John Birchensha (c.1605-1681) is chiefly remembered for the impression that his theories about music made on the mathematicians, natural philosophers and virtuosi of the Royal Society in the 1660s and 1670s, and for inventing a system that he claimed would enable even those without practical experience of music to learn to compose in a short time by means of 'a few easy, certain, and perfect Rules'. His great aim was to publish a treatise on music in its philosophical, mathematical and practical aspects entitled Syntagma musicÿ. Unfortunately, the book never appeared, and no final manuscript of it survives. Recent research, however, has brought to light a number of manuscripts which allow us at last to form a more complete view of Birchensha's ideas and to gain at least a flavour of the lost Syntagma musicÿ.