Since, as everyone knows, Ludwig von Beethoven wrote only nine symphonies, how come the London Symphony Orchestra under conductor Wyn Morris made a recording the other day of Beethoven's Tenth?

And how come the Royal Liverpool Philharmonic under Walter Weller is giving the Tenth Symphony's first-ever public performance in October? Is this all a joke?Far from it, say renowned Beethoven expert Barry Cooper and scholars who are convinced that Cooper's five years of sleuthing have recovered what Beethoven was writing when he died 161 years ago.

It is a fascinating tale that begins on Beethoven's deathbed in 1827.

Tormented by pain and poverty, the great composer asked the London Philharmonic Society to organize a benefit performance for him. Instead, the society sent 100 pounds - $175 now, but worth a great deal more then - to help with Beethoven's "comforts and necessities."

The help came too late. But Beethoven was so grateful he promised by letter he would give London his Tenth Symphony to "prove to those magnanimous Englishmen how greatly I appreciate their sympathy for me in my sad fate."

Sketches for the symphony, he wrote, "are already in my desk."

Beethoven died eight days later. And researchers found no new symphony in his desk or anywhere else.

Karl Holz, Beethoven's secretary, insisted that the composer had played him the new symphony's opening. But with no physical evidence, scholars for 150 years discounted Holz's tale. . .

. . . Until five years ago, when Cooper found among Beethoven manuscripts in a West Berlin library a set of sketches precisely matching Holz's description of the music Beethoven played on the piano.

All the experts had identified these sketches as an overture Beethoven never finished. But Cooper, 39, a lecturer in music at Aberdeen University and author of several books on Beethoven, found a note in the composer's handwriting on one page of the notebook saying, "end of first movement." The next page referred to "the new symphony."

Cooper discussed his "Tenth Symphony" theory in an article in a scholarly journal. The week it went to press the curator of Bonn's Beethoven archive announced the discovery of additional sketches closely resembling those in Berlin.

"By combining the two sets," Cooper says, "I began to find what Beethoven had in mind for the first movement."

Intrigued, he collected every scrap of Beethoven's notes - none lasting more than 20 bars, or a few seconds - and laid them end to end. Suddenly he had the shape of a symphonic first movement.

That was hardly the end of it. Cooper turned it into proper music.

"I tried to keep very close to the sketches, to reconstruct the movement as Beethoven envisaged it at that time," he says.

"I had to fill in some harmonies and compose a few linking sections myself, but I did not invent any new themes. Those are all Beethoven's.

"One is hesitant to do this sort of thing, because I'm not Beethoven and therefore I cannot do it as well as Beethoven. But everyone wants to hear the music.

"Only a few specialists who have studied learned journals have any idea. So I'm trying to make it more widely available, to give a kind of artist's impression of what he had in mind."

Music critics who have heard the result say it sounds more like early Beethoven than something written when he was 56 and dying.

"Having listened to it for 15 hours at the recording session, I can say it is extremely convincing," said Alexander Waugh, an executive of the company that is releasing the 19-minute "Tenth" on the Pickwick label in Britain and MCA in the United States.

"It shows Beethoven kicking off in a new direction, looking back toward the romantic period of his Fifth and Sixth symphonies," Waugh said in an interview.

"The recording was edited last night - we were all up until 2 a.m. doing it - and we're trying to rush it out by the time of the world premiere."

That performance, by the inheritor of the society to which Beethoven pledged it, is in London Oct. 18. It will be the first public chance to hear the Tenth Symphony Beethoven never finished.