)

of Tone X from Tone A for Experiment 3 (where SC=8).

As stated earlier, one of the tenets of grouping theory (e.g., Bregman 1990) is that it should be harder to compare across perceptual groups than within them. To test this

66 hypothesis, the data from the SC0 condition were examined more closely. Grouping theory predicts that the patterns used in SC0 should segregate into two groups, with the first consisting of the first four tones in a pattern (by virtue of their having identical pitches), and the second consisting of the final two tones (i.e., Tones X and B). Since these groups will segregate more with increasing pitch distance between tone A and tone

X, it should be harder to judge the relative timing of tone X the greater its distance in pitch from tone A.

A 5 x 8 repeated-measures ANOVA (with 5 levels of X Pitch and 8 levels of X

Time) was performed on PC scores from the SC0 condition of Experiment 3. Notably, there was no significant effect of X Pitch . Instead, these data displayed only a significant effect of X Time, F(7,56) = 11.49, Mse = .046, p < .0001. As in Experiment 2, this indicates that listeners performed worse on the task the closer Tone X fell toward the temporal midpoint of the AXB sequence. Thus, it appears as if the Auditory Motion

(AM) hypothesis is a better predictor of the results of Experiment 3 than grouping theory.

As stated earlier, the AM hypothesis predicts that if the beginning of an auditory sequence leads a listener to extrapolate null (or no) pitch motion, the kappa effect should be abolished. Crucially, however, this account does not predict a main effect of X Pitch on accuracy.

PSE and JND values for the data of Experiment 3 were also examined. PSE scores were subjected to a mixed-factor ANOVA with one between-subjects factor, Serial

Context, and one repeated-measures factor, X Pitch. A significant effect of X Pitch on

PSE was obtained, F (4, 76) = 3.88, Mse = 696.36, p < .01. Similar to the findings of

Experiment 2, as the Tone X moves further from Tone A in pitch, the PSE for timing

67 decreases, consistent with the kappa effect. This is shown in Figure 18. The variable of

Serial Context did not significantly influence PSE scores, nor did the interaction of Serial

Context with X Pitch; however, as in Experiment 2, several subjects needed to be dropped from the PSE and JND analyses due to inadequate probit fits (three participants from the SC0 condition, three from the SC4 condition, and two from the SC8 condition); as a result there may have been insufficient power to test for these more subtle effects.

Figure 18. PSE scores as a function of X Pitch in Experiment 3.

JND scores from Experiment 3 were also analyzed with the same mixed-factor design. No significant effects or their interactions were present. It appears that neither

68 Serial Context nor X Pitch significantly influence difference limen in this task. However, this result may be due to the lack of power inherent in this design; as alluded to earlier, seven participants’ data was excluded from this analysis due to inadequate probit fits.

Summary

The major change in Experiment 3 was the addition of a serial context cell, comprising a three-tone sequence, to the beginning of the three AXB tones present in

Experiment 2. Some of these serial contexts implied no pitch motion relative to the rest of the sequence.

The Auditory Motion hypothesis predicts that if the beginning of an auditory sequence leads a listener to extrapolate null (or no) pitch motion, the kappa effect should be abolished in sequences where the serial context does not imply or reinforce a pitch motion; in order for the kappa effect to obtain, it is hypothesized that the listener’s attention may need to be guided through the auditory sequence in a consistent motion- like fashion. Alternatively, if a serial context does imply some pitch motion, this hypothesis predicts a reinforcement of a perception of pitch motion associated with the auditory sequence as a whole, leading to a reinstatement of the kappa effect. An alternative prediction can be formulated with respect to the phenomenon of auditory grouping, namely that the patterns in the SC0 condition of Experiment 3 will segregate into two groups, the first group consisting of the first four tones (which all have the same pitch), and the second group consisting of the final two tones (which each have a different pitch). Because it should be harder to compare across groups than within groups, and since these groups will segregate more with increasing pitch distance

69 between tone A and tone X, then it follows from this hypothesis that it should be harder to judge the timing of tone X relative to tone A, the greater its distance in pitch from tone

A. In effect, auditory grouping predicts a main effect of X pitch on accuracy of time judgments.

No effect of X Pitch on accuracy (measured as either PC or as JND) was found for SC0 patterns in Experiment 3, indicating a lack of support for the predictions of grouping theory. Support for the AM hypothesis, however, was obtained, in the form of a significant interaction between the variables of X Pitch and Serial Context (see Figure

12). Essentially, listeners displayed the kappa effect in the SC4 and SC8 conditions

(where the serial context reinforces the pitch motion of the kappa cell) but not in the SC0 condition (where the serial context implies null pitch motion with respect to the kappa cell). If the kappa effect depends on a listener’s attention being guided through an auditory pattern in a consistent motion-like fashion, then disrupting the pitch trajectory of an auditory pattern (e.g., by indicating null pitch motion in the first half of the sequence and instantiating a pitch velocity in the second half) should disrupt the kappa effect.

CHAPTER 5

KAPPA WITH OPPOSING SERIAL CONTEXT

Experiment 3 illustrates that kappa may be abolished in situations where the serial context of a pattern differs from the kappa cell in terms of its implied pitch motion. If the kappa effect depends on the motion-like characteristics of a pattern, disrupting these characteristics should disrupt kappa. Specifically, Experiment 3 indicates that when the serial context of a pattern (i.e., the tones leading up to a kappa cell) implies null or no pitch motion, the kappa effect is dramatically weakened (and, statistically speaking, non- existent).

The Auditory Motion hypothesis claims that implied, motion-like properties of a sequence give rise to the kappa effect. Therefore, disrupting the motion-like properties of a sequence may disrupt or abolish the kappa effect. As illustrated in Experiment 3, disrupting the motion-like properties of a sequence consisted of manipulating the pitch distance between tones in the serial context, such that successive tones were 0 semitones apart, i.e., all tones in the serial context were of the same pitch.

In Experiment 4, we again disrupt the motion-like properties of a sequence, to see whether the kappa effect remains. Here, however, the serial context will possess a different pitch direction than the tones comprising the kappa cell (see Figure 19). The

71 serial context of the pattern will thus lead a listener to extrapolate motion-like properties different from those in the kappa cell.

B __ Higher

Kappa Cell

Frequency __

| Serial | Context Cell

Lower 1 2 3 4 5 6 Serial position

Figure 19. Schematic of a sequence in Experiment 4.

According to the Auditory Motion hypothesis, this type of context manipulation should result in the abolishment of the kappa effect. Sequences in which the pitch motion in the serial context leads a listener to extrapolate pitch motion inconsistent with that present in the kappa cell should not display kappa. Alternatively, if the Auditory Motion hypothesis is incorrect, we may expect to see kappa present in these sequences as well.

