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The Structure of Recognizable Diatonic Tunings

Author: Easley Blackwood

Publisher: Princeton University Press

Published: 2014-07-14

Total Pages: 329

ISBN-13: 1400854075

In a comprehensive work with important implications for tuning theory and musicology, Easley Blackwood, a distinguished-composer, establishes a mathematical basis for the family of diatonic tunings generated by combinations of perfect fifths and octaves. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Tuning, Timbre, Spectrum, Scale

Author: William A. Sethares

Publisher: Springer Science & Business Media

Published: 2013-06-05

Total Pages: 346

ISBN-13: 1447141776

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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.

Treatise on Harpsichord Tuning

Author: Jean Denis

Publisher: Cambridge University Press

Published: 1987-04-09

Total Pages: 140

ISBN-13: 9780521314022

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A translation of Jean Denis's Treatise on Harpsichord Tuning (1643/50), with notes and an introduction.

Mathematics and Music

Author: Gerard Assayag

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 294

ISBN-13: 3662049279

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In Western Civilization Mathematics and Music have a long and interesting history in common, with several interactions, traditionally associated with the name of Pythagoras but also with a significant number of other mathematicians, like Leibniz, for instance. Mathematical models can be found for almost all levels of musical activities from composition to sound production by traditional instruments or by digital means. Modern music theory has been incorporating more and more mathematical content during the last decades. This book offers a journey into recent work relating music and mathematics. It contains a large variety of articles, covering the historical aspects, the influence of logic and mathematical thought in composition, perception and understanding of music and the computational aspects of musical sound processing. The authors illustrate the rich and deep interactions that exist between Mathematics and Music.

Polytempic Polymicrotonal Music

Author: Peter Alexander Thoegersen

Publisher: CRC Press

Published: 2022-09-08

Total Pages: 219

ISBN-13: 100063132X

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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.

The Monteverdi Vespers of 1610 : Music, Context, Performance

Author: Jeffrey Kurtzman

Publisher: Clarendon Press

Published: 2000-01-06

Total Pages: 626

ISBN-13: 0191590711

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This is a thorough-going study of Monteverdi's Vespers, the single most significant and most widely known musical print from before the time of J.S. Bach. The author examines Monteverdi's Vespers from multiple perspectives, combining his own research with all that is known and thought of the Vespers by other scholars. The historical origin as well as the musical and liturgical context of the Vespers are surveyed; similarly the controversial historiography of the Vespers in the nineteenth and twentieth centuries is scrutinized and evaluated. A series of analytical chapters attempt to clarify Monteverdi's compositional process and the relationship between music and text in the light of recent research on modal and tonal aspects of early seventeenth century music. The final section is devoted to thirteen chapters investigating performance practice issues of the early seventeenth century and their application to the Vespers, including general and specific recommendations for performance where appropriate. The book concludes with a series of informational appendices, including the psalm cursus for Vespers of all major feasts in the liturgical calendar, texts, and structural outlines for the Vespers compositions based on a cantus firmus, an analytical discography, and bibliographies of seventeenth-century musical and theoretical sources.

Exploring Musical Spaces

Author: Julian Hook

Publisher: Oxford University Press

Published: 2022-09-08

Total Pages: 681

ISBN-13: 0190246014

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Exploring Musical Spaces is a comprehensive synthesis of mathematical techniques in music theory, written with the aim of making these techniques accessible to music scholars without extensive prior training in mathematics. The book adopts a visual orientation, introducing from the outset a number of simple geometric models--the first examples of the musical spaces of the book's title--depicting relationships among musical entities of various kinds such as notes, chords, scales, or rhythmic values. These spaces take many forms and become a unifying thread in initiating readers into several areas of active recent scholarship, including transformation theory, neo-Riemannian theory, geometric music theory, diatonic theory, and scale theory. Concepts and techniques from mathematical set theory, graph theory, group theory, geometry, and topology are introduced as needed to address musical questions. Musical examples ranging from Bach to the late twentieth century keep the underlying musical motivations close at hand. The book includes hundreds of figures to aid in visualizing the structure of the spaces, as well as exercises offering readers hands-on practice with a diverse assortment of concepts and techniques.

Harmonic Experience

Author: W. A. Mathieu

Publisher: Simon and Schuster

Published: 1997-08-01

Total Pages: 576

ISBN-13: 1620554011

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An exploration of musical harmony from its ancient fundamentals to its most complex modern progressions, addressing how and why it resonates emotionally and spiritually in the individual. W. A. Mathieu, an accomplished author and recording artist, presents a way of learning music that reconnects modern-day musicians with the source from which music was originally generated. As the author states, "The rules of music--including counterpoint and harmony--were not formed in our brains but in the resonance chambers of our bodies." His theory of music reconciles the ancient harmonic system of just intonation with the modern system of twelve-tone temperament. Saying that the way we think music is far from the way we do music, Mathieu explains why certain combinations of sounds are experienced by the listener as harmonious. His prose often resembles the rhythms and cadences of music itself, and his many musical examples allow readers to discover their own musical responses.

The Arithmetic of Listening

Author: Kyle Gann

Publisher: University of Illinois Press

Published: 2019-09-16

Total Pages: 344

ISBN-13: 0252051424

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"Tuning is the secret lens through which the history of music falls into focus," says Kyle Gann. Yet in Western circles, no other musical issue is so ignored, so taken for granted, so shoved into the corners of musical discourse. A classroom essential and an invaluable reference, The Arithmetic of Listening offers beginners the grounding in music theory necessary to find their own way into microtonality and the places it may take them. Moving from ancient Greece to the present, Kyle Gann delves into the infinite tunings available to any musician who feels straitjacketed by obedience to standardized Western European tuning. He introduces the concept of the harmonic series and demonstrates its relationship to equal-tempered and well-tempered tuning. He also explores recent experimental tuning models that exploit smaller intervals between pitches to create new sounds and harmonies. Systematic and accessible, The Arithmetic of Listening provides a much-needed primer for the wide range of tuning systems that have informed Western music. Audio examples demonstrating the musical ideas in The Arithmetic of Listening can be found at: https://www.kylegann.com/Arithmetic.html

Temperament

Author: Stuart Isacoff

Publisher: Vintage

Published: 2003-02-04

Total Pages: 290

ISBN-13: 0375703306

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Few music lovers realize that the arrangement of notes on today’s pianos was once regarded as a crime against God and nature, or that such legendary thinkers as Pythagoras, Plato, da Vinci, Galileo, Kepler, Descartes, Newton and Rousseau played a role in the controversy. Indeed, from the time of the Ancient Greeks through the eras of Renaissance scientists and Enlightenment philosophers, the relationship between the notes of the musical scale was seen as a key to the very nature of the universe. In this engaging and accessible account, Stuart Isacoff leads us through the battles over that scale, placing them in the context of quarrels in the worlds of art, philosophy, religion, politics and science. The contentious adoption of the modern tuning system known as equal temperament called into question beliefs that had lasted nearly two millenia–and also made possible the music of Beethoven, Schubert, Chopin, Debussy, and all who followed. Filled with original insights, fascinating anecdotes, and portraits of some of the greatest geniuses of all time, Temperament is that rare book that will delight the novice and expert alike.