Jonathan Mills's head was spinning. He had come up with a brilliant stroke of inspiration for his first programme as the new director of the Edinburgh International Festival. Central to it would be a production of Monteverdi's seminal 1607 opera L'Orfeo, a work that, in part, established opera as a viable dramatic form. As he explained in The Herald yesterday, Mills sees L'Orfeo not just as a great opera but as "the great idea" which redefined the way music would be written.

Excited as he was, he immediately faced an issue: what to put with L'Orfeo in the programme? As the root of Monteverdi's opera is the relationship between text and music, Mills decided to let the idea spin off into a historical survey of that issue. Words and music: which comes first? Which is the priority? Hence the raft of apparently unrelated operas in this year's festival by composers as historically and stylistically diverse as Monteverdi, Vivaldi, Salieri, Richard Strauss, Stravinsky and - with more than a lick of Broadway - Leonard Bernstein.

The theme will also be explored across dance and theatre components of the festival programme by the Trisha Brown Dance Company, the Vienna Schauspielhaus and, obliquely, by the Wooster Group.

In the music programme itself, one of Mills's first thoughts was "we could have wall-to-wall Monteverdi". Not possible. There is no such thing as wall-to-wall Monteverdi. Sure, Monteverdi wrote it, but over the ages much of the music has disappeared. Look at a sampling from the worklist. Endimion, dance music, 1604. Music lost. L'Arianna, opera, 1608. Music lost except for the famous lament. Andromeda, opera, 1620. Music lost. Apollo, dramatic cantata. Music lost. Le Nozze d'Enea, opera, 1641. Music lost. And so on.

For a very specific reason, Mills thus turned his attention towards Monteverdi's madrigals. Basically, the director wanted to explore Monteverdi's work, which was as polemical as it was musical, from a different direction. And the madrigals, as well as featuring rich seams of some of the most beautiful, expressive and dramatic music ever composed, also provided an insight into the way Monteverdi's musical thought, language and structures developed.

There are about 250 madrigals, which Monteverdi grouped into a series of eight books. (There is a ninth, posthumous, collection.) The madrigals were written over a 60-year period, from about 1580. As well as being a generally untapped goldmine of glorious music, they also range across the broad development of the composer's style and language, covering, en route, a vast spectrum of styles and types, from the lament (an invention of Monteverdi's) to dramatic scenes that are almost operas in miniature.

This treasure trove of musical riches drew Mills like a magnet. He makes an analogy with the visual arts, where you might have a grand, wide-canvas oil painting and, by the same artist, a whole series of smaller-scale, broadly related works on paper. "The madrigals are very important works in themselves, but they're also wonderful little laboratory sketches for larger pieces and scenes. Monteverdi's always working out dramatic moments, he's always word-painting, and the music is teeming with energy."

To reflect these qualities, Mills is bringing to the festival the harpsichordist and director Rinaldo Alessandrini and his sensational vocal octet and instrumental group Concerto Italiano, who will give performances in five early-evening concerts in Greyfriars Kirk of selections from all eight books of madrigals.

Where next, wondered Mills? He needed to find what he calls "a response" to the concentration of Monteverdi's music. One possibility was to look at the work of other composers at the Mantuan court, who were writing the "ridiculous counterpoint" to which Monteverdi was laying siege. Wisely, perhaps, Mills eschewed this option. What, he thought, if he went back even further in time and started from the eleventh century in Europe, going right up to Orfeo in 1607?

Thus the door opened for the 11-concert series entitled Harmony and Humanity, ushering in to the festival the music of medieval and later masters, including 1000-year-old music from Provence; the music of Josquin Desprez; Machaut with his amazing Messe de Nostre Dame; Dufay; William Byrd's masses; the dark, voluptuous and intensely chromatic music of Gesualdo; the pure, blemish-free musical perfection of Palestrina; and Bach's Motets. All will be played at the hands of some of the most renowned and accomplished exponents in the field, including the cult vocal ensemble Anonymous 4, the Orlando Consort, Paul Hillier's Theatre of Voices, the Tallis Scholars, Claudio Cavina's La Venexiana and the Huelgas Ensemble, a group Mills reckons might turn out to be a sensation of the festival.

The Harmony and Humanity series, like the Monteverdi madrigal concerts, will be 6pm shows in Greyfriars Kirk (with the exception of the second Anonymous 4 concert, which will be at 9pm).

Will it all work? It's a gamble. It's unfamiliar territory to concert audiences. It's not just that this music has no currency in recent Edinburgh Festival practice; there is no significant long-running series of early-music concerts in Edinburgh at any other time of the year. Indeed, there is little of it performed in Scotland at all (pace Cappella Nova, the Georgian Concert Society and one or two others). It is simply not part of the diet of even the most avid music-lovers.

So is there an appetite for it? Will people take a chance, either out of curiosity or because it's the Edinburgh Festival? Jonathan Mills obviously reckons there will be a public response, and advance sales tend to support his view. He sees it very much as an integral part of having an international festival in Edinburgh, not as the imposition of a new director out to address a gap in festival programming or to indulge any predilection for early music.

"Look at Edinburgh," he says. "It's not just a Georgian, Enlightenment town. It's a medieval town as well. It is so striking to me as an outsider from Australia just how ancient parts of this city are.

"Edinburgh is a great festival city, not just in the contained density of it, and not just in the fact that it is architecturally beautiful, but in that it actually has several architectural histories to tell in parallel. There is a medieval history, there's an enlightenment history and there are certain forms of modern history as well."

Mills sees no dichotomy between all of this and the early- music elements in his programme. Quite the reverse, in fact. "It sounds very thoughtful and high-minded, but it all builds towards the festival experience. And the performers bringing this music to Edinburgh are among the best in the world."