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Perceptual and response organization of rhythmic patterns 1988

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PERCEPTUAL AND RESPONSE ORGANIZATION OF RHYTHMIC PATTERNS by MICHAEL J. CANIC B.P.E., The U n i v e r s i t y of B r i t i s h Columbia, 1981 M.P.E., The U n i v e r s i t y of B r i t i s h Columbia, 1983 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES (Department of I n t e r d i s c i p l i n a r y Studies: Psychology/Physical Education/Music) We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA March, 198 8 © Michael J . Canic, 1988 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. ~ ^ , I n t e r d i s c i p l i n a r y Studies Department of The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 March 4, 1988 Date DE-6(3/81) - i i - A B S T R A C T Four studies were undertaken to i n v e s t i g a t e the advance planning and perception of simple rhythmic patterns. Subjects l i s t e n e d to patterns of i d e n t i c a l , computer- generated tones and then reproduced them as accurately as p o s s i b l e by tapping on a s i n g l e response key. Section One focussed on the advance planning of isochronous rhythmic patterns i n which subjects performed the a d d i t i o n a l task of i n i t i a t i n g p a t t e r n reproduction as q u i c k l y as p o s s i b l e . In Experiment 1, subjects l i s t e n e d to patterns of one to s i x tones with i n t e r s t i m u l u s i n t e r v a l s (ISIs) of 300 ms. The reproduction phase involved no stimulus u n c e r t a i n t y . Reaction time (RT) was found to increase l i n e a r l y with number of response events. Advance planning thus occurs f o r patterns reproduced as slow as 300 ms per response event. Stimulus u n c e r t a i n t y i s not a necessary c o n d i t i o n f o r RT to increase with response complexity. In Experiment 2 , subjects reproduced patterns of one to eight tones with ISIs of 2 0 0 , 4 0 0 , 6 0 0 , and 800 ms. A l i n e a r RT trend was found only at the 200-ms ra t e . Patterns slower than t h i s rate d i d not d i s p l a y "response coherence". Patterns at the 200-ms and 400-ms rates showed evidence of grouping through the accenting of f i r s t and l a s t i n t e r v a l s . These patterns' displayed "perceptual coherence". Section Two focussed on the perceptual o r g a n i z a t i o n of patterns i n which patt e r n s t r u c t u r e s could suggest the grouping of events as two equal- duration i n t e r v a l s . In Experiment 3 , subjects reproduced two - I l l - s e r i e s of patterns, one s e r i e s i n which the suggested gr o u p i n g - i n t e r v a l s were i n i t i a t e d by external-world events, and one i n which they were not. Pattern s t r u c t u r e s i n the l a t t e r s e r i e s were not suggestive enough to induce grouping of events as two equal-duration i n t e r v a l s . Patterns were ins t e a d grouped as two i n t e r v a l s of unequal duration showing that the r e l a t i v e temporal p o s i t i o n s of external-world events dominates i n simple perceptual grouping. Experiment 4 i n v e s t i g a t e d the upper temporal l i m i t of perceptual grouping- •intervals and the infl u e n c e of number of group c o n s t i t u e n t s . Results showed that perceptual grouping of events that span more than 1800 ms i s seldom accomplished and that grouping occurs when i n t e r v a l s contain up to seven c o n s t i t u e n t s . - iv - TABLE OF CONTENTS Page ABSTRACT ... . i i TABLE OF CONTENTS..'. ' . i v LIST OF TABLES • v i LIST OF FIGURES : v i i i ACKNOWLEDGEMENT x GENERAL INTRODUCTION : 1 What i s Rhythm? Per c e i v e d Rhythm? 2 Rhythm, Tempo and Meter 5 Programs, Programming, Subprograms and Preprogramming 7 Purpose 11 L i m i t a t i o n s • 13 SECTION ONE: The Advance Planning and Timing of Isochronous Response Patterns • 17 Methodology 19 Parameters of Response Complexity 23 Task S e l e c t i o n 25 Synthesis 28 Experiment One 30 Method '. 31 Res u l t s . 37 D i s c u s s i o n 47 Experiment Two 51 Method • 54 Res u l t s 61 D i s c u s s i o n 77 General D i s c u s s i o n 84 SECTION TWO: The P e r c e p t u a l Organization of Rhythmic Patterns 88 Sub j e c t i v e Rhythmization 89 G e s t a l t P r i n c i p l e s of Grouping 90 Pe r c e p t i o n of Temporal Ratios . ... 94 Processes i n Rhythm Pe r c e p t i o n 10.1 Summary 102 - v - Experiment Three .''. 106 Method ' . 108 Res u l t s 112 Discussion.' 120 Experiment Four 125 Method • 127 Resul t s '. 12 9 D i s c u s s i o n 136 General D i s c u s s i o n 146 SUMMARY & CONCLUSIONS 149 FOOTNOTES 153 REFERENCES 154 - v i - L I S T OF TABLES Page Table 1. Mean IRI and Terminal Event (TE) Durations 45 (ms) and Corresponding SD 1s as a Function of S e r i a l P o s i t i o n and P a t t e r n Length. Table 2. Mean and SD of . I n t r a t r i a l and I n t e r t r i a l IRI 46 SD's (ms) as a Function of P a t t e r n Length. Table 3. Mean RT and Corresponding SD's (ms) as a .65 Func t i o n of Response Rate and P a t t e r n Length. Table 4. Mean IRI Durations and Corresponding SD 1s (ms) 71 as a Function of Response Rate and S e r i a l P osition.. Table 5. Mean DT Durations and Corresponding SD's (ms) 75 as a Function of Response Rate and S e r i a l P o s i t i o n . Table 6. C l a s s i f i c a t i o n and Frequency of E r r o r T r i a l s 76 i n R e l a t i o n to the T o t a l Number of T r i a l s and the Next Superordinate E r r o r Category. Table 7. A l l P o s s i b l e 2-unit and 4-unit Clocks f o r a 99 Rhythmic P a t t e r n . Table 8. Stimulus Patterns f o r Experiment 3. 109 Table 9. Mean IRI,and T o t a l P a t t e r n (T) Durations 117 (ms) and Corresponding SD's as a Function of S e r i a l P o s i t i o n f o r Each P a t t e r n . Table 10. Mean P r o p o r t i o n a l Reproduction E r r o r as a 119 Func t i o n of Pattern-Type and the Number (Even/Odd) of Shorter Temporal I n t e r v a l s . - v i i - Table 11. Mean R e l a t i v e D u r a t i o n s o f S h o r t e r Temporal 121 I n t e r v a l s t o Longer Temporal. I n t e r v a l s as a F u n c t i o n of P a t t e r n - T y p e . Table 12. S t i m u l u s p a t t e r n s f o r Experiment 4. 128 Table 13. Mean D u r a t i o n s (ms), Co r r e s p o n d i n g SD 1s 130 and P r o p o r t i o n a l E r r o r (PE) Scores f o r .Shorter and Longer IRI's.. T able 14. F i r s t I n t e r v a l D u r a t i o n s (ms) and R e s u l t a n t 133 Evid e n c e f o r Grouping Based on Agogic A c c e n t i n g o f the F i r s t and L a s t I R I 1 s . - v i i i - L I S T OF FIGURES Page F i g u r e 1. Time l i n e of a t y p i c a l t r i a l f o r a 3-tone 34 p a t t e r n . F i g u r e 2.• Mean r e a c t i o n time (RT) across 39 t r i a l s - 72 observations per p o i n t . F i g u r e 3. Mean r e a c t i o n time (RT) as a f u n c t i o n of 41 number of tap s . a._ Resu l t s f o r 12 subjects - 108 observations per p o i n t , b. Resu l t s f o r 11 subjects - 99 observations per p o i n t . F i g u r e 4. Response apparatus and computer i n t e r f a c e 55 systems f o r Experiment 2. F i g u r e 5. Time l i n e of a t y p i c a l t r i a l f o r a 3-tone 59 p a t t e r n . F i g u r e 6. Mean r e a c t i o n time (RT) as a f u n c t i o n of 63 number of taps f o r the 200 ms response r a t e . A: Regression l i n e c a l c u l a t e d over a l l but the f i r s t task c o n d i t i o n s . B: Regression l i n e c a l c u l a t e d over a l l task c o n d i t i o n s . F i g u r e 7. Mean inte r r e s p o n s e i n t e r v a l . (IRI) durations 66 as a f u n c t i o n of p a t t e r n length. a. 200 ms r a t e , b. 400 ms r a t e , c. 600 ms ra t e , and d. 800 ms r a t e . F i g u r e 8. Mean down-time (DT) durations ,as a f u n c t i o n 73 of response r a t e and p a t t e r n length. - ix - F i g u r e 9. Mean r e a c t i o n time (RT) as a f u n c t i o n o f number of t a p s . F i g u r e 10. Mean r e a c t i o n time (RT) as a f u n c t i o n o f t o t a l p a t t e r n d u r a t i o n . F i g u r e 11. P r o p o r t i o n a l E r r o r v e r s u s C r i t e r i o n Long I n t e r v a l D u r a t i o n . F i g u r e 12. P r o p o r t i o n a l E r r o r v e r s u s C r i t e r i o n T o t a l P a t t e r n D u r a t i o n . F i g u r e 13. Mean R e p r o d u c t i o n R a t i o ( s h o r t - t o - l p n g i n t e r v a l ) f o r each S e r i a l P o s i t i o n . a. c r i t e r i o n r a t i o : 0.25, b. c r i t e r i o n r a t i o : 0.20, c. c r i t e r i o n r a t i o : 0.17, d. c r i t e r i o n r a t i o n 0.14. - x - ACKNOWLEDGEMENT I am g r a t e f u l f o r the support and guidance I have r e c e i v e d throughout my Ph.D. program. Over the 7 years that I have known him, Dr. Ian Franks has i n v e s t e d enormous time and e f f o r t towards my academic development. I am t r u l y indebted and hope that he f e e l s h i s input has been j u s t i f i e d . Dr. Ward has provided many s t i m u l a t i n g d i s c u s s i o n s with regards to my research, and to the broader i s s u e s of philosophy, science and s o c i e t y . He i s a true s c h o l a r . P r o f e s s o r Hultberg has s k i l l f u l l y advised me and introduced me t o the r i c h t r a d i t i o n of rhythm i n music. P r o f e s s o r Schutz has always provided thorough and c o n s t r u c t i v e c r i t i c i s m . His r i g o r o u s approach to knowledge and to the e d u c a t i o n a l process i s admired and appreciated. P r o f e s s o r Tees has generously provided h i s vast e x p e r t i s e i n the areas of rhythm p e r c e p t i o n and p e r c e p t i o n i n g e n e r a l . I am g r a t e f u l to Prof. S. Keele and Prof. G. Stelmach f o r a c t i n g as E x t e r n a l Examiners and to Dr. G. S i n c l a i r and P r o f . R. Corteen f o r a c t i n g as U n i v e r s i t y Examiners f o r my o r a l defence. I am g r a t e f u l to P r o f e s s o r W.R. Morford and P r o f e s s o r S. I i d a f o r t h e i r continued support throughout my graduate c a r e e r . I acknowledge Dr. R. Mosher, f o r i t was l a r g e l y through h i s impetus t h a t I continued my graduate education at t h i s p a r t i c u l a r time. I am g r a t e f u l to family and f r i e n d s who have supported me throughout t h i s p e r i o d , most notably, my parents, my s i s t e r Cyndi, and Lee Jensen. I am g r a t e f u l f o r the f i n a n c i a l a s s i s t a n c e that has been pro v i d e d me through the U.B.C. U n i v e r s i t y Graduate F e l l o w s h i p fund, the Tina & Morris Wagner Foundation, the Governments of Canada and B r i t i s h Columbia and my f a t h e r . F i n a l l y , I wish to thank George Patterson, Don Smith, Gord Robertson, Andy Bhakthan, Paul Nagelkerke, Mr. Hsu, Dave Brecht, and Shawn Abbott f o r programming, t e c h n i c a l and p r o d u c t i o n a s s i s t a n c e , and to Dr. Joan V i c k e r s f o r her comments on the I n t r o d u c t i o n to t h i s d i s s e r t a t i o n . - 1 - GENERAL INTRODUCTION Rhythm i s a fundamental aspect of e x i s t e n c e . I t i s inherent i n the a c t i v i t y of l i v i n g organisms and n o n - l i v i n g matter. Rhythm i s apparent, at a macro l e v e l , i n the r e v o l u t i o n s of p l a n e t a r y bodies, and at a micro l e v e l , i n the v i b r a t o r y motions of atoms and molecules. B i o l o g i c a l systems are r e p l e t e with rhythmic a c t i v i t y and p a t t e r n s of behavior. These may be as common as the migratory p a t t e r n s of animals or as unique as the b r i e f but r e g u l a r appearance of the 17- year c i c a d a . Some rhythms are fundamental to human e x i s t e n c e . C i r c a d i a n rhythms, f o r example, are manifest i n a l t e r n a t e p e r i o d s of r e s t and a c t i v i t y ; c a r d i a c and r e s p i r a t o r y rhythms r e f l e c t the e n e r g e t i c demands of a c t i v i t y . And e l e c t r i c a l a c t i v i t y i n the b r a i n i s c h a r a c t e r i z e d by rhythmic p a t t e r n s 'of v a r i o u s f r e q u e n c i e s . We can i n t e n t i o n a l l y create rhythms i n such forms as poetry, music and dance. We can create symbolic r e p r e s e n t a t i o n s of rhythmic p a t t e r n s , we can produce rhythms through a v a r i e t y of modes and'we p e r c e p t u a l l y organize rhythmic, p a t t e r n s when exposed to them. How i s i t that we p e r c e p t u a l l y organize rhythmic pa t t e r n s ? Does p e r c e p t u a l o r g a n i z a t i o n r e v e a l i t s e l f i n the r e p r o d u c t i o n of such p a t t e r n s ? What processes u n d e r l i e the p r e p a r a t i o n of rhythmic p a t t e r n production? The present work i s concerned with these general questions. The work i s comprised of two s e c t i o n s . The focus of the f i r s t s e c t i o n i s - 2 - on the advance p l a n n i n g and response t i m i n g o f i s o c h r o n o u s r h y t h m i c p a t t e r n s t h a t v a r y i n tempo (rate) and c o m p l e x i t y (number o f e v e n t s ) . The second s e c t i o n i s concerned w i t h the p e r c e p t u a l o r g a n i z a t i o n o f rhythmic p a t t e r n s t h a t v a r y i n d u r a t i o n , tempo and event frequency. The b a s i c method employed i s t o have s u b j e c t s reproduce p a t t e r n s o f i d e n t i c a l , computer-generated a u d i t o r y tones by t a p p i n g w i t h a s i n g l e f i n g e r on a response key. Each s e c t i o n of s t u d i e s i s preceded by an i n t r o d u c t i o n and development of t h e u n d e r l y i n g t h e o r e t i c a l i s s u e s . The remainder o f t h i s G e n e r a l I n t r o d u c t i o n i s devoted t o the e x p l a n a t i o n of c e n t r a l concepts, and o u t l i n i n g the purpose and l i m i t a t i o n s o f the r e p o r t e d s t u d i e s . What i s Rhythm? P e r c e i v e d Rhythm? I t would, a t f i r s t thought, appear r a t h e r s e l f - e v i d e n t what rhythm i s . Rhythm e n t a i l s p e r i o d i c i t y . A p e r i o d i m p l i e s c o n t r a s t between/among s t a t e s / e v e n t s w i t h i n a s i n g l e p e r i o d i c c y c l e . The s i m p l e s t r h y t h m i c p a t t e r n i s thus the a l t e r n a t i o n o f s t r e s s and r e l e a s e (Cooper, 1973). Yet, i f matt e r s were so s i m p l e , Ruckmich (1913, 1915, 1918) c o u l d h a r d l y have co m p i l e d a g e n e r a l b i b l i o g r a p h y of rhythm c o n t a i n i n g oyer 500 e n t r i e s ! What about p e r c e i v e d rhythm? Rhythm can be p e r c e i v e d b e f o r e a p e r i o d i c c y c l e i s completed. We b e g i n t o • p e r c e p t u a l l y o r g a n i z e a s t i m u l u s p a t t e r n as soon as i t i s i n i t i a t e d (Garner, 1974). P e r c e i v e d rhythm suggests - 3 - c o n t i n u i t y , and ,connectivity among events. Thackray (1969) re p o r t e d evidence that a fundamental f a c t o r i n rhythm p e r c e p t i o n i s the a b i l i t y to p e r c e i v e and memorize a rhythmic s t r u c t u r e as a whole. In a c l a s s i c e a r l y work on the psychology of music, Seashore (1938) wrote, "There are two fundamental f a c t o r s i n the p e r c e p t i o n of rhythm: an i n s t i n c t i v e tendency to group impressions i n hearing and a c a p a c i t y f o r doing t h i s with p r e c i s i o n i n time and s t r e s s . " (Seashore, 1938, p.138). Grouping of events (in time) thus seems c r u c i a l to the n o t i o n of p e r c e i v e d rhythm. The r e l a t i v e t i m i n g of events, however, while e s s e n t i a l to most Western music, i s not e s s e n t i a l to " f r e e " rhythm which appears i n some Indian songs and ancient European f o l k music (Apel, 1972). In f r e e rhythm, .measure i s by groups of notes, but the r e l a t i v e lengths of the notes themselves are not measured. Grouping i s seldom d i s c u s s e d without reference to "accenting" (Berry, 1976; Lerdahl & Jackendoff, 1983). A c c e n t i n g i s . t h a t process by which an event i s made d i s t i n c t from, and more s a l i e n t than, surrounding events. I t r e s u l t s i n c o n t r a s t among events i n a p a t t e r n . For a u d i t o r y p a t t e r n s , an event may be produced and/or p e r c e i v e d as accented in' at l e a s t three ways. F i r s t , an event may be louder than surrounding events (dynamic a c c e n t ) . I t may be higher i n p i t c h than other events (tonic a c c e n t ) . T h i r d l y , i t may be longer i n d u r a t i o n than surrounding events (agogic accent) (Cooper, 1973). In t h e i r landmark book, "The - 4 - Rhythmic S t r u c t u r e of Music", Cooper and Meyer (1960) suggested that rhythm i s the way i n which one or more unaccented beats are grouped i n time i n r e l a t i o n to an accented beat. They noted, however, that a c c e n t i n g alone does not determine rhythmic grouping. As i s c h a r a c t e r i s t i c of p e r c e p t i o n i n general, the s u b j e c t i v e experience of rhythm r e s u l t s from an i n t e r a c t i o n of stimulus s t r u c t u r e and i n t e r n a l structure' (e.g. memory, e x p e c t a t i o n s ) . We might t h i n k of o b j e c t i v e rhythm as rhythmic s t r u c t u r e inherent i n the stimulus p a t t e r n and s u b j e c t i v e rhythm as the rhythmic s t r u c t u r e imposed by the perc'eiver. The p e r c e p t i o n o f rhythm, i f s i m i l a r to the p e r c e p t i o n of time, should not be t r e a t e d too much l i k e a "sensory" pro.cess. O r n s t e i n (1969) has provided evidence that the pe r c e p t i o n of time depends g r e a t l y on the q u a n t i t a t i v e and q u a l i t a t i v e aspects of the information that are (or are not) present i n the d e f i n e d i n t e r v a l . In f a c t , even i n the l a t e - 19th century i t was thought that' the experience of time depends on stimulus i n t e n s i t i e s , stimulus frequencies, d i f f e r e n c e s among s t i m u l i , a t t e n t i o n p a i d to the s t i m u l i and s t i m u l i - g e n e r a t e d a s s o c i a t i o n s and expectations (Guyau, 1890, c i t e d i n Ornstein, 1969). I f t h i s i s the case, and i n c o n s i d e r a t i o n of Fr'ankenhaeuser' s (1959) f i n d i n g that temporal experience i s al s o i n f l u e n c e d by emotions and a t t i t u d e s , then i t i s not s u r p r i s i n g that the experience of - 5 - p e r c e i v i n g rhythm can be so r i c h and d i v e r s e ... and so pe r s o n a l . Rhythm, Tempo and Meter In the terminology of music, rhythm i s d i s t i n g u i s h e d from tempo and meter. I n t e r e s t i n g l y , there i s not u n i v e r s a l agreement on the meaning of the terms or the r e l a t i o n among them. "Tempo" r e f e r s to the rate of a composition (Apel, 1972). More s p e c i f i c a l l y , i t i s the r a t e of the u n d e r l y i n g "beat" of a p a t t e r n . Many notes can be spaced c l o s e l y together i n time but the u n d e r l y i n g beat (as determined by cont e x t u a l f a c t o r s ) may i n d i c a t e a slow tempo. Conversely, s i m i l a r f a c t o r s may i n d i c a t e a f a s t tempo when notes are not spaced c l o s e l y together. Occurrence of a beat may be e x t e r n a l or i n t e r n a l to the subject (Apel, 1972). Some have suggested t h a t rhythmic o r g a n i z a t i o n does not depend on tempo (Cooper & Meyer, 1960). In f a c t , i t i s not uncommon to f i n d t h a t current models of rhythm p e r c e p t i o n (for example, Povel & Essens, 1985) overlook the p o s s i b l e r o l e of tempo. Yet, -others have argued t h a t t h i s p o s i t i o n i s i n e r r o r and that the pe r c e p t i o n of rhythm i s i n t e g r a l l y t i e d to the tempo of a p a t t e r n (Clarke, 1982,1985; Handel & Oshinsky, 1981; Michon, 1974). F r a i s s e (1963) has suggested that rhythm i s l o s t when sounds are separated by around two seconds. While t h i s may seem unduly b r i e f when one cons i d e r s the powerful i n f l u e n c e of context on rhythm p e r c e p t i o n , i t - 6 - does draw focus t o the is s u e of the i n f l u e n c e of tempo on rhythm. "Meter" r e f e r s t o a higher-order temporal u n i t - the grouping of beats to form a s t r u c t u r e the -very nature of which i n f l u e n c e s accenting w i t h i n the u n i t . In music, meter i s i n d i c a t e d by a time signature, such as "4/4", i n which the second number s i g n i f i e s the type of note r e c e i v i n g a beat ( i . e . a quarter note) and the f i r s t number s i g n i f i e s the number of such notes that are grouped .in a measure. The s u b j e c t i v e experience of metric o r g a n i z a t i o n and beats, however, i s not n e c e s s a r i l y determined by the symbolic r e p r e s e n t a t i o n o f musical s t r u c t u r e . Radocy and Boyle e x p l a i n : Meter signatures s p e c i f y which u n i t of n o t a t i o n r e c e i v e s a beat; i n p r a c t i c e , however, the u n i t designated by a meter sig n a t u r e as r e c e i v i n g the beat i s not always the same as the beat which 'is f e l t i n response to the music ... When the tempo of the music i s quick, the e f f e c t on the l i s t e n e r o f t e n i s t o make the notated measure, r a t h e r than the m e t r i c a l beat, the u n i t of the beat. (Radocy & Boyle, 1979, pp. 70-71.) There i s l i t t l e dispute that rhythmic o r g a n i z a t i o n i s i n f l u e n c e d by meter; Clarke (1985) presented subjects with a notated rhythmic p a t t e r n set i n 10 d i f f e r e n t m e t r i c a l contexts. Interresponse i n t e r v a l s i n the production of t h i s standard p a t t e r n were found t o vary as a f u n c t i o n of the m e t r i c a l context i n which i t was presented. G a b r i e l s s o n , Bengtsson, and G a b r i e l s s o n (1983) repo r t e d the lengthening of notes that completed musical groups at va r i o u s l e v e l s of - 7 - s t r u c t u r e . Essens and Povel (1985) showed that p a t t e r n s conceivable i n a m e t r i c a l framework are represented and reproduced more a c c u r a t e l y than p a t t e r n s t h a t are not. F i n a l l y , c o n s i d e r the complex i n t e r a c t i o n of rhythm, tempo and meter. Shaffer, Clarke, and Todd (1985) have s t u d i e d the s k i l l e d performance of a complex rhythmic pi e c e and concluded t h a t the performer i s allowed two degrees of freedom i n producing rhythm. One i s f o r mapping meter onto a time s c a l e thus determining tempo, and the other i s f o r the expressive t i m i n g of groups of events i n r e l a t i o n to the meter. Programs, Programming, Subprograms and Preprogramming To understand how we p l a n and c o n t r o l the execution of rhythmic movement patt e r n s (or, f o r that matter, any movement pattern) we should be f a m i l i a r with r e l e v a n t concepts i n the f i e l d of motor c o n t r o l . The current n o t i o n of a "motor program" i s that of a ge n e r a l i z e d , c e n t r a l l y - s t o r e d , a b s t r a c t r e p r e s e n t a t i o n of a pl a n of a c t i o n that, once i n i t i a t e d , assumes c o n t r o l of movement (Schmidt, 1987). I t i s thought to be a g e n e r a l i z e d a c t i o n p l a n i n that c e r t a i n parameters must be input t o the program (e.g. o v e r a l l movement dur a t i o n , o v e r a l l f o r c e , muscle s e l e c t i o n ) to s a t i s f y the s p e c i f i c requirements of the task at hand. I t assumes c o n t r o l of movement i n that i t determines the o r i g i n a l p a t t e r n of a c t i o n . That p a t t e r n of a c t i o n , however, can be modified f o l l o w i n g the p e r i o d of one r e a c t i o n time ( R T ) i n response t o - 8 - feedback or non feedback-related v o l u n t a r y reprogramming of the response. In the absence of c o n t r a i n d i c a t o r y feedback or- a v o l u n t a r y change of plan, the motor program runs through i t s e n t i r e t y . This conception owes much to the t h e o r e t i c a l i n s i g h t s of Keele (1968)', who i n t e g r a t e d f i n d i n g s from a number of f i e l d s i n support of the programmed c o n t r o l of s k i l l e d motor performance. C i t i n g the temporal l i m i t a t i o n s i n p r o c e s s i n g feedback, the' reduced a t t e n t i o n a l demands a s s o c i a t e d with i n c r e a s i n g s k i l l , and the r o l e of memory i n a n t i c i p a t i n g and s k i l l f u l l y producing and reproducing movement, Keele proposed that muscle commands are s t r u c t u r e d p r i o r to the i n i t i a t i o n , of a movement sequence, and t h a t the e n t i r e sequence i s then executed u n i n f l u e n c e d by p e r i p h e r a l feedback. While t h i s i s no longer b e l i e v e d to be s t r i c t l y t r u e (see above), the ideas, as a-whole, were instrumental i n c r e a t i n g a s h i f t i n the t h e o r e t i c a l emphasis i n the f i e l d of motor behavior. "Programming" r e f e r s to the p r e p a r a t i o n and i n i t i a t i o n of a response (Schmidt, 1987). The processes i n v o l v e d i n response-programming have been a source of much resea r c h and controversy i n recent years. Ivry (1986) has argued f o r s e p a r a t i n g the processes of program- c o n s t r u c t i o n from those of program implementation. Program c o n s t r u c t i o n i n v o l v e s those processes t h a t can take p l a c e p r i o r to the d e c i s i o n t o i n i t i a t e a response, i f the r e l e v a n t parameters are known. In the case of a simple RT task, a l l of the r e l e v a n t response parameters are known i n advance so the e n t i r e program can be - 9 - c o n s t r u c t e d . F o r a c h o i c e RT t a s k , o n l y t h o s e parameters known i n advance of the s i g n a l t o respond can be p r e p a r e d - t h u s , the motor program i s p a r t i a l l y c o n s t r u c t e d (Rosenbaum, I n h o f f , & Gordon, 1984) . In f a c t , i t i s c u r r e n t l y acknowledged t h a t programming ( c o n s t r u c t i o n ) of l a t t e r / u n c e r t a i n p a r t s o f a movement sequence may co-occur w i t h the e x e c u t i o n o f e a r l i e r / k n o w n p a r t s (Rosenbaum, H i n d o r f f , & Munro, 1987; Semjen & G a r c i a - C o l e r a , 1986). The program (or program p a r t s ) , once c o n s t r u c t e d , i s presumably s t o r e d i n t o some type o f s h o r t - t e r m memory b u f f e r ( S t e r n b e r g , M o n s e l l , K n o l l , & Wright, 1978). Program i m p l e m e n t a t i o n i n v o l v e s those p r o c e s s e s t h a t t a k e p l a c e a f t e r a d e c i s i o n t o i n i t i a t e a response. I t has been suggested t h a t these p r o c e s s e s i n v o l v e the t r a n s l a t i o n o f a b s t r a c t codes i n t o s e t s of motor commands (Semjen & G a r c i a - C o l e r a , 1984), or t h e r e t r i e v a l of s p e c i f i c p a r t s of the program from a b u f f e r ( S t e r n b e r g e t a l . , 1978) . The c o n s t r u c t e d program i s not implemented e a r l i e r s i n c e , presumably, i m p l e m e n t a t i o n i s i n some way t i e d t o response e x e c u t i o n . T h i s n o t i o n w i l l be d e a l t w i t h i n more d e t a i l i n Experiment 1. For the purpose o f the s t u d i e s r e p o r t e d here, i t w i l l be i n t e r e s t i n g t o note t h a t b o t h c o n s t r u c t i o n and im p l e m e n t a t i o n p r o c e s s e s are thought t o i n v o l v e l a r g e l y independent f o r c e and t i m i n g components and, indeed, t h e r e i s even evidence t h a t s e p a r a t e f u n c t i o n a l u n i t s o f b r a i n o r g a n i z a t i o n u n d e r l i e t h e s e components (Keele & I v r y , 1987). - 10 - One of t h e most e l a b o r a t e and most r e s e a r c h e d frameworks o u t l i n i n g the p r o c e s s e s of,program imp l e m e n t a t i o n was developed by S t e r n b e r g et a l . (1978). They p o s t u l a t e d t h a t a motor program i s comprised of one or more "subprograms". A subprogram r e p r e s e n t s a s i n g l e u n i t of e x e c u t i o n i n the motor program - a f u n c t i o n a l response u n i t . For example, the program f o r a response p a t t e r n o f "n" t a p p i n g movements would c o n s i s t o f "n" subprograms - one f o r each movement. S t e r n b e r g and h i s c o l l e a g u e s p r e s e n t e d data t o support the t h e o r e t i c a l p o s i t i o n t h a t program imp l e m e n t a t i o n f i r s t i n v o l v e s the s e l f - t e r m i n a t i n g , s e r i a l s e a r c h / r e t r i e v a l of the f i r s t subprogram from a n o n - s h r i n k i n g b u f f e r . The r e t r i e v e d subprogram i s then "unpacked" (broken down i n t o i t s c o n s t i t u e n t s - e.g. a s t r e s s group i n speech can be made up of one or more s y l l a b l e s ) , the motor commands f o r the c o n s t i t u e n t s are s p e c i f i e d and, f i n a l l y , response' e x e c u t i o n i s i n i t i a t e d . Along w i t h s t i m u l u s p r o c e s s i n g , t h i s i m p l e m e n t a t i o n procedure t a k e s p l a c e d u r i n g the RT p e r i o d . The procedure then r e p e a t s i t s e l f f o r each a d d i t i o n a l subprogram. The S t e r n b e r g e t a l . model r e l i e s h e a v i l y on a c o r r e s p o n d i n g l i n e a r i n c r e a s e of RTs and q u a d r a t i c i n c r e a s e of i n t e r r e s p o n s e i n t e r v a l s ( I R I s ) . However, r e c e n t f i n d i n g s , f o r example i n the h a n d w r i t i n g s t u d i e s of H u l s t i j n and van Galen (1983), and T e u l i n g s , M u l l i n s and Stelmach.