CONTENTS
Introduction
The basics of the theory of symmetry
Definitions of symmetry
Isometric transformations and symmetry groups
Specific properties of symmetries in arts and generalizations of the theory of symmetry
Visual modeling of musical works and their symmetry structure
The symmetry of rhythmic structure
Absolute and relative transformations of rhythmic structure
Permutational equality and permutational proportionality of rhythmic entities
Symmetry analysis of rhythmic structure
Symmetry of music meter
The symmetry of melodic structure
Scales with different semi-tone intervals
Tempering as the symmetrization of scales
Formalized system for numerical notation of tonal pitches
Intervals and chords in the formalized system
Related tonalities and symmetry of coefficients of similarity
Symmetry transformations of melodic structure
Isometric transformations of melodic structure
Proportionality transformations of melodic structure
Relative symmetry transformations of melodic structure
The symmetry of counterpoint
Symmetry of melodic line
Optimization of melodic line
Optimal conjoining of chords and simultaneous conducting of melodic lines
Symmetry transformations of polyphonic melody structure
The symmetry of harmony
Symmetry of interval and seventh-chord structure of scales
Symmetry of fifth-chord coefficients of stability
Symmetry of harmonic functions
Extensions of tonalities by using isometric transformations of chords
Symmetry of seventh-chord structure of scales
Symmetry of chromatic seventh-chords
Symmetry of chromatic seven-chords
The symmetry of tonality
Formalization of direct diatonic modulations by means of fifth-chords
Indirect modulations by means of fifth-chords and their optimization
Formalization of direct diatonic modulations by means of seventh-chords
Formalization of enharmonic modulations
Symmetry transformations of chords as the basis of chromatic modulations
The symmetry of form
Static symmetry
Repetitive symmetry
Antisymmetry
Dynamic symmetry and golden section
The symmetry analysis of musical work
Symmetry as the organization principle of artwork and its esthetic meaning
Exact construction laws in art
Temporal arts, rhythm and periodicity
Symmetry as perception factor and the basis of "good form"
Dissymetry as a dynamic component of artwork
Antisymmetry, complementarity, bivalence, and ambiguity
The role of symmetry in music work
Bibliography
English translation: Ana Smiljanic
Notography: Konstantin Stefanovic
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