Musical Techniques

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.

• Preface  xiiiIntroduction xvPart 1. Laying the Foundations 1Introduction to Part 1 3Chapter 1. Sounds, Creation and Generation of Notes  51.1. Physical and physiological notions of a sound 51.1.1. Auditory apparatus  51.1.2. Physical concepts of a sound 71.1.3. Further information on acoustics and acoustic physiology 81.1.4. Idea of minimum audible gap/interval between two frequencies  161.1.5. Why have we told this whole story, then? 22Chapter 2. Generation of Notes 232.1. Concept of octave 232.1.1. Choice of inner division of an octave  242.2. Modes of generation/creation/construction of notes  252.3. Physical/natural generation of notes 262.3.1. Harmonics 262.3.2. Fractional harmonics 262.3.3. Initial conclusions 292.3.4. Order of appearance and initial naming of the notes 292.3.5. A few important additional remarks 322.4. Generation of perfect fifth notes 332.4.1. Generation with ascending fifths  332.4.2. Generation with descending fifths  372.4.3. Conclusions on fifth-based constructions of notes  392.5. Important remarks on “physical”/”fifths” generation  402.6. Generation of tempered notes 402.6.1. Notion of the ear’s logarithmic sensitivity 412.6.2. Examples of electronic generation of tempered notes  432.6.3. Relative gaps between tempered and electronic notes 432.7. In summary and in conclusion on generation of notes 462.8. Comparison of gaps between all the notes thus created  492.8.1. Note on pitch-perfect hearing… or is it?  53Chapter 3. Recreation: Frequencies, Sounds and Timbres 553.1. Differences between a pure frequency and the timbre of an instrument  553.2. Timbre of an instrument, harmonics and harmony 583.2.1. Relations between timbres and spectra 603.3. Recomposition of a signal from sine waves 633.3.1. Subtractive synthesis 633.3.2. Additive synthesis  633.3.3. Recreation: harmonic drawbars 64Chapter 4. Intervals  694.1. Gap/space/distance/interval between two notes 694.2. Measuring the intervals  704.2.1. The savart 704.2.2. The cent  714.3. Intervals between notes  734.3.1. Second interval: major tone and minor tone  744.3.2. Major third and minor third interval 754.4. Overview of the main intervals encountered  754.5. Quality of an interval 764.5.1. Instrumentation  764.5.2. Tempo 764.5.3. Dynamics of amplitudes 764.5.4. Register  764.6. Reversal of an interval 774.7. Commas…ss  774.7.1. Pythagorean comma 784.7.2. Syntonic comma 794.7.3. A few remarks about commas  804.7.4. Enharmonic comma  804.7.5. Other theoretical commas and a few additional elements 804.7.6. Final remarks 824.7.7. In summary, commas and C°  83Chapter 5. Harshness, Consonance and Dissonance  855.1. Consonance and dissonance 855.1.1. Consonant interval  855.1.2. Dissonant interval 865.2. Harshness of intervals 865.3. Consonance and dissonance, tension and resolution of an interval  875.3.1. Consonance of an interval  875.3.2. Dissonance of an interval 895.3.3. Savarts, ΔF, consonance, pleasing values or beating of frequencies  90Part 2. Scales and Modes 93Introduction to Part 2 95Chapter 6. Scales  976.1. Introduction to the construction of scales  976.2. Natural or physical scale 986.2.1. Harmonics 986.3. Pythagorean or physiological diatonic. scale  1006.3.1. Principle  1006.3.2. The why and wherefore of the 7-note scale 1016.3.3. Names of the notes in the Pythagorean scale  1046.3.4. The series “tone-tone-semi/ tone-tone-tone-tone-semi/tone”?  