(1986), and the hand m a n i p u l a t i o n s t u d i e s .of H a r r i n g t o n and Haaland (1987) have f a i l e d t o r e p l i c a t e t h i s correspondence and, as a - 11 - r e s u l t , have cast doubt on some aspects of t h i s conceptual scheme. Even so, i t has proved, and continues to prove, u s e f u l as a t h e o r e t i c a l framework from which many i n t e r e s t i n g hypotheses are generated. "Preprogramming" i s not r e f e r r e d to u n e q u i v o c a l l y i n the l i t e r a t u r e . Perhaps i t has been most f r e q u e n t l y taken as synonymous with response-programming that occurs p r i o r to response i n i t i a t i o n (Schmidt, 1987). Presumably, the i n i t i a t i o n of a l l movements or movement p a r t s that are l e s s than one RT i n d u r a t i o n i s accomplished through preprogramming. What i s not c l e a r i s how t h i s n o t i o n t i e s i n with the programming of movement during continuous a c t i v i t y - and not j u s t the l a t e r programming of a p r e v i o u s l y known movement p a r t . It doesn't appear to make sense t o speak of preprogramming as o c c u r r i n g only i n the absence of any movement, yet i f preprogramming occurs during ongoing a c t i v i t y , then how are d i s t i n c t movement p a r t s i d e n t i f i e d ? Preprogramming w i l l be used here to r e f e r t o only those processes that take p l a c e p r i o r to the d e c i s i o n t o i n i t i a t e a response. That i s , preprogramming i s d e f i n e d as the programming operations that occur i n advance of the s i g n a l to respond - the processes of program c o n s t r u c t i o n i n a simple RT paradigm. Purpose of the Studies The s t u d i e s i n Secti o n One are designed to provide a b e t t e r understanding of the i n t e r r e l a t i o n among response - 12 - programming, response t i m i n g and'response a r t i c u l a t i o n . Previous s t u d i e s have t y p i c a l l y i n v e s t i g a t e d the programming of response p a t t e r n s of v a r y i n g l e v e l s of complexity t h a t are executed as q u i c k l y as p o s s i b l e . But what happens with slower, isochronous response patterns? To what extent i s programming r e q u i r e d p r i o r to response i n i t i a t i o n ? Does t h i s vary with the r a t e of response? One f o c a l t h e o r e t i c a l q u e s t i o n i n the f i r s t s e c t i o n i s : why do s u b j e c t s not completely preprogram a l l aspects of a known response p a t t e r n (or at l e a s t the f i r s t response unit) i n advance of the s i g n a l to respond? What processes u n d e r l i e the delay i n i n i t i a t i n g a complex response pattern? The research t o date has l a r g e l y ignored t h i s question. An attempt i s made to answer i t i n the present work by t e s t i n g one of two competing hypotheses. The s t u d i e s i n S e c t i o n Two continue the recent r e s e a r c h t h r u s t devoted to uncovering the p r i n c i p l e s of p e r c e p t u a l o r g a n i z a t i o n f o r rhythmic p a t t e r n s . A primary assumption here i s t h a t p e r c e p t u a l o r g a n i z a t i o n or grouping i s r e f l e c t e d i n the a c c e n t i n g of reproduced p a t t e r n s ; the output form of the p a t t e r n s i n these s t u d i e s can r e f l e c t only agogic (duration) accenting. Yet, as Keele, Ivry and Pokorny (1987) have shown, acc e n t i n g of t h i s type can be i n f l u e n c e d by f o r c e v a r i a t i o n s i n response pro d u c t i o n . In the l i t e r a t u r e , much reference i s made to o r g a n i z a t i o n with respect to a fundamental temporal i n t e r v a l or r e f e r e n t - a " b e a t - i n t e r v a l " . What f a c t o r s c o n t r i b u t e to - 13 - the determination of a b e a t - i n t e r v a l ? I t has g e n e r a l l y been assumed t h a t a b e a t - i n t e r v a l must be i n i t i a t e d by an e x t e r n a l - w o r l d event. But i s t h i s necessary i f other cues suggest the same pe r c e p t u a l o r g a n i z a t i o n ? A l s o of i n t e r e s t i s how the number of events i n a p a t t e r n and event frequency (rate) i n f l u e n c e the s e l e c t i o n of a b e a t - i n t e r v a l . I f there i s a d u r a t i o n range that the b e a t - i n t e r v a l must f a l l , w i t h i n , as there s u r e l y must be (the p e r t i n e n t l i t e r a t u r e with respect t o t h i s i s s u e w i l l be d i s c u s s e d i n S e c t i o n Two), then manipulating the above v a r i a b l e s should allow us to expose i t . L i m i t a t i o n s There are s e v e r a l l i m i t a t i o n s to the s t u d i e s presented here. These r e l a t e to v a r i o u s aspects of v a l i d i t y . F i r s t , with respect to i n t e r n a l v a l i d i t y and method, the method of reproducing a u d i t o r y stimulus p a t t e r n s i s being used, i n pa r t , to make i n f e r e n c e s regarding p e r c e p t i o n . Yet, there i s evidence t o suggest t h a t the mechanisms i n v o l v e d i n reproducing an a u d i t o r y rhythmic p a t t e r n , producing the same p a t t e r n from n o t a t i o n , and judging temporal r e l a t i o n s i n that p a t t e r n , are not i d e n t i c a l ( A l l a n , 1979; Keele &• Ivry, 1987; Sternberg, K n o l l , & Zukofsky, 1982; Summers, Hawkins, & Mayers, 1987; Vroon, 1976). D e v i a t i o n of the response from the c r i t e r i o n may be a r e s u l t of p e r c e p t u a l or response b i a s e s . I t i s argued here that even though each method has l i m i t a t i o n s , the method of reproduction i s the most d i r e c t - 14 - s i n c e the s t i m u l u s and response are bo t h i n the form o f a rhy t h m i c p a t t e r n . J o i n t use o f these methods i s not a p p r o p r i a t e f o r the s t u d i e s o u t l i n e d s i n c e the i n v e s t i g a t i o n of programming p r e c l u d e s an " e s t i m a t i o n " response, and the p e r c e p t i o n o f s p e c i f i c t i m e - i n t e r v a l s p r e c l u d e s t h e p r e s e n t a t i o n o f a t r a n s c r i b e d s t i m u l u s . The second l i m i t a t i o n concerns v a l i d i t y and the methods of a n a l y s i s . Most of the e x p e r i m e n t a l r e s u l t s p r e s e n t e d here are a n a l y z e d a c c o r d i n g t o some type of A n a l y s i s o f V a r i a n c e (ANOVA) pr o c e d u r e . ANOVA makes c e r t a i n assumptions r e g a r d i n g the d i s t r i b u t i o n s of the da t a b e i n g a n a l y z e d . These assumptions are t y p i c a l l y not met w i t h RT d a t a . RT da t a are thought t o be almost always non-normally d i s t r i b u t e d - i n p a r t i c u l a r , t h e y are skewed toward h i g h e r v a l u e s of RT ( R a t c l i f f , 1979). In a d d i t i o n , the assumption o f independent means and v a r i a n c e s i s r a r e l y met ( P i e t e r s , 1983) . However, ANOVA tends t o be, f o r the most p a r t , a ro b u s t t e s t even when the u n d e r l y i n g assumptions are not c o m p l e t e l y met (Glass & Hopkins, 1984) . From a t h e o r e t i c a l p o i n t o f view, i n f e r e n t i a l s t a t i s t i c a l t e s t s a p p l i e d t o group data do not n e c e s s a r i l y uncover what i s happening at the l e v e l o f t h e i n d i v i d u a l . The use o f a s i m i l a r response s t r a t e g y a c r o s s s u b j e c t s may y i e l d v a r i a b l e r e s u l t s w h i l e the use o f d i s s i m i l a r s t r a t e g i e s may y i e l d e q u i v a l e n t r e s u l t s . I n d i v i d u a l d i f f e r e n c e s and t h e i r causes are d i f f i c u l t t o i d e n t i f y and i n t e r p r e t . - 15 - The t h i r d l i m i t a t i o n i s with respect t o e x t e r n a l v a l i d i t y . At the l e v e l of stimulus p r e s e n t a t i o n , there i s evidence that v a r i a b i l i t y i n rhythmic performance depends on the modality of p r e s e n t a t i o n - v i s u a l s t i m u l i r e s u l t i n the g r e a t e s t performance v a r i a b i l i t y while a u d i t o r y s t i m u l i r e s u l t i n the l e a s t (Kolers & Brewster, 1985). Therefore, the present r e s u l t s - S e c t i o n Two, i n p a r t i c u l a r - may not be g e n e r a l i z a b l e t o other stimulus m o d a l i t i e s . However, by u t i l i z i n g the modality that r e s u l t s i n l e a s t v a r i a b i l i t y we are more l i k e l y to uncover d i f f e r e n c e s that could be missed i f the v i s u a l modality were used f o r stimulus p r e s e n t a t i o n . The subjects i n the reported s t u d i e s are p r i m a r i l y North-American, u n i v e r s i t y students. The rhythmic backgrounds of these subjects are s p e c i f i c not only to t h e i r p e r s o n a l h i s t o r i e s but a l s o to t h e i r c u l t u r e . Davies (1978) has suggested t h a t Western music, while t o n a l l y very complex, i s r h y t h m i c a l l y q u i t e simple. Other forms of music, most notably Indian and A f r i c a n music, are 'rhythmically very complex (Dowling & H'arwood, 1986) A In a d d i t i o n , a strong r e l a t i o n s h i p has been found between pulse forms of e t h n i c music and the rhythms of the corresponding language (Clynes & Walker, 1982). Thus, past rhythmic experience i s l i k e l y very d i f f e r e n t among c u l t u r a l populations and these d i f f e r e n c e s may be evident i n the types of tasks performed i n the present s t u d i e s . A f i n a l l i m i t a t i o n i s one of e c o l o g i c a l v a l i d i t y with respect to music. While i t i s g e n e r a l l y recognized that, - 16 - "without rhythm, there would be no music" (Radocy & Boyle, 197 9), i t i s t r u e that without music there i s much rhythm. And rhythm e x t e r n a l to music may be d i f f e r e n t from rhythm i n t e r n a l t o music. The s t u d i e s reported here i n v o l v e stimulus and response p a t t e r n s that vary only i n the time i n t e r v a l s between event-onsets. P i t c h , loudness and timbre are a l l c o n t r o l l e d and kept constant (though the constant values f o r these dimensions are d i f f e r e n t i n Experiment 2 of S e c t i o n One). Als o , event durations are kept constant i n the stimulus p a t t e r n s . The p e r c e p t i o n of these c o n t r o l l e d , computer-generated rhythms may be very d i f f e r e n t from the p e r c e p t i o n of rhythm i n a r i c h context such as music. SECTION ONE:' The Advance Planning and Timing of Isochronous Response Patterns What processes u n d e r l i e the p r e p a r a t i o n of response p a t t e r n s ? S p e c i f i c a l l y , are there d i f f e r e n c e s i n the p r e p a r a t i o n of response p a t t e r n s t h a t vary i n complexity? The measure commonly used when i n v e s t i g a t i n g these questions i s the RT to i n i t i a t e a response. For response p a t t e r n s of v a r i o u s types, RT has been found to increase with i n c r e a s i n g response complexity. Freeman (1907) was l i k e l y the f i r s t t o i n v e s t i g a t e t h i s r e l a t i o n s h i p . He found that simple RT was g r e a t e r when subj e c t s had to draw a geometric f i g u r e or move to a s p e c i f i e d p o i n t than when they had to draw around a c i r c u l a r t r a c k or merely make a v e r t i c a l movement. In a c l a s s i c paper, Henry and Rogers (1960) showed that i n c r e a s i n g the complexity of a simple hand movement by s p e c i f y i n g t a r g e t l o c a t i o n s and d i r e c t i o n a l changes r e s u l t e d i n g r e a t e r simple RTs. In more recent years, s i m i l a r RT analyses have been a p p l i e d to a number of tasks, i n c l u d i n g handwriting ( H u l s t i j n & van Galen, 1983/ Stelmach & Teulings, 1983; Teulings et a l . , 1986; Teulings, ThomassenS van Galen, 1983), speech (Eriksen, P o l l a c k & Montague, 1970; Klapp, 1974; Klapp, Anderson & B e r r i a n , 1973; Sternberg et a l . , 1978) and keystrokes and t a p p i n g (Fischman, 1984; Klapp & Rodriguez, 1982; Klapp, Wyatt & Lingo, 1974; Rosenbaum et a l . , 1987; Semjen & G a r c i a - C o l e r a , 1986; Semjen, G a r c i a - C o l e r a & Requin, - 18 - 1984). The u n d e r l y i n g assumption has been t h a t d i f f e r e n t i a l RTs can h e l p t o uncover and e x p l a i n , among o t h e r t h i n g s , the p r o c e s s e s i n v o l v e d i n what has v a r i o u s l y been r e f e r r e d t o as the "advance p l a n n i n g " , "programming", or " p r e p a r a t i o n " of a motor response. While t h e r e i s evidence s u p p o r t i n g the e f f e c t o f response c o m p l e x i t y on RT, the r e s e a r c h f i n d i n g s have not been u n e q u i v o c a l . E r i k s e n e t a l . (1970) and Klapp e t a l . (1973) have found t h a t c h o i c e RT i n c r e a s e s as a f u n c t i o n of the number of s y l l a b l e s t o be spoken but not s i m p l e RT. Klapp et a l . (1974) observed lengthened c h o i c e RTs f o r l o n g as opposed t o s h o r t key p r e s s e s but, a g a i n , no s i m p l e RT e f f e c t s . K e r r (1979) attempted t o r e p l i c a t e the Klapp et a l . (1974) f i n d i n g s but i n s t e a d found no sim p l e RT or c h o i c e RT e f f e c t s . T e u l i n g s et a l . (1986) r e p o r t e d c o n f l i c t i n g r e s u l t s w i t h r e s p e c t t o s i m p l e RT and t h e number of h a n d w r i t t e n s t r o k e s . Chamberlin and M a g i l l (1987) f a i l e d t o f i n d i n c r e a s e s i n sim p l e o r c h o i c e RT as a f u n c t i o n o f number o f t a p p i n g movements. R e s u l t s such as the s e have l e d some r e s e a r c h e r s t o q u e s t i o n the r e l i a b i l i t y and i n t e r p r e t a t i o n of si m p l e RT e f f e c t s (Klapp, 1981). What these r e s u l t s do i n d i c a t e i s t h a t methodology, the d e f i n e d parameter o f response c o m p l e x i t y , and t a s k s e l e c t i o n may be imp o r t a n t c o n s i d e r a t i o n s i n the d e s i g n of experiments concerned w i t h response p r e p a r a t i o n and motor programming. Each of the s e are c o n s i d e r e d i n t u r n . - 19 - Methodology Both simple RT and choice RT methods are necessary to r e v e a l a f u l l understanding of the p r e p a r a t i o n of response p a t t e r n s . These methods h i g h l i g h t d i f f e r e n t response processes. I t i s thought that the response processes that choice RT index are t h o s e • i n v o l v e d i n both motor program c o n s t r u c t i o n and implementation; simple RT indexes' only those response processes i n v o l v e d i n program implementation (Sternberg et a l . , 1978; Ivry, 1986). Does t h i s imply that the choice RT method i s more r e v e a l i n g and the simple RT method i s merely redundant? L i k e l y not. Simple RT allows a f i n e r probing of the processes i n v o l v e d i n response implementation. The confounds present i n choice RT paradigms ( i . e . stimulus d i s c r i m i n a t i o n , stimulus-response, response- response, and stimulus-response ensemble c o m p a t i b i l i t i e s , and response s e l e c t i o n ) are avoided i n simple RT paradigms. S t i l l , some have endorsed the choice RT method to the e x c l u s i o n of the simple RT method. Klapp (1981) has been perhaps the most v o c a l c r i t i c of u s i n g simple RT e f f e c t s t o i n f e r motor programming. His p o s i t i o n has been that a response known i n advance can be completely preprogrammed. While not denying the e x i s t e n c e of simple RT e f f e c t s , these e f f e c t s are i n t e r p r e t e d as having a b a s i s other than motor programming. One argument (Klapp, c i t e d i n Henry, 1980) i s that simple RT e f f e c t s may r e f l e c t p e r i p h e r a l f a c t o r s (such as v a r i a b l e limb-segment i n e r t i a s and d i f f e r e n t i a l d i g i t RTs) as opposed to c e n t r a l processes - 20 - (see a l s o Anson, 1982). Fischman (1984) t e s t e d t h i s hypothesis by measuring both premotor and motor simple RT components f o r a s e r i a l t a r g e t - t a p p i n g task. The r e s u l t i n g i n c r e a s e i n simple RT as a f u n c t i o n of the number of taps was a t t r i b u t e d almost e x c l u s i v e l y to the premotor component. This, i n l i g h t of the f a c t t h a t the i n i t i a l movement segment was standardized across response p a t t e r n s , provides good evidence against the p e r i p h e r a l f a c t o r s i n t e r p r e t a t i o n . I t has been suggested t h a t simple RT e f f e c t s may only be evident f o r l a r g e - s c a l e movements as opposed t o small f i n g e r movements (Klapp, 1980). However, t h i s seems u n l i k e l y s i n c e simple RT i s thought to r e f l e c t processes that u n d e r l i e parameters other than movement extent (Hayes & Marteniuk, 1976). Sternberg et a l . (1978) reported an i n c r e a s e i n simple RT as a f u n c t i o n of number of typed l e t t e r s but the l e t t e r s (and thus response l o c a t i o n s ) were not i d e n t i c a l . There i s a l s o concern t h a t an i n c r e a s e i n simple RT may be due to a v a r i a b l e speed/accuracy t r a d e - o f f across l e v e l s of complexity (Klapp, 1981). There i s p r e s e n t l y i n s u f f i c i e n t evidence to comment on t h i s i s s u e . Other arguments are t h a t simple RT e f f e c t s may r e s u l t from i n s u f f i c i e n t l y m o t i v a t i n g the subject to respond as q u i c k l y as p o s s i b l e (Klapp et a l . , 1979), and that simple RT e f f e c t s can be e l i m i n a t e d with p r a c t i c e (Klapp et a l . , 1974). Of course, even with e x p l i c i t i n s t r u c t i o n s , feedback, and a p p r o p r i a t e r e i n f o r c e r s i t 'may be that m o t i v a t i o n i s i n s u f f i c i e n t . The best we can do i s to emphasize these - 21 - m o t i v a t i o n a l s t r a t e g i e s and assume that the subject i s being induced to respond as i n s t r u c t e d . These s t r a t e g i e s have been employed i n past s t u d i e s . The argument with respect to p r a c t i c e seems u n l i k e l y i n l i g h t of the Sternberg et a l . (1978) r e s u l t s which showed a s i g n i f i c a n t i n c r e a s i n g t r e n d i n simple RT even a f t e r high l e v e l s of p r a c t i c e . However, p r a c t i c e d i d r e s u l t i n an o v e r a l l decrease i n mean RT and the RT r e g r e s s i o n c o e f f i c i e n t . This decrease was asymptotic over s e s s i o n s . Yet, even i f no i n c r e a s i n g t r e n d were found a f t e r much p r a c t i c e , i t could simply mean that the " u n i t s " of programming change as one becomes more s k i l l e d . A f i n a l argument i s d e r i v e d from a study i n which a l i n e a r r e l a t i o n s h i p between simple RT and number of spoken words was found but d i f f e r e n t - task c o n d i t i o n s produced d i f f e r e n t r e g r e s s i o n c o e f f i c i e n t s (Klapp et a l . , 1979). The "repeat" c o n d i t i o n , i n which subjects had to repeat the number "one" (from one to f i v e times), y i e l d e d a s i g n i f i c a n t l y l a r g e r c o e f f i c i e n t than the "count" c o n d i t i o n , i n which s u b j e c t s had to count ascending i n t e g e r s s t a r t i n g with "one" (up to f i v e i n t e g e r s ) . This d i f f e r e n c e prompted the c o n c l u s i o n , "...we can r e j e c t the motor-programming i n t e r p r e t a t i o n f o r r e s u l t s of t h i s type" (p.99). However, r a t h e r than a t t r i b u t i n g d i f f e r e n t i a l RT r e g r e s s i o n c o e f f i c i e n t s to processes other than motor programming,'it would be more u s e f u l to e x p l a i n these d i f f e r e n c e s w i t h i n a motor programming framework. For example, counting numbers may simply be a more f a m i l i a r and w e l l - l e a r n e d task than - 22 - r e p e a t i n g them i n which case, as noted e a r l i e r , a s m a l l e r c o e f f i c i e n t would r e s u l t ..