TITLES can serve as words of invitation into the world of an artwork.

So how's this for a ballet title: ''Quartet for Strings''? Does that excite your curiosity or set you quivering with anticipation? Well, then, what about this one: ''Telemann Overture Suite in E-Minor''?

Those are the titles of two new works the New York City Ballet has been offering during its winter season at the New York State Theater. ''Quartet,'' to Verdi, is a neatly made but uncompelling piece by Peter Martins. ''Telemann'' is the promising choreographic debut of Melissa Barak, a member of the company. However, what is worth considering here is not the artistic quality of those ballets, but their titles and what those titles reveal both about the New York City Ballet and about much recent American choreography for ballet and modern dance alike.

American dance is obsessed with, or even tyrannized by, music. Of course, dance and music have been partners for ages and deserve to continue their pas de deux. Yet fundamentally dance does not need music. Dance needs rhythm. And rhythms can be established by the regular or irregular ways bodies move in space, even without vocal or instrumental accompaniment. Thus some choreographers have created effective dances in silence, or to sound effects.

Most choreographers, though, like music, and it's not hard to understand why. Music sounds good. It can intensify mood or atmosphere. And its formal sonic patterns can suggest movement patterns.

Nevertheless, dance is not a subdivision of music, but an independent art. And dance works are more than music-appreciation lessons.

Much of American dance's addiction to music can be traced to the influence of George Balanchine, a great choreographer who was musically sensitive to an extraordinary degree and who titled many, but by no means all, of his ballets after the scores to which they were set. He even renamed some productions to honor their music. Thus his ''Ballet Imperial'' of 1941 has since 1973 been known as ''Tchaikovsky Piano Concerto No. 2'' and ''Le Palais de Cristal,'' created in 1947, became ''Symphony in C'' a year later.

Until his death, he continued naming ballets after scores. Among his works being danced this season by New York City Ballet are ''Divertimento No. 15,'' ''Duo Concertant,'' ''Kammermusik No. 2,'' ''Stravinsky Violin Concerto'' and ''Tchaikovsky Suite No. 3.'' Other choreographers for the company have sometimes followed his example, as ''Quartet'' and ''Telemann'' demonstrate. And ballet and modern-dance groups around the country often choose similar musical titles for works.

There's nothing necessarily wrong with this practice. Choreographers should have the freedom to call dances anything they choose, just as abstract painters have been known to give canvases with slashing lines and vibrant colors such noncommittal titles as ''No. 17'' or ''May 23.''

Yet this proliferation of musically titled dances makes me fear that many choreographers may be limiting their inspiration to music alone. Balanchine once termed music a floor for dancing, an image implying that dances are like houses. But houses have features other than floors. For instance, they have windows and doors by which the outside world can be let in or out.

So, too, other factors than music can influence dance. Indeed, aspiring choreographers might find it valuable to study painting and sculpture to gain a sense of volume, shape and grouping. Literature and mythology may provide ideas for dramatic or emotional content. Historical periods, and an awareness of the clothes and etiquette of those periods, might challenge choreographers to devise striking ways of moving. And there is no reason to ignore the excitement of contemporary life outside the dance studio.

Of course, audiences have often had to sigh over emotionally excessive or dramatically lugubrious dances filled with grimaces, pompous poses and frantic arm waving. And such histrionics have turned up in both expressionist modern dance and ballets inspired by literary classics. However, audiences today must do their own sighing over musically based dances in which, to the sounds of the notes, performers jump about with more precision than expression, as if they were nothing more than metronomes with feet.

In addition to rousing fears that titles based on scores may indicate a restriction of choreographic imagination, such titles are bothersome simply because they are dull. How can they possibly rouse an audience's interest? Is anyone so prosaic as to think ''Tchaikovsky Piano Concerto No. 2'' is more appealing than ''Ballet Imperial''?

Conceivably, choreographers may not want to reveal too much with their titles and thereby rob theatergoers of the thrill of discovering a new work's content. Balanchine himself may have occasionally wished to surprise audiences. One of the most cumbersome and, for anyone not fluent in German, unpronounceable titles in the entire Balanchine canon is ''Robert Schumann's 'Davidsbündlertänze.' '' That title is simultaneously musically correct and emotionally neutral, hinting nothing whatsoever about what goes on in this work from 1980. At first, the ballet appears to depict people at a party. Then Balanchine throws in his surprises. The choreographic tone gradually darkens until one realizes that this is not just a ballet about a party but a somber portrait of a man on the brink of madness. A first viewing of ''Schumann,'' as it is sometimes called, can be genuinely startling.