Imagine that Shakespeare had titled that play “The Murder of Gonzago” rather than “Hamlet” and you will have a good notion of the conceit of Richard Rodney Bennett’s “The Mines of Sulphur,” which had its City Opera premiere on Sunday afternoon.

Since we know who the killer is from the start, “Mines” is not a mystery per se, but rather a Victorian-Gothic summer-stock sort of potboiler. The story is rather simple. Three nefarious characters (one of whom, in dry English style is named Tovey, after the most influential of all British music critics) kill a landowner for his wife’s jewelry. Hiding out at his estate on the moors, they are visited by a traveling troupe of players, who trade a performance of a play for shelter. The play, called “The Mines of Sulphur,” is about a plot to kill a count. You can pretty much guess the rest.

For a critic, it was refreshing to attend a performance where there were no preconceived notions, since the work and the composer are both relatively obscure. Many people who think they know of Richard Rodney Bennett, who was primarily a film composer, are actually confusing him with the American cinema arranger Robert Russell Bennett who, like the British Bennett in question, lived on the fringes of the classical music world (he once wrote a symphony about the Brooklyn Dodgers). If only “The Mines of Sulphur” hadn’t been such a dud, the experience of listening to something new would have been highly pleasurable.

Musically, it is easy to hear why this piece is such a marginal one. This is movie music pure and simple, totally reactive to the proceedings on the stage. There is never even a hint of melody in the score – not a scintilla, not an iota, not a subatomic particle of tunefulness. This may sound like a rant against the modern but is far from it. I don’t care if it is dodecaphonic, neoclassical, atonal, aleatoric, or diatonic, music has little dramatic value without any sense of melody whatsoever.

Oddly, there was quite a bit of inventiveness in the orchestral parts. Music director George Manahan led his instrumentalists in a reasonably clean version, although there were certainly passages that did not hold together that well.

And what of the singers? Well, it is a bit of a fool’s errand to evaluate them, since they were never asked to string two sentences together. Each sung utterance was simply a line of dialogue with a definitive ending; therefore, any considerations of lyricism or phrasing went out of the window. Breath control was a nonissue as there was always a chance to pause between lines. Further, because of the microphone system at the New York State Theater, volume level was suspect. And since the individual roles were at best two-dimensional, there was little opportunity to judge whether the singers could act with their voices.

I suppose the most praise should go to Mark Duffin as the chief killer and Caroline Worra as “the girl in the play,” since they had the most to do and, as I often opine at City Opera, seemed to do it well.

Considering how little they had to work with, the production crew at City Opera did an excellent job of mounting this already dated theatric. The set of James Noone was a functional, three-story affair complete with dramatic staircases used in a dreamlike manner. The lighting of Kevin Adams was suitably spooky and occasionally bejeweled.

A much more difficult task was mastered by director David Schweizer. There are really no characters in this story, and there is no character development. Everyone is a medieval archetype whose lines are about as emotional as those of Everyman. Casting falls into three distinct categories: young and attractive, middle aged and dowdy, or old and grizzled. There was even a mime. How Mr. Schweizer made any of this interesting shows his ability to improvise.

Among the touches that enhance the experience for the crowd is the decision to have the evil trio come up out of the audience when Act II begins. When the killers become the audience for the play within the play, it focused our attention on the moral relativism of the action. Of course, it also calls into question why we are watching such an objectionable performance on the stage within the stage; in fact, I asked myself that question several times in the course of the opera.

And did I mention that there were no melodies?

“The Mines of Sulphur” will be performed again tonight & October 27 and November 2 & 5 at the New York State Theater (Lincoln Center, 212-870-5570).