̂  A l t e r n a t i v e l y , programming, i n the case o f the repeat c o n d i t i o n , may i n v o l v e a d d i t i o n a l p r o c e s s e s , the d u r a t i o n s o f which depend on the number of u n i t s t o be spoken. The a d d i t i o n a l p r o c e s s e s c o u l d r e f l e c t a set of i n s t r u c t i o n s - one f o r each time the number of ( i d e n t i c a l ) response u n i t s executed i s t o be compared w i t h the t o t a l r e q u i r e d . A n a l o g o u s l y , S t e r n b e r g et a l . (1978) found t h a t , f o r t y p e d k e y s t r o k e s , the' s i m p l e RT r e g r e s s i o n c o e f f i c i e n t was g r e a t e r f o r a l t e r n a t i n g hands than f o r a s i n g l e hand. I t may be t h a t programming f o r a l t e r n a t e hand t y p i n g a l s o i n v o l v e s a d d i t i o n a l p r o c e s s e s - one f o r each time a change of hands must.be made. Al t h o u g h some concerns s t i l l remain, t h e r e appears t.o be no d e c i s i v e evidence opposed t o a programming i n t e r p r e t a t i o n f o r s i m p l e RT e f f e c t s . What, th e n , are the b e n e f i t s of u s i n g the s i m p l e RT method? As p r e v i o u s l y s t a t e d , i n a d d i t i o n t o a v o i d i n g c h o i c e RT confounds, the s i m p l e RT method a l l o w s a f i n e r p r o b i n g o f the p r o c e s s e s i n v o l v e d i n the i m p l e m e n t a t i o n of a motor program. Indeed, o n l y the s i m p l e RT method can address t h e q u e s t i o n , "Why must some p r o c e s s e s be d e l a y e d u n t i l the s i g n a l t o respond, even though the s u b j e c t knows i n advance e x a c t l y what he/she i s t o do?" The c h o i c e RT method alone cannot unambiguously s e p a r a t e the p r o c e s s e s o f program c o n s t r u c t i o n from those of program i m p l e m e n t a t i o n . T h i s i s e v i d e n t when we examine programming models. Simple RT d a t a l e d t o t h e S t e r n b e r g e t a l . (1978) - 23 - model which p o s t u l a t e s d i s t i n c t stages to account f o r p r o c e s s i n g that follows the c o n s t r u c t i o n of a motor program. On the other hand, the H i e r a r c h i c a l E d i t o r Model of Rosenbaum et a l . (1984; see a l s o Rosenbaum et a l . , 1987), while very impressive i n e x p l a i n i n g how choice RT v a r i e s as a f u n c t i o n of the number of response elements p r i o r to and f o l l o w i n g an u n c e r t a i n response element> e x p l a i n s simple RT e f f e c t s simply by means of a " t r e e - t r a v e r s a l process". Simple RT i n c r e a s e s f o r longer p a t t e r n s because the d i s t a n c e along a "node path" from the top of a .pattern " t r e e " to i t s f i r s t t e r m i n a l node i n c r e a s e s . While p r o v i d i n g a metaphor, t h i s does l i t t l e t o suggest or e x p l a i n the processes that u n d e r l i e simple RT e f f e c t s . The goal of research i n t o response programming i s a u n i f i e d model - one t h a t e x p l a i n s both simple and choice RT processes. I t appears that both simple and' choice RT methods are necessary, f o r the u l t i m a t e development of such a model. Parameters of Response Complexity There are many candidate parameters of response complexity (see Hayes & Marteniuk, 1976, and.Kerr, 1978, f o r reviews). C o n t r a s t i n g simple and choice RT methods can t e l l us which parameters are and are not programmed p r i o r t o a stimulus s i g n a l . For instance, Ivry (198 6) has found t h a t choice RT v a r i e s with the need f o r i n s t r u c t i o n s to d e a c t i v a t e f o r c e output, while simple RT does not. Thus, f o r a known response, f o r c e d e a c t i v a t i o n can be programmed i n advance of the response s i g n a l . Choice RT s t u d i e s t y p i c a l l y i n v e s t i g a t e - 24 - the e f f e c t s of uncertainty along one or more response parameters. In movement precuing studies, f o r example, these have included the limb, d i r e c t i o n and extent of a movement (Goodman & Kelso, 1980; L a r i s h & Frekany, 1985; Rosenbaum, 1980) as w e l l as d i g i t and movement duration (Zelaznik & Hahn, 1985). In force-timing studies, i t has been the s e r i a l p o s i t i o n of a stressed tap i n a s e r i e s of otherwise i d e n t i c a l taps (Semjen & Garcia-Colera, 1986; Semjen et a l . , 1984). Experimental design can allow various uncertain parameters and thus choice RT can index many (contrived) parameters of response complexity. Yet, as Kerr (1978) has cautioned, "...task-defined parameters...that we i d e n t i f y as important may be very d i f f e r e n t from the i n t e r n a l values that t r u l y a f f e c t the motor c o n t r o l system" (p.66). I t i s suggested here that c o n t r i v e d parameters of response complexity should not automatically be assumed to r e f l e c t the " n a t u r a l " parameters i n t r i n s i c to the motor c o n t r o l system. The parameters that most r e l i a b l y lend themselves to i n v e s t i g a t i o n by the simple RT method are: 1) number of response u n i t s (subprograms), and 2) response duration. The response u n i t may be i d e n t i c a l with an i n d i v i d u a l response element or may represent a group of elements - much as an IRI i s comprised of response onset and o f f s e t times. What determines t h i s f u n c t i o n a l grouping i s not always c l e a r . For the c l e a r i n t e r p r e t a t i o n of r e s u l t s , a s t a t e d requirement has been that response patterns be comprised of elements thought to be fundamentally i d e n t i c a l ( i . e . the "element-invariance" - 25 - r e q u i r e m e n t , S t e r n b e r g et a l . , 1978). An i n c r e a s e i n RT as number of response u n i t s i n c r e a s e s (each comprised o f one or more elements) would r e f l e c t p r o c e s s e s s e n s i t i v e t o t h i s parameter o f c o m p l e x i t y . The i n c r e a s e , when observed, i s t y p i c a l l y a l i n e a r one. S e p a r a t i n g "number" from " d u r a t i o n " as response p a r a m e t e r s ' i s d i f f i c u l t s i n c e p a t t e r n s w i t h more response u n i t s ' n o r m a l l y t a k e l o n g e r t o execute. I f number of response u n i t s i s h e l d c o n s t a n t and response d u r a t i o n v a r i e d , then t h e r e i s the r i s k of a l l o w i n g complete " o n - l i n e " c o n t r o l f o r the l a t e r events o f slower p a t t e r n s . While t h e r e i s some evidence t h a t c h o i c e RT i n c r e a s e s as a f u n c t i o n of response d u r a t i o n (Klapp, 1977; Klapp et a l . , 1974), r e c e n t s t u d i e s have measured RT t r e n d s f o r both t o t a l response d u r a t i o n and movement v e l o c i t y , and. found t h a t RT i n c r e a s e s i n i n v e r s e p r o p o r t i o n o n l y t o the l a t t e r v a r i a b l e ( F a l k e n b e r g & N e w e l l , 1980; see a l s o , C a r l t o n , R obertson, C a r l t o n & N e w e l l , 1985). Task S e l e c t i o n The s e l e c t i o n o f an a p p r o p r i a t e t a s k i s imp o r t a n t t o ensure t h a t the d e f i n e d parameter of c o m p l e x i t y i s not confounded w i t h o t h e r v a r i a b l e s (see, f o r example, Fischman, 1984). C o n s i d e r h a n d w r i t i n g and speech. In the case o f h a n d w r i t i n g , r e s e a r c h e r s have t r i e d w i t h l i m i t e d success t o show an i n c r e a s e i n sim p l e RT as a f u n c t i o n of t h e number of response u n i t s - the response u n i t b e i n g , presumably, e i t h e r - 26 - a l e t t e r or a stroke. Teulings et a l . (1986) have noted t h a t the continuous nature of handwriting may w e l l u n d e r l i e i t s r e s i s t a n c e t o decomposition i n t o d i s t i n c t u n i t s and thus the i n c o n s i s t e n t r e s u l t s . In a d d i t i o n , the f a c t t h at stroke lengths and durations are v a r i a b l e and t h a t movement i n handwriting occurs along the h o r i z o n t a l as w e l l as the v e r t i c a l a x i s i n d i c a t e s that the elements of handwriting f a i l to meet the element-invariance requirement (see above). The v a r i a b i l i t y among stroke durations, i n p a r t i c u l a r , presents a problem. The amount of p r o c e s s i n g r e q u i r e d p r i o r to response i n i t i a t i o n can,be i n f l u e n c e d by the (variable) rate- of u n i t execution. In the case of slower r a t e s , p r o c e s s i n g requirements p r i o r to execution may be reduced due to time allowance f o r o n - l i n e p r o c e s s i n g during execution. As a r e s u l t , simple RT could f a i l to i n c r e a s e as number of strokes i n c r e a s e . In f a c t , H u l s t i j h and van Galen (1983) have suggested that t h e . f a i l u r e to show r e l i a b l e l a t e n c y e f f e c t s with handwriting may be due to the r e l a t i v e l y low maximum output r a t e that i s observed. They argue that a low output r a t e might mean there i s no need t o program an e n t i r e sequence, indeed, no need to program more than one l e t t e r i n advance of the s i g n a l t o respond. Thus, the method of i n v e s t i g a t i o n (choice or simple RT) and chosen parameter of complexity (number of response u n i t s ) can f a i l t o r e v e a l RT e f f e c t s i f the s e l e c t e d task i s not a p p r o p r i a t e . The response u n i t i n speech appears to be the s t r e s s - group (a segment of speech a s s o c i a t e d with primary s t r e s s ) . - 27 - Simple RT has been found to increase l i n e a r l y as number of stress-groups increase (Sternberg et a l . , 1978). Yet, as with handwriting, the response u n i t durations have -not been c o n t r o l l e d . Although maximum output rates are high f o r speech, thus i n c r e a s i n g the necessity f o r processing p r i o r t o the s i g n a l to respond, the lack of c o n t r o l f o r u n i t duration r e s t r i c t s our a b i l i t y to e x p l a i n the processes that u n d e r l i e latency e f f e c t s and response execution. Other problems a r i s e when studying RT e f f e c t s of speech production (see Sternberg et a l . , 1978). Most importantly, measurement of l a t e n c i e s (and IRIs). t y p i c a l l y depend on i d e n t i f y i n g a vocal response that exceeds a s p e c i f i e d l e v e l of i n t e n s i t y . Vocal i n t e n s i t y , however, v a r i e s considerably with the length of a sequence, the volume of a i r i n the lungs at any given time and the nature and context of the s p e c i f i c stresses to be v o c a l i z e d . Contrast the task of producing keystrokes. When performed with a s i n g l e f i n g e r on a s i n g l e key, keystrokes are simple and r e l a t i v e l y i n v a r i a n t movements. S i g n i f i c a n t movement occurs only i n one plane, the maximum output rate i s high (up to 12 taps per second, c i t e d i n Seashore, 1938), requirements of s p a t i a l accuracy encourage response consistency, response u n i t s are r e l a t i v e l y d i s c r e t e , and stroke-onset times can be p r e c i s e l y defined and measured. I f time i s not c o n t r o l l e d and measured then subjects might impose unknown rhythmic s t r u c t u r e s upon response sequences thus clouding the i n t e r p r e t a t i o n of RT e f f e c t s . This task - 28 - seems i d e a l l y s u i t e d t o t h e i n v e s t i g a t i o n o f response c o m p l e x i t y ( d e f i n e d as the number of response u n i t s ) and s i m p l e RT e f f e c t s . Yet, o n l y G a r c i a - C o l e r a and Semjen(1987; a l s o Semjen & G a r c i a - C o l e r a , 1986, and Semjen et a l . , 1984) have r e g u l a r l y employed t h i s t a s k t o t h e s e ends. S y n t h e s i s The s t u d i e s r e p o r t e d here are s p e c i f i c a l l y concerned w i t h response programming a f t e r the s i g n a l t o respond ( i . e . program i m p l e m e n t a t i o n ) . The s i m p l e RT paradigm i s t h u s employed. In t h i s paradigm the response p a t t e r n i s t y p i c a l l y produced as f a s t as p o s s i b l e . T h i s i s t o maximize programming requirements and minimize " o n - l i n e " movement c o n t r o l . S u b j e c t s , here, reproduce s e r i e s o f i s o c h r o n o u s a u d i t o r y tones - r h y t h m i c p a t t e r n s - by t a p p i n g a s i n g l e response key. P l a c i n g temporal c o n s t r a i n t s on t h e response p a t t e r n a l l o w s e x a m i n a t i o n of how v a r i o u s response r a t e s ( i . e . tempi) a f f e c t the amount of r e q u i r e d programming. I t a l s o a l l o w s measurement of the a c c u r a c y and c o n s i s t e n c y o f response t i m i n g . RT e f f e c t s o f response c o m p l e x i t y are i n v e s t i g a t e d - c o m p l e x i t y b e i n g d e f i n e d as the number of response u n i t s . Why i s n ' t the f i r s t response u n i t c o m p l e t e l y programmed ( c o n s t r u c t e d and implemented) and s i m p l y " t r i g g e r e d " g i v e n the s i g n a l t o respond? In t h i s paradigm, i s s t i m u l u s " u n c e r t a i n t y " t h e r o o t cause o f programming d e l a y ? What can - 29 - response t i m i n g t e l l us about perceptual and response organization? These questions are the focus of Section One. - 30 - Experiment 1 The purpose of t h i s study i s to examine a fundamental issue regarding the nature of response processing that has, fo r the most par t , gone unattended. Namely, i n a simple RT paradigm, why do we not program a l l aspects of a known response, or at l e a s t the f i r s t response u n i t , and simply " t r i g g e r " i t i n response to a stimulus? Why are the operations that f o l l o w the c o n s t r u c t i o n of a motor program not i n i t i a t e d u n t i l a f t e r the s i g n a l to respond? Two p o s s i b l e explanations have been put f o r t h (Sternberg et a l . , 1978). Consider again that "programming" i s thought to i n v o l v e program con s t r u c t i o n processes (which i n the case of a known response can take place before the s i g n a l to respond) and program implementation processes. I t may be that the i n i t i a t i o n of implementation processes automatically leads to response execution. I n i t i a t i n g these processes p r i o r to the stimulus would then cause the subject to erroneously respond on catch t r i a l s . A l t e r n a t i v e l y , the implemented program stored i n a motor b u f f e r might be subject to r a p i d decay or i n t e r f e r e n c e i n the event of stimulus processing. This would delay the i n i t i a t i o n of at l e a s t some programming operations u n t i l a f t e r the s i g n a l to respond. In t h i s study, the f i r s t of the above hypotheses i s t e s t e d - namely, that only the threat and experience of" catch t r i a l s prevents program- implementation p r i o r to the s i g n a l to respond. I f t h i s i s the case, then removing catch t r i a l s , and thus the t h r e a t , should r e s u l t i n no simple RT - 31 - d i f f e r e n c e s across l e v e l s of complexity. The programmed response can be t r i g g e r e d . In f a c t , i t has p r e v i o u s l y been assumed that i n the absence of temporal, s p a t i a l or event u n c e r t a i n t y subjects are able to o v e r t l y i n i t i a t e a response j u s t a f t e r the s i g n a l to respond (Quesada & Schmidt, 1970). Other questions are also of i n t e r e s t here. Does the ti m i n g of an isochronous response pattern have i m p l i c a t i o n s f o r the preparation of that pattern? How accurately and c o n s i s t e n t l y do subjects reproduce isochronous patterns i n an RT paradigm? How many response u n i t s can be programmed i n advance of response i n i t i a t i o n ? Speech, typing and tapping studies have found a l i n e a r increase i n RT through f i v e response u n i t s (Fischman, 1984, Sternberg et a l . , 1978). The patterns i n the present study contain up to s i x response u n i t s . Method Subjects. Twelve male and female students from the U n i v e r s i t y of B r i t i s h Columbia p a r t i c i p a t e d i n the study as part of a course requirement. Subjects ranged i n age. from 21 to 24 years. A $20.00 p r i z e was o f f e r e d to the subject who best performed the j o i n t task of r a p i d l y i n i t i a t i n g and accurately reproducing the response patterns. Apparatus. Stimulus events were produced as tones through an Apple l i e microcomputer and heard through headphones. Stimulus tone durations and toneless i n t e r v a l durations were also c o n t r o l l e d through the Apple l i e . - 32 - R e p r o d u c t i o n o f i n d i v i d u a l tone d u r a t i o n s and subsequent i n t e r v a l s was r e a l i z e d by s u b j e c t s p r e s s i n g and l i f t i n g from a s p e c i f i e d key on the computer keyboard w i t h t h e p r e f e r r e d f i n g e r o f the dominant hand. A minimum f o r c e o f 1.2 Newtons (N) was r e q u i r e d t o depress a key. The r e s t i n g f o r c e g e n e r a t e d by the weight o f a f i n g e r was found t o range from •0.5-0.6 N. T h i s meant t h a t an a d d i t i o n a l f o r c e • o f 0.6-. 0.7 N was r e q u i r e d t o produce key d e p r e s s i o n . The same f i n g e r and key were t o be used f o r the d u r a t i o n o f t h e experiment. Reproduced tones were of an i n t e n s i t y and frequency i d e n t i c a l t o t h o s e o f t h e s t i m u l u s t o n e s . The reproduced tone d u r a t i o n s , t o n e l e s s i n t e r v a l s , and the l a t e n c y t o i n i t i a t e the f i r s t event i n each t r i a l were a l l r e c o r d e d by t h e computer. S t i m u l u s P a t t e r n s . S u b j e c t s were i n s t r u c t e d t o reproduce s i x d i f f e r e n t s t i m u l u s p a t t e r n s . The p a t t e r n s c o n s i s t e d o f one t o s i x 100 ms tones ( e v e n t s ) . A l l tones were o f an i d e n t i c a l i n t e n s i t y and produced at a frequency o f 1420 Hz. A d j a c e n t tones i n m u l t i - t o n e p a t t e r n s were s e p a r a t e d by t o n e l e s s i n t e r v a l s o f 200 ms r e s u l t i n g i n i n t e r s t i m u l u s i n t e r v a l s ( i . e . the time from tone-onset t o tone-onset) o f 300 ms. P r o c e d u r e . S u b j e c t s were s e a t e d at a t a b l e and i n s t r u c t e d as t o the n a t u r e o f the study. A d e m o n s t r a t i o n o f the procedure was viewed. Then, wearing headphones and r e s t i n g t h e f i n g e r t i p s o f t h e • p r e f e r r e d hand on t h e computer keyboard, s u b j e c t s l i s t e n e d t o a s t i m u l u s p a t t e r n c o n s i s t i n g - 33 - o f one t o s i x t o n e s . P r e s e n t a t i o n o f t h e s t i m u l u s p a t t e r n was preceded by a one second Ready tone (of e q u a l i n t e n s i t y t o t h e s t i m u l u s tones but produced a t a frequency o f 4 00 Hz) and a P r e - P r e s e n t a t i o n i n t e r v a l a l s o one second i n d u r a t i o n . The f i n a l s t i m u l u s tone i n t h e p a t t e r n was f o l l o w e d by a P o s t - P r e s e n t a t i o n i n t e r v a l o f 1200 ms. The o f f s e t o f a Warning tone ( i d e n t i c a l i n a l l a s p e c t s t o the Ready tone) was th e s i g n a l f o r s u b j e c t s t o i n i t i a t e r e p r o d u c t i o n o f t h e s t i m u l u s p a t t e r n (see F i g u r e 1). F o l l o w i n g r e p r o d u c t i o n o f the f i n a l tone the. e x p e r i m e n t e r p r e s s e d a key on the keyboard thus e n d i n g t h e t r i a l and p r e p a r i n g t h e computer f o r t h e subsequent t r i a l . A 6 X 10 f a c t o r i a l repeated-measures d e s i g n was employed. S u b j e c t s performed 10 c o n s e c u t i v e t r i a l s f o r each s t i m u l u s p a t t e r n . The o r d e r o f p a t t e r n p r e s e n t a t i o n a c r o s s s u b j e c t s was determined by a b a l a n c e d L a t i n Square d e s i g n . R e p r o d u c t i o n o f a l l s i x s t i m u l u s p a t t e r n s c o n c l u d e d the study. The t w o f o l d t a s k was: 1) t o i n i t i a t e r e p r o d u c t i o n o f t h e s t i m u l u s p a t t e r n as q u i c k l y as p o s s i b l e f o l l o w i n g t h e o f f s e t o f the. warning tone, and 2) t o reproduce the t i m i n g o f each s t i m u l u s p a t t e r n as a c c u r a t e l y as p o s s i b l e . E q u a l emphasis was p l a c e d on t h e two.aspects o f the t a s k . A n a l y s i s . Mean RT was the p r i m a r y measure o f i n t e r e s t . RTs g r e a t e r than 1000 ms were o m i t t e d from t h e a n a l y s e s . I n l i g h t o f t h e r e s u l t s from p r e v i o u s s t u d i e s , RTs t h i s slow would c l e a r l y be e r r o r s and r e v e a l n o t h i n g about response programming (the s l o w e s t , mean s i m p l e RTs found i n the - 34 - F i g u r e 1. Time l i n e o f a t y p i c a l t r i a l f o r a 3-tone p a t t e r n . READY TONE STIMULUS TONES WARNING INTERRESPONSE TONE INTERVALS 1.0 1 .1 .1 i . o AX 1.0 .2 .2 cn w 1.2 4° r A S E C O N D S - 3 6 - l i t e r a t u r e f o r studies of t h i s sort are i n the range of 345 ms to 380 ms - Semjen & Garcia-Colera, 1984, Expt. 1). Omitted RT data were replaced with s i n g l e subject means f o r the same c o n d i t i o n . T h i s ' c o r r e c t i o n procedure was u t i l i z e d only i n cases where the t o t a l number of missing data points was two or l e s s per c e l l . The interresponse i n t e r v a l (IRI) was the-primary measure used i n the a n a l y s i s of duration data. The IRI i s the combined duration of a reproduced tone and the subsequent toneless i n t e r v a l - i n other words, the duration from tone- onset to tone-onset (see Figure 1). Since i n d i v i d u a l onset and o f f s e t durations are thought to generally r e f l e c t response a r t i c u l a t i o n rather than timing processes (Clarke, 1985; Sternberg, K n o l l , & Zukofsky, 1982), the IRI i s commonly used as the f u n c t i o n a l measure f o r temporal p a t t e r n reproduction (Povel, 1981; Semjen & Garcia-Colera, 1986; Vorberg & Hambuch, 1984). For each subject f i v e dependent v a r i a b l e s were c a l c u l a t e d . These included: mean i n t r a t r i a l IRIs and i n t - r a t r i a l standard deviations (for m u l t i - I R I patterns) , the mean and standard d e v i a t i o n of mean i n t r a t r i a l IRIs, and the mean i n t r a t r i a l standard d e v i a t i o n . These v a r i a b l e s represent, r e s p e c t i v e l y : the mean and v a r i a b i l i t y of IRI scores w i t h i n each t r i a l , the mean'and v a r i a b i l i t y of t r i a l means, and the mean w i t h i n - t r i a l v a r i a b i l i t y . Comparisons made across conditions allowed f o r inferences regarding the accuracy and consistency of pattern reproduction. An i n t r a t r i a l standard d e v i a t i o n was c a l c u l a t e d f o r a l l IRIs w i t h i n each p a t t e r n , and f o r j u s t the f i r s t two IRIs common to each multi-IRI p a t t e r n . The l a t t e r measure gives a more accurate comparison when i n t r a t r i a l v a r i a b i l i t y i s concentrated at the beginning of the response p a t t e r n . The d u r a t i o n of the f i n a l response or "terminal event i n t e r v a l " was a l s o measured and analyzed since, by design, i t was not followed by a measurable i n t e r v a l . IRIs of l e s s than 100 ms or grea t e r than 500 ms were considered to be e r r o r s since they represent more than a two- t h i r d s d e v i a t i o n from the c r i t e r i o n i n t e r v a l s . These data were omitted from the analyses. Non-usable t r i a l data r e s u l t i n g from the subject p r e s s i n g more than one key, us i n g more than one f i n g e r , or i n c o r r e c t l y reproducing the number of response elements were s i m i l a r l y omitted. The omitted IRI data were r e p l a c e d with s i n g l e subject means f o r the same c o n d i t i o n and s e r i a l p o s i t i o n . Omitted t e r m i n a l event data were r e p l a c e d with s i n g l e subject means f o r the same c o n d i t i o n . These c o r r e c t i o n procedures were u t i l i z e d only i n cases where the .total number of missing data p o i n t s was two or l e s s per c e l l . In f a c t , c o r r e c t e d IRI and t e r m i n a l event data accounted f o r 1.4% and'1.9% of the data used i n the analyses, r e s p e c t i v e l y . R e s u l t s Latency Data. P r e l i m i n a r y a n a l y s i s of the data r e v e a l e d - 38 - that mean RTs were t y p i c a l f o r s t u d i e s of t h i s s o r t ( c f . Sternberg et a l . , 1978). As a r e s u l t , RTs of l e s s than 100 ms were considered e r r o r s of a n t i c i p a t i o n - and not a normal mode of response given the absence of catch t r i a l s . C o r r e c t e d l a t e n c y data (both f a s t and slow) accounted f o r 3.9% of the data analyzed. A n a l y s i s of variance (ANOVA) uncovered a s i g n i f i c a n t t r i a l s e f f e c t , F(9,99)=4.05, Greenhouse-Geisser £=.012. 3 Tukey post hoc a n a l y s i s revealed that only the f i r s t t r i a l was s i g n i f i c a n t l y d i f f e r e n t from the others (see Figure 2). D i f f e r e n c e s were s i g n i f i c a n t at JD<.01 f o r a l l but the second and f i n a l t r i a l s (]p_<.05) . To exclude the e f f e c t s of l e a r n i n g and/or f a m i l i a r i z a t i o n with the task, f i r s t t r i a l s were omitted from a l l subsequent analyses. Mean r e a c t i o n time data are shown i n Figure 3a. Trend a n a l y s i s r e v e a l e d only a s i g n i f i c a n t l i n e a r orthogonal component, F(1, 11)=5.66, p_=.037. V i s u a l i n s p e c t i o n of the raw data, however, revealed that the mean performance of one p a r t i c u l a r subject, while not deviant enough to be excluded from the a n a l y s i s based on a p r i o r i c r i t e r i a , was both very slow across r e s p e c t i v e c o n d i t i o n s (mean RTs: 289, 369, 442, 537, 358, 198 ms) and h i g h l y v a r i a b l e (mean standard d e v i a t i o n s : 127, 82, 160, 131, 81, 24 ms). Indeed, and perhaps as a r e s u l t , group standard d e v i a t i o n s (58, 69, 79, 114, 71, 86 ms) were unusually high. This subject's data appear, i n p a r t i c u l a r , t o have c o n t r i b u t e d t o the unusually high mean and standard d e v i a t i o n i n the four taps c o n d i t i o n . - 39 - F i g u r e 2. Mean r e a c t i o n time. (RT) a c r o s s t r i a l s - 72 o b s e r v a t i o n s per p o i n t . 320 300 - _ 2 8 0 - 'c/T 1x260 - 240 - 220 ' 1 1 I I L 1 2 3 4 5 - 41 - Figure 3. Mean r e a c t i o n time (RT) as a fu n c t i o n of number of taps. a. Results f o r 12 subjects - 108 observations per p o i n t , b. Results f o r 11 subjects - 99 observations per po i n t .   - 44 - Despite the r e l a t i v e l y good f i t of the r e g r e s s i o n l i n e , i t i s not beyond.question that an i n c r e a s i n g l i n e a r r e l a t i o n s h i p that plateaus a f t e r four taps i s the best r e p r e s e n t a t i o n of the data here. A subsequent a n a l y s i s was t h e r e f o r e conducted i n which a l l l a t e n c y data from the subje'ct i n question were e l i m i n a t e d . The r e s u l t i n g mean data are shown i n F i g u r e 3b. Indeed, the new data were found to be s l i g h t l y l e s s v a r i a b l e o v e r a l l , most n o t i c a b l y i n the four taps c o n d i t i o n (58, 60, 57, 86, 68, 87 ms). As w e l l , RT f o r the four taps c o n d i t i o n f e l l more i n t o l i n e with the p r e d i c t e d e f f e c t . In a d d i t i o n to the r e l i a b l e l i n e a r e f f e c t , F (1, 10) =9.38, p_=.012 (the only s i g n i f i c a n t t r e n d ) , the o v e r a l l • c o n d i t i o n s e f f e c t was found to be s i g n i f i c a n t , F (5, 50)=4.06, Huynh-Feldt £=.005. The c a l c u l a t e d r e g r e s s i o n c o e f f i c i e n t i n d i c a t e d t h a t l a t e n c y i n c r e a s e d at 'a r a t e of 10.2 ms/tap (RT (ms) = 10.2 X Number of Taps + 213). L i n e a r r e g r e s s i o n accounted f o r 93% of the v a r i a n c e among mean l a t e n c i e s . I n t e r v a l Data. Mean c o n d i t i o n IRIs are presented i n Table 1. Reproduced s e r i a l p o s i t i o n and c o n d i t i o n means were c l o s e approximations of the c r i t e r i o n i n t e r v a l s of 300 ms. ANOVA re v e a l e d no s i g n i f i c a n t d i f f e r e n c e s e i t h e r w i t h i n or between c o n d i t i o n s . O v e r a l l accuracy d i d not s y s t e m a t i c a l l y vary across c o n d i t i o n s . Mean i n t e r t r i a l standard d e v i a t i o n s are presented i n Table 2. Subjects' response t i m i n g across t r i a l s was c l e a r l y l e s s v a r i a b l e as p a t t e r n length i n c r e a s e d . I n t r a t r i a l standard d e v i a t i o n s f o r a l l IRIs and f o r the f i r s t two IRIs common to each multi-IRI p a t t e r n are a l s o d i s p l a y e d - 4 5 - Table -1 Mean IRI and Terminal Event (TE) Durations (ms) and Corresponding SD's as a Function of S e r i a l P o s i t i o n and Patte r n Length Mean Duration IRI S e r i a l P o s i t i o n TE Number ,— of Taps 1 2 3 4 5 M M SD 113 24 M 289 18 289 18 131 18 M SD 292 18 303 33 298 24 123 17 M SD 301 16 306 20 308 22 305 17 127 14 M 302 19 307 16 298 20 307 21 303 17 124 13 M SD 299 19 304 18 298 15 307 19 310 17 304 13 127 13 - 46 - Table 2 Mean and SD of I n t r a t r i a l and I n t e r t r i a l IRI SD's (ms) as a Function of P a t t e r n Length Number of I R I 1 s 1 2 3 4 5 I n t r a t r i a l SD 1s A l l s e r i a l p o s i t i o n s M - 17.92 17.63 18.96 18.44 SD - 12.36 4.90 5.43 8.54 1st 2 s e r i a l p o s i t i o n s M - 17.92 13.65 16.90 17.04 SD - 12.36 3.10 8.62 11.12 I n t e r t r i a l SD 1s M . 