In May 1747, Johann Sebastian Bach, near the end of his career and life, traveled to the court of Frederick the Great, his fellow composer. There, the king gave him a theme on which to improvise a fugue. How bad could this fugue have been, huh? But, in later days, Bach did much more with the king’s theme. He produced a large, long work called “Musical Offering,” containing more fugues, and canons, and a trio sonata. It is regarded as one of the greatest feats of musical intellection in history.

The Amsterdam Baroque Orchestra offered “Musical Offering” in Zankel Hall on Tuesday night. This was the second of its two concerts within the Carnegie building, the other having taken place last week. The orchestra was founded in 1979 by the conductor, harpsichordist, and all-around musician Ton Koopman. It was he who led his small group on Tuesday night, from the harpsichord.

And it was he who began “Musical Offering” with an extended “ricercare.” Mr. Koopman seemed to be merely getting through the piece, rather than really playing it and showing forth its musical worth. He was rather plodding, mechanical, as his group at large would be. There was precious little beauty or musicality as the orchestra went through the “Offering.” It was enough to give “period practice” a very bad name.

This was even apart from the sound of the group — which was beyond austerity into severity, sickliness, and painfulness. Someone once quipped that Bach, if he had had access to indoor plumbing, would have used it. I could not help thinking on Tuesday night that, if he knew about modern instruments, he would want them employed.

Not that the sound was incapable of growing on you. The violist, Jane Rogers, gave us a striking plaintiveness. But mainly — for sonic and other reasons — this performance was like a long visit to the dentist’s office, in B minor. There was only the loud rumble of the Zankel subway to relieve it.

(I should note that Bach wrote his “Offering” in C minor, but the key as he knew it sounds to modern ears like B minor. The world tunes differently now. But the Amsterdam Baroque Orchestra, of course, tunes Baroquely.)

You are perhaps familiar with the point that Bach encompassed everything: He subsumed and exalted everything that had come before him, and he anticipated everything that would come after him. You cannot think of a musical idea or notion — certainly not a worthy one — that is missing from Bach.

I say all this in order to remark that Bach’s “Coffee” Cantata, composed in 1734, can be considered a comic opera. Yes, a little comic opera. It is about — and isn’t it interesting to say that a Bach cantata is “about” something? — a struggle between a father and a daughter. The father, conservative, is against the new fad of coffee-drinking. The daughter is just wild about joe. Bach has the father sing in an old style of music. The daughter sings in a more modish.

Singing that role was Bettina Pahn, a German soprano. She was smart and endearing — daughterly, in fact. But her lightish, slightly breathy voice could have used a bit more support. Singing the father was a German bassbaritone, Klaus Mertens. He, too, was smart and endearing — robust but not blustery. The two singers did a little bit of acting, which was just the right amount. There was even a coffee pot and a cup onstage; Ms. Pahn pretended to take a sip or two.

In the background, Mr. Koopman’s band was fairly lively and engaged, even if we heard some more of that plodding, thumping quality. And I should relate what the program notes told us about the Carnegie Hall premiere of Bach’s “Coffee” Cantata. Lawrence Tibbett was the father, which is very interesting. Even more interesting is that one of the violinists was Jascha Heifetz.

There is a third singer in this work, a tenor who delivers two recitatives, acting as our narrator or host. He was Otto Bouwknegt, a Dutchman. Mr. Bouwknegt handled his part ably, except for one unfortunate stumble. And he began the cantata in an interesting way. The orchestra was tuning at length — tuning and tuning — and Mr. Bouwknegt rushed in from the back of the hall, exclaiming, “Stop, stop, stop with your tuning! I want to begin the piece!”(I am paraphrasing a little.)

The orchestra had tuned at length before Bach’s “Musical Offering,” too. And I was reminded of one of my favorite musical and personal stories.

A little cousin of mine had sat with me during the first half of an orchestra concert. In the second half, he sat with his parents, elsewhere in the auditorium. As the orchestra was tuning up, preparing to begin the second half, this little boy leaned over to his parents and said in a loud whisper, “Don’t worry: It’ll get better.”