Christiaan Huygens (1629-1695)

Christiaan Huygens is primarily known as one of the greatest scientists of the Dutch Golden Age, but his contributions to music are less well known. Although only a few short musical pieces by his hand have survived, Huygens was by no means unknown in the world of music. He played various instruments, including the viola da gamba, the lute, and the harpsichord, and throughout his life he devoted himself intensively to music theory. His scientific background led him to study the physical basis of music, with a particular interest in tone ratios and tuning systems. One of his most groundbreaking contributions was his work on the 31-tone system, an innovative method of dividing an octave into 31 equal parts. Christiaan Huygens described these ideas in his Lettre touchant le cycle harmonique (Rotterdam, 1691) and in Novus cyclus harmonicus (Leiden, 1724). Earlier, in 1661, he had already made notes in which he achieved the following:

• He developed an elegant method for calculating string lengths for any regular tuning, which he applied exclusively to meantone temperament.
• He devised a way to use logarithms in the calculation of string lengths and interval sizes.
• He demonstrated the close relationship between meantone temperament and the 31-tone tuning.
• He recognised the possible consonant nature of septimal intervals such as 4:7 and 5:7, indicating that these were approximated respectively by the augmented sixth and augmented fourth in both meantone temperament and the 31-tone tuning.

Huygens’ name is inextricably associated with the division of the octave into 31 equal parts. He was, however, not the first to describe a 31-tone division, as Nicola Vicentino (1555), Fabio Colonna (1618), and Lemme Rossi (1666) had done so earlier. Huygens was not aware of their writings and instruments, except for Vicentino’s archicembalo, of which he had heard via Salinas. Huygens did not, however, intend to create a system with 31 tones; he merely pointed out that the 31-tone equal temperament provides a more elegant description of the intervals than meantone temperament, which he considered the best: “Optimum est Temperamentum in chordarum systemate, cum ex diapente quarta pars commatis ubique deciditur.” Huygens was the inventor of numerous devices and also designed a keyboard instrument with 31 strings per octave. The keyboard with twelve standard keys per octave was placed above the strings and was movable. Through a system of pins, the keys would each play twelve of the 31 strings, and transposition consisted of shifting the keyboard. This design was probably never realised.

Also read the article by A.D. Fokker: Het muzikale toonstelsel van Christiaan Huygens, de normale diëzenstemming (Dutch) in the online archive. And also see the page about Huygens’ contemporary Quirinus van Blankenburg (1654-1739). Huygens also corresponded with Joan Albert Ban (1597-1644).