26.85 17.67 12.28 8.45 8.15 £D • 12.10 . 7.33 8.54 3.90 2.51 - 47 - i n Table 2. Shown are the mean i n t r a t r i a l standard d e v i a t i o n s ( c o l l a p s e d across t r i a l s and s u b j e c t s ) , and the mean w i t h i n - s u b j e c t standard d e v i a t i o n s of i n t r a t r i a l standard d e v i a t i o n s . Mean i n t r a t r i a l v a r i a b i l i t y d i d not s y s t e m a t i c a l l y vary as p a t t e r n length i n c r e a s e d . However, the co n s i s t e n c y of v a r i a b i l i t y (within-subjects) f o r the 3-IRI p a t t e r n was c l e a r l y g r e a t e r than f o r the other p a t t e r n s . T h i s was the only p a t t e r n i n which the consistency of i n t r a t r i a l v a r i a b i l i t y was gr e a t e s t f o r j u s t the f i r s t two IRIs i n d i c a t i n g that, f o r the other p a t t e r n s , w i t h i n - s u b j e c t s v a r i a b i l i t y was concentrated at the beginning o f the p a t t e r n . Terminal Event Data. Terminal event data are shown i n Table 1. ANOVA uncovered no s i g n i f i c a n t d i f f e r e n c e s among t e r m i n a l event i n t e r v a l s . ^However, the a l t e r n a t i n g long and short durations suggested the performance of a post hoc t r e n d a n a l y s i s i n order to determine i f t h i s p a r t i c u l a r higher- order t r e n d was s i g n i f i c a n t . Not s u r p r i s i n g l y , the a n a l y s i s d i d r e v e a l a s i g n i f i c a n t q u i n t i c e f f e c t , F(1,10)=6;07, E=.033. This e f f e c t , i n a d d i t i o n t o the observation t h a t the reproduced i n t e r v a l s were s u b s t a n t i a l l y longer than the . c r i t e r i o n i n t e r v a l of 100 ms, underscore the idea that response onset times r e f l e c t a r t i c u l a t i v e and not n e c e s s a r i l y t i m i n g processes. D i s c u s s i o n The c l a i m t h a t simple RT incr e a s e s as a l i n e a r f u n c t i o n of the number of response u n i t s - s i n g l e f i n g e r taps - i s - 48 - supported i n t h i s study. The primary i n t e n t of t h i s study was t o determine i f such a f i n d i n g would occur i n the absence of c a t c h t r i a l s , and,thus speak to the hypothesis that the processes of program implementation a u t o m a t i c a l l y l e a d to response execution and, t h e r e f o r e , are delayed u n t i l a f t e r the stimulus only when the paradigm i n v o l v e s catch ' t r i a l s . These r e s u l t s do not support t h i s hypothesis. In a simple RT paradigm, stimulus u n c e r t a i n t y i s not a necessary c o n d i t i o n f o r programming' delay. Why, then, should a subject wait u n t i l the s i g n a l t o respond t o implement a programmed response i f he/she knows what i s to be done, when i t i s to be done and that i t always must be done? The present f i n d i n g s are c o n s i s t e n t with the Sternberg et a l . (1978) suggestion that program implementation i s delayed because p l a c i n g the implemented but y e t - t o - b e - t r i g g e r e d program i n a motor b u f f e r would subject i t to r a p i d decay, or i n t e r f e r e n c e i n the event of stimulus p r o c e s s i n g . T y p i c a l l y , subjects are to respond'as q u i c k l y as p o s s i b l e i n s t u d i e s of t h i s s o r t . Yet, the l i n e a r i n c r e a s e i n RT re p o r t e d here f o r the reproduction of response tones separated by around 300 ms i n d i c a t e s that, even at t h i s r e l a t i v e l y slow .rate, the e n t i r e p a t t e r n was t r e a t e d i n some way as a coherent response. In terms of the Sternberg et a l . model, RT i n c r e a s e d because the s e a r c h / r e t r i e v a l process was faced with an i n c r e a s i n g pool of subprograms. The l i n e a r i n c r e a s e i n RT i s c o n s i s t e n t with the model of Sternberg and h i s co l l e a g u e s . However, t h e i r model a l s o - 49 - p r e d i c t s t hat movement d u r a t i o n per response u n i t should i n c r e a s e as the length of the response p a t t e r n i n c r e a s e s . That was not the case here. P a t t e r n length d i d not a f f e c t the mean reprod u c t i o n of IRIs. R e c a l l , though, that the p a t t e r n s i n the present study were reproduced at a s p e c i f i e d r a t e . The Sternberg et a l . model was based on response, p a t t e r n s t h a t are produced,as f a s t as p o s s i b l e . The a d d i t i o n a l time-per-unit p r e d i c t e d by t h e i r model might w e l l be "absorbed" i n the longer IRIs of the p a t t e r n s i n t h i s study. Therefore, we are unable to comment on the -duration aspect of the Sternberg et a l . model. With respect to the r e p r o d u c t i o n of IRIs, mean i n t r a t r i a l v a r i a b i l i t y was s i m i l a r across conditions' although w i t h i n - s u b j e c t c o n s i s t e n c y of i n t r a t r i a l v a r i a b i l i t y was g r e a t e s t i n the 3-IRI p a t t e r n . We might speculate t h a t with the m a j o r i t y of popular Western musical rhythm being i n the s t r u c t u r e of 4/4 time, the 3-IRI ( i . e . 4-tap) p a t t e r n induced s u b j e c t s to access a learned s t r u c t u r e ; t h e r e f o r e , i n t r a p a t t e r n v a r i a b i l i t y was c o n s i s t e n t . The i n t e r t r i a l v a r i a b i l i t y f i n d i n g s are the most • i n t e r e s t i n g of the IRI data. For the longer p a t t e r n s , s u b j e c t s were more c o n s i s t e n t i n t h e i r mean r a t e of response across t r i a l s . I t may be that the feedback from reproducing longer p a t t e r n s and/or the exposure to longer stimulus p a t t e r n s more thoroughly embeds the temporal or' rhythmic q u a l i t i e s of the p a t t e r n . The p e r c e p t i o n of only two s e q u e n t i a l events does not suggest the phenomenon of a - 50 - "pattern" so much as i t does temporal d i s t i n c t i v e n e s s . As pat t e r n length increases so does the expansion of temporal s t r u c t u r e f o r r e l a t i o n s between adjacent and non-adjacent i n t e r v a l s . The general f i n d i n g of a l i n e a r RT fu n c t i o n f o r in c r e a s i n g response complexity i s extended to.the reproduction of up to s i x response u n i t s . In the next study, programming requirements f o r various response rates and a broader range of response complexity ( i . e . number of events) are i n v e s t i g a t e d . The e f f e c t s of response rate on response ti m i n g and a r t i c u l a t i o n ( i . e : tone-onset times) are al s o studied. Comment on the q u i n t i c e f f e c t observed f o r termi n a l event durations i n t h i s f i r s t Experiment w i l l be reserved u n t i l the general d i s c u s s i o n f o r Section One. - 51 - Experiment 2 How does the r e q u i r e d : r a t e of response execution i n f l u e n c e programming requirements p r i o r t o response i n i t i a t i o n ? Rapid movement p a t t e r n s are t r e a t e d as coherent responses and t h i s i s r e f l e c t e d i n d i f f e r e n t i a l RTs such as those found i n Experiment 1. We would not expect t h i s same e f f e c t f o r slower p a t t e r n s i f they are not t r e a t e d as coherent responses. H u l s t i j n and van Galen (1983) have suggested that f o r handwriting (a r e l a t i v e l y slow output form) e i t h e r p a r t of a handwritten sequence i s f u l l y programmed or the e n t i r e sequence i s p a r t i a l l y programmed i n advance of response i n i t i a t i o n (see a l s o Stelmach & T e u l i n g s , 1983). The remaining, programming i s done " o n - l i n e " . Harrington and Haaland (1987) i n v e s t i g a t e d RT and IRI p r o f i l e s f o r s e r i e s of hand manipulation movements and concluded that the f i r s t two response u n i t s are completely programmed p r i o r to response i n i t i a t i o n . Although i t seems c l e a r t hat response p a t t e r n s are c o n t r o l l e d i n p a r t through o n - l i n e programming, the i s s u e of how. much programming i s done p r i o r t o and a f t e r response i n i t i a t i o n remains, u n c e r t a i n . Semjen and G a r c i a - C o l e r a (198 6) found that simple and choice RTs to i n i t i a t e a f i v e f i n g e r - t a p p a t t e r n decreased as response r a t e decreased from 300 ms to 600 ms per response. No such d i f f e r e n c e s were.found when tapping r a t e v a r i e d between 140 ms and 300 ms. Indeed, whereas r a p i d p a t t e r n s may t r u l y be prepared as response "patterns", slow p a t t e r n s may be produced as s e r i e s of separable responses or response "chunks" . Programming requirements f o r response rates of 2 0 0 , 4 0 0 , 6 0 0 , and 800 ms per response u n i t are i n v e s t i g a t e d . In the case of a simple tapping task, i t i s pr e d i c t e d that RT w i l l increase as a functi o n of number of response u n i t s f o r the 200-ms c o n d i t i o n but not f o r the 600-ms or 800-ms co n d i t i o n s . There i s no precedent i n the l i t e r a t u r e f o r making a p r e d i c t i o n regarding the 400-ms c o n d i t i o n . Previous i n v e s t i g a t i o n s have yet to discover a r e l i a b l e " c e i l i n g " to the number of response u n i t s that r e s u l t i n an increase i n simple RT. Of course, i t i s hardly p l a u s i b l e that RT increases i n d e f i n i t e l y f o r i n c r e a s i n g l y long response patterns regardless of how r a p i d l y they are produced. Analogously, choice RT does not- continue to increase when the number of stimulus-response a l t e r n a t i v e s becomes very high (Seibel, 1 9 6 3 , showed t h i s when t e s t i n g up to .1032 a l t e r n a t i v e s (!)). What would a l i m i t to the simple RT e f f e c t mean -(with respect to number of response units) ? I t could mean, again, that the response patt e r n i s not t r e a t e d as a coherent whole - that the number of subprograms subject to a s e a r c h / r e t r i e v a l process i s l i m i t e d . A RT l i m i t i s thus l i k e l y dependent on both response rate and the t o t a l number of response u n i t s . Both response rate and the number of response u n i t s are manipulated i n the present study.- As a r e s u l t , t o t a l response duration a l s o v a r i e s . A s i g n i f i c a n t l i n e a r RT trend f o r more than one - 53 - response rate would shed l i g h t on whether response duration and/or the number of response u n i t s i s the c r i t i c a l parameter of response complexity i n a simple RT paradigm. Would d i f f e r e n t timing p r o f i l e s be expected among response patterns reproduced at d i f f e r e n t rates? Povel and Essens (1985) have suggested that temporal patterns are accented i n a way that r e f l e c t s t h e i r perceptual o r g a n i z a t i o n . S p e c i f i c a l l y , they have proposed that i s o l a t e d events, the second i n a c l u s t e r of two events, and the i n i t i a l and f i n a l events i n c l u s t e r s of more than two events, are p s y c h o l o g i c a l l y accented regardless of the combination i n which such c l u s t e r s occur.in a temporal p a t t e r n . However, t h e i r model f a i l s to consider pattern tempo. The i n t e r a c t i o n of rhythm and tempo i n pattern perception i s considered by many to be c r u c i a l and should'not be ignored (for example, Clarke, 1985). I f slow stimulus patterns are perceived more as a pa t t e r n of s t i m u l i than as a u n i t a r y stimulus pattern, then such patterns should not d i s p l a y evidence of the p s y c h o l o g i c a l accenting suggested by'Povel and Essens. One way i n which the accenting of an i n t e r v a l - i s r e a l i z e d i s to lengthen the duration of that i n t e r v a l ( i . e . an agogic accent). The accenting of isochronous patterns that vary i n tempo i s i n v e s t i g a t e d here by determining the r e l a t i o n s h i p s among IRIs (durations) w i t h i n each c o n d i t i o n . Measurable accenting of these patterns may help to reveal how they are p e r c e p t u a l l y organized. - 54 - F i n a l l y , the a r t i c u l a t i v e p r o p e r t i e s ( i . e . tone-onset times) of response p a t t e r n s are examined. Although a somewhat n e g l e c t e d measure of performance (recent exceptions being G a r c i a - C o l e r a & Semjen, 1987; Keele et a l . , 1987), response a r t i c u l a t i o n , as an emergent fe a t u r e of performance, may provide i n s i g h t t o the c o n t r o l of response p a t t e r n s produced at d i f f e r e n t r a t e s . Method • • Subjects. Eleven male and female students from the U n i v e r s i t y of B r i t i s h Columbia p a r t i c i p a t e d i n the study as an o p t i o n a l course requirement. ( D i f f e r e n t s u b j e c t s p a r t i c i p a t e d i n each of the four s t u d i e s r e p o r t e d h e r e ) . Subjects ranged i n age from 20 to 39 years. A l l but two of the s u b j e c t s had at l e a s t the e q u i v a l e n t of one high school course i n t y p i n g . Apparatus. The experiment was c o n t r o l l e d through' an IBM "XT" microcomputer. A c i r c u i t board was designed to i n t e r f a c e a "Tecmar Labmaster" data a c q u i s i t i o n , m u l t i - f u n c t i o n board t h a t was r e s i d e n t i n the computer with an apparatus comprised of 11 LEDs, miniature speakers and push button response switches (see F i g u r e 4). For t h i s study, only two speakers (one f o r the ready and warning tones, one f o r the stimulus tones) and one response key were f u n c t i o n a l . A l l LEDs were covered with black tape. The designated c i r c u l a r response key was 1.2 cm i n diameter. On i t s black s u r f a c e was a red, 0.9 cm tape square. Stimulus events were - 55 - Figure 4. Response apparatus and computer i n t e r f a c e systems f o r Experiment 2. IBM PC/XT CPU I TECMAR L ABM ASTER I MOTHER C- BOARD 1̂ (^EX^RIME^TER^) DAUGHTER BOARD J J L DIGITAL I/O VARNING SPEAKER VARNING LED STIMULUS SPEAKERS RESPONSE SVITCHES STIMULUS LEDs PORT C PORT A SOSMP CIRCUIT BOARD SOSMP APPARATUS —o o o o o o o o o o o - 57 - produced as tones through the stimulus speaker-. The ready and warning tones were produced through the second speaker. Tone durations and toneless i n t e r v a l durations were c o n t r o l l e d through the computer. Reproduction of the stimulus patterns was r e a l i z e d by pressing and l i f t i n g from the response key with the index f i n g e r of the dominant hand. Reproduced tones were i d e n t i c a l to the stimulus tones i n i n t e n s i t y and frequency. Response durations, toneless i n t e r v a l s and the latency to i n i t i a t e the f i r s t event i n each t r i a l were a l l recorded by the computer. Stimulus Patterns. Subjects reproduced 29 d i f f e r e n t stimulus patterns. The patterns consisted of one to eight 100 ms tones. Multi-tone patterns were presented with •interstimulus i n t e r v a l s (ISIs) of 200, 400, 600, and 800 ms ( r e s u l t i n g i n 28 d i f f e r e n t p a t t e r n s ) . The s i n g l e tone p a t t e r n was not associated with an I S I . A l l tones were equal i n i n t e n s i t y and frequency. Procedure. Subjects were seated at a t a b l e d i r e c t l y i n fro n t of the apparatus and i n s t r u c t e d as to the nature and procedure of the experiment. They rested t h e i r dominant 'hand on.or near the apparatus so that t h e i r index f i n g e r was res t i n g , on the response key. Subjects were i n s t r u c t e d to maintain contact with the response key at l e a s t through completion of the f i r s t response tone. Subjects l i s t e n e d to., one of 29 stimulus patterns. Presentation of the stimulus p a t t e r n was preceded by a one second Ready tone (lower i n frequency than the stimulus tones) and a Pre-Presentation - 58 - i n t e r v a l a l s o one second i n duration. The f i n a l stimulus tone i n the pa t t e r n was followed by a Post-Presentation i n t e r v a l ranging between 2100 and 2700 ms. The off s e t ' of a Warning tone ( i d e n t i c a l i n a l l aspects to the Ready tone) was the s i g n a l f o r subjects to i n i t i a t e reproduction of the stimulus p a t t e r n (see Figure 5). Following reproduction of the f i n a l tone the experimenter pressed a key on the computer keyboard thus i n i t i a t i n g the subsequent t r i a l . Subjects consecutively performed 12 p r a c t i c e t r i a l s and 24 performance t r i a l s f o r each patte r n . Of these, 16.7% were catch t r i a l s . High between-subje'cts v a r i a b i l i t y f o r RT i n Experiment 1 (see the Results section) may have been a r e s u l t of some subjects a n t i c i p a t i n g the s i g n a l to respond. Catch t r i a l s were included i n the present study i n order to, c o n t r o l f o r any a n t i c i p a t i o n that might have otherwise occurred. The Warning tone continued f o r four seconds i n the event of a catch t r i a l . P r a c t i c e t r i a l s were included i n order t o reduce v a r i a b i l i t y . Testing covered three days f o r each subject. Each day involved two- one-hour sessions separated by a r e s t p e r i o d of f i v e minutes. The twofold task was: 1) to i n i t i a t e reproduction of the stimulus p a t t e r n as q u i c k l y as p o s s i b l e f o l l o w i n g the o f f s e t of the warning tone, and 2) to reproduce the tim i n g of each stimulus p a t t e r n as accurately as p o s s i b l e . Equal emphasis was placed on the two aspects of the task. A n a l y s i s . Mean RT was again the primary measure of i n t e r e s t . For each subject the co n d i t i o n mean RTs and - 59 - F i g u r e 5. Time l i n e of a t y p i c a l t r i a l f o r a 3-tone p a t t e r n . (4.0 s f o r catch t r i a l s ) READY TONE 1.0 STIMULUS TONES 1 . 1 . 1 1.0 • 3 2.1 (to 2.7) WARNING TONE 1.0 INTERRESPONSE INTERVALS xx S E C O N D S - 61 - standard d e v i a t i o n s were c a l c u l a t e d . I n d i v i d u a l t r i a l RTs that exceeded two standard d e v i a t i o n s from.the c o n d i t i o n mean were considered e r r o r s as were mean RTs gr e a t e r than 500 ms. E r r o r f u l data were not i n c l u d e d i n the analyses. For IRIs, e r r o r s were d e f i n e d as those scores f a l l i n g o u t s i d e of an allowed t o l e r a n c e range. For the 200-ms rate a t o l e r a n c e range of +50% was allowed. For the 400-, 600-, and 800-ms r a t e s a t o l e r a n c e of +25% was allowed. The s h o r t e r response du r a t i o n s of the 200-ms patte r n s are more s e n s i t i v e to mechanical and p h y s i o l o g i c a l v a r i a b i l i t y , thus the gr e a t e r t o l e r a n c e range was allowed. 'Given the accuracy and con s i s t e n c y of su b j e c t s RTs and IRIs i n Experiment 1, the c r i t e r i a f o r acceptable RT and IRI performance were reduced i n the present study. Tone-onset times or "down-times" (DTs) were not subject to t o l e r a n c e ranges f o r acceptable performance. Since they are thought t o r e f l e c t a r t i c u l a t i v e and not t i m i n g f e a t u r e s of a response p a t t e r n ( r e c a l l that the combined IRI r e f l e c t s p a t t e r n t i m i n g ) , performance c r i t e r i a were not deemed to be app r o p r i a t e . R e s u l t s One subject experienced great d i f f i c u l t y i n co n c e n t r a t i n g on both aspects of the task and t h i s was r e f l e c t e d i n h i s performance. As a r e s u l t , the sub j e c t ' s data were omitted from a l l analyses. Latency Data. As p r e d i c t e d , t r e n d a n a l y s i s uncovered a s i g n i f i c a n t l i n e a r orthogonal component f o r the 200-ms response r a t e , F(1,9)=11.25, p_=.009, along with a s i g n i f i c a n t o v e r a l l e f f e c t , F(7, 63)=3.01, Huynh-Feldt £=.0'09 (see F i g u r e 6).- No other higher-order trends were s i g n i f i c a n t . The r e g r e s s i o n c o e f f i c i e n t was c a l c u l a t e d to be 4.9 ms/tap-(RT (ms) = 4.9 X Number of Taps + 211). However, the s i n g l e - t a p RT i s c l e a r l y d i s t i n c t from the m u l t i - t a p RTs. This f i n d i n g i s not uncommon and w i l l be d i s c u s s e d l a t e r . Taking i n t o account j u s t the m u l t i - t a p p a t t e r n s , the r e g r e s s i o n c o e f f i c i e n t was 3.0 ms/tap (RT (ms) = 3.0 X Number of Taps + 222). S i m i l a r t r e n d analyses r e v e a l e d no e f f e c t s f o r the other rates'. S u r p r i s i n g l y , however, RTs across c o n d i t i o n s f o r the other r a t e s were not c o n s i s t e n t l y low (see Table 3). S t i l l , as can be seen i n the r i g h t hand column of the t a b l e , .the o v e r a l l mean RT was gr e a t e s t f o r the 200-ms response r a t e . I n t e r v a l Data. The time p r o f i l e s f o r the reprod u c t i o n of IRIs are shown i n Fig u r e 7. For patte r n s at the 200-ms and 400-ms r a t e s , the f i r s t and l a s t i n t e r v a l s were reproduced longer than the i n t e r i o r i n t e r v a l s . There was no apparent t r e n d i n the pa t t e r n s produced at slower r a t e s with the exception of the elongated f i r s t i n t e r v a l at the 800-ms r a t e . Means of the f i r s t and l a s t i n t e r v a l s f o r each r a t e are c o n t r a s t e d with the means of the i n t e r i o r i n t e r v a l s i n Table 4. Subsequent analyses of these data r e v e a l e d s i g n i f i c a n t d i f f e r e n c e s f o r the 200-ms rate, F (1, 9)=52.87, - 63 - Figure 6. Mean r e a c t i o n time (RT) as a f u n c t i o n of number of taps f o r the 200 ms response ra t e . A: Regression l i n e c a l c u l a t e d over a l l but the f i r s t task c o n d i t i o n s . B: Regression l i n e c a l c u l a t e d over a l l task c o n d i t i o n s .  - 65 - Table 3 Mean RT and Corresponding SD's (ms) as a Function of Response Rate and P a t t e r n Length Number of Taps Response Rate 2 ' 3 4 5 6 7 8 M 400 ms M 242 221 227 233 229 226 220 228 £D 49 42 36 39 33 29 ' 28 29 600 ms M 242 239 214 235 216 238 225 230 • SR 57 43 38 36 36 ' 36 28 29 800 ms M 241 224 216 248 237 239 227 233 Sn 5 3 - 3 3 35 57 40 36 44 31 200 ms M sn 237 24 - 66 - Figure 7. Mean interresponse i n t e r v a l (IRI) durations as a fun c t i o n of patter n length. a. '200-ms ra t e , b. 400-ms ra t e , c. 600-ms rate , d. 80,0-ms r a t e .   520 h 3 4 5 N U M B E R O F IRIs N U M B E R O F IRIs - 71 - Table 4 Mean IRI Durations and Corresponding SD's (ms) as a Function of Response Rate and S e r i a l P o s i t i o n S e r i a l P o s i t i o n Response Rate F i r s t & Last Elements I n t e r i o r Elements 200 ms M £D 183 17 169 14 400 ms M £D 351 .16 345 13 600 ms M £D 543 19 541 20 800 ms M £D 709 33 704 29 - 72 - jo<.001, and 400-ms r a t e , F ( l , 9 ) = 10.11, £=.011. R e l i a b l e d i f f e r e n c e s were not found f o r t h e o t h e r response r a t e s . Down Time Data. The time p r o f i l e s f o r DTs are shown i n F i g u r e 8. For p a t t e r n s at jthe 200-ms r a t e , f i r s t and l a s t DTs were l o n g e r than i n t e r i o r DTs. For a l l o t h e r response r a t e s the f i r s t DT was the s h o r t e s t i n the p a t t e r n . In Table 5, the mean o f the f i r s t and l a s t DTs f o r p a t t e r n s reproduced at t h e 200-ms r a t e i s c o n t r a s t e d w i t h the mean of the i n t e r i o r DTs. Subsequent a n a l y s i s r e v e a l e d a s i g n i f i c a n t d i f f e r e n c e between th e s e means, F(1,9)=31.92, rK.001. F or the o t h e r response r a t e s , ;the means o f the f i r s t DT are c o n t r a s t e d w i t h the means of a l l o t h e r DTs. R e l i a b l e d i f f e r e n c e s were found at the 400-ms r a t e , F(1,9)=7.62, p_=.022, t h e 600-ms r a t e , F (1, 9) =16 . 94, £=.003, and the 800-ms r a t e , F (1, 9) =30 . 66, p_<.001. V i s u a l a n a l y s i s of the data made c l e a r t h a t the q u i n t i c ( a l t e r n a t i n g ) e f f e c t observed f o r f i n a l DTs a c r o s s l e v e l s of c o m p l e x i t y i n the f i r s t experiment was not r e p l i c a t e d f o r any of the response r a t e s i n the p r e s e n t study. E r r o r s . G e n e r a l and r e l e v a n t s p e c i f i c e r r o r d ata are p r e s e n t e d i n Table 6. T o t a l performance e r r o r s were q u i t e h i g h - 14.4%. That no " s h o r t " IRIs were found f o r the 200- ms p a t t e r n s i s not s u r p r i s i n g . That the m a j o r i t y of s h o r t I R I s o c c u r r e d i n the 400-ms p a t t e r n s i s p u z z l i n g . Perhaps most i n t e r e s t i n g i s the f a c t , t h a t 77% of the " l o n g " I R I s were found f o r t h e 200-ms p a t t e r n s and t h a t , of t h e s e , 66% o c c u r r e d i n the l a s t s e r i a l p o s i t i o n (whereas 22% would be - 73 - F i g u r e 8. Mean down-time (DT) durations as a f u n c t i o n of response r a t e and p a t t e r n length.  - 75 - Table 5 Mean DT Durations and Corresponding SD's (ms) as a Function of Response Rate and S e r i a l P o s i t i o n S e r i a l P o s i t i o n Response Rate F i r s t & Last Elements I n t e r i o r Elements M 200 ms M £D 91 12 8'2 9 85 10 Response Rate S e r i a l P o s i t i o n F i r s t Element A l l Other Elements 40 0 ms M 116 31 122 31 121 31 600 ms M SD. 127 40 139 42 137 42 800 ms M SD 128 44 141 48 138 47 - 76 - Table 6 C l a s s i f i c a t i o n and Frequency of E r r o r T r i a l s i n R e l a t i o n to the T o t a l Number of T r i a l s and the Next Superordinate E r r o r Category E r r o r s E r r o r s % of % of Next and Number T o t a l Superordinate P a t t e r n Type T r i a l s E r r o r Category T o t a l Performance E r r o r s 835 14 . 4% Non-RT E r r o r s 442 7 . 6% Short IRI's 298 5 .1% 2 00 ms 400 ms 0 161 0% 54% Long IRI's 94 200 ms 72 Last ser. pos. 6- tap p a t t e r n 7- tap p a t t e r n 8- tap p a t t e r n 400, 600, 800 ms 22 Last ser. pos. E x t r a tap(s) 50 200 ms 42 6- tap p a t t e r n 7- tap p a t t e r n 8- tap p a t t e r n RT E r r o r s 393 1 . 6% 0.9% 77% 66% * 18% 29% 24% 23% 38% * 84% 14% 29% 50% 6.8% Catch T r i a l E r r o r s 22 1.9% ** These percentages were c a l c u l a t e d from the t o t a l m u l t i - IRI p a t t e r n s . A s i n g l e - I R I that was lengthened could not be c l a s s i f i e d as a " l a s t " s e r i a l p o s i t i o n . Four of 72 long IRI's i n the 200 ms pa t t e r n s , and one of the 22 long IRI's i n the other p a t t e r n s f e l l i n t o the s i n g l e - I R I category. By chance, long IRI e r r o r s should have occurred i n the l a s t s e r i a l p o s i t i o n 22% of the t i m e . 4 This e r r o r score was c a l c u l a t e d as a percentage of the t o t a l catch t r i a l s . - 77 - p r e d i c t e d by chance f o r m u l t i - I R I p a t t e r n s ) . This i s l i k e l y explained- by the f a c t that at times subjects stopped tapping e x a c t l y one tap before the end of the p a t t e r n . The experimenter had to remind them to reproduce one a d d i t i o n a l tap. Conversely, subjects also made er r o r s of reproducing too many taps. Again, these er r o r s were concentrated i n the 200-ms patterns and, s p e c i f i c a l l y , i n the longest patterns at t h i s r a t e . I t i s c l e a r that subjects experienced r e l a t i v e d i f f i c u l t y i n reproducing the correct number of taps f o r longer patterns at the f a s t e s t r a t e . RT e r r o r s revealed no systematic tendencies across response rate or response length. This was to be expected, however, since RTs were eliminated on the basis of exceeding • twice the subject's standard d e v i a t i o n f o r each c o n d i t i o n . For one c o n d i t i o n performed by a s i n g l e subject the mean • c o n d i t i o n RT exceeded 500 ms and was thus eliminated. Discussion RT, programming, response rate and response length. Execution rate determines how much processing must be done i n advance of response i n i t i a t i o n . Patterns at the 2'00-ms response rate d i s p l a y response coherence. In terms of the Sternberg et a l . (1978) model, RT increases with the number of pooled subprograms that must be searched. S i m i l a r increases are not observed ; f o r the slower rates which i n d i c a t e s that the number of subprograms searched does' not increase with i n c r e a s i n g pattern length - the patterns do not - 78 - d i s p l a y response coherence. The p r e d i c t i o n s regarding •programming requirements f o r isochronous patterns reproduced at various rates are confirmed. The 400-ms response ra t e , f o r which no p r e d i c t i o n was made, f a i l e d to d i s p l a y coherence i n response programming. Three i n t e r e s t i n g aspects of the RT data require e l a b o r a t i o n : 1) the d i s t i n c t l y low RT f o r the s i n g l e - t a p c o n d i t i o n , 2) the pattern of RT means across conditions f o r each of the 400-ms, 600-ms and 800-ms response r a t e s , and 3) the high mean RT f o r the f i v e - t a p c o n d i t i o n at the 200-ms ra t e . We might account f o r the deviant s i n g l e - t a p RT by r e f e r r i n g again to the element-invariance requirement introduced by Sternberg and h i s colleagues (1978). S p e c i f i c a l l y , they argued that the production of a s i n g l e element may be fundamentally d i f f e r e n t from the production of multi-element patterns which have a beginning element, a terminating element, and vary only i n the number of i n t e r i o r elements they possess. Their one-handed typing data, and the data presented here, sho.w a g r e a t l y reduced single-element RT i n r e l a t i o n to the trend of multi-element RTs. However, the general evidence i n t h i s regard has been c o n f l i c t i n g . With respect to handwriting, H u l s t i j n and van Galen (1983, expt. 1) found that simple RT increased l i n e a r l y from two to four l e t t e r s a f t e r a s i g n i f i c a n t decrease from one to two l e t t e r s . However, a second experiment revealed an in c r e a s i n g trend from one to four l e t t e r s . Teulings et a l . (1986, expts. 1,2) found that i n patterns of one to s i x - 79 - continuous curved-strokes, and one to f i v e continuous s t r a i g h t - s t r o k e s , RT was g r e a t e s t i n the s i n g l e stroke • c o n d i t i o n . Yet, a t h i r d experiment showed that with the h o r i z o n t a l p r o g r e s s i o n of s u c c e s s i v e w r i t t e n strokes e l i m i n a t e d , the deviant s i n g l e stroke RT f e l l i n t o l i n e and a small - n o n s i g n i f i c a n t i n c r e a s e r e s u l t e d . Sternberg et a l . (1978) found no d e v i a t i o n s from an i n c r e a s i n g l i n e a r t r e n d f o r the s i n g l e response u n i t i n speech or two-handed t y p i n g . In our f i r s t experiment, the s i n g l e - t a p RT d i d not d e v i a t e from the t r e n d of m u l t i - t a p RTs. Unfortunately, evidence r e g a r d i n g the element-invariance requirement i s clouded and no c o n c l u s i o n s can be drawn i n t h i s regard. Perhaps more importantly, i n c o n s i d e r a t i o n of the present design, i s the f a c t t h a t a s i n g l e tap r e q u i r e s no t i m i n g component, whereas f o r m u l t i - t a p p a t t e r n s an•IRI must be programmed. This a d d i t i o n a l operation would add a constant time to m u l t i - t a p RTs. Yet, t h i s e x p l a n a t i o n i s not supported i n the r e s u l t s of Experiment 1. The i n c o n s i s t e n t p a t t e r n of RT means across c o n d i t i o n s f o r each of the three slower response r a t e s i s a s u r p r i s i n g f i n d i n g . We might speculate, and indeed i t was observed, t h a t r e p r o d u c t i o n of the slower p a t t e r n s does not r e q u i r e as much a t t e n t i o n or " e f f o r t " as f o r the 200-ms p a t t e r n s . I f s u b j e c t s are not c o n s i s t e n t l y a t t e n t i v e f o r the slower p a t t e r n s , then they may p e r c e i v e them as more or l e s s coherent, and may employ d i f f e r e n t response s t r a t e g i e s i n - 80 - executing them. We would then expect an i n c o n s i s t e n t p a t t e r n of RT means to r e s u l t . For the 200-ms c o n d i t i o n , RT continued to increase through, eight taps although' the small increment of the slope and the r e l a t i v e l y high f i v e - t a p RT make t h i s i n t e r p r e t a t i o n somewhat tenuous. I t may be that RT "plateaus" at t h i s number of response u n i t s (or t o t a l response d u r a t i o n ) . In general, i n t e r p r e t a t i o n i s l i k e l y to be d i f f i c u l t f o r designs that i n v o l v e p r a c t i c e t r i a l s - as t h i s one d i d - since the regression c o e f f i c i e n t f o r RT decreases with l e a r n i n g and, as i t does, becomes more d i f f i c u l t to d i s t i n g u i s h from a h o r i z o n t a l r e l a t i o n s h i p or plateau e f f e c t . Response timing and rhythmic o r g a n i z a t i o n . IRI p r o f i l e s show that, r e l a t i v e to i n t e r i o r p a t t e r n i n t e r v a l s , the f i r s t and l a s t i n t e r v a l s i n a pattern are lengthened f o r the 200-ms and 400-ms rates but not for the slower r a t e s . S i m i l a r r e s u l t s have been found by Semjen and Garcia-Colera, (1986 - for p a t t e r n rates up t o 300-ms but not f o r a rate of 600-ms), Povel (1981) , and, for piano performance, by Povel (1977), Shaffer (1980) and Shaffer et al.' (1985). R e c a l l that the c l u s t e r i n g of s t i m u l i w i t h i n a pattern is'thought to r e s u l t i n p s y c h o l o g i c a l "accenting" of c e r t a i n pattern elements. For c l u s t e r s of more than two elements, Povel and Essens (1985) have argued that the f i r s t and l a s t elements are accented. Shaffer et a l . (1985) have suggested that t h i s i s how "coherent sequences" are. organized. - 81 - I f t h i s i s the case, then i t appears that only those patterns presented at the 200-ms and 400-ms rates d i s p l a y perceptual coherence. The h i e r a r c h i c a l s t r u c t u r i n g of temporal patterns as evidenced by accenting i s what Miction (1974), among others, considers as c h a r a c t e r i s t i c of rhythmic patterns. The conclusion here i s that, in' the context presented, patterns of isochronous elements separated by more than 400-ms are not perceived as "rhythmic" patterns. Within more elaborate contexts, of course, such as those i n music, pauses between elements may be greater i n duration yet rhythm i s s t i l l maintained. Response a r t i c u l a t i o n and system dynamics. DT p r o f i l e s r e v e a l the nature of p a t t e r n - a r t i c u l a t i o n as opposed to patt e r n - t i m i n g . In patterns reproduced at the f a s t e s t rate, the f i r s t and l a s t DTs are lengthened. Why? Since i t takes time to overcome i n e r t i a and accelerate the response segment to a v e l o c i t y that w i l l correspond with the des i r e d frequency of response, the f i r s t DT contact i s lengthened. In terms of the Kay, Kelso, Saltzman, and Schoner (1987) L i m i t - C y c l e • O s c i l l a t o r model, the " s t i f f n e s s " required f o r the generation of a r a p i d rhythmic patt e r n i s not yet achieved ( s t i f f n e s s i s argued to be the c o n t r o l parameter that u n d e r l i e s peak vel o c i t y / f r e q u e n c y and amplitude/frequency r e l a t i o n s h i p s ) . The explanation with respect to the f i n a l DT i s s i m i l a r . Presumably, as subjects approach the end of a r a p i d l y reproduced patt e r n they slow t h e i r movement (i.e.' decrease the s t i f f n e s s component of the system) so as not to reproduce an e x t r a response. Indeed, f o r high-frequency, low- • amplitude movement patterns, t h i s decrease i s l i k e l y a n t i c i p a t e d i n advance. As a r e s u l t , slowing should occur before the l a s t element i s produced - p r e c i s e l y what was found f o r the 200-ms patterns. I f there i s ample time to modulate s t i f f n e s s i n the 'reproduction of patterns at slower response rates then why are the DTs not equivalent across s e r i a l p o s i t i o n s ? Why are they c o n s i s t e n t l y shorter f o r the f i r s t tap? Simply, the task employed here was also a RT task. I t was imperative to accelerate the response segment maximally to produce the • i n i t i a l tap as q u i c k l y as p o s s i b l e before achieving the s t i f f n e s s required to generate responses at the de s i r e d frequency. This i n t e r p r e t a t i o n of DT r e s u l t s , while s p e c u l a t i v e , addresses an important question with respect to response c o n t r o l . S p e c i f i c a l l y , to what extent do response programming, feedback, and response system dynamics i n t e r a c t and account f o r the features of response production? A s p e c i f i c and i n t e r e s t i n g question that r e s u l t s from the present study i s : Are e r r o r f u l patterns where an extra tap i s produced due to improperly programming too many responses (a programming i n t e r p r e t a t i o n ) , inadequately processing feedback i n time to terminate the response (a feedback i n t e r p r e t a t i o n ) , or a f a i l u r e to modulate s t i f f n e s s a p p r o p r i a t e l y (a dynamical i n t e r p r e t a t i o n ) ? Of course, these a l t e r n a t i v e s are not n e c e s s a r i l y e x c l u s i v e to one-another. - 83 - One f i n a l observation i s of i n t e r e s t here. I t was v i s u a l l y apparent that to produce patterns at the three slower response rates subjects could quite comfortably move only t h e i r index f i n g e r . To achieve the f a s t e r 200-ms rate, however, they t y p i c a l l y v i b r a t e d e i t h e r about t h e i r w r i s t or t h e i r elbow. Of course, the l i n e a r v e l o c i t y of a d i s t a l p oint along a r a d i a l arm v i b r a t i n g at a f i x e d frequency increases as the length of the arm increases. Thus, a d i f f e r e n t and l a r g e r coordinative s t r u c t u r e may have been employed i n order to r e a l i z e the high v e l o c i t i e s required at the d i s t a l limb segment (see Kugler, Kelso, & Turvey, 1980/ Kelso, Holt, Kugler, & Turvey, 1980). One outcome of t h i s would be the necessity to overcome a greater i n e r t i a when stopping a movement and thus a greater l i k e l i h o o d of producing an e x t r a tap. However, e m p i r i c a l research i s required t o shed more l i g h t on t h i s issue. - 84 - GENERAL DISCUSSION The major f i n d i n g s and i m p l i c a t i o n s of Section One are summarized i n four p a r t s . The Design of "Programming" Experiments At the outset, a t t e n t i o n was drawn to three areas of concern i n the design of experiments that i n v e s t i g a t e programming operations: methodology, the parameters of response complexity, and task s e l e c t i o n . The simple RT method was adopted here i n order to examine the processes of response implementation and the conditions under which such processes would be executed p r i o r t o response i n i t i a t i o n . The r e s u l t a n t f i n d i n g s f o r various response ra t e s , l e v e l s of complexity, and varying stimulus uncertainty, lend support to the use of t h i s method. Based on the l i n e a r , i n c r e a s i n g RT trends found f o r the •300-ms rat e i n Experiment 1, the 200-ms rate i n Experiment 2, and the r e s u l t s of previous studies (e.g. Garcia-Colera & Semjen, 1987), "number of response u n i t s " . i s a strong candidate f o r a parameter of response complexity. Unfortunately, since no s i m i l a r trend was found f o r the 400- ms ra t e , t h i s parameter cannot be separated from " t o t a l response duration". Because of d i f f e r e n t designs, equipment and procedures, RT trends cannot be compared across Experiments 1 and 2. What i s needed to resolve t h i s issue i s a study i n which, again, response rate and number of response u n i t s i s covaried, but the response rates are kept w i t h i n a - 85 - range known to r e s u l t i n an i n c r e a s i n g , l i n e a r RT trend ( i . e . at or below 300-ms). In terms of the r e s u l t s , s i n g l e key tapping proved to be a r e l i a b l e task. Producing these simple and r e l a t i v e l y . i n v a r i a n t movements also allowed f o r the accurate measurement of DTs and IRIs, and t h e i r subsequent analyses. Programming Requirements and Response Rate Isochronous patterns were used as s t i m u l i as opposed to "a s - f a s t - a s - p o s s i b l e " patterns, i n order to c o n t r o l f o r and determine the in f l u e n c e of response rate on programming p r i o r to response i n i t i a t i o n . Findings from the two studies i n d i c a t e that only those patterns executed at a rate at dr below 300-ms d i s p l a y coherence and are programmed accordingly (although, Franks and van Donkelaar, 1987, have uncovered some evidence f o r an increase between two and three taps at a 400-ms r a t e ) . Patterns executed at slower rates are not tr e a t e d as coherent•as evidenced by the n o n - s i g n i f i c a n t RT trends. The greater RT slope f o r the 300-ms rat e i n Experiment 1 compared to the 200-ms rate i n Experiment 2 (10.2 ms/tap vs. 3.0 ms/tap) i s l i k e l y due to the absence of p r a c t i c e t r i a l s i n the former study - r e c a l l that Sternberg et a l . (1978) found that the magnitude of the regression c o e f f i c i e n t decreases with l e a r n i n g . The RT r e s u l t s • r e p o r t e d here are consistent with.the t h e o r e t i c a l d i s t i n c t i o n between program co n s t r u c t i o n and program implementation (Ivry, 1986). S p e c i f i c a l l y , the program f o r a known response pattern i s constructed i n - 86 - advance of the s i g n a l t o respond. But the implementation of the program i s delayed u n t i l a f t e r the s i g n a l to respond. The d u r a t i o n of program implementation f o r the f i r s t response u n i t (RT) i s d i r e c t l y r e l a t e d to the number, of response u n i t s i n the p a t t e r n . Stimulus U n c e r t a i n t y ' Experiment 1 i s the f i r s t study to show t h a t RT in c r e a s e s l i n e a r l y with response complexity even i n the absence of e x t e r n a l l y - i n d u c e d stimulus u n c e r t a i n t y . I f the i n i t i a t i o n of program implementation a u t o m a t i c a l l y l e d to response execution then removing catch t r i a l s should allow f o r implementing the program p r i o r to the s i g n a l to respond, and thus no simple RT e f f e c t s would r e s u l t . Yet, t h i s was not the case. An a l t e r n a t i v e explanation that remains i s that p l a c i n g an implemented but y e t - t o - b e - t r i g g e r e d program i n a motor b u f f e r would subject i t t o r a p i d decay or i n t e r f e r e n c e i n the event of stimulus p r o c e s s i n g (Sternberg et a l . , 197 8 ) . Response Timing and Response A r t i c u l a t i o n The r e p r o d u c t i o n of isochronous stimulus p a t t e r n s r e v e a l e d s e v e r a l i n t e r e s t i n g f i n d i n g s . F i r s t , i n Experiment 1, i n t e r t r i a l v a r i a b i l i t y decreased with i n c r e a s i n g p a t t e r n l e n g t h . The development of a well-defined-temporal s t r u c t u r e may be d i r e c t l y r e l a t e d to the number of temporal i n t e r v a l s i n a p a t t e r n . Longer p a t t e r n s allow f o r an expanded network of r e l a t i o n s among adjacent and non-adjacent i n t e r v a l s . - 87 - Second, i n Experiment 2 , IRI p r o f i l e s showed t h a t t h e 200-ms and 400-ms p a t t e r n s were o r g a n i z e d as acc e n t e d c l u s t e r s o f tones ( i . e . r h y t h m i c p a t t e r n s ) . The f i r s t and l a s t I R I s i n th e s e p a t t e r n s were c o n s i s t e n t l y l e n g t h e n e d i n r e l a t i o n t o i n t e r i o r I R I s . C u r i o u s l y , s i m i l a r a c c e n t i n g was not observed f o r r e p r o d u c t i o n o f t h e 300-ms p a t t e r n s i n Experiment 1, a l t h o u g h , w i t h fewer t r i a l s , a r h y t h m i c o r g a n i z a t i o n may not y e t have developed. F i n a l l y , t h e r e s u l t s o f Experiment 2 g i v e a p r e l i m i n a r y i n d i c a t i o n t h a t measuring response a r t i c u l a t i o n may be u s e f u l i n r e f l e c t i n g t h e dynamic f e a t u r e s o f movement p r o d u c t i o n . I t would appear t o t a k e time b o t h t o a c c e l e r a t e a response segment t o a v e l o c i t y t h a t corresponds w i t h a r a p i d response r a t e , and t o d e c e l e r a t e t h a t segment i n o r d e r t o a v o i d making more responses than d e s i r e d . (However, t h i s does not presume a s p e c i f i c cause f o r the e r r o r d a t a d i s c u s s e d e a r l i e r ) . RT s t u d i e s demand maximal a c c e l e r a t i o n i n t h e p r o d u c t i o n o f a f i r s t response u n i t which e x p l a i n s why DTs are not e q u i v a l e n t f o r response p a t t e r n s reproduced at slo w e r r a t e s . - 88 - SECTION TWO: The Perceptual Organization of Rhythmic Patterns What are the p r i n c i p l e s that govern the perceptual o r g a n i z a t i o n and representation of rhythmic patterns? Since the mid-1800's t h i s question has been i n v e s t i g a t e d - with e s p e c i a l v i g o r over the l a s t 20 years. Although the focus here i s not n e c e s s a r i l y rhythm i n a musical context, much has been learned from studying rhythm i n such a context. In t h i s s e c t i o n , the.major e f f o r t s i n the study of rhythm perception w i l l be reviewed. The'principles that govern rhythm perception must u l t i m a t e l y account f o r a number of s u b j e c t i v e phenomena. These in c l u d e : the groupings of events i n a pattern, the accenting, of events, the o r d i n a l and r a t i o r e l a t i o n s among events, the absolute durations of events, and the l i m i t s i n p e r c e i v i n g each of these. In a d d i t i o n , account must be made of the f a c t that r e c o g n i t i o n of patterns that vary i n "expressive" t i m i n g s t i l l occurs (Clarke, 1985). How f a r such expression can be "stretched" before r e c o g n i t i o n i s l o s t , and how that depends on the nature of the s p e c i f i c pattern, i s p r e s e n t l y unknown. Is i t meaningful to t a l k of the experience of rhythm as j u s t "perceptual"? L i k e l y not. Since g l o b a l aspects of a rhythmic p a t t e r n are extended i n time, memory becomes i n e x t r i c a b l y l i n k e d with rhythm perception (Dowling & Harwood, 198 6) . Memory demands have been used to e x p l a i n why - 89 - low s c o r e s are observed f o r l o n g e r items i n t e s t s o f rhythm p e r c e p t i o n , performance and movement (Thackray, 1969). The development of a r h y t h m i c o r g a n i z a t i o n a l l o w s us t o • a n t i c i p a t e and p r e d i c t what w i l l f o l l o w ( F r a i s s e , 1982). The p e r c e p t i o n o f rhythm i s a l s o s e n s i t i v e t o l e a r n i n g . Sloboda (1985) r e c o u n t s the p o w e r f u l e x p e r i e n c e o f suddenly r e a l i z i n g a new r e l a t i o n s h i p among events i n a l o n g - f a m i l i a r p i e c e o f music - an experience'well-known by s e r i o u s music l i s t e n e r s . F i n a l l y , by way o f i n t r o d u c t i o n , the p e r c e p t i o n emerging from c o n c u r r e n t , c o n f l i c t i n g r h y t h m i c p a t t e r n s (polyrhythms) i s a whole o t h e r , and c h a l l e n g i n g , area o f i n v e s t i g a t i o n (see Deutsch, 1983; Handel & Oshinsky, 1981; Handel & Lawson, 1983; Yeston, 1976). Because o f t h e seemingly boundless d i v e r s i t y o f polyrhythms, some have suggested t h a t , " ... i t • i s u n c l e a r whether t h e r e i s a l e v e l or l e v e l s at which g e n e r a l i z a t i o n s about rhythm can emerge." (Handel & Lawson, 1983, p. 12.0) . The p e r c e p t i o n o f rhythm as emergent from the p r e s e n t a t i o n o f polyrhythms w i l l be not be d i s c u s s e d i n t h i s s e c t i o n . S u b j e c t i v e R h y t h m i z a t i o n A p a t t e r n o f i d e n t i c a l sounds s e p a r a t e d by e q u a l t i m e - i n t e r v a l s i s s p o n t a n e o u s l y p e r c e i v e d i n groupings o f two, t h r e e , or f o u r events ( B o l t o n , 1894). T h i s h o l d s f o r I S I d u r a t i o n s o f 115 ms'to 1500-2000 ms ( B o l t o n , 1894; MacDougall, 1903; F r a i s s e , 1956). B o l t o n (1894) found t h a t the s i z e o f the g r o u p i n g i n c r e a s e s w i t h t h e r a t e o f - 90 - p r e s e n t a t i o n . MacDougall (1903) showed that i f subjects produce groups of two, four or s i x i n t e r v a l s , the rate of production increases with the s i z e of the group. In performances of E r i k Satie's piano piece "Vexations", Clarke (1982) observed that the music was segmented i n t o fewer groups when played at f a s t e r tempi. These e a r l y studies demonstrated that optimal group s i z e i n t e r a c t s with tempo. Gesta l t P r i n c i p l e s of Grouping A number of Gestalt grouping p r i n c i p l e s are a p p l i c a b l e to the perceptual organization of rhythmic patterns. The law of Pragnanz states that the p s y c h o l o g i c a l organization of a perceptual f i e l d w i l l be as "good" as the p r e v a i l i n g conditions allow. Garner and h i s colleagues were the f i r s t to invoke t h i s notion with respect to temporal patterns (Garner, 1962; Garner & Clement, 1963; Royer & Garner, 1966) . I t was shown that patterns of dichotomous elements which have few a l t e r n a t i v e modes of organization are considered 'simple, easy to organize, and thus good (Royer & Garner, 1966). Such patterns have a' higher p s y c h o l o g i c a l redundancy and are l e s s uncertain than more complex patterns. This notion of goodness was l a t e r shown,to have temporal l i m i t s , r e i t e r a t i n g the notion that grouping i n t e r a c t s with tempo. On the b a s i s of experimental evidence, Garner and Gottwald (1968) defined pattern perception as occurring when (constant) stimulus presentation rates are greater than two elements per second, and p a t t e r n l e a r n i n g as occurring at - 91 - lower r a t e s . They argued that the perception of a patt e r n i s i n t e g r a t e d and phenomenally immediate while the l e a r n i n g of a patte r n i s an a c t i v e , i n t e l l e c t u a l i z e d , extended process. This d i s t i n c t i o n , while u s e f u l at the time, can be regarded as too l i m i t e d i n l i g h t of the f a c t that most rhythmic patterns are not isochronous and that, even i n the case of