An alternative to the predictions of the Auditory Motion hypothesis can once again be formulated with respect to Bregman’s (1990) discussion of Auditory Scene

Analysis; these predictions are also related to the phenomenon of auditory grouping.

72 In the first stage of Auditory Scene Analysis, sounds are grouped together. According to

Bregman (1990), the principles by which an organism groups sounds together seem to be analogous, broadly speaking, to Gestalt principles. One Gestalt principle of immediate consequence for the current study is the principle of “continuity”; that is, sequential sounds with the same pitch trajectory will tend to group together. The principle of continuity makes the prediction that the patterns of Experiment 4 will segregate into two groups, the first group consisting of the first four tones (all of which descend in pitch), and the second group consisting of the final two tones (which instantiate an ascending trajectory).

Again, the greater the difference, in pitch, between the final tone of the first group

(tone A) and the initial tone of the second group (tone X), the more these “groups” will segregate, again on the basis of the principle of pitch proximity referred to in the previous chapter. Since it should be more difficult to compare “across” perceptual groups than

“within” them, it follows from this hypothesis that it should be harder to judge the timing of tone X relative to tone A, the greater its distance in pitch from tone A. In effect, auditory grouping again predicts a main effect of X pitch on accuracy of time judgments.

Method

Participants

Twelve participants were recruited from an undergraduate psychology course at

OSU and participated in return for course credit. As in all previous experiments, subjects were required to have good hearing in both years and less than ten years of formal musical training.

Apparatus

The apparatus was the same as in all previous experiments.

Stimuli

As in previous experiments, all tones were pure tones with a duration of

200 ms. Like Experiment 3, on each trial, listeners heard six-tone sequences, and for all sequences, Tones A & B (i.e., tones at the 4th and 6th serial positions) were

C5 (523 Hz) & G#5 (831 Hz), respectively. Tones A & B were always separated by an ISI (Inter-Stimulus Interval) of 1200 ms.

The major change from Experiment 3 was in the structure of the three-tone serial context listeners heard before the kappa cell (where the kappa cell may again be denoted A – X – B). On each trial, listeners heard a three-tone serial context before the kappa cell. However, in Experiment 4, this serial context differed from the kappa cell with respect to pitch direction. In Experiment 4, the serial context descended in pitch, whereas the tones within the kappa cell consistently ascended in pitch, as shown in Figure 19.

For all sequences, this serial context was C6 - G#5 - E5; successive tones in the serial context were thus separated from each other by 4 semitones. The last tone in the serial context, E5, was also separated from the first tone in the kappa cell, C5, by 4 semitones. All tones in the serial context were again pure tones with a duration of 200 ms, and each tone was followed by a silent ISI of 500 ms.

74 Tone X assumed one of 5 pitch values, corresponding to the same pitch values it could take on in Experiments 2 & 3 (see Table 1). As in all previous experiments, Tone X also assumed one of eight timing values. Expressed in terms of inter-stimulus interval, or ISI, between Tone A and Tone X, these were: 430,

450, 470, 490, 510, 530, 550, or 570 ms. All subjects experienced all levels of

Tone X timing.

Design

The primary design of Experiment 4 was a 5 x 8 repeated-measures design. The variable of X Pitch (expressed as the distance in semitones between Tones A & X) served as one within-subjects variable. The variable of X Time served as another within-subjects variable, with the eight levels of timing given above. This resulted in 40 patterns unique to each subject.

Procedure

The procedure for Experiment 4 was identical to the procedure for Experiment 3.

Results & Discussion

A 5 x 8 repeated-measures ANOVA was calculated on the p(B) scores from

Experiment 4. A significant main effect of X Time was obtained, F(7, 77) = 45.186, Mse

= .062, p < .0001. As shown in Figure 20, subjects were more likely to respond “B” if

Tone X was closer to Tone B in time, similar to the results of previous experiments, and

75 indicating that the temporal manipulation of the X Tone was effective in influencing listeners’ responses.

Figure 20. Effect of X Time on p(B) judgments in Experiment 4.

No other main effects or their interactions were significant. In particular, the data from Experiment 4 displayed no main effect of X Pitch. Figure 21 indicates the null kappa effect in showing that the pitch of tone X exerted no systematic effects on temporal judgments. For comparison purposes, the SC4 condition from Experiment 3 is plotted as well; this condition possessed a similar of absolute pitch motion in the serial context (i.e.,

4 st between consecutive ascending tones), but in the opposite direction of the serial context from Experiment 4 (in which the serial context descends in pitch). In particular, this finding parallels the results from the SC0 condition of Experiment 3, where the serial 76 context of a kappa judgment contained motion-like properties that conflicted with those of the kappa cell. Recall that in Experiment 3, the SC0 condition contained a serial context that implied null or no pitch motion, relative to the trajectory established by the kappa cell. In this condition of Experiment 4, the serial context for the kappa cell may be said to conflict with the kappa cell in the same way, in the sense that the pitch direction of the serial context conflicts with the pitch direction of the kappa cell; the kappa cell for both experiments implies pitch motion upwards, yet in the SC0 condition of Experiment

3, the serial context implies null pitch motion, while in Experiment 4, the serial context implies a downward pitch motion.

Figure 21. Null effect of X Pitch on p(B) judgments in Experiment 4. The SC 4

condition from Experiment 3 is plotted for comparison.

77 In addition, PC scores from Experiment 4 were subjected to a 5 x 8 repeated- measures ANOVA with 5 levels of X Pitch and 8 levels of X Time. The data displayed only a significant effect of X Time, F = 11.355, Mse = .058, p < .001. No effect of X

Pitch was present, nor was the interaction of X Time and X Pitch, as would be effected if the kappa effect were to obtain. As in the SC 0 condition of Experiment 3, this indicates that listeners performed worse on the task the closer Tone X fell toward the temporal midpoint of the AXB sequence. Indeed, the data appear virtually indistinguishable from that presented in Figure 14. Thus, it appears as if the Auditory Motion (AM) hypothesis is a better predictor of the results of Experiment 4 than grouping theory. A grouping account makes the prediction that the patterns of Experiment 4 will segregate into two groups because of the principle of continuity; that is, the first group consists of the first four tones (all descending in pitch), and the second group consists of the final two tones

(ascending in pitch); it should therefore be more difficult to judge the relative timing of

Tone X the further away it is in pitch from Tone A (due to the principle of pitch proximity). This predicts a main effect of X Pitch on accuracy for this task, which is not present in the data.

