Finishing composers' unfinished work

Finishing the unfinished seems to be a constant obsession with some music historians. The list of important works left unfinished is not particularly long, but it does involve some particularly beloved composers. Beethoven was working on a Tenth Symphony, of which he left some sketches. Mozart was working on a ''Requiem,'' which was finally rather weakly finished by F.X. Sussmayr. Schubert wrote only two whole movements of his Eighth Symphony and some sketches of a scherzo before abandoning the work altogether.

Bruckner completed three movements of his Ninth, leaving behind several hundred pages of sketches, scorings, and instructions for the final movement. Mahler completed an adagio and a small movement he entitled a purgatorio, and he fully sketched out the rest of his Tenth Symphony. Puccini never lived to finish ''Turandot,'' so Franco Alfano was asked to complete the opera based on sketches the composer had already written out.

Of the above list, Puccini's ''Turandot'' and Mozart's ''Requiem'' are the only works to have entered the standard repertoire, complete with their un-original endings. Mahler's Tenth was put into performance shape by the late Deryck Cooke, and this version was given a hearing at the New York Philharmonic a few weeks back, under the direction of Kurt Sanderling. I've also heard an inadequate performance by the Boston Symphony Orchestra of the version in 1979. Recorded performances by James Levine and the Philadelphia Orchestra (RCA digital CTC2-3726) and Simon Rattle and the Bournemouth Symphony (British EMI digital SLS-5206) have been available for several years now.

There is something odd about finishing musical compositions. Nobody runs around trying to finish unfinished Da Vincis, or uncompleted Michelangelos. Yet with music, there is the compulsion to finish, even if the effort is based only on sketches and motifs.

Mahler - a furious reviser - only sketched out his Tenth Symphony. Therefore, we will never know what he would have done to make it a worthy successor to the extraordinary ''Das Lied von der Erde'' and the Ninth Symphony. Mr. Cooke had the good sense to declare that his effort simply represented ''the stage the work had reached when Mahler died, in a practical performing version.'' He also noted it was impossible to ''complete'' the Tenth - only Mahler could do that. Even today, the august Mahlerians such as Rafael Kubelik and Leonard Bernstein refuse to perform the completed Mahler Tenth.

One hears the potential scope of the work, the emotional torture of the adagio (which is frequently heard alone in concerts), followed by a long but unassuming scherzo Mahler would clearly have improved upon. The fourth movement, a demonic outburst of frighteningly strong Mahlerian dimension, is succeeded by an intermittently glorious finale that brings this uneven musical journey to an end.

More emphatic is the case to be made against finishing the Bruckner Ninth. This symphony has just been given its final movement, based on extensive sketches and scorings by Bruckner. William Carragan has put it together, and the American Symphony Orchestra, under co-principal conductor Moshe Atzmon, offered the world premiere reading of it in Carnegie Hall Jan. 8.

At Mr. Carragan's own admission, only 70 percent of the score actually exists , some sections in as many as five versions. There are places where nothing exists at all, though Carragan convincingly maintains they were written but are simply missing.

So a major labor of love and affectionate hypothesis notwithstanding, there is just enough missing in the finale of the Ninth, even in sketch form, to call the entire project into question. In performance with the American Symphony Orchestra it too often sounded skimpy - lacking the stirring underpinnings, the richness of orchestrational textures, the utter transcendency of vision - that mark Bruckner's late music.

Some of the harmonically daring things the composer was exploring in this symphony come to light in the finale, and the big chorale that dominates the movement is impressive indeed. But then there is the coda, which has no vitality or originality and sounds too much like the coda to the Eighth to be really convincing.

Of course this is based on one listening and on Carragan's first try.

Bruckner and Mahler kept improving on themselves, finding new ways to say new things. For both, from their last works, it was clear that new vistas were opening up to them. Had they finished their works, something altogether exceptional would have come of them - this much is clear from both projects.

But trying to treat either of these versions as valid samples of the composer's craft would be like calling legitimate an art restorer's attempts to put arms and a head on Venus de Milo - we would have someone's educated guess as to what it might have looked like but we will never know for sure. Should we even be bothering?