isochronous patterns, r a p i d patterns extended over a very long p e r i o d are neither i n t e g r a t e d nor immediate. A number of researchers (Preusser, Garner & Gottwald, 1970; R e s t l e , 1967; Restle, 1970; Restle and Brown, 1970; Royer and Garner, 1970), extended the p r i n c i p l e s of s e r i a l p a t t e r n o r g a n i z a t i o n to include the Ge s t a l t laws of s i m i l a r i t y and good continuation . With respect to s i m i l a r i t y , these researchers showed that a "run" - a s e r i e s of consecutive elements of one type i n a l a r g e r p a t t e r n of mixed elements - i s a p s y c h o l o g i c a l l y meaningful u n i t . P r e f e r r e d grouping places the longest run at e i t h e r the beginning or the end of a pattern depending on whether the element-type ,is regarded as f i g u r e or ground (Preusser, Garner & Gottwald, 1970). With respect to good continuation, patterns that have a " d i r e c t i o n a l s i m p l i c i t y " of e i t h e r i n c r e a s i n g or decreasing run-lengths are also p r e f e r r e d (Royer & Garner, 1970). The d e s c r i p t i o n of rhythmic pattern perception based on G e s t a l t grouping p r i n c i p l e s was found to be inadequate f o r seve r a l reasons. One main reason was that there was no account of higher-order groupings or r e l a t i o n s h i p s between - 92 - G e s t a l t - d e t e r m i n e d groups - i n s h o r t , t h e r e was no h i e r a r c h i c a l o r g a n i z a t i o n . In a paper of c o n s i d e r a b l e f o r e s i g h t , L a s h l e y (1951) d i s c u s s e d r h y t h m i c a c t i o n , and h i e r a r c h i c a l c o n c e p t i o n s o f b e h a v i o r as p o s s i b l e s o l u t i o n s t o t h e problem o f s e r i a l o r d e r i n b e h a v i o r . The emerging r e s e a r c h i n ' r h y t h m p e r c e p t i o n i n t h e 1 9 7 0's, and beyond, f o l l o w e d h i s l e a d , and t h e o r i z a t i o n i n t h e area e x p e r i e n c e d a quantum l e a p . Tenney and P o l a n s k y (1980) proposed a tem p o r a l g e s t a l t model of p e r c e p t i o n t h a t o u t l i n e s t h e h i e r a r c h i c a l o r g a n i z a t i o n o f p a t t e r n s o f time-spans i n monophonic music. They suggested t h a t elements i n a m u s i c a l p i e c e are grouped a c c o r d i n g t o the G e s t a l t laws of s i m i l a r i t y , good c o n t i n u a t i o n and p r o x i m i t y . With r e s p e c t t o p r o x i m i t y f i t was s t a t e d t h a t , a l l e l s e b e i n g e q u a l , l i s t e n e r s t e n d t o p l a c e group bo u n d a r i e s at i n t e r v a l s t h a t are l o n g e r than the i m m e d i a t e l y p r e c e d i n g and s u c c e e d i n g i n t e r v a l s - p r o x i m a l elements are grouped t o g e t h e r . Higher l e v e l s o f o r g a n i z a t i o n r e s u l t by a p p l y i n g the laws t o l o w e r - l e v e l groups. T h i s p r o c e s s c o n t i n u e s u n t i l no h i g h e r - l e v e l group can be o r g a n i z e d . The model, which i n t e g r a t e s t h e parameters of t i m e , p i t c h and i n t e n s i t y , was a p p l i e d t o m u s i c a l p i e c e s composed by Varese, Webern and Debussy. The p r e d i c t e d segmentations were compared w i t h the- segmentations made by e x p e r t s i n the music a n a l y s i s l i t e r a t u r e . R e s u l t s showed t h a t t h e p r e d i c t e d o r g a n i z a t i o n s compared w e l l w i t h t h o s e suggested i n t h e - 93 - l i t e r a t u r e . These researchers a t t r i b u t e d deviations from the model to the f a c t that i t does not account f o r : timbre as a parameter, harmonic f a c t o r s , motivic f a c t o r s , and f u r t h e r , does not allow f o r single-event perceptual groups. We can question the model on several counts. F i r s t , because of the model's high degree of h i e r a r c h i c a l o r g a n i z a t i o n , s u b s t a n t i a l "recognition-delays" ( i . e . the time from the p h y s i c a l i n i t i a t i o n of an o r g a n i z a t i o n a l u n i t u n t i l the time that the u n i t i s recognized as completed) are i m p l i c i t at higher l e v e l s since group boundaries are determined i n comparison to preceding and succeeding time i n t e r v a l s . Given such recognition-delays and the need f o r memory and- a n t i c i p a t i o n , does i t make sense to- speak of "perceptual processing"? This problem i s acknowledged by the authors. Second, the r e a l i t y of u n l i m i t e d higher-order grouping can be questioned. Is t h i s r e a l l y a sub j e c t i v e phenomenon; what purpose would i t serve? Third, while proposing an org a n i z a t i o n based on the o r d i n a l r e l a t i o n s between time-spans, the model does not consider t h e i r r a t i o r e l a t i o n s and how these might influence' perceptual o r g a n i z a t i o n . With the exception of the Garner.and Gottwald (1968) study on perception, l e a r n i n g and the i n t e r v a l r e l a t i o n s of ISIs, most Gestalt d e s c r i p t i o n s of rhythmic pa t t e r n perception are r e s t r i c t e d to the o r d i n a l r e l a t i o n s h i p s between i n t e r v a l s . In developing a generative theory of t o n a l music, Lerdahl and Jackendoff (1983; also Jackendoff & Lerdahl, - 94 - 1981) have proposed a s e r i e s of Grouping (and M e t r i c a l ) "Well-Formedness" and "Preference" r u l e s . The former e s t a b l i s h the formal s t r u c t u r e of grouping patterns and t h e i r r e l a t i o n s h i p to the s e r i e s of musical events that form a piece, and the l a t t e r determine which of the formally p o s s i b l e s t r u c t u r e s correspond to the l i s t e n e r ' s a c t u a l i n t u i t i o n s . This theory marked a s i g n i f i c a n t advance i n that some con s i d e r a t i o n was given to r e l a t i v e t i m i n g among Gestalt-determined groups. For example, one Grouping Preference Rule states a preference f o r group s u b d i v i s i o n i n t o two.parts of equal length. While unquestionably a step i n the r i g h t d i r e c t i o n , the treatment of r e l a t i v e t i m i n g i n rhythm perception requires a much more comprehensive a n a l y s i s . Perception of Temporal Ratios I t i s a f a i r l y robust f i n d i n g that subjects' reproductions of unequal temporal i n t e r v a l s are biased towards a r a t i o of e i t h e r 2:1 or 1:1. F r a i s s e (1946) demonstrated t h i s f i n d i n g f o r patterns with a long i n t e r v a l l e s s than twice the duration of a shorter i n t e r v a l . Povel (1981) r e p l i c a t e d t h i s f i n d i n g and extended i t f o r patterns with a long/short r a t i o of more than 2:1. Summers, Sargent and Hawkins (1984) observed t h i s trend f o r three-event patterns. Sternberg et a l . (1982) e x t e n s i v e l y researched the judgement, production .and reproduction of temporal r a t i o s . The reproduction research y i e l d e d general support f o r the - 95 - above f i n d i n g s . Presented pa t t e r n s that d e v i a t e d the most from a 2:1 r a t i o ( i . e . 8:1, 6:1 and 8:7, 6:5) were c l e a r l y reproduced with a tendency towards 2:1. This e f f e c t was not as c l e a r , however, f o r patterns with long/short r a t i o s c l o s e r to 2:1 ( i . e . 4:1 and 4:3). These r e s u l t s , i n general, support the n o t i o n that temporal r a t i o s are reproduced i n accordance with p r e f e r r e d rhythmic s t r u c t u r e s - 2:1 or 1:1. This i s not s u r p r i s i n g , c o n s i d e r i n g F r a i s s e ' s (1956) report that an average of 86% of tone durations i n a r e p r e s e n t a t i v e sample of Western music stood i n the r e l a t i o n of 2:1. As with the e a r l i e r G e s t a l t d e s c r i p t i o n s of rhythm p e r c e p t i o n , the above g e n e r a l i z a t i o n says nothing about p o s s i b l e h i e r a r c h i c a l o r g a n i z a t i o n s of more complex rhythmic p a t t e r n s . Martin (1972) developed a model to' answer t h i s c r i t i c i s m . He suggested that rhythmic pat t e r n s are organized i n the form of b i n a r y t r e e s and proposed r u l e s f o r determining the r e l a t i v e t i m i n g and r e l a t i v e accent f o r each event w i t h i n a p a t t e r n . . Events may be e x t e r n a l - w o r l d events, or i n t e r n a l - w o r l d events which do not occupy a space i n the e x t e r n a l p h y s i c a l p a t t e r n but do have a p s y c h o l o g i c a l r e a l i t y . While p r o v i d i n g a good account f o r simple examples of speech and music, Martin's model i s l i m i t e d i n s e v e r a l r e s p e c t s . F i r s t , i t a p p l i e s only to sequences that c o n t a i n a t o t a l of 2 n events. C l e a r l y , we often group and accent rhythmic p a t t e r n s by threes r a t h e r than twos (dancing a waltz would be r a t h e r d i f f i c u l t , otherwise!). Second, given a long sequence of events, the model n e c e s s i t a t e s a m u l t i - l e v e l - 96 - hierarchy (e.g 4 l e v e l s f o r 16 events, 5 l e v e l s f o r 32 events, etc.) that would p r e d i c t d i s t i n c t accent l e v e l s f o r each event. Povel (1981) i n v e s t i g a t e d the perception of various temporal r a t i o s w i t h i n the context of rhythmic patterns. He o u t l i n e d and t e s t e d a "beat-based" model f o r rhythmic p a t t e r n perception i n which the i n i t i a l step i s the segmentation of a p a t t e r n i n t o equal i n t e r v a l s bordered by p s y c h o l o g i c a l l y accented, external-world events c a l l e d "beats". Shorter temporal i n t e r v a l s w i t h i n the pattern are represented as s u b d i v i s i o n s of the b e a t - i n t e r v a l . For example, the p a t t e r n "250/250/250/250/1000" ( a l l u n i t s i n ms) i s organized as two- 1000 ms b e a t - i n t e r v a l s , the f i r s t subdivided i n t o four equal i n t e r v a l u n i t s . On the other hand, the p a t t e r n "250/250/250/250/800" would not conform to a beat-based model since i t cannot be segmented i n t o equal b e a t - i n t e r v a l s . Note that b e a t - i n t e r v a l s are consistent with the G e s t a l t laws of s i m i l a r i t y , and r e g u l a r i t y - the tendency to group things i n t o regular bundles rather than i r r e g u l a r ones. Povel found, i n general, that the reproduction of patterns that conformed to a beat-based model was more accurate than f o r patterns that d i d not. Povel's model and f i n d i n g s were i n c o n c l u s i v e f o r several reasons. F i r s t , although i t was stated that b e a t - i n t e r v a l s t y p i c a l l y range between 250; and 150 0 ms, no account was given f o r how to s e l e c t among candidate b e a t - i n t e r v a l s w i t h i n t h i s range. More complex rhythmic patterns are l i k e l y to have - 97 - more than one i n t e r v a l that could serve as the b e a t - i n t e r v a l . Second, only external-world events are allowed to i n i t i a t e a b e a t - i n t e r v a l . In music, however, i t i s common to have r e s t notations l a s t i n g the duration of one beat, one measure or longer. In .Povel's scheme, any patter n l a c k i n g a r e c u r r i n g , external-world event would be poorly organized and reproduced. Third, r u l e s f o r beat s u b d i v i s i o n were.not determined, with the exception that the f i r s t l e v e l of s u b d i v i s i o n below the b e a t - i n t e r v a l can only be of one type. Povel and Essens (1985; also Essens & Povel, 1985; Essens, 198 6) developed a model f o r rhythmic p a t t e r n perception based on the accenting of l o c a l events and the f i t t i n g of a "best" i n t e r n a l clock to these accents. In patterns of i d e n t i c a l tones d i f f e r i n g only i n t h e i r ISIs, we p s y c h o l o g i c a l l y accent i s o l a t e d tones, the second i n a c l u s t e r of two tones, and the i n i t i a l and f i n a l tones i n a c l u s t e r of more than two tones. Consider a sample p a t t e r n : / / / / / • • / / • / . / / / . where "/" i n d i c a t e s an external-world event and the subsequent i n t e r v a l ( i . e . an I S I ) , and "." i n d i c a t e s a s i l e n t pause of equal duration to the ISI. According to the accent r u l e s , the f o l l o w i n g representation would r e s u l t : I ! ? ! I I / / / / / • • / / . / . / / / . where " 1 " represents a l o c a l accent. A competition between p o s s i b l e clocks then takes place. Clocks can vary according to t h e i r u n i t s i z e ( i . e . the number of ISIs or duration - 98 - between " t i c k s " ) and t h e i r l o c a t i o n ( i . e . t h e i r s t a r t i n g l o c a t i o n ) . The clock u n i t must be an i n t e g e r d i v i s o r of the t o t a l p a t t e r n d u r a t i o n that i s greater than two. Clock u n i t s of only one i n t e r v a l do not c o n t r i b u t e t o a higher order o r g a n i z a t i o n and thus are not considered. Clock i n d u c t i o n s t r e n g t h i s based on the c a l c u l a t i o n of how many c l o c k t i c k s c p i n c i d e with l o c a l l y accented, unaccented, or s i l e n t events. Clock s e l e c t i o n i s determined by the amount of counter- evidence a cl o c k meets i n a p a t t e r n . I f the p o s s i b l e c l o c k s f o r the above p a t t e r n are considered (see Table 7), then c l o c k (3) i s s e l e c t e d as the p r e f e r r e d c l o c k f o r p a t t e r n p e r c e p t i o n . Every c l o c k t i c k c o i n c i d e s with the acc e n t i n g of a l o c a l f e a t u r e . , Fol l o w i n g the generation of the best clock, .any unaccented or s i l e n t i n t e r v a l s that c o i n c i d e with clock t i c k s are accented as "beats". In cases where a best c l o c k cannot be determined from counter-evidence, i t i s determined by the ease of p a t t e r n coding. For example, e q u a l l y spaced s u b i n t e r v a l s (up to three) or empty u n i t i n t e r v a l s are more e a s i l y represented than complex i n t e g e r r e l a t i o n s among u n i t s u b i n t e r v a l s . S e v e r a l concerns a r i s e from t h i s model. F i r s t , there i s no expla n a t i o n of why cl o c k u n i t s must be l e s s than (as opposed t o l e s s than or equal to) 1/2 the t o t a l p a t t e r n d u r a t i o n . Indeed, t h i s requirement r e s u l t s i n a f a i l u r e to e x p l a i n the Povel (1981) f i n d i n g s that the patt e r n s "250/250/250/750", and "250/250/250/250/1000" were w e l l - 9 9 - Table 7 A l l P o s s i b l e 2 - u n i t and 4-unit. C l o c k s f o r a Rhythmic P a t t e r n > i i i i i / / / / / . . / / . / . / / / . 2-unit - - - - - - - - ( i ) - - - - - - - - (2) 4-unit - - - - (3) " " " " " (4) (5) - " " - (6) (" - " represents t i c k l o c a t i o n ) - 100 - reproduced - each presumably as two equal b e a t - i n t e r v a l s varying i n s u b d i v i s i o n frequency. Second, what i f a pattern i s interspersed with a few r a p i d elements? Let us consider again the sample pa t t e r n : / / / / / . . / / . / . / / / • A and subdivide the fourth event i n t o three s u b i n t e r v a l s . This means that s i l e n t i n t e r v a l s must be i n s e r t e d throughout the r e s t of the p a t t e r n to match the shortest fundamental s u b i n t e r v a l . The e n t i r e accenting pattern would change as a r e s u l t (the previous pattern of clock' t i c k s i s displayed) . 1 I I I 1 I I 1 T ? ? ? 1 / . . / . . / . . / / / / . / . . / / / . . / . . / R e c a l l that clock u n i t s can not be e a s i l y subdivided i n t o more than three equal u n i t s . This new representation r e s u l t s i n many complex subd i v i s i o n s and necessitates the search f o r a new c l o c k . This does not seem c o r r e c t . In music, a .constant beat and meter can be maintained even i n the event of a b r i e f p e r i o d of very r a p i d notes. F i n a l l y , there i s no regard i n the model f o r the absolute durations of i n t e r v a l s and, thus, p a t t e r n tempo. And i t may be that t h i s oversight u n d e r l i e s the second problem wi t h the model noted above. S p e c i f i c a l l y , i f fundamental i n t e r v a l s and clock u n i t s were required to be - 101 - w i t h i n an absolute range of, durations then the modelling problems created by the i n t r u s i o n of a few, r a p i d events might be avoided. Processes i n Rhythm Perception The Povel and Essens (1985) model i s presented by 'the authors as a d e s c r i p t i v e , not a process, model. Lon'guet- Higgins and Lee (1982, 1984) have developed a process model of rhythm perception that emphasizes the i d e n t i f i c a t i o n of m e t r i c a l u n i t s . On the basis of the f i r s t I S I, the l i s t e n e r forms a hypothesis and p r e d i c t s the occurrence of the next beat. Confirmation of this' hypothesis leads to a new hypothesis regarding recurrence of the combined, h i g h e r - l e v e l i n t e r v a l . I f s u c c e s s f u l , t h i s process continues up to a maximum m e t r i c a l - u n i t duration of around two to three seconds. Disconfirmation of a hypothesis causes the l i s t e n e r e i t h e r to update the hypothesis by using the second ISI as the reference i n t e r v a l or to s t r e t c h the f i r s t ISI to include the duration .from the second to t h i r d beats. Results of the model's p r e d i c t i o n s were encouraging but a 'f a i l u r e to account f o r organization i n the event of changing tempos, changing meters, expressive v a r i a t i o n s i n ' timing, and the i n f l u e n c e of Gestalt grouping p r i n c i p l e s e i t h e r i n support of or counter to the p r e d i c t i o n s based on r e l a t i v e note lengths, a l l c o n s t i t u t e l i m i t a t i o n s . In addition,_Lee (1985) has argued that the i n a b i l i t y to e x p l a i n how m e t r i c a l evidence e a r l i e r i n a pattern i s weighted more - 102 - than l a t e r evidence, as w e l l as what determines whether contrary evidence i s regarded as a counter-example or merely as an exception to the hypothesis, presents d i f f i c u l t i e s f o r the model. Summary A comprehensive model of rhythm perception i s c u r r e n t l y not to be found. At l e a s t part of the problem i s that t h e o r e t i c i a n s have often overlooked the r o l e of f a c t o r s that were introduced at the outset of t h i s s e c t i o n , and demonstrated throughout, to be c r i t i c a l i n the .perception of rhythm. One fundamental f a c t o r i s Gestalt o r g a n i z a t i o n . Although de a l i n g , f o r the most par t , with o r d i n a l r e l a t i o n s between events, the p r i n c i p l e s of Gestalt grouping are s a l i e n t i n the perceptual organization of temporal events. The h i e r a r c h i c a l organization of temporal s t r u c t u r e i s another fundamental f a c t o r . However, as evidenced i n the Martin' (1972) and Tenney and Polansky (1980) models, e x c e s s i v e l y " v e r t i c a l " h i e r a r c h i c a l s t r u c t u r e i s both i n e f f i c i e n t and u n l i k e l y given the accumulating durations required f o r higher l e v e l s of s t r u c t u r e . Consider a l s o , as Sloboda and Parker (1985) have i n s i g h t f u l l y noted, that a rhythmic patt e r n may not be perceived as a f u l l y coordinated s t r u c t u r e , e s p e c i a l l y the f i r s t time i t i s heard. Again, t h i s addresses the r o l e of memory i n f i l l i n g the gaps or exposing new r e l a t i o n s h i p s i n pr e v i o u s l y "incomplete" rhythmic s t r u c t u r e . ' - 103 - The importance of r e l a t i v e t i m i n g i n rhythm p e r c e p t i o n i s unquestionable. Much of the work of Povel and h i s col l e a g u e s c l e a r l y shows how c e r t a i n r a t i o r e l a t i o n s and s u b d i v i s i o n frequencies are p r e f e r r e d both w i t h i n and outside of a m e t r i c a l context. With the current emphasis on r e l a t i v e timing, the absolute durations of the i n t e r v a l s i n v e s t i g a t e d must not be taken f o r granted. Fundamental b e a t - i n t e r v a l s and hi g h e r - order metric groupings l i k e l y occur w i t h i n a more-or-less f i x e d range of d u r a t i o n s . R e c a l l that the i n t e r a c t i o n of grouping and tempo was one of the o r i g i n a l areas of i n v e s t i g a t i o n i n rhythm p e r c e p t i o n . F l e x i b i l i t y i s necessary i n a comprehensive model of rhythm p e r c e p t i o n . Perceptual o r g a n i z a t i o n i s maintained i n the presence of changing meters (higher-order temporal u n i t s ) , changing tempi (beat r a t e s ) , and expressive v a r i a t i o n s w i t h i n each of these. Rhythm p e r c e p t i o n may best be c h a r a c t e r i z e d as the dynamic i n t e r p l a y among l o c a l , g l o b a l , and what I w i l l c a l l r e g i o n a l f e a t u r e s i n a temporal stimulus p a t t e r n . A c r u c i a l process i n rhythm p e r c e p t i o n i s the- i d e n t i f i c a t i o n of the b e a t - i n t e r v a l . I f a b e a t - i n t e r v a l must f a l l roughly w i t h i n a range of 250-1800 ms ( b e a t - i n t e r v a l ranges w i l l be d i s c u s s e d more thoroughly i n Experiment 4), then, presumably, both h i g h e r - o r d e r and l o w e r - l e v e l u n i t s should be organized i n terms of that i n t e r v a l . The b e a t - i n t e r v a l i s a r e g i o n a l f e a t u r e . - 104 - Although t h i s i s speculative, I would suggest a loose analogy to K i n c h l a and Wolfe's (1979) "middle-out" processing i n which the order of stimulus processing o r i g i n a t e s from more o p t i m a l l y - s i z e d features and proceeds i n d i r e c t i o n s of both i n c r e a s i n g and decreasing s i z e . In terms of accommodating changing meters and expressive timing, decreasing the r o l e of memory processes i n perception, and given the f l e x i b i l i t y f o r changing tempi, i t makes sense f o r t h i s stimulus l e v e l - the b e a t - i n t e r v a l - to d i s p l a y processing dominance ( i . e . i n general, t o be perceived more e a s i l y , remembered longer and more accurately, and be more r e s i s t a n t to i n t e r f e r e n c e - see Ward, 1983) even though i t does not n e c e s s a r i l y have temporal precedence i n e x t r a c t i o n from the stimulus p a t t e r n . However, as Ward (1983) has noted, temporal precedence i s only one p o s s i b l e cause of processing dominance. Processing by means of a "top-down" hierarchy (once i t i s constructed) does not allow f o r the f l e x i b i l i t y required of r e a l - w o r l d rhythm perception. Although there i s c u r r e n t l y no evidence i n support of the processing dominance of . r e g i o n a l features, t h i s may be a d i r e c t i o n to consider i n the search f o r a broader understanding of rhythm perception. The studies i n t h i s s e c t i o n i n v e s t i g a t e the conditions under which perceptual events are organized i n t o coherent groups. Does the grouping of stimulus events require that patterns be d i v i d e d i n t o i n t e r v a l s of equal duration? Must external-world events i n i t i a t e the perceived grouping- - 105 - i n t e r v a l s i n simple rhythmic patterns? Is the perceptual grouping of auditory s t i m u l i subject to l i m i t s of duration or number of events? Of c e n t r a l i n t e r e s t here are the r e g i o n a l features of auditory stimulus patterns. I n d i v i d u a l events are the l o c a l features; r e g i o n a l features emerge from the grouping of these. And with the c y c l i c a l presentation of each pattern, subjects may perceive h i g h e r - l e v e l g l o b a l features, although the i n v e s t i g a t i o n of t h i s i s beyond the scope of the present s t u d i e s . Consistent with the concerns discussed throughout the i n t r o d u c t i o n to t h i s s e c t i o n , the data reported here are analyzed with respect t o t h e i r absolute timing, r e l a t i v e t iming, and o r d i n a l r e l a t i o n s h i p s , i n order to provide a more complete p i c t u r e of rhythmic' p a t t e r n perception and reproduction. - 106 - Experiment 3 A common feature among models of rhythm perception i s that the r e l a t i v e t iming of external-world events determines the s e l e c t i o n of higher-order (beat or metrical) grouping- i n t e r v a l s (Longuet-H'iggins & Lee, 1982; Povel, 1981; Povel & Essens, 1985). T y p i c a l l y , the higher-order g r o u p i n g - i n t e r v a l must be i n i t i a t e d , i f p o s s i b l e , by an external-world event. As i s often the case i n music, though, a m e t r i c a l context can be preserved even i f the measure i s not i n i t i a t e d by an external-world event.11 Apel (1972) reminds us that a beat may be e x t e r n a l or i n t e r n a l to the subject. Canic and Franks (1985) found that w e l l - p r a c t i c e d patterns could- be accurately reproduced i f the f i r s t higher-order i n t e r v a l was d i v i d e d i n t o s u b i n t e r v a l s of equal duration and the second such i n t e r v a l was empty of external-world events. Sternberg et a l . (1982, expt. 12) showed that f o r the production of b e a t - f r a c t i o n s , subjects were j u s t as accurate when the s t a r t of production coincided with a given "beat" as when i t began ju s t a f t e r the given beat - that i s , when the- b e a t - i n t e r v a l was not i n i t i a t e d by a subject-generated event. Yet, i n the l a t t e r case, the i n i t i a t i o n of the f i r s t b e a t - f r a c t i o n was minimally delayed with respect to the given beat. For simple rhythmic patterns, do subjects perceive higher-order groupings of equal duration when each higher- order i n t e r v a l i s not i n i t i a t e d by an external-world event? Do such patterns provide s u f f i c i e n t context f o r the perceptual o r g a n i z a t i o n of equal duration higher-order - 107 - groupings? We