PSE and JND scores from Experiment 4 were also examined (The data from two participants had to be removed due to inadequate probit fits). PSE scores from

Experiment 4 were subjected to a one-way repeated-measures ANOVA with one variable, X Pitch, which had 5 levels. No significant differences in PSE were found as a function of X Pitch. JND scores from Experiment 4 were also subjected to a one-way repeated-measures ANOVA with 5 levels of the X Pitch variable; no significant effect of

X Pitch on JND scores was found.

78 Summary

In Experiment 4, the motion-like properties of a sequence were again disrupted.

Here the serial context possessed a different pitch direction compared to the kappa cell

(see Figure 19). The serial context in the patterns of Experiment 4 lead a listener to extrapolate a descending pitch trajectory, while the tones in the kappa cell instantiate an ascending pitch trajectory.

According to the Auditory Motion hypothesis, this type of context manipulation should result in the abolishment of the kappa effect. When the trajectory of the serial context leads a listener to extrapolate pitch motion inconsistent with the trajectory of the kappa cell, listeners should not display the kappa effect. No kappa effect was found in the data of Experiment 4, providing support for the AM hypothesis. As in Experiment 3, if the kappa effect depends on a listener’s attention being guided through an auditory pattern in a consistent motion-like fashion, then disrupting the pitch trajectory of an auditory pattern (e.g., by instantiating a pitch trajectory in the serial context that is the opposite direction from the pitch trajectory instantiated by the kappa cell) should disrupt the kappa effect.

An alternative to the above prediction comes from grouping theory. The Gestalt principle of continuity, as utilized in the first stage of Auditory Scene Analysis, makes the prediction that the patterns of Experiment 4 will segregate into two groups, the first group consisting of the first four tones (descending in pitch), and the second group consisting of the final two tones (ascending in pitch). Since it should be more difficult to compare “across” perceptual groups than “within” them, it follows from this hypothesis that it should be harder to judge the timing of tone X relative to tone A the greater its

79 distance in pitch from tone A, in essence predicting a main effect of X pitch on accuracy of the temporal judgment in Experiment 4. However, no effect of X Pitch on accuracy was found in Experiment 4, again indicating a lack of support for the predictions of grouping theory.

CHAPTER 6

KAPPA CELLS WITH GREATER PITCH MOTION

The data from Experiments 3 and 4 provide preliminary support for the Auditory

Motion (AM) hypothesis, i.e., the idea that the kappa effect should be abolished in those sequences that lead a listener to extrapolate null pitch motion. One may ask, however, if this is always the case. If the kappa effect depends on a listener’s tendency to extrapolate motion, then there may exist situations in which the sense of auditory motion in the kappa cell is so great that it overwhelms any effect of serial context. That is, there be may be situations in which the pitch motion present in the kappa cell is so great that the kappa effect is displayed, regardless of serial context.

Experiment 5 examines these issues. The stimuli from Experiment 5 are designed to be very similar to those of Experiment 3. However, the kappa cells of Experiment 5 contain greater pitch motion (operationally defined as the pitch distance between successive tones) than those in previous experiments.

The Auditory Motion hypothesis implies that the kappa effect obtains in situations in which a listener’s attention is guided through an auditory sequence in a consistent motion-like fashion. The sequences of Experiment 5 also contain a three-tone serial context cell added to the beginning of the kappa cell. As shown in Experiments 3 and 4, disrupting the motion-like properties of a sequence (e.g., by altering the pitch trajectory

81 of the serial context to make it different from the trajectory of the kappa cell) may reduce or abolish the kappa effect. This manifested in a significant effect of the Serial Context variable in Experiment 3. Recall that listeners in the SC0 condition of Experiment 3

(where the pitch distance in semitones between successive tones in the serial context cells for those patterns was equal to 0) did not display the kappa effect, while listeners in the

SC4 and SC8 conditions (corresponding, respectively, to distances of 4 or 8 st between successive tones in the serial context) did display the kappa effect.

As in Experiment 3, the design used in Experiment 5 will divide listeners into three Serial Context conditions: SC0, SC4, and SC8. In Experiment 5, like in Experiment

3, one Serial Context condition (SC0) will imply null pitch motion. The Auditory Motion hypothesis predicts that if the beginning of an auditory sequence (i.e., the serial context cell, for the present experiments) leads a listener to extrapolate null pitch motion, the kappa effect should be abolished in these kinds of sequences. In other words, the AM hypothesis predicts no kappa effect for the patterns of SC0.

An alternative to the predictions of the Auditory Motion hypothesis can be formulated with respect to auditory grouping. As in Experiment 3, auditory grouping makes the prediction that patterns implying null pitch motion in Experiment 5 (i.e., patterns in the SC0 condition) will segregate into two groups, the first group consisting of the first four tones (all having the same pitch), and the second group consisting of the final two tones, due to the Gestalt principle of pitch proximity espoused in Auditory

Scene Analysis (Bregman, 1990). Since it should be harder to compare across groups than within them, and since these groups will segregate more with increasing pitch distance between tone A and tone X, then it should be harder to judge the relative timing

82 of tone X the greater its distance in pitch from tone A. As in Experiment 3, auditory grouping predicts a main effect of X pitch on accuracy.

However, there exists a third alternative to these two sets of hypotheses. If the pitch velocity present in the kappa cell (defined as average pitch change/time) is increased, the sense of auditory motion in the kappa cell might be so great as to overwhelm any effect of serial context. In other words, in cases where the pitch velocity of the kappa cell is relatively large, the kappa effect may still obtain in these sequences even when the serial context implies a null pitch motion. We may refer to this as the

Modified Auditory Motion (MAM) hypothesis. In essence, the MAM hypothesis describes a limiting set of circumstances for the kappa effect; though kappa seems to depend on the motion-like relationships between the serial context and kappa cells, the pitch velocity of the kappa cell is important as well. If the kappa effect does indeed depend on the imputed motion in the kappa cell (as well as on the consistency of motion- like properties from the serial context to the kappa cell), it follows that the greater the imputed motion (defined here as pitch velocity), the more likely a listener will be to display the kappa effect. Support for the MAM hypothesis would be seen if the SC0 patterns of Experiment 5 displayed the kappa effect, as the only change in these patterns from the SC0 condition of Experiment 3 will be the greater pitch motion present in the kappa cells of Experiment 5.

83 Method

Participants

Thirty-four participants from an undergraduate psychology course at OSU participated in return for course credit. All subjects were required to have good hearing in both years and less than ten years of formal musical training.

Apparatus

The apparatus was the same as in all previous experiments.

