And long before Bartok, he wrote music in compound meter, overthrowing the tradition that subdivided musical time into multiples of twos and threes. One such fugue, written in 1803 in the knock-knee time signature of 5/8, will appear on Mr. Ilic’s third Reicha disc next year.

“I was fascinated by the way he broke the rules,” Mr. Ilic said. “He has a musical style that’s pretty close to Haydn in terms of the surface, but then he modulates in really weird ways and it’s in 5/8.”

What’s especially strange about Reicha is that this unconventional streak was embedded in a sober, even pedantic personality and a compositional work ethic rooted in the past. His voluminous writings for solo piano — Mr. Ilic estimates that his five albums will cover about a third of the output — are related in spirit to those of Bach. Fugues were an obsession.

As a theorist, Reicha was driven by a desire to bring the same structure and logic to music education that he saw in other sciences. Louise Bernard de Raymond, a musicologist in Paris, said in a phone interview that in Reicha’s work “there is also the desire to understand music through other fields: mathematics, Kantian philosophy. There is a general desire to forge a form of musical education that is systematic and rational — a belief in progress.”

To his students, Reicha appears to have been a wonderfully open-minded teacher. “Nothing offends him,” Gounod wrote in his memoirs, “everything amuses him; everything is of interest; and what I like best about him is that he always wants to know why.”