might consider, by way of analogy, the importance of context i n p i t c h perception. Lockhead and Byrd (1981) i n v e s t i g a t e d " p r a c t i c a l l y p e r f e c t p i t c h " - the a b i l i t y to i d e n t i f y any note of the musical s c a l e . They found that m u s i c a l l y - t r a i n e d subjects with t h i s a b i l i t y performed almost f l a w l e s s l y i n recognizing musical notes as played on a piano; however, performance was s i g n i f i c a n t l y poorer f o r the i d e n t i f i c a t i o n of variable-frequency sine waves generated by a computer c o n t r o l l e d o s c i l l a t o r . We' i n v e s t i g a t e , here, patterns which are d i v i s i b l e i n t o two i n t e r v a l s of equal duration. For a l l patterns the f i r s t i n t e r v a l i s d i v i d e d i n t o s u b i n t e r v a l s of equal duration. In one group of patterns the second i n t e r v a l i s i n i t i a t e d by an external-world event - the only event i n the i n t e r v a l . In the other group of patterns the second i n t e r v a l contains no external-world events. An underlying assumption, consistent with a l l but Povel and Essens. (1985), i s that the duration of a higher-order grouping does not have to be l e s s than h a l f the duration of the e n t i r e p a t t e r n . I f the presented patterns are p e r c e p t u a l l y organized as two higher-order i n t e r v a l s of equal duration then the accuracy of p a t t e r n reproduction would not be expected to d i f f e r . Opposing p r i n c i p l e s of organization may be at work, however. The G e s t a l t p r i n c i p l e s of s i m i l a r i t y , symmetry and r e g u l a r i t y would suggest the organization of rhythmic patterns i n t o higher-order i n t e r v a l s of equal duration (see Jackendoff & Lerdahl, 1981; West, Howell, & Cross, 1985). - 108 - This tendency may be opposed i f there- i s no extern"al-world event to i n i t i a t e each i n t e r v a l - the higher-order grouping may not be r e a l i z e d . I t may also be opposed by a "Grouping Preference Rule" proposed by Jackendoff and Lerdahl (1981) that s t r o n g l y discourages s i n g l e event groups. I f these patterns are not a l l p e r c e p t u a l l y organized i n the same way then the (agogic) accenting of events i s l i k e l y to r e f l e c t these d i f f e r e n c e s . I t i s generally accepted that events at the beginning and the end of stimulus groups are p s y c h o l o g i c a l l y accented (Fraisse, 1978, 1982; Povel & Essens, 1985). Can beats that are i n t e r n a l to the perce i v e r occupy these p o s i t i o n s ? Method Subjects. Twenty-four male and female students from the U n i v e r s i t y of B r i t i s h Columbia p a r t i c i p a t e d i n the study as part of a course requirement. Subjects ranged i n age from 21 to 33 years. A $20.00 p r i z e was o f f e r e d to the subject who most accurately reproduced the response patterns. Apparatus. The apparatus was the same as described i n Experiment 1. Stimulus Patterns. Subjects were i n s t r u c t e d to reproduce eight d i f f e r e n t stimulus patterns. Two pa t t e r n - types were presented f o r each of four d i f f e r e n t p a t t e r n durations (see Table 8). A l l patterns could be d i v i d e d i n t o two i n t e r v a l s of equal duration with the f i r s t i n t e r v a l f u r t h e r d i v i d e d i n t o equal duration s u b i n t e r v a l s . For h a l f - 109 - Table 8 Stimulus Patterns f o r Experiment 3 Pattern-Type Pattern Representation / Ratio X / • • / « • / • • • • • • (1200 ms) 1:1:2 E /../ X /../../.. / (1800 ms) 1:1:1:3 E /../../ X /../../../.. / (2400 ms) 1:1:1:1:4 E /../..I.J X /../../../../.. / ' (3000 ms) 1:1:1:1:1:5 E /../../../../ "/" represents an external-world event (100 ms! "." represents a s i l e n t i n t e r v a l (100 ms) 'X" represents patterns i n which both i n t e r v a l s are i n i t i a t e d by an external-world event 'E" represents patterns i n which the second i n t e r v a l i s empty For the sake of c l a r i t y a break has been i n s e r t e d a r t i f i c i a l l y d i v i d i n g each patt e r n i n t o two i n t e r v a l s of equal duration. - 110 - of the patterns the second i n t e r v a l was i n i t i a t e d w ith an external-world event ("X"-type p a t t e r n s ) ; the other h a l f contained no external-world event ("E"-type p a t t e r n s ) . The p h y s i c a l c h a r a c t e r i s t i c s of the tones and the tone durations (100 ms each) were the same as i n Experiment 1. Procedure. Subjects were seated at a t a b l e and i n s t r u c t e d as to the nature of the study. A demonstration of the procedure was viewed. The time l i n e f o r stimulus presentation was the same as i n Experiment 1 (see Figure 1) with the f o l l o w i n g exceptions: Stimulus, patterns were those shown i n Table 8, subjects l i s t e n e d to 20 cycles of each stimulus .pattern, the Post-Presentation i n t e r v a l ( p r i o r to the 1000 ms Warning tone) ranged from 1500 to 2700 ms, and subjects reproduced each pattern c y c l i c a l l y u n t i l keypressing no longer generated response tones (after 20 c y c l e s ) . One t r i a l was performed f o r each stimulus p a t t e r n . The order of presentation across subjects was determined by a balanced L a t i n Square design. Reproduction of a l l eight stimulus patterns concluded the study. The task was to reproduce the timing of each stimulus p a t t e r n as accurately as p o s s i b l e . In a d d i t i o n , h a l f of the subjects were i n s t r u c t e d to i n i t i a t e reproduction of the stimulus p a t t e r n as q u i c k l y as p o s s i b l e f o l l o w i n g the o f f s e t of the warning tone. This c o n d i t i o n was added to i n v e s t i g a t e the e f f e c t s of response complexity and duration on RT. However, with the c y c l i c a l (rather than singular) presentation of each stimulus pattern, the s i z e of the - I l l - implemented response program i s l i k e l y to vary among subjects. A n a l y s i s . The fundamental u n i t of comparison was the IRI. R e l a t i v e measures of the shortest temporal i n t e r v a l s (300 ms) to the longest i n t e r v a l s (600-1500 ms) were not p o s s i b l e f o r the patterns with the empty second i n t e r v a l since there i s no external-world event that acts as a marker i n time. As a r e s u l t , patterns of the same type were compared with respect t o : 1) t o t a l pattern duration, 2) the p r o f i l e s across the shorter IRI durations common to each pat t e r n , 3) i n t e r i n d i v i d u a l v a r i a b i l i t y i n the reproduction of shorter IRIs and t o t a l pattern durations. T o t a l durations f o r X-type and E-type patterns were compared by c a l c u l a t i n g a p r o p o r t i o n a l e r r o r score equal to (x-c)/c where "x" i s - t h e reproduced p a t t e r n duration and "c" i s the c r i t e r i o n duration ( i . e . 1200, 1800, 2400, 3000 ms). There i s general agreement that f i l l e d i n t e r v a l s are estimated as being longer i n duration than u n f i l l e d i n t e r v a l s ( A l l a n , 1979; Ornstein, 1969; Poppel, 1978). To t e s t t h i s hypothesis, the r e l a t i v e durations of higher-order i n t e r v a l s were compared i n the X-type patterns. RT t o i n i t i a t e the c y c l i c a l reproduction of the response patte r n was also measured. Comparisons were made across i n s t r u c t i o n conditions (RT vs. C o n t r o l ) , and w i t h i n the RT group i n contrast with response complexity (defined as the number of taps per one cycle of the pattern) and t o t a l p a t t e r n duration. - 112 - R e s u l t s Latency data. RT was s i g n i f i c a n t l y d i f f e r e n t across i n s t r u c t i o n c o n d i t i o n s , £(1,22) = 11.04, £=.003. Mean RT was 1397 ms f o r the C o n t r o l group and 351 ms f o r the RT group. As no v i s i b l e trends were obvious f o r the data of the C o n t r o l group, f u r t h e r analyses were not performed. V i s u a l analyses of the RT group data suggested that RT inc r e a s e s with number of taps per one c y c l e of the p a t t e r n (see Fi g u r e 9) and total- p a t t e r n d u r a t i o n (see Fi g u r e 10). However, these observations, were not s t a t i s t i c a l l y supported by t r e n d analyses (£=.212 and £=.061, r e s p e c t i v e l y , f o r the l i n e a r orthogonal components - no other components were c l o s e r to s i g n i f i c a n c e ) . The f a i l u r e to reach s i g n i f i c a n c e i s l i k e l y due to the extremely high between-subjects standard d e v i a t i o n s which ranged from 120 to 212 ms. I n t e r v a l data. No d i f f e r e n c e s were found between i n s t r u c t i o n c o n d i t i o n s f o r any of the i n t e r v a l data t e s t s so these data were combined. Means and standard d e v i a t i o n s .for the reproduced i n t e r v a l data are shown i n Table 9. ANOVA was performed on the p r o p o r t i o n a l e r r o r scores f o r the t o t a l p a t t e r n d u r a t i o n s (see A n a l y s i s s e c t i o n f o r e x p l a n a t i o n ) ; t h i s allowed comparisons across p a t t e r n s of d i f f e r e n t t o t a l d u r a t i o n s . 'A s i g n i f i c a n t d i f f e r e n c e between'X-type and E- type p a t t e r n s was revealed, £(1,23) = 6.66, £=.017; the X- type p a t t e r n s were reproduced more a c c u r a t e l y . There were no r e l i a b l e p r o p o r t i o n a l e r r o r d i f f e r e n c e s across t o t a l p a t t e r n d u r a t i o n s , nor were there f o r the i n t e r a c t i o n of d u r a t i o n X - 113 - Figure 9. Mean r e a c t i o n time (RT) taps. as a funct i o n of number of  - 115 - Figure 10. Mean r e a c t i o n time (RT) as a f u n c t i o n of t o t a l p a t t e r n duration. 400 380 h 280 1 1 1 ' 1 I 600 1200 1800 2400 3000 3600 TOTAL PATTERN DURATION (ms) - 117 - Table 9 Mean IRI and Total Pattern (T) Durations (ms) and Corresponding SDs as a Function of S e r i a l P o s i t i o n f o r Each Pattern IRI S e r i a l P o s i t i o n Pattern,-Type 1 2 3 4 5 Last X • 285 294 608 1187 (1200 ms) 12 14 36 38 E 299 824 1123 39 91 85 X 2 92 290 289 849 1720 (1800 ms) 24 18 13 113 119 E 295 305 1125 1725 38 38 233 161 X 2 92 2 94'' 288 300 1134 2308 (2400 ms) 23 26 21 10 165 174 E 296 293 299 1319 2207 46 34 43 230 240 X 296 296 291 295 299 1339 2816 (3000 ms) 36 31 27 30 14 263 259 E 299 293 ': 286 307 1605 2790 49 41 : 34 41 278 310 "X" represents patterns i n which both s u b i n t e r v a l s are i n i t i a t e d by an external-world event "E" . represents patterns i n which the second s u b i n t e r v a l i s empty - 118 - pattern-type. As can be seen i n Table 9, the superior performance of X-type patterns was not consistent f o r a l l pat t e r n durations. A subsequent ANOVA was undertaken to see i f t h i s inconsistency might be a t t r i b u t e d to an a d d i t i o n a l .factor; s p e c i f i c a l l y , patterns with an even number of shorter durations i n the f i r s t i n t e r v a l generally appear to be b e t t e r reproduced than those with an odd number of such durations (see Table 10). This i n s i g h t was supported, £(1,23) = 6.70, £=.016. The duration p r o f i l e s f o r the shorter IRIs ( i . e . s e r i a l p o s i t i o n trends) were compared across pattern-types at each duration. A s i g n i f i c a n t i n t e r a c t i o n e f f e c t ( s e r i a l p o s i t i o n X pattern-type) was found f o r the four shorter i n t e r v a l s common to the 3000-ms patterns, £(3,69) = 13.04, Greenhouse- Geisser £<.001, fo r the three i n t e r v a l s common to the 2400-ms patterns, £(2,46) = 4.54, Huynh-Feldt £=.023, and f o r the two i n t e r v a l s 'common to the 1800-ms patterns, £(1,23) = 6.28, £=.020. A comparison of the s i n g l e shorter i n t e r v a l s common to the 1200-ms patterns f a i l e d to reach s t a t i s t i c a l s i g n i f i c a n c e , £(1,23) = 3.63, £=.070. No main e f f e c t s of pattern-type were uncovered i n d i c a t i n g that d i f f e r e n c e s i n performance were l a r g e l y a t t r i b u t a b l e to reproduction of the la r g e s t temporal i n t e r v a l . Only one e f f e c t of s e r i a l p o s i t i o n was found - f o r the 3000-ms patterns, £(3,69) = 14.61, Greenhouse-Geisser £<.001. The r e l a t i v e durations of each shorter i n t e r v a l (common to both pattern-types) to the t o t a l pattern' duration are - 119 - Table 10, Mean P r o p o r t i o n a l Reproduction E r r o r as a Function of Pattern-Type and the Number (Even/Odd) of Shorter Temporal I n t e r v a l s Pattern-Type Number of Shorter Temporal I n t e r v a l s 1 2 3 4 5 X (even) .011 .039 (odd) .045 .061 E (even) .041 .070 (odd) .064 • .080 The P r o p o r t i o n a l Reproduction E r r o r (PRE) i s equal to the reproduced patt e r n duration minus the c r i t e r i o n p a t t e r n duration a l l d i v i d e d by the c r i t e r i o n p a t t e r n duration. The Mean PRE i s equal to the mean of the absolute values of the PREs. - 120 - shown i n Table 11'. These data h i g h l i g h t the f i n d i n g that even when the t o t a l d u r a t i o n of the X-type p a t t e r n s was reduced, the r e l a t i v e t i m i n g of i n t e r v a l s w i t h i n each p a t t e r n was w e l l maintained. Four separate ANOVAs were conducted to c o n t r a s t the durat i o n s of the f i r s t and second b e a t - i n t e r v a l s w i t h i n the X-type p a t t e r n s . The second i n t e r v a l d u r a t i o n (shown under the heading "Last") i s l e s s than the f i r s t i n t e r v a l d u r a t i o n ( c a l c u l a t e d by s u b t r a c t i n g ; "Last" from "T") i n a l l cases except f o r the 1200-ms p a t t e r n (see Table 9). However, these f i n d i n g s were not s t a t i s t i c a l l y s i g n i f i c a n t . D i s c u s s i o n Povel (1981; a l s o Povel & Essens, 1985; Essens & Povel, 1985) showed that patterns d i v i s i b l e i n t o equal i n t e r v a l s i n i t i a t e d by ex t e r n a l - w o r l d events were a c c u r a t e l y reproduced. Yet we know from music that a m e t r i c a l context can be preserved even i f each measure i s not i n i t i a t e d by an ext e r n a l - w o r l d event. The main purpose of t h i s study was to determine i f a minimal context would be s u f f i c i e n t f o r subjects t o pe r c e i v e higher-order groupings of equal d u r a t i o n when each grouping i s not i n i t i a t e d by an ex t e r n a l - w o r l d event. Three p i e c e s of evidence suggest that the context p r o v i d e d here was i n s u f f i c i e n t f o r such an o r g a n i z a t i o n . F i r s t , the o v e r a l l reproduction of p a t t e r n durations was b e t t e r f o r the X-type than the E-type p a t t e r n s . Second, the du r a t i o n p r o f i l e s f o r the sh o r t e r IRIs were d i f f e r e n t across - 121 - Table 11 Mean R e l a t i v e Durations of Shorter Temporal I n t e r v a l s to Longer Temporal I n t e r v a l s as a Function of Pattern-Type Reproduction Ratio C r i t e r i o n Pattern-Type Ratio Sl/T S2/T S3/T S4/T X .240 (1200 ms) ' .250 E .266 X .170 .169 • (1800 ms) • .167 E .171 .177 X .127 .127 .125 (2400 ms) . .125 E .134 .133 .135 X .105 .105 .103 .105 (3000 ms) .100 E .107 .105 .102 .110 "Sn/T" represents the r a t i o of the nth shorter temporal i n t e r v a l (300 ms) to the t o t a l p a t t e r n duration - 122 - the two pattern-types. Third, f o r each of the 10 corresponding shorter IRIs and each of the 4 t o t a l durations, i n t e r s u b j e c t v a r i a b i l i t y was greater f o r the E-type patterns (see Table 9). This i n d i c a t e s that subjects, as a whole, were not p e r c e i v i n g and reproducing the E-type patterns i n a consistent way. These patterns proved to be more d i f f i c u l t to organize than the X-type patterns. Although Canic and Franks (1985) d i d f i n d that E-type patterns could be w e l l reproduced, the patterns i n t h e i r study were more h i g h l y learned than the patterns reproduced here. There was no main e f f e c t of pattern-type f o r the reproduction of shorter IRIs (just the i n t e r a c t i o n e f f e c t noted above). This i n d i c a t e s that d i f f e r e n c e s were a t t r i b u t a b l e almost e n t i r e l y to the reproduction of the longer IRIs R e c a l l that Sternberg et a l . (1982) found that subjects accurately produced b e a t - f r a c t i o n s whether or not production began on the external-world beat. I f the E-type patterns were not organized as two i n t e r v a l s of equal duration then how were they organized? The duration p r o f i l e s of the shorter IRIs may give us a clue here. For each E-type pattern with m u l t i p l e shorter IRIs, the l a s t IRI i s longest i n duration. I f we again apply the r u l e that i n t e r v a l s that end perceptual groups are accented - a g o g i c a l l y , i n t h i s case - then i t appears that a l l the short i n t e r v a l s are grouped together and the longer i n t e r v a l i s t r e a t e d as a d i s t i n c t u n i t . The E-type patterns are organized as two higher-order i n t e r v a l s of d i f f e r i n g - 123 - d u r a t i o n s . The p r i n c i p l e s t h a t would suggest the o r g a n i z a t i o n of two equal d u r a t i o n i n t e r v a l s are overridden by the l a c k of co n t e x t u a l cues. T h i s e x p l a n a t i o n i s supported by the observation that e q u i v a l e n t longer ISIs (e.g. 900 ms f o r the X-type 1800-ms pa t t e r n s and the E-type 1200-ms pattern) were always b e t t e r reproduced i n the X-type p a t t e r n s . In the presence of a m e t r i c a l (equal i n t e r v a l ) context, r e p r o d u c t i o n of a longer i n t e r v a l i s degraded l e s s than when i t occurs i n the absence of such a context - when i t occurs i n i s o l a t i o n . Why should the e r r o r always be i n the d i r e c t i o n of reducing the longer i n t e r v a l ? There i s some evidence that an " i n d i f f e r e n c e i n t e r v a l " (that i n t e r v a l of time t h a t i s n e i t h e r overestimated or underestimated) e x i s t s around 700 ms (Coren, Porac, & Ward, 1984; but c f . Poppel, 1978; and Woodrow, 1951). Longer i n t e r v a l s are underestimated and s h o r t e r i n t e r v a l s are overestimated. In the r e s u l t s presented here, the longer ISIs are underestimated i n every case of both pattern-types with the exception o f the 600-ms ISI i n one X-type p a t t e r n . The sh o r t e r ISIs are not overestimated, however. But i f we consider that they are grouped as a u n i t , then the u n i t durations are underestimated as they almost always should be. Of course, there are a l t e r n a t i v e e x p l a n a t i o n s . F i r s t , Essens and Povel found that non-metrical p a t t e r n s are reproduced so that the r a t i o of longer to s h o r t e r durations approaches 2:1. The second exp l a n a t i o n i s found i n Helson's - 124 - (1964) a d a p t a t i o n - l e v e l theory. The c e n t r a l i d e a adapted to the present study i s t h a t s t i m u l i are organized so t h a t t h e i r d i f f e r e n c e s along a common dimension are reduced. C o n s i s t e n t with both explanations, f o r p a t t e r n s with w e l l - d e f i n e d (multiple) s h o r t e r IRIs, the longer IRI w i l l be reduced. A comparison of the two higher-order i n t e r v a l s i n X-type p a t t e r n s showed that the mean f i r s t i n t e r v a l d u r a t i o n i s longer than the second i n t e r v a l f o r every case but one. This provides weak evidence f o r the " f i l l e d - i n t e r v a l i l l u s i o n " (Coren, Porac, & Ward, 1984) - the observation t h a t f i l l e d i n t e r v a l s are estimated as longer than u n f i l l e d i n t e r v a l s ( in t h i s case, when t h e i r d urations exceed that of the i n d i f f e r e n c e i n t e r v a l ) . F i n a l l y , the mean RT data provide some support f o r the p o s i t i o n t h a t RT inc r e a s e s as a f u n c t i o n of number of response u n i t s and/or response d u r a t i o n . However, s i n c e these p a t t e r n s were reproduced c y c l i c a l l y , the high between- subj e c t s v a r i a b i l i t y i n d i c a t e s that subjects may not have implemented response programs of the same s i z e . The data, while suggestive, p o i n t to the c o n c l u s i o n that t h i s procedure i s not optimal f o r the i n v e s t i g a t i o n of RT e f f e c t s . - 125 - Experiment 4 The a b i l i t y to p e r c e p t u a l l y organize a b r i e f p a t t e r n of i d e n t i c a l temporal s t i m u l i i n t o groups of equal duration requires that each group be i n i t i a t e d by an external-world event. What other l i m i t s are there to the grouping of i n t e r v a l s ? The two l i m i t s r e f e r r e d to most frequently i n the l i t e r a t u r e are the duration of the group and the number of s u b i n t e r v a l s per group. Much of the focus, with respect to group duration, has been on the i n t e r v a l range which allows f o r the perception of b e a t - i n t e r v a l s . The Harvard D i c t i o n a r y of Music reported that b e a t - i n t e r v a l s t y p i c a l l y range from 42 9 to 1200 ms (Apel, 1972). Lerdahl and Jackendoff (1983) suggested a broader range of 375 to 1500 ms while Povel (1981) st a t e d that b e a t - i n t e r v a l s i n Western music range from 250 to 1500 ms. Based on h i s review of the l i t e r a t u r e , F r a i s s e (1978, 1982) concluded that grouping occurs f o r i n t e r v a l durations of up to 1800 ms. The general p o s i t i o n of these i n v e s t i g a t o r s i s that adjacent or non-adjacent s t i m u l i separated by long i n t e r v a l s are not grouped together and perceived as a coherent patt e r n of beats since they lose t h e i r perceptual c o n t i n u i t y . Conversely, s t i m u l i separated by very short i n t e r v a l s are not perceived as beats but as f r a c t i o n s of beats due to t h e i r r a p i d i t y . Is there a maximum number of equal s u b i n t e r v a l s by which a beat can be divided? In music the question i s u s u a l l y - 126 - framed at the next higher l e v e l of orga n i z a t i o n : how many beats are contained i n a s i n g l e metric u n i t - a measure? As was noted i n Section One, however, the perceptual d i s t i n c t i o n between m e t r i c a l and beat org a n i z a t i o n i s not always an unambiguous one (Radocy & Boyle, 1979). Most Western rhythm i s confined to meters i n v o l v i n g u n i t s of 2, 3, or 4 beats (Davies, 1978). Lerdahl and Jackendoff (1983) have proposed a number of " M e t r i c a l Well-Formedness Rules", one of which states that " ... at each m e t r i c a l l e v e l , strong beats are spaced e i t h e r two or three beats apart". In a non-musical context, Essens (1986) has determined that h i e r a r c h i c a l l e v e l s i n the orga n i z a t i o n of temporal patterns must r e l a t e as integers l e s s than f i v e . Yet, Deutsch (1983) found that when subjects synchronize with d i c h o t i c a l l y presented, isochronous stimulus patterns that vary i n t h e i r integer, i n t e r v a l r e l a t i o n s , the base rate ISI (1200 ms) was more c o n s i s t e n t l y performed when the other (faster) rate stood i n a r e l a t i o n of 5:1 than when the r e l a t i o n was 4:1, 3:1, or 2:1. This f i n d i n g i s consistent with Getty's (197 6) discovery that the variance i n reproducing an i n t e r v a l decreases as the number of s u b i n t e r v a l s i t i s d i v i d e d i n t o increases. The purpose of t h i s study i s to determine i f grouping occurs when the suggested g r o u p i n g - i n t e r v a l s : 1) exceed 1800 ms, and 2) are d i v i d e d i n t o more than 4 s u b i n t e r v a l s of equal duration. Agogic accenting i s again the dependent measure used to evidence grouping. I t has been appl i e d by Garcia- - 127 - Colera and Semjen (1987) who reported that, i n general, f i r s t and l a s t p a t t e r n events were lengthened r e l a t i v e to i n t e r i o r events i n patterns of 3 to 8 i n t e r v a l s (although t h i s f i n d i n g was not supported s t a t i s t i c a l l y ) . Method Subjects. Twenty-two male and female students from the U n i v e r s i t y of B r i t i s h Columbia p a r t i c i p a t e d i n the study as part of a course requirement. Subjects ranged i n age from 2 0 to 27 years. A $20.00 p r i z e was o f f e r e d to the subject who most accurately reproduced the response patterns. Apparatus. The apparatus was the same as described i n Experiment 1. Stimulus Patterns. Subjects were i n s t r u c t e d to reproduce 12' d i f f e r e n t stimulus patterns (see Table 12). As i n Experiment 3, a l l patterns can be d i v i d e d i n t o two i n t e r v a l s of equal duration with the f i r s t i n t e r v a l f u r t h e r d i v i d e d i n t o equal duration s u b i n t e r v a l s . Patterns v a r i e d i n the number of s u b i n t e r v a l s they contained ( i . e . 4, 5, 6, 7). A l l patterns were of the "X-type" described i n the previous experiment. That i s , each suggested g r o u p i n g - i n t e r v a l was i n i t i a t e d by an external-world event. The p h y s i c a l c h a r a c t e r i s t i c s of the tones, and the tone durations were the same as i n Experiment 3. Procedure. The procedure was i d e n t i c a l with that of Experiment 3 with the f o l l o w i n g exceptions: There were 12 stimulus patterns - those shown i n Table 12, the Post- - 128 - Table 12 Stimulus Patterns f o r Experiment 4 Pattern-Rate Pattern Representation / I n t e r v a l Duration 200 ms /./././. / 800 ms /././././. / 1000 /./././././. 7 1200 /././././././. 1 1400 300 ms /../../../.. / 1200 . . /../../../../../ 1500 /. ./. ../../. ./. ./. . / 1800 /../../'../../../../.. / 2100 4 00 ms /.../. /. . 7 . , . 7 . , . 7 . . . / /., . 7 . , , 7 . , . 7 . , , 7 . . . / / / / . 7 . . /.. , 7 . . . 7 . , .../.. . 