§133. Practical Studies of Chord-types

Chapters in this book

1. Frontmatter 1
2. Table of Contents 7
3. Introduction 15
4. Editor’s Preface 27
5. Preface 29
6. Chapter I – The Harmonic Material of the Tempered Chromatic System
7. §1. The Tempered Chromatic System and its Notation 39
8. §2. Premises for the Investigation of Harmonic Material 41
9. §3. The Orientation Scheme of Chord-types 43
10. §4. The Harmonic Scheme of Chord-types 45
11. §5. Inversion of a Chord-type. Symmetrical and Asymmetrical Chord-types 46
12. §6. Types of Two-note Chords 48
13. §7. Types of Three-note Chords 48
14. §8. Types of Four-note Chords 51
15. §9. Types of Five-note Chords 53
16. §10. The Negative of a Chord-type 54
17. §11. Types of Six-note Chords 58
18. §12. The Harmonic Possibilities of the Tempered Chromatic System 62
19. §13. Types of Multi-note Chords 63
20. §14. Pitch-systems Contained in the Tempered Chromatic System 64
21. §15. Conclusions and Prospects 67
22. Chapter II – Sonic Characteristics of the Harmonic Material
23. §16. Consonance and Dissonance 69
24. §17. Dissonant Elements 70
25. §18. The Principle of Harmonic Inversion 72
26. §19. Dissonant Characteristics of Chords 74
27. §20. Influence of Consonant Components 76
28. §21. Family Characteristics of Chords 77
29. §22. Increasing the Dissonant Characteristic 80
30. §23. Merging of Dissonant Characteristics 83
31. §24. Semitone Clash of Semitone and Tritone Elements 86
32. §25. Summary 89
33. Chapter IIIa – Classification of the Harmonic Material
34. §26. The Concept of a Harmony in Classical Harmony 93
35. §27. Transient Chords 95
36. §28. Incomplete Harmonies 96
37. §29. The Formation of New Harmonies 97
38. §30. The Concept of a Harmony in Modern Harmony 98
39. §31. The Concept of the Characteristic Maximum 101
40. §32. The Concept of the Characteristic Nucleus 102
41. §33. Consonant Harmonies as Maxima with the Negative Dissonant Characteristic 104
42. §34. The Characteristic Maximum 6 104
43. §35. The Characteristic Maximum 2 105
44. §36. Characteristic Maxima 1 and 01 107
45. §37. Characteristic Maxima 0, 26, and 026 108
46. §38. Characteristic Maxima 16 and 016 110
47. §39. Characteristic Maxima 12 and 012 111
48. §40. Characteristic Maxima 126 112
49. §41. Characteristic Maxima 0126 115
50. §42. Characteristic Maxima 166 and 1266 117
51. §43. Characteristic Maxima 112 and 0112 119
52. §44. Characteristic Maxima 1126 120
53. §45. Characteristic Maxima 01126 123
54. §46. Characteristic Maxima 11266 125
55. §47. The Characteristic Maximum 011266 127
56. §48. The System of Characteristic-types 128
57. §49. Connections between Chords with Different Dissonant Characteristics 130
58. §50. Boundaries between Characteristic-types 134
59. Chapter IIIb – Triadic Combinations
60. §51. The System of Triadic Combinations 137
61. §52. True and Partial Combinations; Combination Categories 138
62. §53. Basic Triads (Harmonies I) 139
63. §54. Combination Harmonies II 141
64. §55. Partial Combinations with Two Components 146
65. §56. Triadic Combinations III 148
66. §57. The Triadic Combinations IV 150
67. §58. Classification of Chords into Combination Categories 152
68. §59. Representation of Triadic Combinations 153
69. §60. The Significance of the Combination System 155
70. Chapter IV – Disposition of Chords
71. §61. The Concept of Disposition 157
72. §62. The Form, Position, and Inner Disposition of a Chord; Pitch Doublings 158
73. §63. Evaluating the Sound of Dispositions 159
74. §64. Disposition of Basic Triads 160
75. §65. Evaluating the Sound of Inversions and their Dispositions 163
76. §66. Disposition of Consonant Components in Dissonant Chords 164
77. §67. Disposition of Dissonant Intervals 165
78. §68. Disposition of Triadic Combinations 169
79. §69. Disposition of Harmonies II 174
80. §70. Disposition of Partial Combinations with Two Components; Doubled Pitches in Intervals 1 179
81. §71. Disposition of Triadic Combinations III 183
82. §72. Disposition of the Triadic Combination IV; Softening of Semitone Clashes of Intervals 1 through Disposition 185
83. §73. Disposition of Chords in a Harmonic Progression 191
84. §74. Disposition of Chords and Compositional Practice 194
85. Chapter V – Expression of Chords
86. §75. Real and Imaginary Pitches 195
87. §76. Appearance and Cancellation of an Imaginary Pitch 196
88. §77. The Counter-canceling Pitch 198
89. §78. The Dying Away of a Harmonic Imaginary Pitch 199
90. §79. Compositional Acceleration of the Dying Away of a Harmonic Imaginary Pitch 201
91. §80. Harmonic Significance of Imaginary Pitches 202
92. §81. Chords Expressed by Real Pitches 204
93. §82. Chords Expressed by Imaginary Pitches 207
94. §83. Composite Expression of Chords in a Single Voice 208
95. §84. Composite Expression of Chords in Polyphony 211
