Does modern music have a romantic streak?

A new romanticism in music? The question is being explored in the New York Philharmonic's unprecedented series of six concerts, an open rehearsal, and numerous symposiums with composers and friends of new music.

''Horizon '83'' poses the question: ''Since 1968, A New Romanticism?'' It is a brave idea, devoting so much time and expense to new and often difficult music composed during this time. More typical of the Philharmonic's efforts at the time is the fact that the late conductor Andre Kostelanetz tried to duplicate the Arthur Fiedler Boston Pops magic in the Big Apple.

Even with various flaws - mostly quite minor in retrospect - ''Horizons'' is emphatically an important addition to the concert scene. The Philharmonic players, it must be noted, seemed to respond to the challenge of the music with dedication, care, and commitment - something rarely seen in standard subscriptions series.

The first three concerts gave a hearty sampling of what ''new romanticism'' might just be all about. Jacob Druckman, the composer-in-residence here, put this ambitious series together, and he has chosen a wide spread of compositional types. The thesis seems to be that music since '68 has become mightily influenced by the Romantic composers of yore, from Berlioz through Mahler.

Curiously, not all of the 12 works heard the opening weekend reveal this influence. The first two programs seemed more like marathons of endurance rather than savvily constructed arguments for the thesis.

But I come not to bury Mr. Druckman (and the Philharmonic) for undertaking this festival, but to praise him (and them). The Philharmonic has taken a bold step during this increasingly conservative era in devoting so much time to the relatively new. After all, new music is not popular. Subscription audiences flee the contemporary almost without exception (they even flee turn-of-the-century music if there is nothing hummable about it).

Everyone in the music business complains about the problem. But few are willing to do much about it, apart from the occasional commissions and world premieres. The Philharmonic's batting average has been higher than most, but this festival puts them in something of a vanguard: There are few other cities where the symphony organization is actively involved in the presentation of new music.

Not that this festival is without flaws. Mr. Druckman's programming is not exactly skillful. The best pieces on the programs tend to be oppressed by the lesser ones. The attempt to include all the New York contemporary performance groups made the two opening programs unwieldy. In some cases, composers on the program have clearly not been touched by anything Romantic or even heartfelt, writing today in the same style as a full decade ago.

''New romanticism'' is most audible in David del Tredici's ''All in the Golden Afternoon.'' This is still more of the composer's ''Alice in Wonderland'' music, and it tends to go on too long for the material presented. But it is consistently entertaining and utterly, if raucously, accessible, with a tune repeated so often it is etched in the mind's ear forever!

Other composers have softened their hard-bitten ways with the musical form called seriality, and the result is quite startling in some cases. One would hardly expect opulence and sheer beauty from Toru Takemitsu, but his ''Far Calls , Coming Far!'' is just that - a shimmering, vibrant work for violin and orchestra that ends long before one wants it to.

The major discovery of the trio of evenings is the John Harbison Violin Concerto. Though it received the drabest, least colorful possible performance from associate concertmaster Charles Rex (beautiful tone, little content) and conductor Arthur Weisberg, one could clearly hear a work of haunting beauty. Mr. Harbison does not venture into new forms, but he broodingly, meltingly exploits contemporary harmonies and eventually incorporates a touch of hoedown fiddling into what emerges as a refreshingly unpretentious American work.

Morton Subotnik's ''Ascent Into Air'' showed a warmer side than usual to his live-with-computer compositional style. Marc-Antonio Consoli's ''Afterimages'' (a world premiere) appeared to lack a clear sense of purpose and forward motion. Donald Martino's ''Triple Concerto for Clarinet, Bass Clarinet, and Contrabass Clarinet'' had an interesting idea (splitting the solo line among three instruments of wide, wide range), but lacked the least hint of spontaneity and beauty in its aggressive tone-clustered meanderings.

Fred Lerdahl's ''Chords'' (world premiere of the revised version) offered some gorgeous moments without real cohesiveness. Sandor Balassa's ''Lupercalia, '' billed as a tribute to Stravinsky, suggested that composer only in a few shrieking chords. Peter Maxwell Davies's ''Ave Maris Stella'' deserved a better performance than it got from the New York New Music Ensemble, though only parts of the score really take wing.

Barbara Kolb's ''Chromatic Fantasy'' proved to be a slender divertissement with Tony Randall the narrator. Leonard Rosenman's exploration of microtonalities, entitled ''Foci I'' (world premiere of the revised version) captured the ear quickly and held interest throughout.

John Adams's ''Grand Pianola Music'' was evidently the composer's attempt to write a controversial, even vulgar work that remains true to its minimalist roots while incorporating a pop beat and harmonies. Mr. Druckman conducted the score rather too seriously, and too many seams showed through. It was constantly entertaining, though a surprisingly hostile segment of the audience thought otherwise - and quite vocally - at performance's finish.

The Horizions comes to an end tonight. Here's hoping the concept does not come to an end as well. The audiences were larger than expected (the price for all seats was $8), and this sort of high-profile series can only help to win further friends to the new. Perhaps the next time around fewer pieces will be better juxtaposed on each program. Maybe the pieces chosen will better bear out the premise of whatever the new series will be named.