Stimuli

All tones were again sine-wave (pure) tones with a duration of 200 ms. On each trial, listeners heard six-tone sequences. As in Experiment 3, stimuli were divided into 3 between-subjects conditions of Serial Context (SC0, SC4, or SC8, corresponding, respectively, to pitch distances of 0, 4, or 8 st between successive tones in the serial context cell). Tone A and Tone B again remained fixed in pitch and time on every trial. For all sequences, Tones A & B were C5 (523 Hz) & E6

(1319 Hz), respectively. Note the increased pitch distance between Tones A & B in Experiment 5 versus Experiment 3; in Experiment 3, Tones A & B were separated by 8 semitones, while in Experiment 5, Tones A & B were separated by

16 semitones. As in Experiment 3, Tones A & B were always separated by an ISI

(Inter-Stimulus Interval) of 1200 ms.

Tone X assumed one of 5 pitch values; these appear in Table 2, along with their distance in semitones (st) from Tone A. Though the timing relationships

84 between Tones, A, X, & B remained constant from Experiment 3, the pitch relationships did not. In Experiment 5, there were thus greater pitch distances between successive tones in the kappa cell, though the kappa cell itself remained unchanged in terms of duration. The kappa cells of Experiment 5 thus implied greater pitch motion relative to the kappa cells of Experiment 3.

Tone X Distance in semitones (st) from Tone A 1 C#5

5 F5

8 G#5

11 B5

15 D#6

Table 2. Possible pitch values for Tone X in Experiment 5.

As in previous experiments, Tone X assumed one of eight timing values.

Expressed in terms of inter-stimulus interval, or ISI, between Tone A and Tone X, these were again: 430, 450, 470, 490, 510, 530, 550, or 570 ms. Listeners experienced all levels of Tone X timing.

As in Experiment 3, a serial context cell was present at the beginning of each pattern. Serial context cells consisted of three tones added to the beginning of a kappa cell. The three tones comprising a serial context cell were all pure

85 tones with an ontime of 200 ms. Each tone was followed by a silent ISI of 500 ms.

Differences in implied pitch motion were conveyed through the pitch distances between successive tones in the serial context cell. As in Experiment 3, three levels of the Serial Context variable were used in Experiment 5, differing in terms of the amount of pitch motion implied in each. Level SC0 (Serial Context

G#4. This serial context implied a moderate amount of pitch motion, yet of an amount different from that implied by the kappa cell. Finally, level SC8 of the

Serial Context Variable corresponded to a pitch distance of 8 ST between successive tones in the serial context cell; the serial context cell was thus C3 -

GS3 - E4. This serial context implied a (relatively) large amount of pitch motion, yet of an amount consistent with that implied by the kappa cell (on average, the pitch change between successive tones in the kappa cell was equal to 8 st).

Design

The primary design of Experiment 5 was a 3 x (5 x 8) mixed factor design. Serial

Context (with the three levels of SC0, SC4, or SC8) served as the between-subjects

86 variable. The variable of X Pitch (again expressed as the distance in semitones between

Tones A & X, i.e., 1, 5, 8, 11, or 15) served as a within-subjects variable. X Time served as another within-subjects variable, with the eight levels described above. This resulted in

40 patterns unique to each subject.

Procedure

The procedure for Experiment 5 was identical to the procedures for Experiments 3

& 4.

Results & Discussion

A 3 x (5 x 8) mixed-factor ANOVA was calculated on p(B) scores from

Experiment 5. This resulted in a significant main effect of X Time, F(7, 217) = 71.247,

Mse = .083, p < .0001, indicating, as in Experiments 1 & 2, that subjects were more likely to respond “B” if Tone X was closer to Tone B in time; the temporal manipulation of the X Tone was thus effective in influencing listeners’ responses (see Figure 22).

87 Figure 22. p(B) scores as a function of the X Time variable in Experiment 1b.

Data from Experiment 5 also displayed an overall effect of X Pitch, F(4, 124) =

26.352, Mse = .111, p < .0001. The kappa effect was present here as a main effect, much as in Experiment 3, and indicates that listeners were more likely to respond “B” (i.e.,

Tone X is closer to Tone B in time) the closer in pitch Tone X was to Tone B. These data are illustrated in Figure 23.

88 Figure 23. p(B) responses as a function of X Pitch for Experiment 5.

Thus far the pattern of main effects in Experiment 5 have been very similar to those of Experiment 3. However, the data from Experiment 5 display an additional main effect that the data from Experiment 3 do not. In contrast to the data from Experiment 3, where no significant effect of Serial Context was present, the data from Experiment 5 display a marginally significant main effect of Serial Context, F(2, 31) = 5.243, Mse =

.282, p < .05. As shown in Figure 24, listeners were slightly (though significantly) less likely to respond “B” (i.e., “closer to Tone B in time”) in the SC0 condition than they were in the SC4 or SC 8 conditions. This is an effect of pitch on time perception, yet of a form different than the “classical” kappa effect. It is clear that the lack of pitch motion in the serial context of patterns in the SC0 condition affected listeners’ responses in

89 Experiment 5. However, the process by which this occurred may be slightly more complex from the processes responsible for the kappa effects seen in other experiments.

It may be the case in Experiment 5 that listeners in the SC0 condition had a stronger memory for the pitch of Tone A (the tone repeated three times in the serial context) and as result their memory for the pitch of Tone X was “pulled” toward the pitch of Tone A, i.e., they misremember Tone X as being lower than it actually was, as might be the case if pitch memory was subject to some kind of “interference” effect in pitch memory, though the experiments demonstrating such effects usually utilize pitch recognition tasks (e.g.,

Deutsch, 1972, 1974) whereas in the present task the listener was explicitly instructed to ignore pitch. If Tone X were indeed misremembered as being lower, we would expect to see results like those present in Figure 24, because misremembering Tone X as being lower than it was would lead to a disproportionate number of “A” responses – a variant of the kappa effects seen in other experiments, but one not dependent on the pitch of Tone X per se. Nevertheless, this main effect was not present in Experiment 3, so presumably its presence in Experiment 5 is due to the increased pitch motion present in the kappa cell of

Experiment 5. (Experiments 3 & 5 are analyzed within the context of a larger design later in the chapter.)

Figure 24. p(B) responses as a function of Serial Context for Experiment 5.

Finally, as in Experiment 3, a significant interaction of X Time with X Pitch was obtained, F(28, 868) = 1.966, Mse = .018, p < .01. Figure 25 illustrates, again, that this is primarily due to an increase in the effect of X Pitch at intermediate values of the X Time variable. No other main effects or their interactions were significant.

91 Distance (ST) of Tone X from Tone A

Figure 25. Interaction of X Time and X Pitch in Experiment 5.

