J O R D A N B . L . S M I T H M A T H E M U S I C A L C O N V E R S A T I O N S S T U D Y D A Y, 1 2 F E B R U A RY 2 0 1 5 R A F F L E S I N S T I T U T I O N E X P L A I N I N G A N D P R E D I C T I N G T H E P E R C E P T I O N O F M U S I C A L S T R U C T U R E
O U T L I N E • What is musical structure? • How do people perceive structure? • Gestalt-based theories • Implication-Realization theory • Listener considerations • Conclusion
https://www.youtube.com/watch?v=nfWlot6h_JM “Shake It Off” by Taylor Swift
W H AT I S S T R U C T U R E ? • How did you hear this piece of music? • How did you perceive this piece of music?
W H AT I S S T R U C T U R E ? • How did you perceive this piece of music? horns voice drums
W H AT I S S T R U C T U R E ? • How did you perceive this piece of music? verse chorus pre- chorus horns voice drums
W H AT I S S T R U C T U R E ? • How did you perceive this piece of music? verse chorus pre- chorus horns voice drums beats sections/ measures/ structure phrases
H O W D O P E O P L E P E R C E I V E S T R U C T U R E ? • Gestalt-based theories • Implication-Realization theory • Listener considerations
G E S TA LT- B A S E D T H E O R I E S Proximity Similarity
G E N E R AT I V E T H E O RY O F T O N A L M U S I C Principle of Proximity Lerdahl and Jackendoof 1983 image credit: http://noike.info/~kenzi/roughly/paper/GTTM/12/12_Psychological_and_Linguistic_Connections.html
G E N E R AT I V E T H E O RY O F T O N A L M U S I C Principle of Similarity Lerdahl and Jackendoof 1983 image credit: http://noike.info/~kenzi/roughly/paper/GTTM/12/12_Psychological_and_Linguistic_Connections.html
G E N E R AT I V E T H E O RY O F T O N A L M U S I C Two rules: Cooperation Conflict
G E N E R AT I V E T H E O RY O F T O N A L M U S I C Conflict of Rules Lerdahl and Jackendoof 1983 image credit: http://noike.info/~kenzi/roughly/paper/GTTM/12/12_Psychological_and_Linguistic_Connections.html
G E N E R AT I V E T H E O RY O F T O N A L M U S I C Goal of GTTM: to devise a set of rules from which a complete hierarchical grouping structure can be inferred Lerdahl and Jackendoof 1983 image credit: http://noike.info/~kenzi/roughly/paper/GTTM/12/12_Psychological_and_Linguistic_Connections.html
G E S TA LT- B A S E D T H E O R I E S Proximity Similarity
G E N E R AT I V E T H E O RY O F T O N A L M U S I C • Fred Lerdahl and Ray Jackendoff, 1983 • Goal of GTTM: to devise a set of rules from which a complete hierarchical grouping structure can be inferred • Inspired by Gestalt theory and by ideas of “universal grammar” in language • Assumes an ideal listener familiar with Western tonal music
? Good Continuation
M E L O D I C E X P E C TAT I O N
M E L O D I C E X P E C TAT I O N
M E L O D I C E X P E C TAT I O N
I M P L I C AT I O N - R E A L I Z AT I O N T H E O RY • Eugene Narmour, 1990 • Goal of I-R Theory: to devise a set of rules from which a complete hierarchical grouping structure can be inferred • …using explicit reference to human cognitive processes • …while carefully separating what is universal from what is culturally learned
I M P L I C AT I O N - R E A L I Z AT I O N T H E O RY • Two expectations are universal: 𝄟 ♩ ♩ ♩ • A + A → A 𝄟 ♩ ♩ ♩ • A + B → C
I M P L I C AT I O N - R E A L I Z AT I O N T H E O RY • Refinements of these expectations, based on interval size and direction, are culturally learned. For example: • Large intervals usually followed by smaller intervals • Large intervals usually followed by a change in direction
I M P L I C AT I O N - R E A L I Z AT I O N T H E O RY • How does expectation lead to structure? • Surprise leads to boundaries • Closure leads to boundaries
W H AT I S S T R U C T U R E ? • How did you perceive this piece of music? horns voice drums
I M P L I C AT I O N - R E A L I Z AT I O N T H E O RY • I-R model focuses almost exclusively on melody as a sequence of intervals. • What about harmony, rhythm, timbre? • Narmour hinted at theory in 1977… • The Analysis and Cognition of Basic Melodic Structures: The Implication-Realization Model published in 1990… • Parts 2–4 forthcoming…
