This chapter includes transcriptions and translations of material on keyboard instruments found in the writings of Jakob Adlung, Marin Mersenne, and Michael Praetorius, as well as technical descriptions of the keyboard instruments used by Johann Sebastian Bach, members of the Couperin family, George Frederick Handel, Domenico Scarlatti, Padre Antonio Soler, and other composers of the period. This chapter provides explicit tuning instructions and analysis of temperaments used in the period, notably meantone, temperament ordinaire, and various circulating and so-called “well temperaments” that appear in treatises written by Denis, Corrette, Kirnberger, Mersenne, Marpurg, Neidhardt, Rameau, Werckmeister, and others.

This chapter deals with the design and construction of keyboard instruments and covers topics such as Mersenne’s Law, keyboard compass, scaling, plucking and striking points, string tension, case and soundboard proportion and structure, as well as technical descriptions of harpsichord, clavichord, and piano mechanisms, including the so-called “English” and “Viennese” hammer actions. Early English, Nuremberg, Berlin, and Vienna wire gauges are compared.

This chapter looks at the mathematization of the study of nature by focusing on how practical mathematicians from the sixteenth century onward understood mathematics as primarily devoted to solving problems through mathematical construction. This constructive understanding of the nature of mathematics is then related to the double movement of physicalizing mathematics (giving physical interpretations to mathematical constructions) and mathematizing physics (understanding physics as basically involving the solution of problems). The work of seventeenth-century thinkers like Galileo, Descartes, and Mersenne is used to further illustrate these ideas, which led to the establishment of mathematical physics as characterized by its problem-solving nature.