In contrast to Experiment 3, no significant interaction of X Pitch and Serial

Context was obtained. That is, the kappa effect was obtained for all levels of Serial

Context. However, the pattern of results is generally similar to Experiment 3, as shown in

Figure 26.

92 Serial Context Condition

Figure 26. Effect (ns) of X Pitch and Serial Context on p(B) in Experiment 5.

As can be seen in Figure 26, the line representing the SC0 condition has a shallower slope than the lines representing the SC4 or SC8 conditions, indicating that the

X Pitch variable had a slightly smaller effect on timing judgments in the SC0 condition.

We might expect to see these results if some version of the Modified Auditory Motion

(MAM) hypothesis is correct. The MAM hypothesis shares with the Auditory Motion

(AM) hypothesis the claim that implied auditory motion is necessary to obtain the kappa effect; however, the AM hypothesis claims that abolishment of the kappa effect will result from any situation in which the implied motion-like characteristics of the serial 93 context differ from those of the kappa cell, due to a listener’s (incorrect) extrapolation of consistent pitch motion beyond the serial context. The MAM hypothesis, in contrast, claims that the greater the pitch motion in a kappa cell, the more likely one is to experience kappa. This is a subtle distinction to be sure, but it may be why we see kappa in the SC0 condition of Experiment 5, but not in the SC0 condition Experiment 3. The only difference in these two conditions is in the amount of auditory pitch motion implied by the kappa cells in both conditions (as defined by amount of pitch change over time).

The greater pitch motion in the SC0 kappa cells of Experiment 5 (vs. Experiment 3) were enough to “overcome” the effect of the null pitch motion implied by the serial context of the SC0 condition so that we see kappa in the SC0 condition for Experiment 5 but not for

Experiment 3.

To test this hypothesis, the p(b) scores from the SC0 condition of Experiment 5 were combined with the p(b) scores from the SC0 condition of Experiment 3. These scores were entered into a 2 x (5 x 8) mixed-factor ANOVA with 5 levels of X Pitch

(denoted as 1, 2, 3, 4, or 5, where higher numbers indicate greater distance, in pitch, from

Tone A to Tone X), 8 levels of X Time serving as the repeated-measures factors, and a new between-subjects factor, Kappa Cell, with two levels, KC4 and KC8, referring to the average amount of pitch change between successive tones in the kappa cell, i.e., 4 st in

Experiment 3 and 8 semitones in Experiment 5. (Though levels of the X Pitch variable do not correspond exactly from Experiment 3 to Experiment 5, the amount of relative pitch change from Tone A to Tone X for a given level of the X Pitch variable remains roughly constant across experiments.)

94 As might be expected, the data displayed a significant effect of X Time, F(7,133)

= 62.924, Mse = .064, p < .001. This is not surprising, given the significant effect of X

Time in both Experiment 3 and Experiment 5. Overall the data displayed a very similar pattern to all other instances where the X Time variable was significant; listeners were more likely to respond “B” if Tone X was closer to Tone B in time (these data are not plotted here, as they appear virtually identical to Figure 22).

A significant effect of X Pitch was also obtained, F(4,76) = 4.291, Mse = .063, p

< .005. As shown in Figure 27, the kappa effect is present in these data. Listeners were more likely, on average, to respond that Tone X was closer to Tone B in time if Tone X was also close to Tone B in pitch.

95 Figure 27. p(B) judgments as a function of X Pitch for the combined SC0

conditions of Experiments 3 & 5. Larger values for X Pitch (x-axis) indicate

greater distances (in semitones) of Tone X from Tone A.

These main effects were qualified, however, by the two-way interaction of X

Pitch with Kappa Cell, F(4, 76) = 2.938, Mse = .063, p < .05. As shown in Figure 28, p(B) scores from the SC0 condition of Experiment 5 displayed the kappa effect (i.e., an effect of X Pitch on p(B) scores), while p(B) scores from the SC0 condition of

Experiment 3 did not. Since the only difference between these two conditions is in the amount of pitch motion present in the kappa cell, this finding provides support for the

MAM hypothesis, which claims that the greater the pitch motion in a kappa cell, the more likely one is to experience kappa.

96 Kappa Cell Condition

Figure 28. p(B) judgments as a function of X Pitch and Kappa Cell conditions for

SC0 patterns. No kappa effect is present for the KC4 condition (Experiment 3)

while a kappa effect is present in the KC8 condition (Experiment 5).

A significant interaction of X Time with Kappa Cell was also obtained, F(7,133)

= 2.281, Mse = .064, p < .05. As illustrated in Figure 29, listeners are more likely to respond “Tone X is closer to Tone B in time” when Tone X is in fact closer to Tone B in time; however, this trend appears more pronounced in the KC4 condition. Also, as can be seen in Figure 29, the trend for the KC4 data appears slightly more ogive than the trend for the KC8 data; viewed in this way, one might interpret this interaction as an effect of 97 Kappa Cell on accuracy, since the trends in Figure 29 may conceived as psychometric functions. Notably, proportion correct (PC) in the KC4 condition was .69, compared with only .63 in the KC8 condition. Nevertheless, a follow-up t-test on PC scores (a measure of overall accuracy) across the two Kappa Cell conditions failed to reach significance.

Kappa Cell Condition

Figure 29. p(B) judgments as a function of X Time and Kappa Cell condition for

SC0 patterns.

98 The data from the SC0 condition of Experiment 5 were once again reanalyzed in terms of Proportion Correct (PC) scores to test a hypothesis from grouping theory, namely that the patterns used in SC0 should segregate into two groups - the first consisting of the first four tones in a pattern, and the second consisting of the final two tones (i.e., Tones X and B). As in Experiment 3, grouping theory predicts that it should be harder to judge the relative timing of tone X the greater its distance in pitch from tone

A, i.e., predicting a main effect of X Pitch on accuracy.

A 5 x 8 repeated-measures ANOVA (with 5 levels of X Pitch and 8 levels of X

Time) was performed on PC scores from the SC0 condition of Experiment 5. As expected, the data displayed a significant effect of X Time, F(7,77) = 10.125, Mse = .074, p < .01. As in Experiment 3, this indicates that listeners performed worse on the task the closer Tone X fell toward the temporal midpoint of the AXB sequence (i.e., the harder the temporal judgment). Interestingly, however, the data also displayed an effect of X

Pitch, though of a form opposite to that predicted by grouping theory.

The effect of X Pitch on accuracy for the SC0 condition of Experiment 5 is displayed in Figure 30. As can be seen, listeners were actually slightly more accurate in judging the timing of Tone X the further away in pitch it was from Tone A. This stands in contrast to grouping theory, which predicts that listeners should be less accurate in judging the timing of Tone X the further away in pitch it is from Tone A.

99 Figure 30. Significant effect of X Pitch on p(B) scores from the SC0 condition of

Experiment 5.

These main effects, however, are qualified by a significant interaction of X Time with X Pitch, F(28, 308) = 3.517, Mse = .028, p < .0001. As seen in Experiments 2 & 3, the effect of the X Time variable is modulated by the effect of the X Pitch variable; listeners perform best on the task when Tone X is close to Tone A (B) in both pitch and time, and worst when Tone X is close to Tone A (B) in time but is far away from Tone A

(B) in pitch. This is shown in Figure 31.

100

Distance (ST) of Tone X from Tone A

Figure 31. Significant interaction of X Time and X Pitch for the SC0 condition of

Experiment 5.

Data from Experiment 5 was reanalyzed in terms of PSE and JND for the 34 participants who participated. Data from 7 participants could not be included in this analysis due to inadequate probit fits. The data of the 27 participants in Experiment 5 for whom psychometric functions could be obtained are shown in figure 32. These PSE scores were subjected to a 3 x (5) mixed-factor ANOVA with one between-subjects factor, Serial Context, and one repeated-measures factor, X Pitch. A significant effect of

101 X Pitch on PSE was obtained, F (4, 96) = 11.56, Mse = 1950, p < .001. As the Tone X moves further from Tone A in pitch, the PSE for timing decreases. This is consistent with the kappa effect. In the absence of any effect of pitch on time perception, PSEs should hover around 500 ms, that level of X Time Distance that would exactly subdivide the ISI between Tones A and B.

Figure 32. PSE scores as a function of X Pitch in Experiment 5.

JND scores of these 27 participants were subjected to the same 3 x (5) mixed- factor ANOVA. No significant effect of Serial Context or X Pitch on JND was observed.

In this experiment, subjects did not show any appreciable changes in difference limen as a function of the Serial Context or X Pitch Distance variables.

102 Summary

Results from Experiment 5 provide support for a version of the Auditory Motion hypothesis. It appears that a sense of auditory motion provided by large pitch/time changes within a kappa cell is sufficient to overwhelm a null pitch motion influence associated with serial context, if the amount of pitch motion is large enough. Kappa may still arise in these sequences even when a serial context preceding a kappa cell implies a null pitch motion. We may refer to this as the Modified Auditory Motion (MAM) hypothesis. Sequences in Experiment 5 implying null pitch motion in the serial context

(yet containing greater pitch motion in the kappa cell than sequences in Experiment 3) displayed the kappa effect. Support for the predictions espoused by grouping theory was not obtained.

103

CHAPTER 7

GENERAL DISCUSSION

In this chapter, the results of Experiments 1 – 5 are first reviewed and discussed.

Next these findings are put into the context of Weber’s Law. Finally, limitations of the current studies are discussed.

Experimental findings

In this section, the main implications of Experiments 1-5 are reviewed and expanded. Experiment 1 provides the baseline data for all following kappa studies in that it assesses listeners’ ability to render judgments about the relative timing of Tone X within a three tone context where the tones flanking Tone X (A, B) are identical to X in pitch. In this experiment, these time judgments were assessed both in the absence of a preceding serial context and in the presence of such a context. The results of this experiment offer modest support for Large and Jones (1999), who claim that longer sequence rhythms allow for the generation of stronger temporal expectancies about future tones than rhythms based on shorter serial contexts. Timing judgments in Experiment 1a consisted of judging whether Tone X was closer to Tone A or Tone B in time. Crucially, these judgments were made without the benefit of any preceding serial context, whereas in Experiment 1b, an isochronous three-tone serial context was added to the beginning of

104 the patterns. It appears that addition of isochronous serial context in Experiment 1b provided a slightly more efficient rhythmic framework in which to make temporal judgments of the X Tone. Listeners averaged better performance for Experiment 1b, with

Context Present sequences (mean PC = .745) than for Experiment 1a, with Context

Absent sequences (mean PC = .723). Thus, it is possible then that an isochronous serial context may have narrowed the listener’s attentional focus, providing greater temporal acuity, i.e., greater sensitivity to a phase discrepancy between the time a listener expected

Tone X to occur (here the midpoint of the temporal interval formed by Tone A and Tone

B) and when that event actually occurred. However, it is noteworthy that the addition of a serial context in this case did not hinder performance relative to the no context condition, which would be predicted if context is viewed simply as “added noise.”

Experiment 2 was designed to replicate Shigeno (1986) and illustrate the classical kappa effect. Building upon the task of Experiment 1a, pitch information was introduced into the three tone sequence. The task remained one of relative time judgment, but the key independent variable in Experiment 2 was the pitch of Tone X. On each of a series of trials, a listener now heard three tones that differed in pitch; they could ascend or descend in pitch. Listeners were told to ignore pitch differences and to judge whether the middle tone was closer to the first (A) or the third (B) tone in time.

The AM hypothesis predicted a main effect of the pitch of Tone X for these sequences. This hypothesis claims that kappa is dependent on pitch/time expectancies induced by the motion-like properties of to-be-judged events. Applying this to the stimuli of Experiment 2, it means that local context (i.e., within Kappa cell) pitch and time intervals between the three Kappa cell tones convey pitch motion; i.e. a rate of change of

105 pitch with respect to the unfolding time intervals between successive events. These motionlike properties are presumed to influence judgments of Tone X such that the pitch/time relationship established in the first time interval implies an expectancy about the pitch/time relationship in the second time interval. Kappa thus results from a perceived distortion in the second time interval, stemming from a violation of the expectancies generated by the first pitch/time interval. In essence, the presence of the kappa effect hinges on (and is invisible without) expectancy violations.

The results of Experiment 2 indicated that the pitch of Tone X significantly affected listeners’ responses to its relative timing. Subjects were more likely to say that

Tone X was closer to Tone A (B) in time if it was also close to Tone A (B) in pitch. In addition to replicating Shigeno (1986), these results extend Shigeno’s (1986) work in the sense that kappa appears to occur in the context of pitch relationships, rather than only in linear frequency relationships per se. These results conflict somewhat with Hirsh et al.

(1990), especially considering the results of Experiment 2 did not find a significant main effect of X Pitch on PC.

The Auditory Motion hypothesis, however, implies that a listener in this experiment perceives tones that are widely separated in pitch as widely separated in time because events in the sequence should be perceived to follow an (implied) motion-like trajectory. Further, if there is a bias to perceive this motion as having a constant rate of pitch change, i.e., a constant auditory velocity, then it would take longer to move between two points on the trajectory that are farther apart in space than to move between two points that are closer together in space; motion-like trajectories thus generate expectancies for certain pitches at certain times.

