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.

"A fascinating and genuinely accessible guide....Educating, enjoyable, and delightfully unscary."—Classical Music What if Bach and Mozart heard richer, more dramatic chords than we hear in music today? What sonorities and moods have we lost in playing music in "equal temperament"—the equal division of the octave into twelve notes that has become our standard tuning method? Thanks to How Equal Temperament Ruined Harmony, "we may soon be able to hear for ourselves what Beethoven really meant when he called B minor 'black'" (Wall Street Journal).In this "comprehensive plea for more variety in tuning methods" (Kirkus Reviews), Ross W. Duffin presents "a serious and well-argued case" (Goldberg Magazine) that "should make any contemporary musician think differently about tuning" (Saturday Guardian). Some images in the ebook are not displayed owing to permissions issues.

Written for musicians by a musician, Meantone Temperaments on Lutes and Viols demystifies tuning systems by providing the basic information, historical context, and practical advice necessary to easily achieve more satisfying tuning results on fretted instruments. Despite the overwhelming organological evidence that many of the finest lutenists, vihuelists, and viola da gamba players in the Renaissance and Baroque eras tuned their instruments in one of the meantone temperaments, most modern early instrument players today still tune to equal temperament. In this handbook richly supplemented with figures, diagrams, and music examples, historical performers will discover why temperaments are necessary and how they work, descriptions of a variety of temperaments, and their application on fretted instruments. This technical book provides downloadable audio tracks and other tools for fretted instrument players to achieve more stable consonances, colorful dissonances, and harmonic progressions that vividly propel the music forward.

"A book that explains how a vexing technical puzzle was solved, making possible some of the most exquisite music ever written."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved

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.

Preface What you are now reading is the written version of an electronic document that explains the mathematical principles for different musical temperaments. The electronic version contains many music examples that you can listen to while you are working with this document at a computer. The written version obviously cannot offer this possibility. It serves therefore merely as a parallel study aid and guide and cannot replace actually working with the electronic text. Musical Temperaments Contents • V II Contents Introduction and Fundamental Properties 1 Pitch and Frequency 1 Preliminary Remarks 1 Frequencies and Intervals 2 Tuning Systems and Frequencies 5 Musical Scales in Different Tunings 5 Pure Tuning 5 Intervals and Triads in Pure Tuning 12 Pythagorean Tuning 23 Intervals and Triads in Pythagorean Tuning 31 Meantone Tuning 34 Intervals and Triads in Meantone Tuning 39 Equal Temperament (Tuning) 42 Intervals and Triads in Equal Temperament (Tuning) 47 Summary 50 Appendices 53 Pictorial explanations 53 Tables of Frequencies and Intervals 54 Operating Instructions 62 Glossary 67 Musical Temperaments Introduction and Fundamental Properties • 1 Introduction and Fundamental Properties Pitch and Frequency Preliminary Remarks It is well known that tones consist of periodically recurring phenomena, that is, beats repeating in a regular pattern. The number of repetitions of beats per second is measured in Hertz: 440 Hertz mean 440 beats per second. This number is also called the frequency of a beat.

The Cambridge History of Western Music Theory is the first comprehensive history of Western music theory to be published in the English language. A collaborative project by leading music theorists and historians, the volume traces the rich panorama of music-theoretical thought from the Ancient Greeks to the present day. Recognizing the variety and complexity of music theory as an historical subject, the volume has been organized within a flexible framework. Some chapters are defined chronologically within a restricted historical domain, whilst others are defined conceptually and span longer historical periods. Together the thirty-one chapters present a synthetic overview of the fascinating and complex subject that is historical music theory. Richly enhanced with illustrations, graphics, examples and cross-citations as well as being thoroughly indexed and supplemented by comprehensive bibliographies of the most important primary and secondary literature, this book will be an invaluable resource for students and scholars alike.

"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