The Kappa Effect in Pitch/Time Context Dissertation
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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 By 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. ii 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. iv 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. v FIELDS OF STUDY Major Field: Psychology vi 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