Cognitive Foundations of Musical Pitch

Contents......Page 10
1. OBJECTIVES AND METHODS......Page 14
The approach of cognitive psychology......Page 16
The plan of the research......Page 20
Outline of the following chapters......Page 23
2. QUANTIFYING TONAL HIERARCHIES AND KEY DISTANCES......Page 27
The tonal hierarchy......Page 29
The first probe tone study: individual differences with a major-key context......Page 32
Replication and extension to minor-key contexts......Page 36
A derived measure of interkey distance......Page 42
A spatial representation of interkey distance......Page 51
Theoretical maps of key relationships......Page 57
3. MUSICAL CORRELATES OF PERCEIVED TONAL HIERARCHIES......Page 61
Tonal consonance......Page 62
Tonal consonance and tonal hierarchies......Page 66
Statistical analyses of tonal compositions......Page 73
Tonal distributions and tonal hierarchies......Page 77
Tonal hierarchies, tonal consonance, and tonal distributions......Page 86
4. A KEY-FINDING ALGORITHM BASED ON TONAL HIERARCHIES......Page 88
The key-finding algorithm......Page 89
Application I: initial segments of preludes of J. S. Bach, Shostakovich, and Chopin......Page 92
Application II: fugue subjects of J. S. Bach and Shostakovich......Page 100
Application III: J. S. Bach\'s C Minor Prelude, Book II......Page 107
Limitations and possible extensions of the algorithm......Page 117
5. PERCEIVED RELATIONS BETWEEN MUSICAL TONES......Page 122
Geometric representations of musical pitch......Page 123
Limitations of geometric models......Page 130
Experimental measures of tonal relations......Page 134
Correlations with tonal consonance and tonal distributions......Page 145
Gestalt theory......Page 149
Three principles of tonal stability......Page 151
Perceptual organization in music: Segmentation and melodic similarity......Page 163
7. QUANTIFYING HARMONIC HIERARCHIES AND KEY DISTANCES......Page 176
Music-theoretical descriptions of harmony......Page 177
Quantifying the harmonic hierarchy......Page 179
Harmonic hierarchy of diatonic triads I-VII......Page 188
Deriving key distances from harmonic hierarchies......Page 193
Perceived harmonic relations and key structure......Page 199
Perceived harmonic relations of diatonic triads I-VII......Page 203
Key context effects on perceived harmonic relations......Page 206
Key structure and memory for chord sequences......Page 210
Key context effects on memory for chord sequences......Page 214
Relational effects on memory for chord sequences......Page 218
Parallels between perceived tonal and harmonic structures......Page 221
9. PERCEIVING MULTIPLE KEYS: MODULATION AND POLYTONALITY......Page 224
Tracing the developing and changing sense of key......Page 225
Tonal hierarchies and polytonality......Page 237
10. TONAL HIERARCHIES IN ATONAL AND NON-WESTERN TONAL MUSIC......Page 251
Tonal hierarchies in 12-tone serial music......Page 252
Tonal hierarchies in North Indian music......Page 264
Tonal hierarchies in Balinese music......Page 277
Tonal hierarchies: some generalizations......Page 279
Properties of the diatonic-harmonic system......Page 282
Properties of pentatonic, octatonic, and North Indian scales......Page 286
Properties emerging from the empirical studies......Page 291
References......Page 300
H......Page 312
O......Page 313
Z......Page 314
F......Page 315
M......Page 316
T......Page 317
W......Page 318