<p>Preface xiii</p> <p>Introduction xv</p> <p><b>Part 1. Laying the Foundations 1</b></p> <p>Introduction to Part 1 3</p> <p><b>Chapter 1. Sounds, Creation and Generation of Notes 5</b></p> <p>1.1. Physical and physiological notions of a sound 5</p> <p>1.1.1. Auditory apparatus 5</p> <p>1.1.2. Physical concepts of a sound 7</p> <p>1.1.3. Further information on acoustics and acoustic physiology 8</p> <p>1.1.4. Idea of minimum audible gap/interval between two frequencies 16</p> <p>1.1.5. Why have we told this whole story, then? 22</p> <p><b>Chapter 2. Generation of Notes 23</b></p> <p>2.1. Concept of octave 23</p> <p>2.1.1. Choice of inner division of an octave 24</p> <p>2.2. Modes of generation/creation/construction of notes 25</p> <p>2.3. Physical/natural generation of notes 26</p> <p>2.3.1. Harmonics 26</p> <p>2.3.2. Fractional harmonics 26</p> <p>2.3.3. Initial conclusions 29</p> <p>2.3.4. Order of appearance and initial naming of the notes 29</p> <p>2.3.5. A few important additional remarks 32</p> <p>2.4. Generation of perfect fifth notes 33</p> <p>2.4.1. Generation with ascending fifths 33</p> <p>2.4.2. Generation with descending fifths 37</p> <p>2.4.3. Conclusions on fifth-based constructions of notes 39</p> <p>2.5. Important remarks on “physical”/”fifths” generation 40</p> <p>2.6. Generation of tempered notes 40</p> <p>2.6.1. Notion of the ear’s logarithmic sensitivity 41</p> <p>2.6.2. Examples of electronic generation of tempered notes 43</p> <p>2.6.3. Relative gaps between tempered and electronic notes 43</p> <p>2.7. In summary and in conclusion on generation of notes 46</p> <p>2.8. Comparison of gaps between all the notes thus created 49</p> <p>2.8.1. Note on pitch-perfect hearing… or is it? 53</p> <p><b>Chapter 3. Recreation: Frequencies, Sounds and Timbres 55</b></p> <p>3.1. Differences between a pure frequency and the timbre of an instrument 55</p> <p>3.2. Timbre of an instrument, harmonics and harmony 58</p> <p>3.2.1. Relations between timbres and spectra 60</p> <p>3.3. Recomposition of a signal from sine waves 63</p> <p>3.3.1. Subtractive synthesis 63</p> <p>3.3.2. Additive synthesis 63</p> <p>3.3.3. Recreation: harmonic drawbars 64</p> <p><b>Chapter 4. Intervals 69</b></p> <p>4.1. Gap/space/distance/interval between two notes 69</p> <p>4.2. Measuring the intervals 70</p> <p>4.2.1. The savart 70</p> <p>4.2.2. The cent 71</p> <p>4.3. Intervals between notes 73</p> <p>4.3.1. Second interval: major tone and minor tone 74</p> <p>4.3.2. Major third and minor third interval 75</p> <p>4.4. Overview of the main intervals encountered 75</p> <p>4.5. Quality of an interval 76</p> <p>4.5.1. Instrumentation 76</p> <p>4.5.2. Tempo 76</p> <p>4.5.3. Dynamics of amplitudes 76</p> <p>4.5.4. Register 76</p> <p>4.6. Reversal of an interval 77</p> <p>4.7. Commas…ss 77</p> <p>4.7.1. Pythagorean comma 78</p> <p>4.7.2. Syntonic comma 79</p> <p>4.7.3. A few remarks about commas 80</p> <p>4.7.4. Enharmonic comma 80</p> <p>4.7.5. Other theoretical commas and a few additional elements 80</p> <p>4.7.6. Final remarks 82</p> <p>4.7.7. In summary, commas and C° 83</p> <p><b>Chapter 5. Harshness, Consonance and Dissonance 85</b></p> <p>5.1. Consonance and dissonance 85</p> <p>5.1.1. Consonant interval 85</p> <p>5.1.2. Dissonant interval 86</p> <p>5.2. Harshness of intervals 86</p> <p>5.3. Consonance and dissonance, tension and resolution of an interval 87</p> <p>5.3.1. Consonance of an interval 87</p> <p>5.3.2. Dissonance of an interval 89</p> <p>5.3.3. Savarts, ΔF, consonance, pleasing values or beating of frequencies 90</p> <p><b>Part 2. Scales and Modes 93</b></p> <p>Introduction to Part 2 95</p> <p><b>Chapter 6. Scales 97</b></p> <p>6.1. Introduction to the construction of scales 97</p> <p>6.2. Natural or physical scale 98</p> <p>6.2.1. Harmonics 98</p> <p>6.3. Pythagorean or physiological diatonic. scale 100</p> <p>6.3.1. Principle 100</p> <p>6.3.2. The why and wherefore of the 7-note scale 101</p> <p>6.3.3. Names of the notes in the Pythagorean scale 104</p> <p>6.3.4. The series “tone-tone-semi/ tone-tone-tone-tone-semi/tone”? 