The problem of tempering keyboard and fretted instruments has occupied the attention of musicians and theorists for hundreds of years. Since the sixteenth century most fretted instruments such as the lute and viola da gamba have employed equal temperament (or an approximation of it based upon the 18:17 rule) or an adaptation of mean-tone tuning, but these systems suffered from ‘tempered’, or ‘impure’, intervals. In 1705 the music theorist Thomas Salmon (born London, 1648; died Mepsal [now Meppershall], Bedfordshire, 1706) proposed a system of intonation for the viola da gamba that employed divided frets (that is, the frets were not tied across the fingerboard in a straight line but were in effect cut apart and glued or inset beneath each string as required) as well as interchangeable fingerboards for different keys (much like the set of crooks for the later Inventionshorn). It was Salmon’s intention to overcome the lack of purity associated with fretting systems that ‘falsify the proportions’ and thus ‘deprive us of that satisfactory pleasure which arises from the exactness of sonorous numbers’. In his system the C major scale was constructed of large and small whole tones having ratios of 9:8 for the intervals C–D, F–G and A–B, 10:9 for the intervals D–E and G–A, and 16:15 for the semitones E–F and B–C. The two sizes of whole tones were divided 18:17:16 and 20:19:18, resulting in the following scale: