Emmanuel Bigand (1993). "The Influence of Implicit Harmony, Rhythm and Musical Training on the Abstraction of `Tension-Relaxation Schemas' in Tonal Musical Phrases" Contemporary Music Review, Vol. 9, 123-137.

Point of view:

psychological: music an informative structure, communicating different emotions, more than just complex acoustical structure

Broad goal:

how is perceptive & cognitive competence used to extract informative structure?

Background:

1. Musical schemas of tension & relaxation (t&r) assimilated into kinetic & emotional schemas. Francès (1958), Imberty (1979,1981)
2. Intuitions about t&r determined by combination of grouping structure, metrical structure & tonal hierarchies; leads to event hierarchy & derivation of t&r hierarchy. Lerdahl & Jackendoff (1983)
3. How do the three components of grouping, meter & tonal hierarchies interact?

Purpose:

to answer four questions:

1. Can two melodies with same rhythmic structure, melodic contour, tempo, dynamic, but different implicit harmonies, generate different t&r networks?
2. Can two melodies differing only in their rhythmical structure generate different t&r schemas?
3. Do pitch and rhythm get processed independently of one another by separate cognitive processes?
4. Are abstraction processes of t&r networks determined by musical training?

Overview:

Wants to measure the t&r schemas generated by a musical phrase. Segments the melody into fragments & asks subjects to evaluate for completeness on a 7-point scale. Completeness of fragment indirectly measures its stability.

Materials:

see Fig. 3 for H1 (R1-3) and H2 (R1-3). Each has 23 stopping points yielding 138 fragments.

Subjects:

18. Half musicians and half non-musicians.

Outcomes show:

1. Influence of tonal hierarchy on t&r schemas. Profiles for H1 & H2 are different. (Musicians- 32 p<0.001; Nonmusicians - 32 p<0.078) See Fig. 5.
2. Influence of rhythmic structure on t&r schemas. Profiles for R1, R2, R3 are different. (M p<0.007; N p<0.001) Compare R1 & R2 - no effect for metrical structure on note stability* (both M&N). Compare R1 & R3 - effect for duration found: the longer the note, the higher the stability. (M&N p<0.01)
3. Interaction between implicit harmony and rhythm: changing rhythmic structure does not have same effect on H1 as H2. (M p<0.007; N not sig.)
4. Strong effect of musical training on abstracting t&r schemas. Non-musicians less developed.* See Fig. 4 * surprising results

Design weaknesses:

1. Subjects listen to all fragments. Subtleties can get lost in the similarities.
2. Random presentation order problematic.

Materials:

eliminates both R3s; fragments presented short to long: one note being added to each hearing

Subjects:

72. Half & half again. 8 groups of 9 subjects. Each group listens to only 1 of 4 melodies.

"Outcomes" highlights:

1. Now for N p<0.001. See Fig. 7 2. Now see effect for metrical structure: note on strong beat is perceived as more stable than on weak. 3. Both groups hear stability increasing when it's on a strong beat, but the gain depends on its tonal function. For M, increasing duration of a note depends on its function. For N, the longer the duration, the higher its musical stability. 4. N similar to M; no difference in competence at task.

Purpose revisited:

1. Two melodies differing only in implicit harmonies do generate different t&r networks. 2. Local t&r schemas are strongly influenced by rhythmic value: both metrical position and durational difference. 3. Interactive relation between pitch and rhythm seems to exist; they are not processed independently. 4. Specific training not needed to structure a musical piece. Musicians might abstract more varied t&r schemas.

Conclusion:

Suggests how one might formalize rules to establish t&r schemas. It involves:

• assigning values to melody notes based on their tonal weight (tonic=3.7; dominant=3.6; third=3.5; other diatonics=3.4; chromatics=3.2 or 3)
• modulations: new key gets same scale of values minus 1 or 2, based on distance to main key.
• durational and metrical weight must be considered.
• see fig. 9
• similarity exists between real and theoretical profiles. A starting point.

Marion Pineau & Emmanuel Bigand (1997). "Effect of Global Structures on Harmonic Priming in Music" L'Année Psychologique, Vol. 97, 385-408.

