The genesis of the scale
[RU] [FR]

L. V. Avdeev, Y. I. Varivoda, V. M. Dubovik, P. B. Ivanov

THE GENESIS OF THE SCALE
The matter of music

St Petersburg: BODLib, 2006

[ in Russian ]


In the history of music, one finds many different tone systems, the musical scales. From the most ancient times, their origin was related to the mathematical relations between the musical sounds. In this book, the history of the development of the theoretical ideas about the structure of the musical scales is presented at a popular level, in comparison with the history of music. Early scales are described along with various combinatory scales, as well as the well-tempered twelve-tone scale, the basis of contemporary music. The principal elements of the modern theory of pitch scale formation are discussed on the basis of the general psychological theory of activity, information theory, quantum mechanics, and the general hierarchical approach. A new universal musical scale of 19 tones is introduced, and the perspectives of the development of the musical pitch systems are outlined. The book does not require any preliminary acquaintance with the theory of music, and the usual secondary school mathematics is enough to understand the mathematic issues involved. The book might be useful for those who like music and are interested in the applications of mathematics.


Contents

INTRODUCTION5
THE WORLD OF SOUND7
1. Sounds in nature and in music7
2. The world of hearing12
3. Ear for music17
THE SENSE OF PITCH: MATHEMATICAL SCALES21
1. The beginning of music21
2. The oscillations of a string and the natural scale24
3. The scale of the Ancient Greece29
4. THe Pythagoras' scale33
5. Other mathematical scales37
THE WELL TEMPERED SCALE41
1. The formation of the 12-tone scale41
2. The structure of the scale45
3. In the search of other possibilities48
4. The ethnic scales54
PITCH PERCEPTION: TOWARDS A THEORY OF SCALING57
1. The psychology of activity57
2. Information and dissonance62
3. Rhythms and timbres67
4. The "zoology" of scales72
5. The 19-tone well tempered scale77
CONCLUSION: THE PERSPECTIVES OF MUSIC87
LITERATURE90


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Also see: [Pitch Scales] [Musical Scales] [Scales in the Visual Arts] [Musical Scale Hierarchy]
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