He was born at Dresden, and studied music under Scholz, Lanska, Grosse and Morlacchi, the rival of Weber. Afterwards he completed his education as a violinist and composer under Spohr, and till 1821 held various appointments in private families, varying him musical occupations with mathematical and other studies bearing chiefly on acoustics and kindred subjects.
For a time also Hauptmann was employed as an architect, but all other pursuits gave place to music, and a grand tragic opera, Mathilde belongs to the period just referred to. In 1822 he entered the orchestra of Cassel, again under Spohr's direction, and it was there that he first taught composition and musical theory--to such men as Ferdinand David, Burgmüller, Kid and others. His compositions at this time chiefly consisted of motets, masses, cantatas and songs. His opera Mathilde was performed at (Tasst with great success.
In 1842 Hauptmann obtained the position of cantor at the Thomas-school of Leipzig (long previously occupied by the great Johann Sebastian Bach) together with that of professor at the conservatoire, and it was in this capacity that his unique gift as a teacher developed itself and was acknowledged by a crowd of enthusiastic and more or less distinguished pupils.
He died on the 3rd of January 1868, and the universal regret felt at his death at Leipzig is said to have been all but equal to that caused by the loss of his friend Mendelssohn many years before. Hauptmann's compositions are marked by symmetry and perfection of workmanship rather than by spontaneous invention.
Amongst his vocal compositions--by far the most important portion of his work--may he mentioned two masses, choral songs for mixed voices (Op. 32, 47), and numerous part songs. The results of his scientific research were embodied in his book Die Natur der Harmonik und Metrik (1853), a standard work of its kind, in which a philosophic explanation of the forms of music is attempted.