[1] He received his doctorate in 1859 at the Humboldt University of Berlin with the dissertation De fidibus graecorum ("On the Stringed Instruments of the Greeks").
Jan received his first teaching position at the Berlinisches Gymnasium zum Grauen Kloster, whose headmaster Johann Friedrich Bellermann [de] was also concerned with the music of ancient Greece.
The work, accompanied by numerous preliminary studies, was reprinted unchanged in 1962 and 1995 and is considered Jan's most important publication, as it replaces the long outdated Antiquae musicae auctores septem by Marcus Meibom (1652).
Jan also got involved in the research debate on the harmonics of kithara music and stood up to the predominant expert in this field, Rudolf Westphal.
Westphal's speculations about possible harmonic laws were largely rejected by Jan and he argued that one should limit oneself to what is certainly recognizable in the ancient theory of harmony.