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".
The son of Ralph Birchensha, an English official in Ireland, and his wife Elizabeth, he lost both his parents while still quite young, and was in the household of George FitzGerald, 16th Earl of Kildare, up to the Irish Rebellion of 1641.
[1] Birchensha's pupils included Silas Taylor, Thomas Salmon, and most famously Samuel Pepys.
[2] Birchensha's great aim was to publish a treatise on music in its philosophical, mathematical and practical aspects (which would have included a definitive summary of his rules of composition), entitled Syntagma musicæ.
A manuscript for Robert Boyle, a relative by marriage of the Earl of Kildare, remains as the major source for his ideas on music.