This is an interesting question. ‘Complete’ is often used as a synonym for ‘best’ – for me, though, I think it more properly should include a sense of how all-encompassing a composer is. Haydn, for example, could be considered one of the most complete composers because he wrote in pretty much every genre available to him.
Richard’s mention of Wagner as one of the most complete operatic composers is certainly on the money, not only because he wrote his own libretti but also because his opera encompass such enormous worlds.
My feeling about Wagner is that, ultimately, what he did was limiting. It was the end of a road rather than part of a journey – partly because his musical language is ultimately conservative and partly because his approach was so closed off.
If we take opera to be an art form that expresses drama in music then I think the composer who achieves that in the most complete manner is Janacek. I don’t think there is another composer who so succinctly and deeply expresses drama and emotion in music. His music hits you straight in the solar plexus; it seems to bypass the bits that everyone else’s music has to travel through and reaches straight for your soul.
The other composer that is inescapable is Verdi. He never achieved the kind of emotional force that Janacek did, but he did compose an opera in Falstaff that is able to dance through a story without showing any compositional mechanics. In listening to Falstaff, one doesn’t hear how the piece was put together, there are no seams, just jewel-like brilliance. In writing Falstaff, Verdi certainly achieved the most complete integration of drama and music that had yet been created.
I would have to bring Puccini in here too. Though there are many things that don’t like about Puccini, most of all that he seems to so transparently manipulate the listeners’ emotions, his skill in creating structures that are musically and emotionally meaningful and in setting language to music are almost without parallel in opera. La boheme has to be here as one of the most complete operas ever written. Though it lacks the apparently effortless brilliance of Falstaff or the emotional shotgun of Janacek, it is still a remarkable compositional achievement and deserves its place as one of the most performed pieces.
Mention should also be made of Mozart whose three great operatic creations – Figaro, Giovanni and Cosi – are of extraordinary, scarcely believable musical brilliance. For my money, Mozart misses out of the ‘complete’ composer because his emotional reach is too limited. I’m not sure if that is connected to the peculiar limitations of the classical musical language he was writing with or his own apparent lack of emotional intelligence – but his characters are too callow, too small-minded to expose full-blown humanity. (Though that being said, Figaro is absolutely on my desert island discs – the finale of Act 2 is possibly the most perfect composition ever written and I would happily listen to it many 1000s of times and still discover new things.)
I think that complete has to mean music that encompasses everything opera is about which – ultimately – is the human experience. Noone does that better than Janacek – in the most brutal contexts he reveals the whole gamut of what it means to be alive.