Just inside the Washington Cathedral's south transept, to the right of the entrance, stands an unobtrusive iron gate. Behind the gate, which is usually locked, a stone stairway winds upward into the belltower. Every story or so, small Gothic windows let in a little light. It is like entering a monastery built in the Middle Ages, except that the stairs aren't worn hollow.

Up, up, until at the top of the stairs is another iron gate, and unlocking it, one finds a massive carillon of 53 bells. But there is more to the tower. A metal stairway circles dizzyingly toward the top floor. Some people just take the elevator.

From the top of the tower is the best view of Washington. It's a view usually enjoyed only by pigeons and, on Sunday mornings, a small band of bellringers who gather to play the cathedral's ten big bells.

The bells range in size from the treble, and F sharp, which weighs 608 pounds, to the tenor, which plays a D and weighs 3,588. They're much too big to play ordinary songs. Each bell swings on a wheel attached to a rope which hangs down into the ringing chamber through a hole in the ceiling. By the time the bell makes one revolution and can strike again, two seconds have passed. As ringing master Rick Dirksen says, "Think of a tune like Yankee Doodle Dandy or Jingle Bells being played at that rate, you can imagine." With that long a wait between notes, Jin . . . gle . . . Bells" would be a dirge.

And so the ringers, each assigned one bell, engage in the English art of change-ringing.

"Treble's going. She's gone," said the woman who was ringing the smallest bell, the bell that always starts a composition.

The ringers intently watched the "sallies," purple pieces of wool woven into the fabric of each rope. The movement of the sallies tells a ringer whose turn it is. Almost as in tennis, there's a handstroke (when a bell is mouth up, the hand pulls the sally when it's in front of the ringer) and a backstroke (after a bell swings down through a revolution and up again, the ringer pulls the tail of the rope).

"You'll wonder," said bellringer Bill Kollar, "are these people having a good time? They are. But they have to concentrate so hard, they haven't time for looking around. When you are ringing there is no world outside that little dais there. Sometimes during compositions, when you are flowing along with the rhythm, you have become so totally quiet, you let your subconscious take over."

If you've ever heard the cathedral's bells ringing -- sometimes for three or more hours at a time -- you know it's not simple. In fact, the goal and the challenge of change-ringing is to play all possible combinations of bells, where each one is played only once, without repeating a combination or "change."

For example, if a composition calls for seven bells, it will take 5,040 different changes before a pattern repeats itself. Try it, try writing all possible combinations of seven bells. Check it out on your pocket calculator: the math is 1x2x3x4x5x6x7. It would take about 3 1/2 hours to play. Anything over 5,000 changes is a successful "peal," an achievement to the bellringers, something to write in the cathedral record books.

Now if you were to use all ten bells in the Cathedral's ring in a similar way, there would be over 3 1/2 million changes. "It would take 101 days to accomplish," says Dirksen. "The neighborhood will be pleased to know we don't intend to do that." They plan to do a bit of ringing in January, though, ringing in the New Year, and then a quarter peal (an hour's worth of ringing), at noon on New Year's Day, and again on Inauguration Day, along with the usual Sunday stint from 12:15 to 1 or so. And sometime in January, they're not sure when, they want to try a full peal.

The Washington Cathedral has the only belltower in the world with both a swinging peal and a carillon. With a good wind behind it, the peal can be heard all the way down in Georgetown, whereas the carillon can only be heard within a few blocks.

The change-ringers don't play songs, the way a carillonneur plays songs on a carillon by hitting keys. They ring "methods," some centuries-old, with names like the Plain Bob Method, Stedman Caters, Grandsire Triples. For example, here's what the start of Plain Bob Minor looks like. (Anything played on six bells is called "minor.") The treble bell is No. 1, the tenor bell No. 6. As in all change-ringing, it starts with "rounds" -- 123456, to get the rhythm going -- and from one change to the next, a bell moves only one space at a time. Say, is this music, or just fun-with-math?

"The real learning process for a ringer," says Dirksen, "isn't memorizing all those numbers -- you'd blow your mind -- but to memorize the path of the bell. The line of the path is exactly the same for all the bells."

When Colleen Kollar first took up change-ringing, "I thought it was musical," she says. "But it was physically and mentally challenging. It doesn't take a lot of strength but it does take coordination.

"If you look out the window at night and notice the cars, you pay for it in the end. I don't do anything else that takes three and a half hours of undivided attention. You can't think about another thing."

She's an acoustical engineer, but doesn't make any connection between that and her interest in bellringing, which she learned in an intensive course at M.I.T. six years ago. She's married to Bill Kollar, and yes, the bells did bring them together.

Of the bellringers, says Bill Kollar, "Most either went to the Cathedral schools or got involved in the Cathedral and then gravitated toward it. You don't grow up saying 'i want to be a bellringer.'"

It's more of an avocation, a hobby. "It's doing something that's different and not easy," says Dirksen, "just like some people like to play enormous doublecrostics that make other people's minds bend."

