The mathematical basis of the arts / by Joseph Schillinger.
| Author/creator | Schillinger, Joseph |
| Format | Book |
| Publication Info | New York : Da Capo Press, 1976, ©1948. |
| Description | x, 696 pages : illustrations ; 24 cm. |
| Subjects |
| Series | Da Capo Press music reprint series Da Capo Press music reprint series. ^A259341 |
| Contents | Part one. Science and esthetics. Art and nature -- Art and evolution -- Mimicry, magic and engineering. Development of art ; Evolution of rhythmic patterns ; Biology of sound ; Varieties of esthetic experience ; History of the arts in five morphological zones -- The physical basis of beauty -- Nature of esthetic symbols. Semantics ; Semantics of melody ; Intentional biomechanical processes ; Definition of melody -- Creation and criteria of art. Engineering vs. spontaneous creation ; Nature of organic art ; Creation vs. imitation -- Mathematics and art. Uniformity and primary selective systems ; Harmonic relations and harmonic coordination ; Other techniques of variation and composition ; Pragmatic validity of theory of regularity -- Part two. Theory of regularity and coordination. Continuum. Definition of an art product by the method of series ; Parametral interpretation of a system ; The first group of art forms ; Time (X₄) as a general parameter ; The second group of art forms ; The third group of art forms ; Correspondences between art forms -- Continuity. Series of values ; Factorial-fractional continuity ; Elements of factorial-fractional continuity ; Determinants -- Periodicity. Simultaneous monomial periodicities ; Polynomial relations of monomial periodicities ; Polynomial relations of polynomial periodic series ; Practical application in art ; Synchronization of the second order ; Periodicity of expansion and contraction ; Progressive symmetry -- Permutation. Displacement ; General permutation ; Permutations of the higher orders ; Mechanical scheme for the permutation of four elements -- Distributive involution. Powers ; General treatment of powers -- Balance, unstable equilibrium, and crystallization of event. Formulae ; Unstable equilibrium in factorial composition of duration groups -- Ratio and rationalization. Ratio, rational, relation, relational ; Rationalization of the second order ; Rationalization of a rectangle ; Ratios of the rational continuum -- Positional rotation. Dimensionality of positional rotation -- Symmetry. Symmetric parallelisms ; Esthetic evaluation on the basis of symmetry ; Rectangular symmetry of extensions in serial development -- Quadrant rotation -- Coordinate expansion -- Composition of density. Technical premise ; Composition of density-groups ; Permutation of the sequent density-groups within the compound sequent density-group ; Phase rotation of ? and ?? through t and d ; Practical application of ?? to ?? -- Part three. Technology of art production. Selective systems. Primary and secondary selective systems ; Temporal scales ; Pitch scales ; Scales of linear configurations and areas (Periodicity of dimensions ; Periodicity of angles ; Rectilinear segments forming angles in alternating directions ; Monomial, binomial and trinomial periodicity of sector radii ; Periodicity of radii and angle values ; Periodicity of arcs and radii ; r₄₃̦ rhythmic groups in linear design ; Planes ; Closed polygons) ; Color scales -- Production of design. Elements of linear design ; Rhythmic design ; Design analysis ; Three compositions in linear design ; Problems in design -- Production of music. Coordination of temporal structures ; Distribution of a duration group ; Synchronization of an attack group ; Distribution of a synchronized duration group ; Synchronization of an instrumental group -- Production of kinetic design. Proportionate distribution within rectangular areas ; Distributive involution in linear design ; Application to dimensions and angles ; Positional rotation applied to kinetic design -- Production of combined arts. The time-space unit in cinematic design ; Correlation of visual and auditory forms -- Appendices. Appendix A. Basic forms of regularity and coordination. Binary and ternary synchronization of genetic factors (Binary synchronization ; Binary synchronization with fractioning ; Ternary synchronization ; Generalization: synchronization of n generators) ; Distributive involution groups (Distributive square of binomials ; Distributive square of trinomials ; Generalization: distributive square of polynomials ; Distributive cube of binomials ; Distributive cube of trinomials ; Generalization: distributive cube of polynomials) ; Groups of variable velocity -- Appendix B. Relative dimensions -- Appendix C. New art forms. Double equal temperament ; Rhythmicon ; Solidrama -- Appendix D. Poetry and prose -- Appendix E. Projects. Books ; Instruments -- Glossary / compiled by Arnold Shaw. |
| Abstract | A work of revolutionary implications in the field of aesthetics, this book formulates the basic laws of mathematical logic underlying all art structures. To mathematicians, engineers and scientists, the Einsteinian approach to the arts will prove stimulating. To painters, composers, motion picture technicians, and industrial designers, Schillinger's original method of rhythmic design will prove a fertile source of fresh techniques. The book runs the gamut from the speculative to the practical, demonstrating how creative works may be synthesized through mathematics. Schillinger achieves that integration of science and art, toward which esthetic philosophers have been working since Leonard da Vinci. The book was organized by Schillinger before his death and published posthumously. |
| General note | Reprint of the edition published by Philosophical Library, New York. |
| General note | Includes index. |
| LCCN | 76008189 |
| ISBN | 0306707810 (hardcover) |
| ISBN | 9780306707810 (hardcover) |
Availability
| Library | Location | Call Number | Status | Item Actions |
|---|---|---|---|---|
| Music | Closed Stacks - Ask at Circulation Desk | NX456 .S35 1976 | ✔ Available | Place Hold |