Combinations of tones that are consonant (“nice”) are those that exhibit no slower beats. Beats occur when two periodic signals are close to the same frequency. For sinusoidal signals, the beat frequency is simply the difference between the two signals. For complex signals, one must also consider differences between multiples of the signal frequency. Thus, consonant combinations are those where the ratio of the frequencies is equal to a rational number. Of particular importance are rational numbers involving the ratio of small integers. The musical fifth corresponds to a frequency ratio of 3 to 2 and is an important part of music. A set of note frequencies used for a musical scale can be justified based on consonant combinations, and variations of the details of those choices, known as temperaments, are useful in music for practical reasons. In particular, the equal-tempered scale used for keyboards, based on multiples of the 12th root of 2, is very common.

This chapter analyzes references to keyboard instruments in the writings of Martin Agricola, Sebastian Virdung, Juan Bermudo, Ercole Bottrigari, Eberhardus Cersne, Paulus Paulirinus, and Hermann Poll, among others. It provides technical descriptions of harpsichords, spinets, virginals, and clavichords made in that period, and includes discussions of pitch, transposition, keyboard compass, as well as tuning and temperaments.

Attention in this final chapter is directed to the private passions of church personnel as revealed in the executors’ accounts of deceased canons, and in particular Jacques de Houchin, remarkable for his bibliophilic sophistication and (apparently) private music-making. Houchin’s book collection at death ran to more than 300 volumes, including large numbers of classical texts, making him one of the most significant private bibliophiles of his age. He also possessed a large number of music books and musical instruments. Centred on this one man’s proclivities, the chapter paints a picture of private music-making within the confines of the church and its cloister, involving canons, vicars and choirboys.