105</p> <p>6.3.5. A few comments 106</p> <p>6.3.6. Uses of the Pythagorean scale, and cases where it cannot be used 107</p> <p>6.4. Major diatonic scale 108</p> <p>6.4.1. Intervals present in a major scale 108</p> <p>6.5. The other major scales 109</p> <p>6.6. Scales and chromatic scales 109</p> <p>6.6.1. Chromatic scale 110</p> <p>6.6.2. Chromatic scales 110</p> <p>6.7. Tempered scale 114</p> <p>6.7.1. Principle of the tempered scale 114</p> <p>6.7.2. Comparisons between physical, Pythagorean and tempered scales 115</p> <p>6.8. Other scales 117</p> <p>6.9. Pentatonic scale 117</p> <p>6.9.1. A little history, which will prove important later on 117</p> <p>6.9.2. Theory 118</p> <p>6.9.3. Reality 120</p> <p>6.9.4. Relations between major and minor pentatonic scales 123</p> <p>6.9.5. Pentatonic scale and system 124</p> <p>6.10. “Blues” scale 125</p> <p>6.11. Altered scale and jazz scale 126</p> <p>6.12 “Tone-tone” (whole-tone) scale 127</p> <p>6.13. Diminished scale or “semitone/tone” scale 128</p> <p>6.14. In summary 128</p> <p>6.15. Technical problems of scales 129</p> <p>6.15.1. Scale and transposition 130</p> <p>6.15.2. Alterations 132</p> <p><b>Chapter 7. Scales, Degrees and Modes 135</b></p> <p>7.1. Scales and degrees 135</p> <p>7.2. Degree of a note in the scale 136</p> <p>7.3. Interesting functions/roles of a few degrees of the scale 136</p> <p>7.4. Modes 137</p> <p>7.4.1. The numerous modes of a major scale 138</p> <p>7.4.2. The original minor modes and their derivatives 142</p> <p>7.4.3. A few normal modes 143</p> <p><b>Part 3. Introduction to the Concept of Harmony: Chords 145</b></p> <p>Introduction to Part 3 147</p> <p><b>Chapter 8. Harmony 149</b></p> <p>8.1. Relations between frequencies 149</p> <p>8.2. How are we to define the concept of harmony? 150</p> <p><b>Chapter 9. Chords 151</b></p> <p>9.1. The different notations 151</p> <p>9.1.1. Convention of notations for notes 151</p> <p>9.2. Chords 152</p> <p>9.3. Diatonic chords 153</p> <p>9.3.1. Diatonic chords with 3 notes: “triads” 154</p> <p>9.3.2. 4-note diatonic chords known as “seventh” chords” 155</p> <p>9.4. “Fourth-based” chords 157</p> <p>9.4.1. Convention of notations of the chords 157</p> <p>9.5. Chord notations 158</p> <p>9.5.1. In the major scale 159</p> <p>9.5.2. In minor scales 161</p> <p>9.5.3. Scales and chords 166</p> <p>9.5.4. List of common chords 169</p> <p>9.5.5. Table of frequently used chords 171</p> <p>9.6. What do these chords sound like? 173</p> <p>9.6.1. In statics 173</p> <p>9.6.2. In dynamics 173</p> <p>9.7. Temporal relations between chords 174</p> <p>9.8. Melody line 175</p> <p>9.9. Peculiarities and characteristics of the content of the chord 175</p> <p>9.10. Relations between melodies and chords 175</p> <p>9.11. The product of the extremes is equal to the product of the means 176</p> <p><b>Part 4. Harmonic Progressions 179</b></p> <p>Introduction to Part 4 181</p> <p><b>Chapter 10. Some Harmonic Rules 183</b></p> <p>10.1. Definition of a chord and the idea of the color of a chord 183</p> <p>10.1.1. Notations used 183</p> <p>10.1.2. Equivalent or harmonious chords 184</p> <p>10.2. A few harmonic rules 184</p> <p>10.2.1. The eight fundamental syntactic rules 185</p> <p>10.2.2. Rules of assembly 186</p> <p>10.2.3. Next steps 187</p> <p>10.2.4. Descending chromatism rule 188</p> <p>10.2.5. Justifications of the eight harmonic rules by descending chromatism 190</p> <p>10.3. Conclusions on harmonic rules 193</p> <p><b>Chapter 11. Examples of Harmonic Progressions 195</b></p> <p>11.1. Harmonic progressions by descending chromatism 195</p> <p>11.1.1. Example 1 195</p> <p>11.1.2. Example 2 196</p> <p>11.1.3. Example 3 197</p> <p>11.2. Codes employed for writing progressions 198</p> <p>11.2.1. Key changes in a progression 199</p> <p>11.2.2. Detailed example of decoding of progressions 202</p> <p>11.3. Hundreds, thousands of substitution progressions… 204</p> <p>11.3.1. Major scale, the best of 204</p> <p>11.3.2. List of harmonious progressions 206</p> <p>11.4. Chromatism in “standards” 213</p> <p>11.5. Families of descending chromatisms 214</p> <p>11.5.1. Family: “1 chromatism at a time” 215</p> <p>11.5.2. Family: “up to two descending chromatisms at once” 217</p> <p>11.5.3. Family: “up to 3 descending chromatisms at once” 220</p> <p>11.5.4. Family: “up to 4 ascending and descending chromatisms at once” 220</p> <p>11.5.5. Conclusions 225</p> <p><b>Chapter 12. Examples of Harmonizations and Compositions 227</b></p> <p>12.1. General points 227</p> <p>12.2. Questions of keys 228</p> <p>12.3. Example of reharmonization 228</p> <p>12.3.1. Blue Moon (by Lorenz Hart and Richard Rodgers) 229</p> <p>12.3.2. Summertime (by G. Gershwin) 239</p> <p>12.3.3. Sweet Georgia Brown (by Bernie, Pinkard and Casey) 243</p> <p>12.4. Example of harmonization 247</p> <p>12.4.1. Madagascar (by Serge Sibony) 247</p> <p>12.5. Conclusion 252</p> <p>Conclusion 253</p> <p>Appendix 255</p> <p>Glossary 273</p> <p>Bibliography 279</p> <p>Index 281</p>