After months of fruitless negotiation, musicians in the Utah Symphony voted this week to go on strike.

That's a serious blow to the cultural life of the community and one that must be resolved as quickly as possible. A long strike could affect the very existence of the orchestra.Unfortunately, the two sides are so far apart that the walkout may last longer than the only other strike in the symphony's history - a five-day impasse in 1983.

Faced with operating deficits, a shortfall in donations, and a shrinkage of the symphony's endowment fund, management asked orchestra members to reduce the symphony season by two weeks and take what amounts to 5 percent salary cut.

The musicians first asked for a 20 percent one-year salary hike. When that was rejected, they sought a larger increase spread over a three-year period, noting that their base pay of $28,000 a year is well below what orchestras with smaller workloads are getting elsewhere.

The symphony season is supposed to begin next week and there is no time to be lost. Canceled playing dates or refunding of tickets would make an already shaky financial situation even worse.

The best thing would be for the musicians to play and talk so the season would not go down the drain.

The musicians must recognize that the symphony management can't make promises or spend money it doesn't have. The non-profit organization showed a $1 million deficit in 1987 and has a current operating deficit of $280,000 on a $5.1 million budget. The endowment fund - badly hurt by last October's stock market crash and the continuing operating deficits - has shrunk from $5 million to $3.5 million.

Clearly, a 20 percent or more salary hike in such circumstances is like asking for the moon.

At the same time, the symphony needs more public support in the form of contributions. The orchestra is a major selling point in the quality of life in the community and in advertising Utah as a good place to live - a significant factor in luring new industry.

This is true, not only of the symphony, but other performing arts as well. Business firms and private individuals should join hands in providing broad-based support to ease the crunch that has the arts living from hand to mouth year after year.

A proposal made a year ago by the new manager of Ballet West ought to be dusted off and examined once more. Trevor A. Cushman, a Massachusetts native, says other communities have had success with a "united" approach to raising money for the arts, instead of the symphony, the ballet, the opera and dance companies, all competing against each other for donations.

In addition, he says the $1.5 million earmarked by the state for support of the arts should be doubled and $1 million a year placed in an endowment fund. After 20 years, the interest would eliminate the need for the state's contribution.

That makes sense, yet doubling the money for the arts may be only a dream, given the financial problems that may face the Legislature next winter. But something has to be done to bolster support of the arts.

Utah has a proud cultural reputation as a well-known center of the arts. To lose that reputation would be more than Utah could afford.