L I S T E N E R C O N S I D E R AT I O N S • Previous theories all posit ideal listeners • i.e., for a given melody, there is a “best” analysis. • But, listeners differ in many ways! • Cultural knowledge • Level of musical training • Listening context • Familiarity with the music
E X P E R I M E N T S A B O U T L I S T E N E R D I F F E R E N C E S • Elizabeth Margulis: What is the effect of repeated listenings? • Listeners heard the same piece four times in a row • Each time, they indicated every single literal repetition they identified • Margulis tallied the correct indications and their lengths
image credit: http://imslp.org/wiki/Pi%C3%A8ces_de_clavecin_%28Rameau,_Jean-Philippe%29
E X P E R I M E N T S A B O U T L I S T E N E R D I F F E R E N C E S • Elizabeth Margulis: What is the effect of repeated listenings? Margulis 2012
L I S T E N E R C O N S I D E R AT I O N S • Some listener disagreements seem less predictable…
Bruderer, McKinney and Kohlrausch 2009
W H AT C A U S E S A L I S T E N E R T O H E A R A B O U N D A RY ? Clarke and Krumhansl 1990: Bruderer et al. 2009: • pause (silence) • change in harmonic • return of material (chordal) progression • change of dynamic • change in melody • new material • change in tempo • change of rhythm • change in rhythm • change of pitch content • change in timbre • change of articulation • change in loudness / dynamics • start of development • breaks • change of register (expansion) • global structure • change of dynamic contour • repetitions • change of texture
W H AT C A U S E S A L I S T E N E R T O H E A R A B O U N D A RY ? 1. Were listeners paying attention to these features, or were these features attention-grabbing? 2. Can we trust the listeners to self-report the correct features?
W H AT C A U S E S A L I S T E N E R T O H E A R A B O U N D A RY ? image credits: various from Google Images Aviezer, Trope and Todorov 2012
What is the viewer paying attention to? What is the listener paying attention to?
E X P E R I M E N T S A B O U T L I S T E N E R D I F F E R E N C E S • I ran an experiment last year on…
E X P E R I M E N T 1 : AT T E N D T O T H E PAT T E R N 38
E X P E R I M E N T 1 : AT T E N D T O T H E PAT T E R N 39
E X P E R I M E N T 2 : B O U N D A RY S A L I E N C E 40
E X P E R I M E N T 2 : B O U N D A RY S A L I E N C E • Hypothesis: focusing on a feature makes changes in that feature more salient. • Participants focused on a single feature while listening to an AB-pattern clip, then rated salience of the change they heard • Independent variable: Match between focal and changing feature varies: match, convolved, or wrong
E X P E R I M E N T 2 : B O U N D A RY S A L I E N C E • Result: Yes, attention did affect the salience of the changes!
E X P E R I M E N T 1 : AT T E N D T O T H E PAT T E R N • Hypothesis: focusing on a feature makes one more likely to perceive groups according to that feature • Participants secretly primed to focus on a feature with a distractor task: detect whether a pattern occurs • Then they indicated their preferred grouping. • Independent variables: relevance of probe; presence of probe.
E X P E R I M E N T 1 : AT T E N D T O T H E PAT T E R N 65/35 50/50
E X P E R I M E N T 1 : AT T E N D T O T H E PAT T E R N • Result: Yes, attention did influence the perceived groupings! • Effect varied with feature
E X P E R I M E N T 1 : D E P E N D E N C E O F G R O U P I N G S T R U C T U R E O N AT T E N T I O N 1.00 2 Mean confidence in grouping preference Mean pattern identification accuracy 0.75 1 0.50 0 0.25 − 1 0.00 − 2 20 30 40 20 30 40 50 Musical training score Musical training score
E X P E R I M E N T I M PA C T • Attention impacts the perception of groupings for listeners • Disagreements between listeners could be caused by differences in attention • Add it to the (growing) list: familiarity, training,
C O N C L U S I O N • Generative Theory of Tonal Music • Explicit set of rules for generating hierarchical analyses of tonal music • Implication-Realization Theory • Expectation has a central role in music perception • Founded in cognitive science; makes testable claims • Listener differences challenge both theories • Consider the non-ideal listener
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