Musical Techniques Frequencies and Harmonics

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 Degrees  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,  F, 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