Polytempic Polymicrotonal Music

This book introduces polytempic polymicrotonality as a new musical aesthetic. It proposes music with more than one microtonal tuning system and discusses examples from the literature to give an historic framework showing that this tendency has been present throughout human musical history. Polytempo is a tool for which polymicrotonal structures can function in relief from its background, and it acts as a frame, or ground structure, that is multidimensional, akin to the advancement of perspective in Renaissance art. The book has historic significance as it is the only book of its category, or genre, in music that features polymicrotonality in music composition or production. It displays examples of music literature for musical precedence in this area, focusing on Charles Ives’s Universe Symphony, unfinished since 1925.

This book introduces polytempic polymicrotonality as a new musical aesthetic. It proposes music with more than one microtonal tuning system and discusses examples from the literature to give an historic framework showing that this tendency has been present throughout human musical history. Polytempo is a tool for which polymicrotonal structures can function in relief from its background, and it acts as a frame, or ground structure, that is multidimensional, akin to the advancement of perspective in Renaissance art. The book has historic significance as it is the only book of its category, or genre, in music that features polymicrotonality in music composition or production. It displays examples of music literature for musical precedence in this area, focusing on Charles Ives’s Universe Symphony, unfinished since 1925.

This book discusses microtonal tunings in the Arabic maqam, prevalent in the Middle East and Central Asia, which employs microtonal intervals from Pythagorean tuning by perfect fifths. The ratio 3/2, as the fifth overtone in the overtone series, is used as a multiplier leading to numeric ratios for all pitches in the tetrachords and pentachords of the maqam. Musicians today are highly curious about expanding the pitch palette and are already employing microtones in their music, from folk rock to classical music. The maqam is among the few extant analyzed systems of music from antiquity that reflect the methods of the Greek Genera, in terms of tuning and function. The book also discusses Charles Ives's use of microtones, Bach and his use of microtones, and a score of Hypercube, the seminal composition discussed in the author’s first book, Polytempic Polymicrotonal Music, which was not published in its entirety in the former book. The text covers microtones philosophically, questioning the efficacy of such tunings. This book is accessible to the beginners in the field and will be beneficial to musical analyses in colleges and universities also by showing detailed analysis of Bach chorales in their original modes, and how their tuning presented complete character shifts by the microtones they contained by mean-tone temperament, an offshoot of Pythagorean tuning during the Baroque.

A commonsense, self-contained introduction to the mathematics and physics of music; essential reading for musicians, music engineers, and anyone interested in the intersection of art and science. “Mathematics can be as effortless as humming a tune, if you know the tune,” writes Gareth Loy. In Musimathics, Loy teaches us the tune, providing a friendly and spirited tour of the mathematics of music—a commonsense, self-contained introduction for the nonspecialist reader. It is designed for musicians who find their art increasingly mediated by technology, and for anyone who is interested in the intersection of art and science. In Volume 1, Loy presents the materials of music (notes, intervals, and scales); the physical properties of music (frequency, amplitude, duration, and timbre); the perception of music and sound (how we hear); and music composition. Calling himself “a composer seduced into mathematics,” Loy provides answers to foundational questions about the mathematics of music accessibly yet rigorously. The examples given are all practical problems in music and audio. Additional material can be found at http://www.musimathics.com.

This classic chronicle of the longstanding challenges of tuning and temperament devotes a chapter to each principal theory, features a glossary and numerous tables, and requires only minimal background in music theory.

Author Thomas Donahue assembles new information and material from previous sources, providing a comprehensive outline of theories and a historical overview that fills a neglected niche in music and keyboard reference."--Jacket.

Tuning, Timbre, Spectrum, Scale focuses on perceptions of consonance and dissonance, and how these are dependent on timbre. This also relates to musical scale: certain timbres sound more consonant in some scales than others. Sensory consonance and the ability to measure it have important implications for the design of audio devices and for musical theory and analysis. Applications include methods of adapting sounds for arbitrary scales, ways to specify scales for nonharmonic sounds, and techniques of sound manipulation based on maximizing (or minimizing) consonance. Special consideration is given here to a new method of adaptive tuning that can automatically adjust the tuning of a piece based its timbral character so as to minimize dissonance. Audio examples illustrating the ideas presented are provided on an accompanying CD. This unique analysis of sound and scale will be of interest to physicists and engineers working in acoustics, as well as to musicians and psychologists.