David Temperley. 2001. The Cognition of Basic Musical Structures Cambridge, MA: MIT Press.

Question: How are musical structures inferred perceptually?

Scope: "Infrastructure" (I. 1-6 below) of Common Practice Music

Cognitive Approach: aim is "descripitive" rather than "suggestive" - generally music theory's aim.

Preference Rule System: "statements of fact about music perception" (p.9) - well formedness rules (WFRs) give legal structures, preference rules (PRs) give favored structures; preference rules are weighted, relative weightings arrived at through trial and error

Computer Modeling: piano roll input (p. 10) with pitch (quantized) and rhythmic information; dynamic programming (p.16); testing model against earlier analyses (Kostka-Payne corpus unless noted) to determine validity of rules.

I. Six Preference Rule Systems (Appendix)

1. Metric Structure:
   • A. Psychological Importance: people generally agree on when to tap along with music. In Povel 1981, subjects played alternating tones at complex ratios. When asked to reproduce the patterns, subjects tended to adjust toward simpler ratios.
   • B. Definitions: Inter-onset interval (IOI) - time span between onset of events; Beat levels - (2 is tactus "felt-beat", 0-1 lower levels, 3-4 higher levels)
   • C. Testing and Sources of Error: (p. 45)
     1. meter often out of phase - long notes at ends of phrases. To compensate, program ignores length at highest level
     2. harmony plays a role in determining meter.
     3. Sometimes a lower level was assigned as the tactus. perhaps finding all levels at once would solve this?
2. Melodic Phrase Structure:
   • A. Psychological Importance: chunking makes information easier to process. In Dowling 1973b, sequences of notes were easier to recognize when not spanning pauses.
   • B. Definitions: phrase - generally 8-10 notes long. Longer phrases are penalized.
   • C. Testing and Sources of Error: tested against Essen Folk Song collection: 75.5% agreement. Sometimes found a different level of grouping. Tonality also seems to be a factor.
3. Contrapuntal Structure:
   • A. Psychological Importance: auditory streaming
   • B. Definitions: black square - pitch event; white square: a rest (p. 97); program output (105-6)
   • C. Testing and Sources of Error: tested against WTC (108)
     1. breaks - single voice broken up into two or more voicesi
     2. missed collision - failure to identify two voices colliding
     3. incorrect collision - collision recorded when none occured
     4. Mislead - failure to connect notes in a stream. Many errors may in fact not be perceptual errors.
4. Pitch Spelling:
   • A. Psychological Importance: difference in affect of minor third versus augmented second (Aldwell and Schacter 1989)
   • B. Definitions: line of fifths - one dimensional projection of fifths. As opposed to cirlce of fifths, Ab and G# are in different places (118, 127); TPC - tonal pitch class; Center of Gravity (COG) - on line of fifths normally two pitches in sharp direction
   • C. Testing and Sources of Error: testing: 98.8%correct
5. Harmonic Structure:
   • A. Psychological Importance: chords within a previously established key "follow better" than others (Krumhansl 1990)
   • B. Testing and Sources of Error: testing 83.7% 1. Limited vocabulary 2. Unequipped for escape tones 3. Harmonic rhythm too fast. altering preference rule scores may improve.
6. Key Structure:
   • A. Psychological Importance: see Harmonic Structure
   • B. Definitions: uses key profiles (174, 180, 186); output (178)
   • C. Testing and Sources of Error: testing - Bach fugue subjects (194-95), Kostka & Payne 84.7% (94.7% early chapters, 79.8% late chapters). May need harmonic input for better scores.

II. Extensions and Implications

1. Revision, Ambiguity, and Expectation
   • A. Revision: "Garden Path" phenomenon ("The old man the boats") and PRs (p. 217)
   • B. Ambiguity: highest score for more than one analysis (p. 226, 230)
   • C. Expectation: in general, expectation for high scores ("continuations" of Schubert lied Schmuckler 1989; "priming" Bharuca 1987 see page 234).
2. Meter, Harmony, and Tonality in Rock
   • A. Syncopation Shift: beats "belong" to next strong beat (p. 245).
   • B. Pentatonic Melodies: independent of harmony ("A Hard Day's Night" p. 256)
   • C. Revised key profiles: the "supermode" (p. 260, 262)
3. Meter and Grouping in African Music
   • A. Greater tolerance for syncopation, but stricter pulse (MPR 3) than Western.
   • B. Hemiola pattern: ambiguous middle level, stable high and low (p. 280)
   • C. The diatonic rhythmic pattern (2-2-1-2-2-2-1): conventional cue to meter?
4. Style, Composition, and Performance
   • A. Composers may adhere to PRs to write in specific style (Huron 2000)
   • B. Analysis scores within style relate to tension (p. 314)
   • C. Perforamance: Ritard at end of phrases - lengthening of OOI? (p.321)
5. Functions of the Infrastructure
   • A. Harmony and Key: drama related to journey through "line of fifths" space.
   • B. Motives, Schema (conventions, "topics"): depend on infrastructure for character
     (Deutsch and Feroe, 1981; Temperly p.333)
6. C. Analysis through PRs: Intellectual appeal (charades, cross-word puzzles, etc.)

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