7 . . . / 1600 2000 2400 2800 For the sake of c l a r i t y a break has been i n s e r t e d a r t i f i c i a l l y d i v i d i n g each pattern i n t o -two i n t e r v a l s of equal duration. - 129 - P r e s e n t a t i o n i n t e r v a l ranged from 1700 to 3700 ms, and subj e c t s were not i n s t r u c t e d t o i n i t i a t e r eproduction of the stimulus p a t t e r n s as q u i c k l y as p o s s i b l e although, l i k e Experiment 3, the o f f s e t of a 1000 ms Warning Tone s i g n a l l e d t h a t p a t t e r n reproduction could begin. Subjects were i n s t r u c t e d t o reproduce the ti m i n g of each stimulus p a t t e r n as a c c u r a t e l y as p o s s i b l e . A n a l y s i s . The IRI was the fundamental u n i t of comparison. The mean absolute durations of each s h o r t e r and longer i n t e r v a l i n a l l of the stimulus p a t t e r n s were c a l c u l a t e d as were the mean p r o p o r t i o n a l e r r o r s f o r these i n t e r v a l s . Agogic ac c e n t i n g of both the f i r s t and l a s t events (in r e l a t i o n t o a l l i n t e r v e n i n g events) i n the f i r s t g r o u p i n g - i n t e r v a l was taken as evidence of grouping. C o n s i s t e n t with the l i t e r a t u r e , the o r d i n a l r e l a t i o n s h i p s among IRI means were s u b j e c t i v e l y analyzed. S t a t i s t i c a l t e s t s were not performed. Indeed, the d i f f e r e n c e s t y p i c a l l y observed i n evidence of acc e n t i n g are c o n s i s t e n t but very subtle.5 P r o p o r t i o n a l e r r o r scores f o r the t o t a l p a t t e r n durations were a l s o c a l c u l a t e d . Mean r e l a t i v e durations of each s h o r t - t o - l o n g i n t e r v a l were c a l c u l a t e d i n order t o determine the accuracy of r e l a t i v e t i m i n g i n p a t t e r n reproduction. R e s u l t s Means and standard d e v i a t i o n s f o r each shorter and longer IRI are shown i n Table 13. Lengthening of the f i r s t - 130 - Table 13 Mean Durations (ms), Corresponding SDs and P r o p o r t i o n a l E r r o r (PE) Scores f o r Shorter and Longer IRIs IRI S e r i a l P o s i t i o n Pattern-Rate 200 1 2 3 4 5 6 7 Last ) ms X 215 208 209 216 868 SD 13 14 13 14 94 PE .075 .039 .045 .081 .086 X 221 215 216 213 217 902 SD 15 14 15 13 16 198 PE , .105 .074 .078 .067 .087 -.098 X 215 212 213 213 208 222 • 1114 SD 13 12 11 12 14 13 234 PE .073 .061 .066 .064 .040 .108 -.072 X 215 213 214 214 210 212 217 1335 SD 20 18 13 13 16 17 18 257 PE . 074 .066 .072 .072 .052 .059 • .087 -.046 i ms X 300 292 288 297 1232 SD 20 16 14 18 143 PE -.001 -.026 -.041 -.009 .027 X 303 297 295 297 303 1511 SD 20 18 • 14 16 17 288 PE .010 -.010 -.016 -.009 .011 .008 X 306 299 301 302 298 307 1959 SD 21 17 16 17 17 16 567 PE .020 -.003 .004 .006 -.005 .024 .088 X 301 298 296 300 297 299 304 2283 SD 20 20 22 22 20 20 24 552 PE .004 -.006 -.013 .000 -.010 -.004 .013 .087 - 131 - 400 ms X . 381 377 371 381 1660 SD 29 25 26 29 205 PE - .048 - . 059 - .071 - .048 .037 X 393 394 386 392 396 2126 SD 22 25 23 25 25 498 PE - .018 - .016 - .036 - .020 - .011 .063 X 385 387 386 389 387 394 2618 SD 29 30 . 26 . 30 " '31 30 852 PE • - . 037 - .031 - .034 - .026 - .033 - .015 .091 X 389 386 386 389 387 392 392 • 3054 SD 23 27 24 26 24 25 23 1017 PE - . 0 2 9 - .036 - .035 - .037 - .033 - .020 - . 019 .091 - 132 - and l a s t s h o r t e r IRIs r e l a t i v e to i n t e r i o r IRIs was taken as evidence o f acce n t i n g and, t h e r e f o r e , p e r c e p t u a l grouping. Presented i n a condensed form, i t can be seen t h a t evidence of grouping s y s t e m a t i c a l l y changes with i n c r e a s i n g i n t e r v a l - d u r a t i o n - the t r a n s i t i o n p o i n t coming above 1800 ms (see Table 14) . P r o p o r t i o n a l E r r o r (PE) scores f o r each IRI are a l s o shown i n Table 13. PE scores f o r a l l 200 ms i n t e r v a l s were p o s i t i v e i n d i c a t i n g t h a t these i n t e r v a l s were reproduced longer than the c r i t e r i o n . PE scores f o r a l l 400 ms i n t e r v a l s were negative i n d i c a t i n g that they were reproduced s h o r t e r than the c r i t e r i o n . PE scores f o r the 300 ms i n t e r v a l s were both p o s i t i v e and negative, and i n general were much lower than those f o r the other durations i n d i c a t i n g t h a t these i n t e r v a l s were most a c c u r a t e l y reproduced. PE scores f o r the longer i n t e r v a l s i n each p a t t e r n are shown i n F i g u r e 11. These data show no apparent t r e n d . But i f we con s i d e r j u s t the reprod u c t i o n of pat t e r n s with s u b i n t e r v a l frequencies of 300 and 400 ms, then a marked in c r e a s e i n e r r o r occurs at 1800 ms. This i s around the i n t e r v a l d u r a t i o n at which suggested grouping no longer occurs. Yet, f o r the long i n t e r v a l durations of l e s s than 1800 ms, the 200 ms data do not seem to f i t . However, i f we p l o t p r o p o r t i o n a l e r r o r versus the t o t a l p a t t e r n d u ration, then the p a t t e r n s i n question . f a l l i n l i n e with the other p a t t e r n s below 3600 ms (2 i n t e r v a l s X 1800 ms) with the exception of the 200/200/200/200/800 ms p a t t e r n (see F i g u r e - 133 - Table 14 F i r s t I n t e r v a l Duration (ms) and Resultant Evidence f o r ' Grouping Based on Agogic Accenting of the F i r s t and Last IRIs I n t e r v a l - D u r a t i o n Evidence of Grouping 800 1000 1200 1200 1400 1500 1600 1800 P o s i t i v e (200-ms rate) (300-ms rate) 2000 2100 Negative P o s i t i v e 2400 2800 Negative - 134 - Figure 11. P r o p o r t i o n a l E r r o r versus C r i t e r i o n Long I n t e r v a l Duration. • = 200 ms s u b i n t e r v a l s , • = 300 ms s u b i n t e r v a l s , • = 400 ms s u b i n t e r v a l s . 0.12 0 300 600 900 1200 1500 1800 2100 2400 2700 3000 CRITERION LONG INTERVAL DURATION - 136 - 12). For t h i s p a t t e rn, the duration of the second i n t e r v a l almost matches that of the f i r s t i n t e r v a l . The r e l a t i v e t iming f o r each patte r n was determined by comparing each shorter IRI to the corresponding longer IRI. Results are displayed separately according to number of shorter i n t e r v a l s i n Figure 13 . When the number of shorter i n t e r v a l s i s f i v e , s i x or seven, the r e l a t i v e t i m i n g f o r patterns at the 300 and 400 ms rates i s w e l l maintained while the same i s not the case f o r the 200 ms patterns. When the number of shorter i n t e r v a l s i s four, a l l patterns were quite w e l l reproduced - moreso, from 400 to 300 to 200 ms patterns. Discussion The main purpose of t h i s study was to determine i f grouping would occur when the suggested gr o u p i n g - i n t e r v a l s exceed 1800 ms (the l a r g e s t i n t e r v a l suggested i n the l i t e r a t u r e , F r a i s s e , 1982) or were d i v i d e d i n t o more than 4 equal duration s u b i n t e r v a l s . A l l patterns with suggested gr o u p i n g - i n t e r v a l s l e s s than or equal to 1800 ms showed evidence of accenting. A l l longer patterns, with the exception of the pattern with the suggested 2100 ms i n t e r v a l s f a i l e d to d i s p l a y accenting. Why should the 2100 ms i n t e r v a l s d i s p l a y accenting and not the 2000 ms i n t e r v a l s ? One p o s s i b l e explanation i s simply that the upper l i m i t f o r group duration i s a fuzzy boundary. Another explanation i s that the boundary i s inf l u e n c e d by the i n t e r a c t i o n of s u b i n t e r v a l rate and number. - 137 - Figure 12. P r o p o r t i o n a l E r r o r versus C r i t e r i o n T o t a l P a t t e r n Duration. • = 200 ms s u b i n t e r v a l s , • = 300 ms s u b i n t e r v a l s , o = 400 ms s u b i n t e r v a l s . 00 m 0.08 0.07 0.06 g 0.05 rt W 0.04 < £ 0.03 O H 0< 0.02 O § 0.01 0.00 -o.oi h -0.02 1 1200 1600 2000 2400 2800 3200 3600 4000 4400 4800 5200 5600 6000 CRITERION TOTAL PATTERN DURATION - 139 - Figure 13. Mean Reproduction R a t i o ( s h o r t - t o - l o n g i n t e r v a l ) f o r each S e r a i l P o s i t i o n . a. c r i t e r i o n r a t i o : 0.25, b. c r i t e r i o n r a t i o : 0.20,'c. c r i t e r i o n r a t i o : 0.17, d. c r i t e r i o n r a t i o : 0.14. • = 200 ms s u b i n t e r v a l s , • = 300 ms s u b i n t e r v a l s , • = 400 ms s u b i n t e r v a l s .    0 . 0 9 1 2 3 4 5 SERIAL POSITION - 144 - Possessing more frequent s u b i n t e r v a l s ( i . e . 300 ms ISIs) may more s t r o n g l y suggest grouping than when s u b i n t e r v a l s are l e s s frequent ( i . e . 400 ms I S I s ) . The p r o p o r t i o n a l e r r o r data showed that s u b i n t e r v a l durations of 300 ms were best reproduced. Subinterval durations of 400 ms were c o n s i s t e n t l y underestimated while s u b i n t e r v a l durations of 200 ms were c o n s i s t e n t l y overestimated. One speculative explanation f o r the l a t t e r f i n d i n g i s that subjects have d i f f i c u l t y i n reproducing such r a p i d patterns unless they are w e l l - p r a c t i c e d . In Experiment 2, patterns with the 200 ms i n t e r v a l s were reproduced f a s t e r than the c r i t e r i o n patterns, but i n that study subjects reproduced each of seven patterns at that rate over 30 separate t r i a l s . I n t u i t i v e l y , however, i t would not seem that d i f f i c u l t t o produce keyboard taps at a rate of five/second. Why should PE be high f o r longer i n t e r v a l s i n the 200 ms patterns but not f o r the e n t i r e pattern duration? To speculate, i f subjects do have d i f f i c u l t y i n producing the 200 ms i n t e r v a l s , and r e a l i z e i t , then perhaps they compensate by shortening the subsequent longer i n t e r v a l s . As a r e s u l t , the PE scores f o r the t o t a l pattern durations are low. That t h i s i s not the case f o r the 200/200/200/200/800 ms p a t t e r n may be because the r e l a t i v e t iming of s h o r t - t o - long i n t e r v a l s i n t h i s pattern (4:1) i s very f a m i l i a r i n Western music and maintaining r e l a t i v e t iming may dominate the need to maintain absolute timing. - 145 - The r e l a t i v e timing data are i n t e r e s t i n g f o r at l e a s t two reasons. F i r s t , they show that timing i s w e l l maintained i n patterns that d i s p l a y no evidence of grouping through accenting. Does accurate r e l a t i v e timing r e s u l t from the a p p l i c a t i o n of some other strategy? Or i s i n t e r v a l lengthening, a measure shown to be u s e f u l i n s e v e r a l of the studies reported i n t h i s work, an incomplete measure of perceptual grouping i n reproduction tasks? Or, perhaps, the processes of memory, and not immediate perception, are responsible f o r being able to reproduce a longer i n t e r v a l j u s t subsequent and of s i m i l a r duration to a s e r i e s of shorter i n t e r v a l s ? Future research may provide an answer to t h i s question. The second reason these data are i n t e r e s t i n g and important i s because they show the inadequacy of measuring only the r e l a t i v e t iming of rhythmic patterns. I f one were to look at j u s t the r e l a t i v e timing data, then the d e v i a t i o n s i n the reproduction of absolute i n t e r v a l durations, and t h e i r p o t e n t i a l s i g n i f i c a n c e , would be overlooked. - 146 - GENERAL DISCUSSION The focus of t h i s second s e c t i o n of s t u d i e s was on how s e l e c t e d v a r i a b l e s i n f l u e n c e the grouping of p a t t e r n elements i n t o equal i n t e r v a l s suggested by p a t t e r n s t r u c t u r e . For simple rhythmic p a t t e r n s , the o r g a n i z a t i o n of elements i n t o two i n t e r v a l s of equal d u r a t i o n occurs when each i n t e r v a l i s i n i t i a t e d by an e x t e r n a l - w o r l d event. In more e l a b o r a t e rhythmic contexts, such as music, t h i s need not be t r u e . But f o r b r i e f p a t t e r n s of i d e n t i c a l elements separated by only two d i f f e r e n t d u r a t i o n s , there i s i n s u f f i c i e n t context t o suggest equal i n t e r v a l grouping i f one i n t e r v a l contains no elements (unless they are w e l l - l e a r n e d as with the Canic & Franks, 1985 study c i t e d e a r l i e r ) . In these cases, s u b j e c t s organize a p a t t e r n as two i n t e r v a l s of unequal d u r a t i o n with the subdivided i n t e r v a l d i s p l a y i n g evidence of agogic a c c e n t i n g . Several models of rhythm p e r c e p t i o n focus s o l e l y on r e l a t i v e t i m i n g and discount the r o l e of absolute i n t e r v a l d u r a t i o n s i n grouping (e.g. Povel & Essens, 1985). An attempt was made here t o determine i f pe r c e p t u a l grouping would occur f o r g r o u p i n g - i n t e r v a l s up to 1800 ms. I t was found that t h i s d u r a t i o n does represent an approximate upper l i m i t t o the grouping of s u b i n t e r v a l s . There was a l s o weak evidence t h a t non-subdivided i n t e r v a l s longer than 1800 ms were p o o r l y reproduced. This i n t e r p r e t a t i o n i s clouded by the f a c t t h a t i n t e r v a l s l e s s than 1800 ms were p o o r l y - 147 - reproduced at the fastest subinterval rate (200-ms ISIs) in Experiment 4. The suggestion that adjacent levels i n the hier a r c h i c a l organization of a rhythmic pattern must relate as simple integers less than 5 was tested. Although such relations v i r t u a l l y exhaust the rhythmic organizations of Western music, rhythm perception and rhythmic action, i n general, extend far beyond t h i s context; there i s l i t t l e reason to suggest that a greater number of intervals cannot be coherently grouped. And, in fact, t h i s i s what was found. Patterns of up to 7 elements can be grouped together as long as the t o t a l pattern duration does not exceed (roughly) 1800 ms. In the discussion of Experiment 3, possible explanations were given for the finding that grouped intervals and longer intervals are underestimated in reproduction. Two possible explanations have received some support i n the time perception l i t e r a t u r e . The f i r s t i s the notion of an "indifference i n t e r v a l " - that intervals longer than around 700 ms are underestimated while shorter intervals are overestimated. This concept f i t s quite well with the reproduction data i n Experiment 3. However, i t did not f i t at a l l well with the data i n Experiment 4. Longer intervals were almost always overestimated and grouped intervals often were (see Table 13). A second finding in Experiment 3 was that, for X-type patterns, f i l l e d (subdivided) intervals were frequently - 148 - reproduced l o n g e r i n d u r a t i o n than u n f i l l e d (non-subdivided) i n t e r v a l s . T h i s was not su p p o r t e d i n t h e r e s u l t s from Experiment 4 . There i s seemingly no s y s t e m a t i c way i n which t h e r e p r o d u c t i o n o f l o n g e r , grouped o r u n f i l l e d i n t e r v a l s d e v i a t e s from t h e c r i t e r i o n d u r a t i o n . I t may be t h a t phenomena observed i n time p e r c e p t i o n (the p e r c e p t i o n o f s i n g l e i n t e r v a l s ) are not found i n t h e more complex c o n t e x t o f rhythm p e r c e p t i o n . I t s h o u l d a l s o be n o t e d t h a t t h e i n d i f f e r e n c e i n t e r v a l and f i l l e d i n t e r v a l i l l u s i o n have been q u e s t i o n e d by some r e s e a r c h e r s o f t i m e p e r c e p t i o n . O r n s t e i n (1969) has reviewed f i n d i n g s and co n c l u d e d t h a t t h e former i s u n r e l i a b l e w h i l e F r a i s s e (1963) has r eached a s i m i l a r c o n c l u s i o n r e g a r d i n g t h e l a t t e r . A f i n a l p ost-hoc f i n d i n g i n Experiment 3 was t h a t p a t t e r n s w i t h an even number o f s u b i n t e r v a l s were reproduced more a c c u r a t e l y than p a t t e r n s w i t h an odd number o f s u b i n t e r v a l s . There was no ev i d e n c e f o r t h i s f i n d i n g i n Experiment 4 . As a r e s u l t , t h e r e i s no apparent e x p l a n a t i o n f o r t h e o b s e r v a t i o n t h a t X-type p a t t e r n s are not always reproduced more a c c u r a t e l y t h a n E-type p a t t e r n s . W h i l e t h e f i n d i n g s i n t h i s s e c t i o n have p r o v i d e d g e n e r a l answers t o t h e q u e s t i o n s asked, t h e use o f a b s o l u t e t i m i n g , r e l a t i v e t i m i n g and o r d i n a l r e l a t i o n s h i p measures have y i e l d e d much d a t a about which we can o n l y s p e c u l a t e . F u r t h e r r e s e a r c h i s r e q u i r e d t o develop a t h e o r e t i c a l framework t h a t can i n t e g r a t e t h e r e s u l t s o b t a i n e d t h r o u g h a l l o f t h e s e measures. - 149 - SUMMARY / CONCLUSIONS In the General I n t r o d u c t i o n i t was asked how we p e r c e p t u a l l y organize and how we p l a n i n advance the r e p r o d u c t i o n of rhythmic p a t t e r n s . A r e c u r r i n g theme throughout the s t u d i e s r e p o r t e d here i s t h a t of "coherence". When i s a stimulus p a t t e r n or a response p a t t e r n t r e a t e d as a coherent whole? What f a c t o r s i n f l u e n c e the coherence of stimulus/response p a t t e r n s ? Issues of response coherence were c e n t r a l t o the f i r s t s e c t i o n . I t was suggested t h a t when program implementation processes act on the e n t i r e response p a t t e r n , then that p a t t e r n i s t r e a t e d as a coherent whole. Simple, isochronous rhythms served as stimulus p a t t e r n s . RT, which i s thought t o r e f l e c t the d u r a t i o n of program implementation processes, was the measure of primary i n t e r e s t . RT was found to i n c r e a s e l i n e a r l y f o r p a t t e r n s with IRIs up to 300 ms. These r a t e s are apparently r a p i d enough t o n e c e s s i t a t e that the response p a t t e r n be t r e a t e d as a coherent whole. Of course, t h i s does not mean the e n t i r e p a t t e r n i s programmed p r i o r t o response i n i t i a t i o n . I t may be t h a t , i n terms of Sternberg and h i s c o l l e a g u e s (1978), the f i r s t response u n i t i s s e a r c h / r e t r i e v e d from an i n c r e a s i n g l y l a r g e pool of response u n i t s . Response r a t e cannot be the only f a c t o r t h a t determines response coherency. RT would undoubtedly not continue t o i n c r e a s e f o r r a p i d , isochronous p a t t e r n s i n d e f i n i t e l y long. An upper l i m i t - e i t h e r i n terms of number of response u n i t s or t o t a l response d u r a t i o n - should be evident here. Late r - 150 - segments of long response patterns can be prepared o n - l i n e - concurrent with execution. Perhaps the question being asked here i s not q u i t e r i g h t . A more important question may be: How much of a head s t a r t , i n terms of programming time, i s required so that on- l i n e programming does not f a l l behind the demands of task execution? I t may be that a RT c e i l i n g i s the by-product of temporal scheduling of o n - l i n e and execution processes, and not e x p l a i n a b l e s o l e l y i n terms of a s a l i e n t output parameter. I f we are asked to produce a movement of continuous duration then duration may be a s a l i e n t parameter. I f we are asked to produce a number of d i s c r e t e movements then number may be a s a l i e n t parameter. Yet, consider that many tasks are ambiguous i n that there may be more than one s a l i e n t output parameters. They may not demand an i n v a r i a n t p a t t e r n of o r g a n i z a t i o n and processing. I t may be that our c o g n i t i v e o r g a n i z a t i o n of a task determines the way i n which the task i s planned and executed. And, f o r many tasks, c o g n i t i v e o r g a n i z a t i o n w i l l vary among i n d i v i d u a l s . Issues of perceptual coherence were c e n t r a l to the second s e c t i o n of s t u d i e s . Stimulus patterns were s t r u c t u r e d so as to suggest the d i v i s i o n of the e n t i r e p a t t e r n i n t o two i n t e r v a l s of equal duration. This f u r t h e r suggested the grouping of s u b i n t e r v a l s that spanned the duration of one " i n t e r v a l " . The lengthening of the f i r s t and l a s t s u b i n t e r v a l s i n a suggested i n t e r v a l - agogic accenting - was - 151 - taken as evidence of grouping. I t was shown t h a t i n a simple context such as t h i s , the suggested grouping does not occur un l e s s both i n t e r v a l s are i n i t i a t e d by e x t e r n a l - w o r l d events. Grouping occurs, but more as a r e s u l t of what i s . t h e r e than what i s n ' t . In G e s t a l t terms, p e r c e p t u a l o r g a n i z a t i o n i s only as good as the p a t t e r n s allow. Grouped i n t e r v a l s of unequal d u r a t i o n are thus p e r c e i v e d . Is the p e r c e p t u a l coherence of a p a t t e r n o f stimulus events dependent upon the t o t a l d u r a t i o n of a suggested g r o u p i n g - i n t e r v a l , or l i m i t e d by number of s u b i n t e r v a l s ? The r e s u l t s presented here s t r o n g l y suggest t h a t grouping of events occurs up to a span of around 1800 ms. Events that span longer i n t e r v a l s are not so coherent. Indeed, the absolute d u r a t i o n s of non-subdivided i n t e r v a l s are w e l l - reproduced up to 1800 ms, at which p o i n t a quantum i n c r e a s e i n p r o p o r t i o n a l r e p r o d u c t i o n e r r o r occurs. S u b i n t e r v a l frequency may a l s o p l a y a r o l e i n the coherence of a g r o u p i n g - i n t e r v a l . There was some evidence t h a t a g r o u p i n g - i n t e r v a l can be longer (2100 ms) i f i t possesses many s u b i n t e r v a l s ( i . e . 7 X 300 ms s u b i n t e r v a l s ) . I t seems i n t u i t i v e l y c o r r e c t that p e r c e p t u a l coherence i s not l i m i t e d by the event r a t e s t h a t l i m i t response coherence - namely, around 300 ms. L i v i n g organisms have an i n v a r i a n t tendency t o organize experience, and i t i s t o our advantage to be able t o p e r c e p t u a l l y group events that are separated by more than 300 ms. (It i s a l s o to our advantage, - 152 - however, not to p e r c e p t u a l l y group events spanning l a r g e p e r i o d s of time, f o r i f we d i d , our experience would be l a r g e l y heterogeneous, perhaps too complex t o i n t e r p r e t or too general t o convey s p e c i f i c meaning). On the other hand, the c a p a c i t y t o act q u i c k l y , and to i n i t i a t e complex a c t i o n s r a p i d l y , i s a l s o t o the advantage of human organisms. I f response coherence were observed f o r long and/or slow response p a t t e r n s , then response i n i t i a t i o n would be slow - c l e a r l y a b i o l o g i c a l disadvantage. As d e f i n e d here, p e r c e p t u a l and response coherence are not subject t o the same l i m i t s . And with l e a r n i n g , these l i m i t s extend i n opposite d i r e c t i o n s . The p e r c e p t i o n of rhythmic r e l a t i o n s h i p s i n a complex p i e c e of music seems to develop with i n c r e a s i n g exposure. New and complex h i g h e r - order groupings are r e a l i z e d , the previous l i m i t s of d u r a t i o n and number of s u b i n t e r v a l s having d i s s o l v e d . The programming of rhythmic p a t t e r n s can s i m i l a r l y transcend previous l i m i t s . With l e a r n i n g , the time r e q u i r e d t o prepare a f i r s t response, and the a d d i t i o n a l time r e q u i r e d as the response p a t t e r n becomes longer, decrease a s y m p t o t i c a l l y . Rhythm e x i s t s w i t h i n us and a l l around us. Understanding coherence, i n the p e r c e p t i o n and p r o d u c t i o n of rhythmic p a t t e r n s , i s c r u c i a l t o the g r e a t e r understanding of human p e r c e p t i o n and a c t i o n . The s t u d i e s reported here are a t h r u s t i n that d i r e c t i o n . 15-31 «- REFLECTIONS Work i s done, then f o r g o t t e n . Therefore i t l a s t s f o r e v e r . Achieve r e s u l t s , But never g l o r y i n them. Achieve r e s u l t s , But never boast. Achieve r e s u l t s , But never be proud. Achieve r e s u l t s , Because t h i s i s the n a t u r a l way. Lao Tzu There can be no challenge without the r i s k of f a i l u r e . Y u i c h i r o Miura Progress During your journey i t may at times seem as i f you are not progressing, that you are no nearer t o your g o a l . You may have to descend i n t o a v a l l e y b efore you can climb a mountain. Thus the paradox of progress. Things are not always what they seem. U t i l i z e f o r e s i g h t . Keep the t r u e path. MJC Great ideas need l a n d i n g gear as w e l l as wings. C D . Jackson Be l i b e r a l i n a l l o w i n g hypotheses and c o n s e r v a t i v e i n conf i r m i n g them. MJC He c o u l d have gone f o r general, but he went f o r h i m s e l f i n s t e a d . Captain W i l l a r d - 153 - FOOTNOTES 1 Farnsworth (1958) reported of early Christian missionaries to A f r i c a who observed natives to beat on t h e i r drums seemingly at random. Their conclusion, that the natives were "poor" i n rhythm, was la t e r shown to be i n error - the African rhythms were very precise but too complicated to be perceptually organized by the foreign l i s t e n e r s ! 2 I thank Prof. R.W. Schutz f o r t h i s suggestion. 3 The reported p. values for repeated measures effects are adjusted according to the fluynh-Feldt procedure when epsilon i s greater than or equal "to 0.75, and according to the Greenhouse-Geisser procedure when epsilon i s less than 0.75, as recommended by Huynh and Feldt (197 6 ) . 4 The t o t a l number of IRI's i n a l l of the multi-IRI patterns i s 27 (i.e. 2+3+4+5+6+7). The t o t a l number of IRI's i n the la s t s e r i a l position i s 6. 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