Christiaan Huygens

Christiaan Huygens (The Hague, 1629 – The Hague, 1695) was a Dutch mathematician, physicist and astronomer whose musical output, though less well known than his scientific work, holds a distinct place in the theory of tuning. The second son of Constantijn Huygens, he received a broad education in languages, mathematics and music, and learnt to play the viola da gamba, the lute and the harpsichord.

His academic career began at Leiden University, between 1645 and 1647, and continued at the Collegium Auriacum in Breda, where he was already known as a mathematician by around 1649. He travelled to Paris on several occasions between 1655 and 1664 and visited London in 1661 and 1663. In the French capital he associated with musicians such as Chambonnières, Pierre de La Barre, Du Mont and Gobert, and attended performances of stage works, among them Cavalli's Xerse and the comédie-ballets of Lully and Molière. In 1663 he was elected a member of the Royal Society of London, and in 1666 he took part in the founding of the Académie des Sciences in Paris, where he resided on a pension from Louis XIV during various periods. When he was not in France, he lived in The Hague with his father. His scientific achievements include the invention of the pendulum clock and the discovery of the rings of Saturn.

Huygens's interest in music arose in the summer of 1661, when his father brought him the tuning instructions for the carillon of Antwerp, which were based on meantone temperament. From there he developed a mathematical description of that system, recorded in his Divisio monochordi, and worked out logarithmic measurements of intervals. Between 1676 and 1678 he studied Mersenne, Zarlino, Salinas and Kircher closely, among others. His Lettre touchant le cycle harmonique, published in 1691, summarises ideas he had already formed three decades earlier and includes a description of an imaginary harpsichord with 31 strings per octave. His manuscript notes also address solmisation, the fingerings of the soprano recorder and the rules for realising the basso continuo. His musical legacy remains a subject of interest: he was the first to use logarithms to underpin the ancient division of the octave into 31 equal parts, a theory that eighteenth-century theorists acknowledged and that the Dutch physicist Fokker revived in the twentieth century as a basis for the study of microtonal intervals.