It is maybe the most charming name on the current New York scene: “Pedals and Pumps: A Festival of Organ Divas.” This is a series of organ recitals held at Trinity Church, at Broadway and Wall Street. They take place on Thursday at 1 o’clock. All the organists are women. And last Thursday’s recitalist was Jane Watts, of Britain. Since 1991, she has been affiliated with the Bach Choir (London).

Trinity literature says that the series “highlights contemporary female musicianship” — a gag-making phrase. There is no female musicianship; only musicianship, good or bad (or in between). The recitalists, I believe, would hate that phrase, if they saw it.

And shouldn’t music be separate from race, gender, and other non-musical things?

But the Trinity series is a nice idea, or, at a minimum, harmless. The setting is beautiful, orderly, and composed. And the recitalists have a new instrument to play on: installed in 2003. Moreover, video monitors dot the church, so that everyone can see hands, feet, etc.

Ms. Watts began her program with a piece by her fellow British organist, Simon Preston. This was his “Alleluyas” — and, in it, Ms. Watts was very, very assured. This would turn out to be a hallmark of her recital. She was correct, sensible, and authoritative. She employed many of the colors that the new organ has to offer. And she knows to wait on her sound — to let it clear out, before the music proceeds.

(At the same time, she does not wait too long, which is equally critical.)

To say again, Ms. Watts was unusually assured — she scarcely put a foot (or hand) wrong. Mr. Preston’s “Alleluyas” was a bracing experience. And when the organ swelled, one’s body seemed to, as well.

We were reminded why the organ is called “the granddaddy of instruments.”

Ms. Watts continued with music of Lloyd Webber. Variations on a Theme from “Phantom of the Opera”? No, this was William Southcombe Lloyd Webber (1914-82), father of Andrew (and of the cellist Julian). Ms. Watts played his Arietta, a gay little tune with embroidery. This little tune is a nothing-burger. But Ms. Watts played it with delicacy and taste.

Then came a work by Marcel Dupré, the great French organ master (1886-1971). This was his Prelude and Fugue in G minor, Op. 7, No. 3. The prelude is ghostly and fleet, reminiscent of the famous last movement of Chopin’s Piano Sonata in B-flat minor. Ms. Watts played it with stunning — I do mean stunning — virtuosity. Her accuracy was uncanny. And the intricate fugue was extremely clean, with every voice clear. And yet those voices formed a proper whole.

Lloyd Webber returned with the Andantino alla cantilena — not a nothing-burger. It is an admirable brief piece, expressing what, to my ears, is typical British melancholy. Ms. Watts gave it its due.

And then she closed the program with a big piece by another French organ master, Alexandre Guilmant (1837-1911). The work in question was the Sonata No. 5 in C minor, Op. 80. It is in five movements, and not exactly a great work — the Adagio is notably weak. But there is greatness in it. And Ms. Watts played it for all it was worth.

The opening movement, Allegro appassionato, was a sheer joy. And the soloist seemed to joy in playing it. Guilmant’s music was bold, grand, arresting, and vivifying. Listeners will not soon forget its pealing ecstasy.

The third movement, Scherzo, had precision and panache, and just a hint of madness. (There are some who say that madness is built into the organ literature.)

As for the last movement, it is a chorale and fugue. In the first, Ms. Watts conveyed the right measured calm; and in the second, she was ennobling and uplifting. Her recital was a most satisfying hour.

Seldom do you hear an instrumentalist so confident and capable as this Jane Watts of Wales (to be specific). She demonstrated total self-possession (in addition to ample musical knowledge and other necessary assets).

And it’s good to have an organ series, for the literature of that instrument is both vast and impressive. Think of the works of Bach alone, so many of which go unheard in the contemporary world. The organ literature is shamefully underheard. So is the choral literature — but we can deal with that some other time.