Musica Mathematica: Traditions and Innovations in Contemporary Music

Description

The concept of «musica mathematica» seeks to accurately examine the intersection of two seemingly radically different subject areas. From the perspective of a European perception, the definition of the science of music was a result of the Pythagorean concept of universal harmony. The Pythagoreans were the first in European culture to raise the issue of uniting music and mathematics, sound and number. In the three parts of the monograph, versatile cases of the intersection of music and mathematics are displayed, moving from philosophical and aesthetic considerations about mathesis to practical studies, discussing the interaction between music and other kinds of art (architecture, painting, poetry and literature), and providing a practical research of contemporary music compositions. Cover Contents List of Analyzed Music Scores Author’s Preface Foreword: Mathesis as a Philosophy of the Beauty of Music Part 1 A Retrospective of the Traditions of Musica Mathematica 1. The Constructive Relationships between Music and Mathematics: The Pythagorean Conception of Universal Music and its Spread in the Worldview of Later Periods 1.1. Music and the Theory of the Quadrivium 1.2. Review of the Harmony of Spheres 1.3. The Phenomenon of Mathesis Universalis 1.4. Expression of Numerical Proportions and Progressions The Fibonacci Progression and the Golden Ratio Phenomenon 1.5. Ars Combinatoria and the Constructivism of Music 2. Semantic Interpretation of the Interaction between Music and Mathematics: Mystic Middle Ages and the Sacral Baroque 2.1. Semantics of the Kabbalah in Music 2.2. Symbolic Thinking and Sacral Numerology 2.3. Codes of the Numerical Alphabets in Music 3. Constructive Aspects of the Interaction between Music and other Arts 3.1. “Frozen Music”: Dialogues between Music and Architecture 3.2. Ut Pictura Musica: The Interaction between Music and Art 3.3. Musical Cryptography as a Common Denominator of the Sound and the Word Application of the Morse Alphabet 4. Musica Mathematica in Practice: Aspects of Analysis Part 2 The Renewal of Mathematical Techniques in Musical Compositions of the 20th and 21st Centuries 1. Constructive Aspects of Music Composition 1.1. The Implications of Numerical Proportions and Progressions in Music 1.1.1. The Number Proportions and Progressions of Antiquity Olivier Messiaen. Quatre études de rythme (1949–1950) Snieguolė Dikčiūtė. The Mystery of Seven Bridges (1991) Steve Reich. Music for Pieces of Wood (1973) Siegfried Thiele. Proportionen (1971) John Cage. First Construction (1939) 1.1.2. Fibonacci and Number Sequences Derived from it Derek Bourgeois. Symphony for Organ, Op. 48 (1975) Steve Reich. Clapping Music (1972) Karlheinz Stockhausen. Klavierstück IX (1961) 1.1.3. The Prime Numbers and other Mathematically Determined Sequences Alain Louvier. L’Isola dei Numeri (1991) Tom Johnson. Music for 88 (1988) 1.2. The Renewal of Polytempo, Polyrhythm, and Polymeter John Adams. Short Ride in a Fast Machine (1986) Conlon Nancarrow. Study for Player Piano No. 15 (premiere in 1962) György Ligeti. Désordre (1985) 1.3. Symmetrical Algorithms and the Confrontation between Symmetries and Asymmetries Morton Feldman. Crippled Symmetry (1983) 1.4. Transformational Elements (Combinatorics, Permutations, Rotations) Olivier Messiaen. Île de feu II (1950) Tom Johnson. Tango (1984) Tom Johnson. The Chord Catalogue (1986) 2. Semantic Aspects of Music Composition 2.1. Cosmological Number Codes and Graphic Constructions 2.2. The Symbols of Magic Number Squares Šarūnas Nakas. Ziqquratu (1998) Dmitri Smirnov. Two Magic Squares (1971) 2.3. The Implications of Sacred Numbers Bronius Kutavičius. The Gates of Jerusalem (1991–5) Snieguolė Dikčiūtė. The Mystery of the Seven Bridges (1991) 2.4. Personalized Semantics: The Significance of Individual Numbers George Crumb. Black Angels (1970) John Cage. Ryoanji (1983) Mikalojus Konstantinas Čiurlionis. Fugue in B-flat, Op. 34/VL 345 (1908–9) Part 3 Innovations of Mathematical Techniques in 20th and 21st Century Music 1. The Mathematized Musical Graph 1.1. A Geometric Prototype as an Algorithm for Musical Composition Jan Rokus van Roosendael. Rotations (1988) John Adams. China Gates (1977) 1.2. L-system Formalities in Music Tom Johnson. Piece No. 14 from the cycle Rational Melodies (1981) Gary Lee Nelson. Summer Song (1991) 1.3. The Numericalization of the Musical Score Morton Feldman. IXION (1958) 2. Implications of Modern Mathematical Theories 2.1. The Practice of Algorithmic Music and Computer-Generated Composition 2.2. Tonal Adaptations of Complicated Mathematical Processes Iannis Xenakis. Nomos alpha (1965) 2.3. Fractal Theory Analogies in Musical Compositions Šarūnas Nakas. Ziqquratu (1998) Vytautas V. Jurgutis. Fractals (1999) Charles Dodge. A Fractal for Wiley Hitchcock (1989) Afterword Bibliography Supplementary Literature on the Subject of this Book Index of Names About the Author