106 Nevertheless, the kappa effect, in some sense, seems to depend on an expectancy violation. The kappa effect is most evident when a listener expects a certain pitch at a time dictated by the assumption of a constant velocity throughout the auditory sequence and this does not happen. When a listener hears the pitch of Tone X, s(he) seems to assume that the timing of Tone X is linked with its pitch, such that the perceived time of

Tone X conforms to that which is expected from its pitch, if a constant velocity was present throughout the sequence.

While Experiment 2 data indicated that kappa is a valid phenomenon, Experiment

3 addressed the question of whether providing a larger serial context (i.e., than the local context within a Kappa cell) for temporal judgments would affect kappa. Serial context was added to each trial by preceding AXB Kappa with a three-tone sequence.

Experiment 2, a serial context was provided for kappa judgments, although some serial contexts implied no pitch motion relative to the rest of the sequence.

Relative timing judgments in Experiment 3 were affected by the independent variable of X Pitch, illustrating the classical kappa effect, and indicating that listeners were more likely to respond “B” (i.e., Tone X is closer to Tone B in time) the closer in pitch Tone X was to Tone B. This effect was qualified, however, by an interaction of X

Pitch with Serial Context. The kappa effect is virtually non-existent for sequences in which the serial context implies a null pitch motion, essentially confirming the predictions of the AM hypothesis. The kappa effect appears to depend on a listener’s

107 attention being guided through an auditory sequence in a consistent motion-like fashion.

If a listener extrapolates the pitch trajectory of a pattern to be one of null pitch motion (as is the case in the Serial Context 0 condition of Experiment 3, i.e., when the serial context contains no pitch changes), the trajectories of the serial context (null pitch motion) and the kappa cell (upward pitch motion) will conflict. This, in turn, leads to a marked reduction or even elimination of the kappa effect.

Experiment 3 thus illustrates that the kappa effect may be abolished, or at least, greatly weakened in situations where the serial context of a pattern differs from the kappa cell in terms of its implied pitch motion. If the kappa effect depends on the motion-like characteristics of a pattern, disrupting these characteristics (i.e., instantiating conflicting pitch trajectories) should disrupt kappa. When the serial context of an auditory sequence implies null pitch motion, the kappa effect is dramatically weakened (and, statistically speaking, non-existent).

Experiment 4 disrupted the motion-like properties of a sequence, although in a different way. In Experiment 4, the serial context possessed a different pitch direction than the kappa cell. Serial context was comprised of tones that descended in pitch, while the kappa cell was again comprised of tones that ascended in pitch, with the first tone of the kappa cell instantiating a “contour change. Here, the serial context of the pattern again led a listener to extrapolate motion-like properties different from those in the kappa cell.

The results of Experiment 4 are predicted by the Auditory Motion hypothesis.

According to this hypothesis, situations in which the implied motion-like characteristics of the serial context differ from those of the kappa cell should weaken or eliminate the

108 kappa effect. The data from Experiment 4 displayed no kappa effect. This finding paralleled the results from the SC0 condition of Experiment 3, where the serial context of a kappa judgment contained motion-like properties that conflicted with those of the kappa cell. In Experiment 4, the serial context conflicted with the kappa cell in the same way, in the sense that the pitch direction of the serial context conflicted with the pitch direction of the kappa cell. In both experiments, the kappa cell implied pitch motion upwards, yet in the SC0 condition of Experiment 3, the serial context implied null pitch motion, while in

Experiment 4, the serial context implied a downward pitch motion.

In these cases, a serial context that conflicts with a kappa cell radically enough

(e.g., by implying null pitch motion, or pitch motion of an opposite trajectory from the kappa cell) may destroy a listener’s expectancy of a constant velocity through the patterns. Jones (1976) has argued that auditory sequences which induce simple pitch/time trajectories facilitate anticipations about future pitch and time locations of subsequent tones within a coherent pattern. A constant velocity auditory motion realizes one such trajectory. In the SC0 condition of Experiment 3, Tone X instantiates a contour change within the sequence. The instant this happens, the listener is provided with information that the assumption of constant velocity is flawed.

However, as discussed previously, Tone X always instantiates a change in the pitch velocity of the sequence (with the exception of when Tone X exactly subdivides the pitch interval from Tone A to Tone B, i.e., one-fifth of the time). The kappa effect, in fact, depends on the flawed assumption of constant velocity being held as true. Why then does a listener discard the assumption of constant velocity when he or she hears a contour

109 change, rather than when he or she hears a pitch interval (e.g., from Tone A to Tone X) that is larger than it should be?

Simply put, contour changes may be more salient than pitch interval changes.

Research has shown that contour changes in an auditory sequence may be more quickly detected (Schiavetto, Cortese, & Alain, 1999), more easily detected (Trainor, McDonald,

& Alain, 2002), and, to the extent that memory may play a role in kappa tasks, better remembered (Dowling, 1978) than changes in interval size. A listener may be able to use the contour change in these sequences as a source of information about the upcoming kappa cell. Namely, a contour change could serve as an indication of sorts to the listener that the assumption of constant velocity does not hold.

X pitch on accuracy of the temporal judgment in Experiment 4. However, no effect of X

Pitch on accuracy was found in Experiment 4, again indicating a lack of support for the predictions of grouping theory.

Experiment 5 asked the question: are there situations where the pitch motion present in the kappa cell is so great as to overwhelm the effect of serial context? The

110 stimuli from Experiment 5 were similar to those of Experiment 3. However, the kappa cells of Experiment 5 contained greater pitch motion (operationally defined here as the pitch distance between successive tones) than the kappa cells in Experiment 3.

Clarke (2001) claims that music is often “metaphorically” perceived as motion.

One way this could happen is through the experience of music in terms of metaphorical motion in virtual space, supported by mappings such as that of pitch and verticality.

Pursuant to this, Eitan and Granot (2006) have claimed that changes in pitch through the course of an auditory sequence may serve as one indicator of this “virtual” motion.

Perhaps the best known phenomenon of a change in pitch being associated with a sensation of motion is the well-known Doppler effect. As a sound source traveling at a constant velocity passes an observer, the observed frequency of the sound will drop.

Crucially, however, the amount of this “Doppler shift” varies as a function of the velocity of the moving sound source (Neuhoff & McBeath, 1996). Specifically, the Doppler shift will be larger (leading to a bigger drop in the observed frequency of the sound) the faster the velocity of the moving sound source.