Says another bellringer, John Matthewson, who works in Pepco's rate department, "When nothing seems to be going right, then you just concentrate on the meditation part of it. In order to really do it well, it has to be subconscious. I can see where people who didn't have some sort of hobby they could use to relax would just stay uptight."

One Sunday after ringing, Matthewson visited a friend and fellow change-ringer, Will Raglan, in his apartment across the street from the Cathedral. Raglan, a transportation analyst for the ICC, hurt his back ringing and was taking some time off from the bells. "Tennis would've done it," he said; and no way even an aggravated congenital problem in his back would keep him away for long.

It happened when he was called upon to help toll someone's passing with a quarter peal. "Aldo Moro died, so that did it," he explained. "I rang the tenor. Big mistake. Nothing happened, I just woke up the next day, a stabbing pain in my back."

Five years ago, spring and summer evenings, Raglan would go up on the roof of his apartment building with a bottle of wine and sit in a deck chair to listen to the bells. Finally he asked around and called the bellmaster, and pretty soon the Cathedral had a new change-ringer.

But not right away. As Dirksen says, it takes three years to get a start in bellringing: "The first six months to a year are just learning to handle the bells safely so you don't kill yourself or anybody else." The bells are stored mouth-down for safety reasons. "Part of the lore," said Raglan, " is regaling beginner with decapitation stories."

About one person in 20 stays beyond the first year. Said Raglan, "The people who succeed as ringers have the highest tolerance of frustration." "It's like basic training in endurance," said Matthewson. They'll be needing to train even more ringers when the belltower to the old Post Office Building is renovated and a ring of bells that was a bicentennial gift from a British foundation is installed, making it the 14th working peal in America -- a mere tink-tink compared to the more than 5,000 peals in the British Isles.

As the beginner well knows, there is the little matter of the mistake. "You're only as good as your weakest bell on a ringing team," says Dirksen. If you repeat a change the method is "false": It doesn't count in bellringer's terms; it's against the rules.

"You can have one ringer plain go to sleep on you," says Dirksen. "By the time you get straightened out, the shock waves to the rest of the band cause everything to fire off."

In a composition that calls for eight bells, the bells strike a total of 240 times a minute, 330 strokes for each bell. "If you're off by a quarter of a second," says Dirksen, "you strike in the wrong position. That's very close tolerance."

It's not like regular music: If the violinist is off by a quarter of a second, does the orchestra stop playing?

The ringers have great admiration for their conductor Quilla Roth. In fact, said Raglan, women make better bellringers. "Men have been taught that it's you up against it. But with the bell you can't win. It doesn't make any difference if you're Mighty Joe Young.

"You've got to be a manipulator. You ARE the bell. Women don't feel that they have to overcome it and prove 'I am stronger than a 3,600-pound bell.'"

"The Cathedral Ring," it reads on the plaque in the ringing chamber. "Cast by the Whitechapel Bell Foundry, Mears and Stainbank, London."

Unlike the bells in the Dorothy Sayers mystery The Nine Tailors, they have no names. They're inscribed, though. For example, the tenor bell says, "I will Magnify Thee Oh God My King." Some were given in memory of people who passed away; one has the name of the donor on it. The bells sit together in a circle up in the belfry, where louvered windows let out the sound from the 301-foot tower. Hanging them in a circle reduces tower sway when they swing.

Most people coming out of church will listen for the rhythm of the change-ringing and know whether it's good or bad, Bill Kollar said. To the untrained ear, listening to the bellringers even while your eyes watch them may not tell who's ringing what: it's that complicated. But as Dirksen pointed out in a recent Smithsonian lecture on campanology -- the study of bells -- it's possible to train your ear:

"Listen to one particular bell and focus your attention on the bell to figure out what change is being rung, or, for that matter, to see if the change is any good." To hear, in bellringer's talk, "if six is making seconds, leading, lying its two blows behind, or if it dodges, steps out of its hunting path." That means the sixth bell is ringing in the second place, in the first, in the sixth place twice or in a retrograde path for two rings.

It gets very cold in the tower, and by the time the day's final composition came 'round, it seemed very chilly indeed. But the ringers were undaunted, warmed by electric heaters suspended over the circular dais where they stood. Matthewson wasn't ringing this one, so he explained what was going on. It was time to bring the bells to a stop, mouth down. "They are ringing the bells down in peal. You'll start getting the harmonics in a minute, it's just lovely." Indeed the air above seemed to swell with a sweet humming, what the ancients might have called the music of the spheres.

There is something about bells.

"If you were to go up to the tower, completely alone, by yourself, at night," said ringing master Dirksen, "and walk into the belfry, where the bells are, the bells not moving, you would be aware of something. There's a feeling. It may have something to do with a knowledge of what sounds can be made, the capability there, I don't know.

"Bells are unique things. It's said that a bell is never still.Because a bell will absorb all the vibration of sounds, movement, and transmit it to a small degree.

"It's not something that you will say, 'Hah, there it is.' It's something you believe. It's like being in a room where you can't see anybody, but you know someone is in the room . . . something other than inanimate objects."