Introduction

1. Tonal and Harmonic Hierarchies

• hierarchy of chords within key
• relatedness of chords
• necessity of perceiving change in chords -- functions depending upon context
• cites some studies showing evidence that listeners can do so (Krumhansl, 1990)

2. Harmonic Expectation

• Bharucha's Connectionist Model: tonal hierarchies represented by strength of connections between three unit levels - notes, chords & keys. The stronger the activation for a chord unit, the more it will be expected.
• Bharucha 1986; Bharucha & Stoeckig 1987's conclusion: Initial context creates expectations for linked chords that, in turn, facilitates their processing, once heard.
• Schmuckler & Boltz 1994: used sequences of chords. For chords less linked to sequence, there was weaker expectation & lower response time.

3. Unanswered Questions

• Are chords processed based on their global or local effects? - Hess, Foss & Carroll 1995: language comprehension. Shows changes in anchoring effects depending upon global or local contexts. Possible application to music?
• Are the components of musical experience sensory or cognitive? - Schmuckler 1989: results favored sensory - Bharucha & Stoeckig 1987: results favored cognitive

4. Goals of Present Study

1. To determine if effects of anchoring could depend on the larger harmonic context.
2. To extend Bharucha & Stoeckig's results to piano sounds and finer harmonic relations.

Overview of Experiments

Subjects hear 8-chord sequences (see Fig. 1) in which target chord is the last. The local context of prime and target will be constant, but the global harmonic context set up by the preceding 6 chords will be varied. In half the experiments, the target is strongly expected (tonic) and the other half it is less expected (subdominant).

Experiment #1

Subjects:

15 volunteers with musical training varying from 0-4 years. No explicit theory knowledge.

Material:

Sound generated on Yamaha Sound Expander piano. 32 chord sequences.

Task:

to evaluate the degree of completion for each sequence using a 7-point scale.

Results:

Higher completion ratings for V-I than I-IV. (see Fig. 2)

Discussion:

• Same chords in different contexts yield different judgments; shows global effects.
• Results confirm theory predictions of tonic being more stable than IV; even subjects with low level of training have internalized ability to deal with these subtleties.

Experiment #2

Goal:

to look at the effect of global harmonic context in a harmonic anchoring paradigm.

Hypothesis:

Expected targets will be identified the fastest when functioning as tonics. If found, this will serve as support that there is a cognitive component to harmonic expectation.

Subjects:

30 volunteers. Half are musicians, half are nonmusicians.

Material:

32 x 2 chord sequences with one set having fifth of last chord raised by semitone.

Task:

Phase 1: subjects practice hearing in-tune/out-of-tune chord pairs.
Phase 2: Judge whether chords are in- or out-of-tune as fast as possible.

Results:

• In all cases (consonant vs dissonant; musicians vs nonmusicians), the expected chord (I) was identified faster than the unexpected.
• Out of tune targets were more likely to be incorrectly identified (confirms Bharucha & Stoekig).

Discussion:

• Confirmation of anchoring effect (Bharucha & Stoekig): target chord is facilitated when related to preceding context.
• Confirms importance of global context: target was interpreted and anticipated based on what came before. Local context was held the same. Only relation between target chord and global context of sequence can account for results.
• Why are results not attributed to sensory components?
  • echoic memory only 2 secs. & would hold prime & target chords only.
  • psychoacoustic factors don't explain differences in response times.
• Why are results attributed to cognitive components?
  • response times can be explained: tonic target chord is quicker to identify because it is activated as a cognitive reference point. Need more time for other chords because their images must be reactivated.

General Discussion

Based on the experimental results showing the effect of global structures on the formation of musical expectations, the authors want to emphasize the ability of various tonal cognition models to include them. They suggest an analogous relationship exists between three types of models in the processing of words in language: (1) data-driven models involving automatic activation of mental lexicons; (2) discourse-based models involving context to determine meaning; and (3) hybrid models that include both the automatic and slower context-driven as sources of activation. Bharucha's connectionist model would most likely be analogous with the first language model and Lehrdahl and Jackendoff's model the second. They offer attempts of both models explaining the global effects, but conclude that as in language, it is probable that harmonic expectations depend equally on both.

• Harmony & Voice-leading Course Page