In a fashion analogous to the Doppler effect phenomenon, the kappa cells from the SC0 condition of Experiment 5 (i.e., patterns which contained not pitch motion in the serial context tones) carried a greater sense of velocity than the kappa cells from the SC0 condition of Experiment 3 by virtue of their (comparatively) large pitch shifts. In other words, Serial Context cells did not change in Experiment 5, relative to Experiment 3.

Thus the only difference in the patterns of Experiment 3 and Experiment 5 was in the pitch relationships of the kappa cell.

111 As shown in Experiments 3 and 4, disrupting the motion-like properties of a sequence with a contour change can disrupt or may even abolish the kappa effect, as the contour change may function as an indication that the assumption of constant velocity is not valid. As in Experiment 3, the serial context of some patterns in Experiment 5 implied null pitch motion. However, the kappa effect appeared with these patterns in

Experiment 5, where it did not in Experiment 3. As this represents the only change to these patterns, one may postulate that it appears that the kappa effect may be reinstated in patterns implying null pitch motion if the sense of auditory motion in the kappa cell is great enough (e.g., a 16 st pitch difference between Tones A and B in Experiment 5 versus an 8 st difference in Experiment 3). Thus the Modified Auditory Motion (MAM) hypothesis claims that kappa is dependent on two things: 1) a sense of pitch motion in the kappa cell and 2) a congruent (if any) serial context for the kappa cell. As shown in

Experiment 5, even though the serial context may not be congruent (and may even in fact imply null pitch motion) the kappa effect may appear if 1) is strong enough, i.e., if there is a strong enough sense of pitch motion in the kappa cell.

In all experiments, support was obtained for a version of the Auditory Motion hypothesis. Recall that Cohen and other authors (Cohen, Hansel, & Sylvester, 1955; Hass

& Hass, 1984; Newman & Lee, 1972; Price-Williams, 1954) have postulated that the mechanism by which the kappa phenomenon manifests is contingent upon a predisposition of an observer (or listener) to perceive a single object moving through time, rather than to perceive a series of different objects that each turn on and off in succession (Cohen, Hansel, & Sylvester, 1955). In other words, subjects perceive events that are widely separated in space (spatial extent or pitch) as widely separated in time

112 because a perceptual object is perceived as traveling along an implied trajectory at a constant velocity; it therefore takes longer to move between two points that are farther apart in space than to move between two points that are closer together. Importantly, though the kappa effect itself depends on a violation of constant velocity, a listener will continue to act as though the assumption holds, i.e., will display the kappa effect, unless given information that this assumption does not hold (through, e.g., a contour change).

Stimuli of the type used by Shigeno (1986; 1993 possessed a very simple frequency/time structure. In the original (1986) task, three tones were presented to the listener, and only the middle tone varied from trial to trial. However, a longer, more complex frequency/time serial context was never provided for these judgments. The present research aimed to address the question: To what extent might auditory kappa be influenced by serial context?

As noted earlier, Jones (1976; Jones and Yee, 1993) claims that in longer auditory sequences, when changes in pitch are both small and unfold relatively quickly, consequent “motion-like” trajectories of a melody has the potential for influencing listeners’ perception. These trajectories guide one’s attending along paths of implied pitch motion, generating expectancies for certain pitches at certain times. Thus, to the degree that the kappa effect is a result of the imputed (auditory) movement of the stimulus serial contexts that preserve salient motion-like characteristics also preserve the kappa effect.

113 Weber’s Law

In its basic form, Weber’s Law states that the amount by which a stimulus must be changed in order for an observer to detect said change is a constant proportion of the stimulus itself. The Weber ratio (here the ratio of JND to PSE) provides this constant. For time perception, some claim the value of this ratio to be equal to around .05 (Getty, 1975;

Halpern & Darwin, 1982; Kristofferson, 1980). However, overall Weber ratios for the current experiments were .12, .18, .16, .13, .17, and .25, for Experiments 1 through 6, respectively. Why the discrepancy?

One reason is the inclusion of additional pitch information in these sequences. In its basic form, Weber’s Law is just as stated above. The generalized version, however, as exemplified by Getty (1975) adds a sensory noise component. Variance in duration discrimination, says Getty, can be parsed in terms of a duration-dependent component

(the simple form of Weber’s Law) plus a duration-independent (or sensory noise) component. As the duration to be discriminated gets smaller, the sensory noise component gets larger, proportionally. This parallels Jones and Huang’s (1982) characterization of auditory kappa; namely, they claim that as temporal judgments are made more difficult, the frequency attributes of the to-be-judged events become more salient. This equates to an effect of frequency information on judgments about time. In other words, as the middle X tone comes closer in time to the midpoint of the temporal interval formed by the A and B tones, the frequency of the X tone becomes more salient.

When it is difficult for subjects to judge to which of two tones (A or B) the X tone is closer in time, the frequency of the X tone strongly affects judgments about its timing, relative to situations in which this temporal judgment is easier. Note this does not explain

114 high values in Experiments 1. Viewed from this perspective, the pitch information of the

X tone functions as a duration-independent source of sensory noise for the listener.

In addition, Halpern and Darwin (1982), although they found an average Weber fraction of around .05, used a series of four clicks which contained no pitch information.

The first three were isochronous, while the last could deviate in either temporal direction from zero up to ten percent of the base IOI. Subjects then made a judgment about whether the last click sounded early or late.

In Experiment 1, in which the kappa cell contained no pitch information, the overall Weber ratio was .12. Though this was the lowest Weber ratio observed in the current set of experiments, it is still relatively high, especially compared to previously observed values of around .05. Perhaps the main reason why this might be the case is that, in the current set of experiments (unlike classical time discrimination studies), one is being asked to not only detect a difference, but to say where in time it is; it is not enough for a subject to say that Tone X departed from isochrony. Rather, the listener must indicate to which Tone (A or B) the middle X tone is closer.

Limitations of Current Research

One limitation of the current research is its (comparatively) non-musical stimuli.

While representing a significant departure from the severely musically deficient stimuli used by Shigeno (1986), mainly in regards to the lack of serial context, the current stimuli are nevertheless relatively simple in terms of rhythmic structure or pitch relationships, while ignoring questions of key or harmony entirely. The current research demonstrates that the kappa effect can be weakened by the type of serial context preceding to-be-

115 judged temporal relationships. However, it remains to be discovered whether more structured, musical sequences elicit the same kinds of perceptual distortions seen here.

Another limitation (and possible direction for current research) of the current research is that here, the presentation rate of stimuli is not manipulated. If (as claimed by the MAM hypothesis) that greater pitch motion leads to an increased kappa effect, then increasing the rate at which the kappa cell unfolds (while keeping pitch relationships constant) may increase the size of the kappa effect. Future experiments will examine this possibility.

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