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This book offers critical demonstrations of various methods and concepts currently used in music analysis. Among the subjects are musical implications, tonal analysis, generative theory, ambiguity, similarity, and the key criteria met with in lawsuits of plagiarism. Finally, can a composer's sexual leanings be derived from his music?
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Assisted by Scott Olsen (Central Florida Community College, USA) This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the "Mathematics of Harmony," a new interdisciplinary direction of modern science. This direction has its origins in "The Elements" of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and
Fibonacci numbers. --- Golden section. --- Mathematics --- Computer science. --- History.
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The Beauty of Fractals includes six essays related to fractals, with perspectives different enough to give you a taste of the breadth of the subject. Each essay is self-contained and expository. Moreover, each of the essays is intended to be accessible to a broad audience that includes college teachers, high school teachers, advanced undergraduate students, and others who wish to learn or teach about topics in fractals that are not regularly in textbooks on fractals.
Fractals. --- Fractals in art. --- Golden section. --- Divine proportion (Mathematics) --- Divine section (Mathematics) --- Extreme and mean ratio --- Golden cut --- Golden mean (Mathematics) --- Golden number (Ratio) --- Golden proportion --- Golden ratio --- Mean of Phidias --- Medial section --- Phi ratio --- Phidias, Mean of --- Geometry, Plane --- Ratio and proportion --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology)
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In this text, the basic mathematical properties of the golden ratio and its occurrence in the dimensions of two- and three-dimensional figures with fivefold symmetry are discussed. Fibonacci series and generalized Finobacci series and their relationship to the golden ratio are also presented.
Fibonacci numbers. --- Golden section. --- Divine proportion (Mathematics) --- Divine section (Mathematics) --- Extreme and mean ratio --- Golden cut --- Golden mean (Mathematics) --- Golden number (Ratio) --- Golden proportion --- Golden ratio --- Mean of Phidias --- Medial section --- Phi ratio --- Phidias, Mean of --- Geometry, Plane --- Ratio and proportion --- Fibonacci sequence --- Numbers, Fibonacci --- Sequence, Fibonacci --- Recurrent sequences (Mathematics)
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This book gives a critical account of various methods used in music analysis. In the first chapter, a number of current approaches such as semiotics, musical implications, Schenkerian analysis, and generative theory are demonstrated on Mozart’s K. 331 theme. Five essays deal with important concepts in music analysis: ambiguity, formal proportions, and similarity within and between works. A further chapter provides a discussion of probability, kinship, and influence – decisive criteria when judging musical plagiarism. The last essay, studying a piece by Schubert, sifts the prospects of deciphering a composer’s sexual leanings from his music.
Musical analysis. --- Analysis, Musical --- Analytical guides (Music) --- Hermeneutics (Music) --- Music --- Music analysis --- Music theory --- Music appreciation --- Analysis, appreciation --- Analytical guides --- Instruction and study --- Analytical;Analytical methods;Applied;Critical;Edlund;Essays;Golden section;Music;Musical ambiguity;Musical hermeneutics;Musical plagiarism;Musical similarity;Schenkerian analysis;Theory;Variations
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