The ringing that some Northwest Washington residents heard around noon yesterday was not all in their heads.

The tintinnabulation that cascaded down on them flowed from the beige stone bell tower of the Washington Cathedral and was one of the most complicated, most dramatic and most uncommon methods for making music.

Inside a brick-and-stone-lined room near the top of the tower, eight ringers, including a Virginia housewife, an assistant headmaster at the National Cathedral School and a computer operator, rang in the New Year by trying a complex mathematical and mental exercise known as a "full peal" of eight of the cathedral's 10 heavy bronze bells.

The trick for each ringer in a full peal is to take part in the ringing of the eight bells, which vary in weight between 712 to 3,588 pounds, in more than 5,000 sequences without repeating a sequence, without stopping and without forgetting one's place in each sequence.

Shortly after noon, four women and four men, all casually dressed and wearing comfortable shoes, grasped their 40-foot long ropes of cotton hemp and started pulling. The rope-pulling swung the bells in the room above them and the tongue of each bell struck a bronze side, creating eight different pitches in tone. They hoped they would have their hands and arms over their heads for the next three hours: the time it would take them to complete the 5,088 different sequences or "changes."

"If a ringer loses his place and forgets what position he has, it has the rapid potential for throwing everybody off," said cathedral bellmaster Richard S. Dirksen, 37, who earns his living as the assistant headmaster for finance at the National Cathedral School.

One missed beat or one momentary loss in memory can doom a peal because stopping and starting again is prohibited.

A full peal is attempted to mark special occasions and holidays. The cathedral's corps of all-volunteer bell ringers, known as the Cathedral Ringing Society, compiled a mixed record in 1981. According to the record book they keep of their successes, and they only record successes, a six-bell peal was completed last New Year's Day in two hours and 49 minutes. The Memorial Day peal and a special peal July 22 ("just for the fun of it with with 'yoked' or silenced clappers") were both successfully completed, Dirksen said.

What that record means is that the ringers failed on the Fourth of July.

Today's pealers carry small books that contain columns of numbers that they must memorize, for these are the sequences that tell them when their bell must be rung.

The importance of mathematics over music accounted for the trio of engineers in the group: Bill and Collen Kollar, a husband-and-wife team from Washington, are consulting engineers, while Richard Simpson of Middlsex, England, is an electronics engineer who is working here temporarily.

The other ringers were Quilla Roth of Washington, who manages a computer time sharing program; Mary Clark, an Arlington housewife and former music teacher who has watched the building of the cathedral and been fascinated by the bells, and Eddie Martin, an English art teacher who recently moved from Washington to West Lafayette, Ind., and Sue Unsworth, also from England, who has been working in the U.S. for a year.

Yesterday's peal was proceeding quite nicely when suddenly "a couple of ringers got crossed up and lost their position," causing other bell ringers to become confused, Dirksen said.

Dirksen tried in vain to restore the rhythm, but it was lost and at a few minutes after 1 p.m. the bells were silenced.

They will remain hushed until Easter.