Musical Techniques

This book is built to start from elementary and fundamental bases to the first degrees of harmony. It provides many theoretical and technical bases of music, presenting in detail relations between physics and music (harmonics, frequency and time spectrum, dissonance, etc.), physiological relations with human body and education.

Preface xiii

Introduction xv

Part 1. Laying the Foundations 1

Introduction to Part 1 3

Chapter 1. Sounds, Creation and Generation of Notes 5

1.1. Physical and physiological notions of a sound 5

1.1.1. Auditory apparatus 5

1.1.2. Physical concepts of a sound 7

1.1.3. Further information on acoustics and acoustic physiology 8

1.1.4. Idea of minimum audible gap/interval between two frequencies 16

1.1.5. Why have we told this whole story, then? 22

Chapter 2. Generation of Notes 23

2.1. Concept of octave 23

2.1.1. Choice of inner division of an octave 24

2.2. Modes of generation/creation/construction of notes 25

2.3. Physical/natural generation of notes 26

2.3.1. Harmonics 26

2.3.2. Fractional harmonics 26

2.3.3. Initial conclusions 29

2.3.4. Order of appearance and initial naming of the notes 29

2.3.5. A few important additional remarks 32

2.4. Generation of perfect fifth notes 33

2.4.1. Generation with ascending fifths 33

2.4.2. Generation with descending fifths 37

2.4.3. Conclusions on fifth-based constructions of notes 39

2.5. Important remarks on “physical”/”fifths” generation 40

2.6. Generation of tempered notes 40

2.6.1. Notion of the ear’s logarithmic sensitivity 41

2.6.2. Examples of electronic generation of tempered notes 43

2.6.3. Relative gaps between tempered and electronic notes 43

2.7. In summary and in conclusion on generation of notes 46

2.8. Comparison of gaps between all the notes thus created 49

2.8.1. Note on pitch-perfect hearing… or is it? 53

Chapter 3. Recreation: Frequencies, Sounds and Timbres 55

3.1. Differences between a pure frequency and the timbre of an instrument 55

3.2. Timbre of an instrument, harmonics and harmony 58

3.2.1. Relations between timbres and spectra 60

3.3. Recomposition of a signal from sine waves 63

3.3.1. Subtractive synthesis 63

3.3.2. Additive synthesis 63

3.3.3. Recreation: harmonic drawbars 64

Chapter 4. Intervals 69

4.1. Gap/space/distance/interval between two notes 69

4.2. Measuring the intervals 70

4.2.1. The savart 70

4.2.2. The cent 71

4.3. Intervals between notes 73

4.3.1. Second interval: major tone and minor tone 74

4.3.2. Major third and minor third interval 75

4.4. Overview of the main intervals encountered 75

4.5. Quality of an interval 76

4.5.1. Instrumentation 76

4.5.2. Tempo 76

4.5.3. Dynamics of amplitudes 76

4.5.4. Register 76

4.6. Reversal of an interval 77

4.7. Commas…ss 77

4.7.1. Pythagorean comma 78

4.7.2. Syntonic comma 79

4.7.3. A few remarks about commas 80

4.7.4. Enharmonic comma 80

4.7.5. Other theoretical commas and a few additional elements 80

4.7.6. Final remarks 82

4.7.7. In summary, commas and C° 83

Chapter 5. Harshness, Consonance and Dissonance 85

5.1. Consonance and dissonance 85

5.1.1. Consonant interval 85

5.1.2. Dissonant interval 86

5.2. Harshness of intervals 86

5.3. Consonance and dissonance, tension and resolution of an interval 87

5.3.1. Consonance of an interval 87

5.3.2. Dissonance of an interval 89

5.3.3. Savarts, ΔF, consonance, pleasing values or beating of frequencies 90

Part 2. Scales and Modes 93

Introduction to Part 2 95

Chapter 6. Scales 97

6.1. Introduction to the construction of scales 97

6.2. Natural or physical scale 98

6.2.1. Harmonics 98

6.3. Pythagorean or physiological diatonic. scale 100

6.3.1. Principle 100

6.3.2. The why and wherefore of the 7-note scale 101

6.3.3. Names of the notes in the Pythagorean scale 104

6.3.4. The series “tone-tone-semi/ tone-tone-tone-tone-semi/tone”? 105

6.3.5. A few comments 106

6.3.6. Uses of the Pythagorean scale, and cases where it cannot be used 107

6.4. Major diatonic scale 108

6.4.1. Intervals present in a major scale 108

6.5. The other major scales 109

6.6. Scales and chromatic scales 109

6.6.1. Chromatic scale 110

6.6.2. Chromatic scales 110

6.7. Tempered scale 114

6.7.1. Principle of the tempered scale 114

6.7.2. Comparisons between physical, Pythagorean and tempered scales 115

6.8. Other scales 117

6.9. Pentatonic scale 117

