Equal temperament in the eighteenth century : the ear versus numbers /

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Includes bibliographical references (pages 161-182) and index.Ears to hear, but do not hear. Introduction ; Late Renaissance intonation ; Later intonation standards ; Eighteenth-dentury views ; Theory vs. practice ; Tuners and the monochord -- Fundamentals. Measurement ; The construction of meantone temperament ; The monochord ; The ear's tolerance for pitch discrepancies ; The meaning of 'diatonic' ; Equal temperament in practice -- Temperament in Italy and France. Equal temperament in Italy ; Equal temperament in France ; Marin Mersenne ; Equal temperament and instruments ; Jean-Philippe Rameau ; Reaction ; The Francophile Marpurg ; Temperament requirements in French music -- Clarifying the issues. The necessity for equal temperament ; Does an unequal temperament make all keys usable? ; Werckmeister and equal temperament ; Well-tempered ; Neidhardt and equal temperament -- Temperament in Germany. The acceptance of equal temperament ; Key characteristics ; Kirnberger and temperament -- Intonation. Flexible intonation ; Eighteenth-century intonation ; The curious story of the Prelleur violin chart ; The influence of traditional theory ; Differentiating between theory and practice ; Orchestral intonation ; Tuning and intonation -- Organ temperament and J.S. Bach. Equal temperament and the organ ; Musical scores ; Equal temperament in Bach's area ; Builders and temperament ; Bach's harmonic requirements ; Postscript -- Expressive intonation. Equal temperament and expressive intonation ; Mathematicians' reaction.Today, many have urged early music specialists to adopt a historical unequal temperament for keyboards and harps, and even for instruments whose frets produce equal temperament naturally. Equal temperament, however, played a significant role during this period, but most writing today has stressed the numbers from early mathematicians who believed that the more just intervals a temperament has, the better it will be. Major writers, however, pressed for equal temperament because it enabled full use of the keyboard, transposition, and enharmonic notes. In contrast, the major and minor semitones of unequal temperaments, and their flats pitched higher than sharps, limited the keyboard's usable compass and made enharmonic notes and transposition impossible. As advanced thinkers were aware, performers with pitch flexibility did not follow the theorists' numbers. An accompaniment in equal temperament offered them free rein to find the best intonation because its ratios for fourths and fifths are closest to the natural ones. Among the many writers who supported equal temperament was Jakob Adlung, who observed that the theorists' calculations gave rise to the argument: "Whether the ear or the numbers should judge if music sounds in or out of tune".