It's a Festival Tuesday at 9.30am.

Donald Macleod and his producer, Serena Field, are huddled over cups of tea at the Queen's Hall café, fine-tuning the morning's script down to the last adjective. In 90 minutes they'll be "handed over the network" - meaning that BBC Radio 3 will be broadcasting live from a little white van parked by the recycling bins round the back of the Queen's Hall.

This year Radio 3 is live-transmitting 15 of the Edinburgh International Festival's 18 morning recitals, and recording a further five concerts (four at the Usher Hall, one at The Hub) to broadcast at a later date. For many listeners who can't make it in the flesh because of geography, work commitments, mobility problems, ticket costs or ticket availability, these radio broadcasts are a way of dipping into festival atmosphere and experiencing the classy rostrum of artists showcased therein.

It's worth noting that because these concerts are EIF productions (ie. they aren't actually hosted by the BBC) it's the festival who runs the show and the radio crew who has to fit in as unobtrusively as possible. And that means getting the timing right. "We have to be ultra-flexible and at the same time water-tight," says Field as she tallies up the tracks she's planning to use during the interval. "Of course, with Donald the whole hall could collapse and he would keep talking, steady as a rock."

Macleod is one of Radio 3's surest pairs of hands. Glasgow-born and a famous BBC voice for more than 30 years, anyone who listens to the station would instantly recognise that inimitable singsong, soothingly knowledgeable intonation. He's been introducing Composer of the Week for nearly 15 years now, and every year takes a holiday in August to come up to Edinburgh and present some of the Queen's Hall series.

"I'm afraid it's a real busman's holiday," he says with a bashful shake of his head. "And it's always a bit of a shock to the system to emerge out of my monastic day-to-day life researching Composer of the Week.

"Listeners accost me at Waverley Station - yesterday I stepped off the train and somebody tapped me on the shoulder and said, 'you realise you are part of my daily life'. People have given me little poems, last year a gentleman presented a drawing of me that he'd done in a restaurant. They say it's nice to meet the face behind the voice. It's all very touching, really."

Macleod knows he can talk at a rate of approximately 174 words per minute, give or take a few. And on this particular morning he knows roughly how long it will take Argentinian mezzo Bernarda Fink to walk onto the stage; how long she'll rest between songs; what she'll sing for her encore, and how long that will take. Even so, he has written reams of extra script, just in case. "The singer might lose her nerve, the pianist might lose his music. I've seen it all happen and had to chat my way through it."

Here's how it all comes together:

10.30am. Set-up in the hall is complete, and relatively simple at that: just a couple of stereo microphones slung across the stage, a pair of mics at the end of the piano and a single stand in front of the singer. For an orchestra it would be 10 times this complex, engineer Paul Sumerling explains, and although the radio team sometimes positions microphones over the audience, the Queen's Hall is small enough for the atmosphere to seep through without needing to amplifying the coughs and fidgeting as well.

10.45am. Macleod is installed upstairs on the balcony, tucked away out of sight of the stage. He sits at a rickety little desk cordoned off with yellow masking tape like a tiny BBC crime scene. At his feet is a huge reel of cables, and the desk is neatly crammed with lamps, a small fader, a glass of water, a blue spotted handkerchief and the all-important green light. "No matter how many times I do this, I still get a dry mouth and heart palpitations," he says, shuffling through his notes one last time and checking his watch.

11am. The Radio 3 network passes from Broadcasting House to the radio van at the Queen's Hall. Macleod begins to speak into an old-fashioned lip mic that looks as though it's been around since the dawn of the BBC. His timing is impeccable - beautifully paced to leave just enough rhetorical silence between phrases and allow the applause to filter through. A few audience members turn to eyeball him as he talks but he carries on without a blink.

11.50am. It's interval down in the radio van and all is not quite so calm. Crowded into the tiny space there's a vast mixing desk, several CD players, two producers, two sound engineers, a TV screen showing the stage, several angle poise lamps, a pile of scores and various versions of the show's running order. Fink retakes the stage for the second half and the producers follow along with the scores, giving Macleod cues 10 seconds before the end of each song.

The team has control of the Radio 3 airwaves from 11 until the 1 o'clock news - or to be more precise, until anywhere from 12.58'30 to 12.59'59. The timing of live broadcasting is an exact science with a moveable target, the producers tell me, teeth gritted in concentration. Because the concert almost certainly won't fill the two hours exactly, the team's mental arithmetic must be fearsome.

Today Fink takes extra time in her encore, really stretching out the nuances. But having made a full eight contingency plans of various-length tracks to fill time until the news kicks in, Field just shrugs. "She's keeping us on our toes. It's all part of the game."

bbc.co.uk/radio3