MORE THAN 60 years ago Igor Stravinsky composed "Pulcinella," a ballet based entirely on music by a "celebrated Italian composer whom I valued and admired: Pergolesi." Many years later, however, it became clear that Pergolesi had relatively little to do with it. The vocal numbers (which are not included in the purely orchestral "Pulcinella" Suite) were indeed drawn from operas and cantatas by Pergolesi, but the bulk of the work was based on the Trio Sonatas, which, we know now, was written by Domenico Gallo, and on the other instrumental pieces in which Pergolesi had no hand.

It appears, in fact, that Pergolesi actually composed none of the instrumental works attributed tohim, and the most familiar of these, the six concertini -- or, more properly, "concerti armonici" -- for string orchestra, have been the most baffling in terms of authentication. Over the years they have been attributed variously to Carlo Ricciotti, to Fortunato Chelleri and to Joham Adam Birkenstock.

Recordings have been released under Ricciotti's name, and the Frankfurt scholar Helmut Hucke, in researching the sources of "Pulcinella," wrote "Probably Chelleri." It turns out now that the corrct answer is "none of the above."

Last year Albert Dunning published conclusive proof that the six concertos were actually composed by amodest Dutch nobleman and amateur musician, Unico Wilhelm, Count of Wassenaer (1692-1766). Dunning's explanatory essay appears with the new recoridng of these works -- the first under Wassenaer's name -- by I Musici. The two-disc set (Phillips 6768.163) also includes a pair of violin concertos whose attribution to Pergolesi is described by Dunning as "extremely doubtful," but for which no other composer is suggested.

Pina Carmirelli is the excellent soloist in the two violin concertos, which are more than agreeable, whoever may have written them. The performances of the six "concerti armonici" are also up to the formidable standards of I Musici, and the sound is both warm and well detailed. Since the violin concertos are hardly indispensable, though, one might question whether it is necessary to spend so much (list price $19.96) to enjoy the six other works, which happen to be available uncut on a single low-proced disc from the Musical Hereitage Society (MHS 3940) in possibly even more fetching performances by the Jean-Francois Pailard Chamber Orchestra.

MHS lists Ricciotti as the composer, and Marvin Paymer's annotation adivses that the "irresponsible" Opera Ommia edition of Pergolesi's works gives a different enumeration for these concertos from that of the original Ricciotti edition. (Ricciotti did have a part in the appearance of these concertos -- as the original publisher.) "Irresponsible" or not, it is the Opera Omnia numbering that is followed on MHS (as it was also by Karl Muenchinger of London), and, to make matters still more interesting, there is a confusion in the labeling of two of the concertos.

Here Nos. 5 and 6 are both listed in B-flat, though one is actually in E-flat, and their numbers are switched. In other words, Ricciotti No. 2/Opera Ominia No. 6, in B-flat (whose finale became the Tarantella in "Pulcinella"), is listed on MHS AS No. 5 in B-flat, and Ricciotti No. 6/Opera omina No. 5, in E-flat, is listed as No. 6 in B-flat. What?

Aside from the compounded confusion, though, the Paillard record is a genuine bargin, offering stylish and enlivening performances of all six concertos on two sides instead of three. The new Philips set is quite appealing in its own right. It brings two new violin concertos to puzzle over, and contains that interesting essay by Dunning on Wassenaer and his background. Those who invest in the Philips for the documentation will not be disappointed; it is good to have that mystery solved at last, and everyone ought to have one or the other of these fine recordings.