Career
He presented at the Royal Society and made an impression on its members in the 1660s and 1670s. Birchensha invented a system that he claimed would enable non-musicians to learn to compose in a short time by means of "a few easy, certain, and perfect Rules". This was at a time when other music theorists were codifying the rules of counterpoint, and writing about other rule-based and combinatorial systems to aid in the composition of music, such as the Arca Musarithmica of Athanasius Kircher.
Information about his life and work remains scanty.
In the 1650s he was known as a viol teacher in London. Birchensha"s pupils included Silas Taylor, Thomas Salmon, and most famously Samuel Pepys.
Pepys recorded impressions of his sessions with Birchensha (and hints at an eventual disillusionment with his teacher) in 1662.