Heinrich Bach was born at Wechmar, and is the father of the so-called Arnstädt Line. After the early death of his father, his older brother Johannes Bach continued his music education and taught him organ playing. They moved to Suhl and Schweinfurt. From 1635 to 1641, he was Ratsmusikant in the Erfurt Ratsmusikanten-Compagnie led by Johannes. From 1641, he became organist in Arnstadt's St. Mary's Church and the Upper Church, a post he kept until his death. In 1642, he married Eva Hoffmann, the younger daughter of Suhl Stadtpfeiffer Hoffmann. Bach died in Arnstadt.