Ján Haluška: Seraching harmony (subtitle: Credo of  a mathematician about music and a little bit also about philosophy), Veda - Pulishing house of the Slovak Academy of Sciences, Bratislava 2006, pp. 295, ISBN 80-224-0918-9, ca 120 color illustrations, 21 tables

 Contents

 Foreword

 Part I  From nature to tones

 1 Where to search harmony?

1.1 Mutual reflexion of spirit and world . . . . . . . . . . . . . . . . . 15

1.2 Excluding of tone system from nature . . . . . . . . . . . . 20

1.3 Reverse direction:  from idea to tone system . . . . . . . . . . . 24

1.4 Music is a relation of one tone to other tones . . . . . . . . . 27

1.5 Excellence of Tone systems . . . . . . . . . . . . . . . 29

1.6 What about any definition of Tone system?  . . . . . . . . . . . . . . . . . . 30

1.7 Tone system theory . . . . . . . . . . . . . . . . . . . 31

2 Extension of human skills

2.1 Tools and natural human abilities . . . . . . . . . . . . . 35

2.2 Invention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.3 About problems of classification . . . . . . . . . . . . . . . . . . . 42

2.4 Material a shapes of instruments. . . . . . . . . . . . . . . . . . . 44

2.5 Aulos and lyra . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3 Ab ovo – interval

3.1 Monochord . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.2 Division of string . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.3 Table of Pythagoras . . . . . . . . . . . . . . . . . . . . . . 77

 4 Measurements with physical equipments

 4.1 Sound waves . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.2 Resonance  . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

4.3 Sequences of harmonics . . . . . . . . . . . . . . . . . . . . . . 87

5 Human psychics and tones

5.1 Pitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

5.2 Loudness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.3 Timbre . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

5.4 Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

 6 Space and auditory  as  integral parts of music

 6.1 What happens in ear . . . . . . . . . . . . . . . . . . . . . . . . 111

6.2 Psychological  research. . . . . . . . . . . . . . . . . . . . . 116

6.3 Acoustical measurements of music halls . . . . . . . . . . . . . . . . . . . . . 119

6.4 A historical overview . . . . . . . . . . . . . . . . . . . . . . . 135

 Part II  Generating tones

 7 Human voice

 7.1 Biological research . . . . . . . . . . . . . . . . . . . . . . . 143

7.2 Soprano, alt, tenor, bas . . . . . . . . . . . . . . . . . . . . . 145

7.3 Functioning of glottis . . . . . . . . . . . . . . . . 148

7.4 Tone timbre of human voice and its relation to language . . . . . . . . . 150

7.5 Some aesthetical aspects . . . . . . . . . . . . . . . . . . . 152

 8 String instruments

 8.1    String instruments without  keys . . . . . . . . . . . . . . 155

8.1.1 The complex production of tone . . . . . . . . . . . . . . . . . 155

8.1.2  Mersenn Laws . . . . . . . . . . . . . . . . . . . 156

8.1.3 Fiddle and loudness . . . . . . . . . . . . . . . 159

8.1.4  Masters of Cremona.Timbre depends on … . . . . 160

8.2    Key string instruments . . . . . . . . . . . . . . . . . . 163

8.2.1 Hammer, tangenta and plectrum . . . . . . . . . . . . 163

8.2.2 Fixed tuning is typical . . . . . . . . . . . . . . . . 167

8.2.3 Illusion of  clavier crescendo, terraced dynamics . . 168

8.2.4 Using of sympathetic vibrations . . . . . . . . . . . 169

8.2.5 Any clavier style? . . . . . . . . . . . . . . . . . . . . . . 171

 9 Wind instruments and organ

 9.1 Wind instruments . . . . . . . . . . . . . . . . . . . . . . . . 175

9.1.1 Relation to string instruments . . . . . . . . . . . . . 175

9.1.2 Labial, lingual and edge instruments . . . . . . . . . 177

9.1.3 Combination of harmonics with the length of the air stlpca 181

9.1.4 Elastic  resistence of the iwind stream . . . . . 187

9.1.5 Is timbre a business of instrument produsers? . . . . . . . . 189

9.2 Organ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

9.2.1 The set of pipes and the double system of ventils . . . . . . . 191

9.2.2 Nomenklature of pipes with respect to the lenght . . . . . . . . . . . 195

9.2.3 Wind press, jealuzions . . . . . . . . . . . . . . . . . . 196

9.2.4 Mensure, various types of pipes . . . . . . . . . . . . . . 197

 10 Percussions

 10.1 Arbitrary forms and sizes are possible . . . . . . . . . . . . . 205

10.2 Noise and dissonant harmonics . . . . . . . . . . . . 206

10.3 Beet, but with love, please! . . . . . . . . . . . . . . . . . . . . 214

10.4 Various structure of harmonics . . . . . . . . . . . . . . . . . . . 214

 

Part III  Tone systems

 11 Modalities major and minor

 11.1 Male and female principles explicitly . . . . . . . . . . . . . . 221

11.2 All flows: consonance and dissonance . . . . . . . . . . . 233

 

12 Temperament

 

12.1 Pythagorena tone system . . . . . . . . . . . . . . . . . . 249

12.2 Just (pure) intonation . . . . . . . . . . . . . . . . . . . 252

12.3 Equal 12–tone temperament . . . . . . . . . . . . 258

12.4 1/4–comma meantone temperament . . . . . . . . . . 265

12.5 Pythagorean versus Equal 12-tone temperament . . . . 268

 13 Have courage for the further work!

 13.1 Impact of scientific research to music . . . . . . . . . . . . . 277

13.2 Impact of music to science . . . . . . . . . . . . . . . 279

13.3 European tradition, culture, consciousness . . . . . . . . . . 279

Literature 282

List of pictures 286

List of tables 290

Index 295