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