6.9.1. A little history, which will prove important later on 117

6.9.2. Theory 118

6.9.3. Reality 120

6.9.4. Relations between major and minor pentatonic scales 123

6.9.5. Pentatonic scale and system 124

6.10. “Blues” scale 125

6.11. Altered scale and jazz scale 126

6.12 “Tone-tone” (whole-tone) scale 127

6.13. Diminished scale or “semitone/tone” scale 128

6.14. In summary 128

6.15. Technical problems of scales 129

6.15.1. Scale and transposition 130

6.15.2. Alterations 132

Chapter 7. Scales, Degrees and Modes 135

7.1. Scales and degrees 135

7.2. Degree of a note in the scale 136

7.3. Interesting functions/roles of a few degrees of the scale 136

7.4. Modes 137

7.4.1. The numerous modes of a major scale 138

7.4.2. The original minor modes and their derivatives 142

7.4.3. A few normal modes 143

Part 3. Introduction to the Concept of Harmony: Chords 145

Introduction to Part 3 147

Chapter 8. Harmony 149

8.1. Relations between frequencies 149

8.2. How are we to define the concept of harmony? 150

Chapter 9. Chords 151

9.1. The different notations 151

9.1.1. Convention of notations for notes 151

9.2. Chords 152

9.3. Diatonic chords 153

9.3.1. Diatonic chords with 3 notes: “triads” 154

9.3.2. 4-note diatonic chords known as “seventh” chords” 155

9.4. “Fourth-based” chords 157

9.4.1. Convention of notations of the chords 157

9.5. Chord notations 158

9.5.1. In the major scale 159

9.5.2. In minor scales 161

9.5.3. Scales and chords 166

9.5.4. List of common chords 169

9.5.5. Table of frequently used chords 171

9.6. What do these chords sound like? 173

9.6.1. In statics 173

9.6.2. In dynamics 173

9.7. Temporal relations between chords 174

9.8. Melody line 175

9.9. Peculiarities and characteristics of the content of the chord 175

9.10. Relations between melodies and chords 175

9.11. The product of the extremes is equal to the product of the means 176

Part 4. Harmonic Progressions 179

Introduction to Part 4 181

Chapter 10. Some Harmonic Rules 183

10.1. Definition of a chord and the idea of the color of a chord 183

10.1.1. Notations used 183

10.1.2. Equivalent or harmonious chords 184

10.2. A few harmonic rules 184

10.2.1. The eight fundamental syntactic rules 185

10.2.2. Rules of assembly 186

10.2.3. Next steps 187

10.2.4. Descending chromatism rule 188

10.2.5. Justifications of the eight harmonic rules by descending chromatism 190

10.3. Conclusions on harmonic rules 193

Chapter 11. Examples of Harmonic Progressions 195

11.1. Harmonic progressions by descending chromatism 195

11.1.1. Example 1 195

11.1.2. Example 2 196

11.1.3. Example 3 197

11.2. Codes employed for writing progressions 198

11.2.1. Key changes in a progression 199

11.2.2. Detailed example of decoding of progressions 202

11.3. Hundreds, thousands of substitution progressions… 204

11.3.1. Major scale, the best of 204

11.3.2. List of harmonious progressions 206

11.4. Chromatism in “standards” 213

11.5. Families of descending chromatisms 214

11.5.1. Family: “1 chromatism at a time” 215

11.5.2. Family: “up to two descending chromatisms at once” 217

11.5.3. Family: “up to 3 descending chromatisms at once” 220

11.5.4. Family: “up to 4 ascending and descending chromatisms at once” 220

11.5.5. Conclusions 225

Chapter 12. Examples of Harmonizations and Compositions 227

12.1. General points 227

12.2. Questions of keys 228

12.3. Example of reharmonization 228

12.3.1. Blue Moon (by Lorenz Hart and Richard Rodgers) 229

12.3.2. Summertime (by G. Gershwin) 239

12.3.3. Sweet Georgia Brown (by Bernie, Pinkard and Casey) 243

12.4. Example of harmonization 247

12.4.1. Madagascar (by Serge Sibony) 247

12.5. Conclusion 252

Conclusion 253

Appendix 255

Glossary 273

Bibliography 279

Index 281

Dominque Paret is Engineer ESIEE / DEA of physics and was responsible for the technical support of an international leader of electronic components for many years. Professor in numerous engineering schools in France and abroad, he runs a company of consultants/technical experts. He is also a seasoned jazz organist.

Serge Sibony is Engineer ESTP, head of products systems construction, research and development director and Professor in several schools of engineers. A jazz pianist and the author of a series of works on musical composition, he is also a creator and independent developer of sharewares related to music.