1056.3.5. A few comments 1066.3.6. Uses of the Pythagorean scale, and cases where it cannot be used  1076.4. Major diatonic scale  1086.4.1. Intervals present in a major scale  1086.5. The other major scales 1096.6. Scales and chromatic scales  1096.6.1. Chromatic scale  1106.6.2. Chromatic scales 1106.7. Tempered scale  1146.7.1. Principle of the tempered scale 1146.7.2. Comparisons between physical, Pythagorean and tempered scales  1156.8. Other scales  1176.9. Pentatonic scale  1176.9.1. A little history, which will prove important later on  1176.9.2. Theory 1186.9.3. Reality 1206.9.4. Relations between major and minor pentatonic scales 1236.9.5. Pentatonic scale and system 1246.10. “Blues” scale 1256.11. Altered scale and jazz scale 1266.12 “Tone-tone” (whole-tone) scale 1276.13. Diminished scale or “semitone/tone” scale 1286.14. In summary  1286.15. Technical problems of scales  1296.15.1. Scale and transposition 1306.15.2. Alterations  132Chapter 7. Scales, Degrees and Modes  1357.1. Scales and degrees 1357.2. Degree of a note in the scale 1367.3. Interesting functions/roles of a few degrees of the scale  1367.4. Modes  1377.4.1. The numerous modes of a major scale 1387.4.2. The original minor modes and their derivatives  1427.4.3. A few normal modes 143Part 3. Introduction to the Concept of Harmony: Chords  145Introduction to Part 3 147Chapter 8. Harmony  1498.1. Relations between frequencies  1498.2. How are we to define the concept of harmony? 150Chapter 9. Chords 1519.1. The different notations  1519.1.1. Convention of notations for notes  1519.2. Chords 1529.3. Diatonic chords  1539.3.1. Diatonic chords with 3 notes: “triads” 1549.3.2. 4-note diatonic chords known as “seventh” chords”  1559.4. “Fourth-based” chords 1579.4.1. Convention of notations of the chords 1579.5. Chord notations  1589.5.1. In the major scale 1599.5.2. In minor scales  1619.5.3. Scales and chords 1669.5.4. List of common chords  1699.5.5. Table of frequently used chords 1719.6. What do these chords sound like? 1739.6.1. In statics  1739.6.2. In dynamics  1739.7. Temporal relations between chords 1749.8. Melody line 1759.9. Peculiarities and characteristics of the content of the chord 1759.10. Relations between melodies and chords  1759.11. The product of the extremes is equal to the product of the means 176Part 4. Harmonic Progressions 179Introduction to Part 4 181Chapter 10. Some Harmonic Rules 18310.1. Definition of a chord and the idea of the color of a chord 18310.1.1. Notations used  18310.1.2. Equivalent or harmonious chords 18410.2. A few harmonic rules  18410.2.1. The eight fundamental syntactic rules 18510.2.2. Rules of assembly  18610.2.3. Next steps  18710.2.4. Descending chromatism rule  18810.2.5. Justifications of the eight harmonic rules by descending chromatism  19010.3. Conclusions on harmonic rules 193Chapter 11. Examples of Harmonic Progressions 19511.1. Harmonic progressions by descending chromatism  19511.1.1. Example 1  19511.1.2. Example 2  19611.1.3. Example 3  19711.2. Codes employed for writing progressions 19811.2.1. Key changes in a progression  19911.2.2. Detailed example of decoding of progressions  20211.3. Hundreds, thousands of substitution progressions… 20411.3.1. Major scale, the best of 20411.3.2. List of harmonious progressions  20611.4. Chromatism in “standards” 21311.5. Families of descending chromatisms  21411.5.1. Family: “1 chromatism at a time” 21511.5.2. Family: “up to two descending chromatisms at once”  21711.5.3. Family: “up to 3 descending chromatisms at once” 22011.5.4. Family: “up to 4 ascending and descending chromatisms at once” 22011.5.5. Conclusions 225Chapter 12. Examples of Harmonizations and Compositions 22712.1. General points  22712.2. Questions of keys 22812.3. Example of reharmonization  22812.3.1. Blue Moon (by Lorenz Hart and Richard Rodgers)  22912.3.2. Summertime (by G. Gershwin) 23912.3.3. Sweet Georgia Brown (by Bernie, Pinkard and Casey) 24312.4. Example of harmonization  24712.4.1. Madagascar (by Serge Sibony) 24712.5. Conclusion  252Conclusion 253Appendix 255Glossary 273Bibliography 279Index 281