SEATTLE -- For 12 of the last 13 summers, opera lovers and Richard Wagner fans have made pilgrimages from around the world to see the Seattle Opera's production of the four-part epic "Der Ring des Niebelungen."

But the last performance of "Die Go tterda mmerung" on Aug. 15 in the 3,000-seat Opera House could ring down the curtain on one of the most ambitious efforts a U.S. opera company has ever undertaken.

Despite the Seattle Opera's overall financial health, the "Ring" cycle won't be produced next year because of the cost, and General Director Speight Jenkins says that if it is ever resumed it would most likely be every other year, or perhaps two years out of three.

For the $3.3 million production in 1986, "82 percent of our money came from outside the state of Washington," Jenkins said. "I felt that it was time . . . to say to the people of the city, the corporate donors, the {individual} donors, 'Look, we can't always depend on the rest of the world paying for our product, which brings so much to us.' "

Last year the "Ring" cycle production had a $1.2 million deficit, a debt retired only after the 1988 cancellation was announced in March.

A double cycle of the "Ring," both the German and English versions, runs this year Aug. 2-15.

"Das Rheingold," "Die Walku re," "Siegfried" and "Die Go tterda mmerung," widely regarded as the most fiscally and artistically challenging series in opera, present a 16 1/2-hour tale of the force of greed and the power of love. Wagner took 26 years to complete the "Ring," scored for a large orchestra and numerous "heroic" singers.

The cost is enough to daunt even the biggest opera companies. Even at Bayreuth, West Germany, where Wagner built a theater to stage the "Ring" in 1876, it is generally presented for four or five years, followed by a one-year break before a new production is given.

Seattle Opera founder Glynn Ross, now 72, put the city on the world opera map with English and German versions of the "Ring," first in individual productions and then with the complete cycle, in 1975. Only in 1985, when a newly designed "Die Walku re" was presented as a prelude to a completely overhauled "Ring," was there less than a full cycle of performances.