96. §85. Non-harmonic Tones in Chords of Composite Expression 214
97. §86. Time Boundaries between Chords of Composite Expression 216
98. §87. Tonal Imaginary Pitches 221
99. §88. Incomplete Expression of Harmonies 224
100. Chapter VIa – Harmonic Motion: Concepts and Principles
101. §89. Possibilities of Motion in Music 227
102. §90. Possibilities of Harmonic Motion 228
103. §91. Links in a Chord Succession 229
104. §92. Partial Harmonic Motion 231
105. §93. Fundamental Harmonic Motion 235
106. §94. Intervals in Fundamental Harmonic Motion; Imaginary Links 236
107. §95. Real Links in Fundamental Harmonic Motion 238
108. §96. Adjacent Partial and Fundamental Harmonic Motions 241
109. §97. Higher-ranked Harmonic Motion or Tonal Motion 242
110. §98. The Significance of Cadential Chord Successions 244
111. §99. The Principle of the Pure Tonic 245
112. §100. Application of the Principle of the Pure Tonic in the Tempered Chromatic System 247
113. §101. Application of the Principle of the Pure Tonic in the Diatonic System 249
114. §102. The Principle of the Leading Tone 250
115. Chapter VIb – Harmonic Motion: Functions and their Combinations
116. §103. The Functional Principle 251
117. §104. Establishing the Tonic 252
118. §105. Types of Representative Pre-tonic Harmonies 253
119. §106. Establishing Possible Representative Pre-tonic Harmonies 254
120. §107. The Classical Functional System of Three Members 256
121. §108. Šín’s Functional System of Five Members 257
122. §109. Stabilization of Relations between Harmonies of the Functional System; the Minor Dominant 259
123. §110. Consonant Combinations of Functions (Interfunctions) 260
124. §111. Dissonant Combinations of Functions 264
125. §112. Functional Ambiguity of Dissonant Combinations 267
126. §113. Evaluating Functional Components According to their Tonal Significance, Disposition, and Representation 274
127. Chapter VIc – Harmonic Motion: Function in Harmonic Progression
128. §114. Harmonic Motion between Functions 277
129. §115. The Functional Aspect of Chords in a Chord Succession 281
130. §116. Unitonal, Bitonal, and Polytonal Combinations 284
131. §117. Local Tonics⁹⁰ and Applied Functions 286
132. §118. Alteration⁹² of Functions 289
133. §119. Modulation 292
134. §120. Loosening Tonally Functional Relations 295
135. §121. Non-Functional (Atonal) Music 299
136. §122. Compositional Order and General Compositional Styling⁹⁶ 305
137. §123. Horizontal Thinking. Voice-leading 309
138. Chapter VII – Problems
139. §124. The Concept of Modern Harmony 315
140. §125. Universal and Artistic Laws 316
141. §126. The Evolution of Compositional Technique 317
142. §127. The Natural Foundation of Music Theory 319
143. §128. The Significance of Experience 321
144. §129. The Search for Law 324
145. §130. Static and Kinetic Conceptions of Harmony 326
146. Chapter VIII – Compositional Practice
147. §131. Composition and Theory 333
148. §132. Modern Melody 334
149. §133. Practical Studies of Chord-types 336
150. §134. Practical Studies of Characteristic-types and Harmonies 339
151. §135. Styling Studies on a Given Harmonic Basis 342
152. §136. Harmonizing a Melody 345
153. §137. Employing Textural Resources Economically 349
154. §138. Resolving Dissonant Chords 351
155. §139. Seeking a Suitable Pre-tonic Combination 355
156. §140. Functional Chord Successions 356
157. §141. Functional Variations in a Chord Progression 359
158. §142. Free Composition 362
159. Chapter IX – Analytical Practice
160. §143. A Method of Harmonic Analysis 369
161. §144. Examining and Evaluating Real Chordal Cross- sections; Seeking New Chord Formations 370
162. §145. Determining Chords from Real and Imaginary Pitches; Rhythmic and Metric Distribution of Chords in a Composition; Transient Chords 371
163. §146. Chordal and Harmonic Character of a Composition; Character of Dispositions 374
164. §147. Examining Transient Chords 377
165. §148. Diatonic Passages; Chromatic Progressions 381
166. §149. Determining the Compositional Order; Evaluating Melodic Lines 383
167. §152. The Formation and Extinction of a Sense of the Tonic 391
168. §153. The Tonally Functional Plan of a Composition; Overall Functional Character 394
169. Tables and Overviews
170. I. Comprehensive Survey of Chord-types 397
171. II. System of Characteristic-types 410
172. III. Characteristic Maxima by Chord-class 412
173. IV. Characteristic Nuclei by Chord-class 414
174. V. Boundaries between Characteristic-types 415
175. VI. Symbols and abbreviations 418
176. Bibliography 423
177. Sources of Examples from Contemporary Music 427
178. Zusammenfassung 429
179. Additional Notes to Some Phenomena of Harmonic and Tonal Thinking 453
180. Order, System, Structure, Function and Mutual Interplay of Theory and Practice 461
181. Conclusion 497
182. References 499
183. Subject Index 503
184. Name Index 507