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Musica Mathematica

Traditions and Innovations in Contemporary Music

by Rima Povilionienė (Author)
Monographs 290 Pages
Series: Methodology of Music Research, Volume 9

Table Of Content

  • Cover
  • Title
  • Copyright
  • About the author
  • About the book
  • This eBook can be cited
  • 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 Compositionsof 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

Rima Povilionienė

Musica Mathematica

Traditions and Innovations in Contemporary Music

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About the author

Rima Povilioniene˙ holds a PhD in Musicology. She is a researcher at the International Semiotics Institute (ISI) at Kaunas University of Technology and an associate professor in the Department of Musicology of the Lithuanian Academy of Music and Theatre.

About the book

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.

This eBook can be cited

This edition of the eBook can be cited. To enable this we have marked the start and end of a page. In cases where a word straddles a page break, the marker is placed inside the word at exactly the same position as in the physical book. This means that occasionally a word might be bifurcated by this marker.

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

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

4. Musica Mathematica in Practice: Aspects of Analysis ←5 | 6→

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

John Cage. First Construction (1939)

1.1.2. Fibonacci and Number Sequences Derived from it

1.1.3. The Prime Numbers and other Mathematically Determined Sequences

1.2. The Renewal of Polytempo, Polyrhythm, and Polymeter

1.3. Symmetrical Algorithms and the Confrontation between Symmetries and Asymmetries

1.4. Transformational Elements (Combinatorics, Permutations, Rotations)

2. Semantic Aspects of Music Composition

2.1. Cosmological Number Codes and Graphic Constructions

2.2. The Symbols of Magic Number Squares

2.3. The Implications of Sacred Numbers

2.4. Personalized Semantics: The Significance of Individual Numbers

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

1.2. L-system Formalities in Music

1.3. The Numericalization of the Musical Score ←6 | 7→

2. Implications of Modern Mathematical Theories

Details

Pages
290
ISBN (PDF)
9783631713822
ISBN (ePUB)
9783631713839
ISBN (MOBI)
9783631713846
ISBN (Book)
9783631713815
Language
English
Publication date
2017 (February)
Tags
interaction of music and mathematics contemporary music analysis numerical proportions in music advanced mathematics musical cryptography music and architecture music and art number symbolism
Published
Frankfurt am Main, Bern, Bruxelles, New York, Oxford, Warszawa, Wien, 2016. 290 pp., 123 fig. b/w.

Biographical notes

Rima Povilionienė (Author)

Rima Povilionienė holds a PhD in Musicology. She is a researcher at the International Semiotics Institute (ISI) at Kaunas University of Technology and an associate professor in the Department of Musicology of the Lithuanian Academy of Music.

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Title: Musica Mathematica