Oliver Kamm has an excellent piece on Comment Is Free about Stockhausen. I don't think it's possible convincingly to disagree with his key point:An impressionable writer in the Daily Telegraph last week quoted one of Stockhausen's acolytes: "Stockhausen gave us the courage to think anything was possible in music." But not everything is possible in music, any more than it is in poetry. If you read a poem you need, at a minimum, to be able to understand the language in which it is written, the conventions of the genre and the tradition of the art form. Musical appreciation does not depend on the ability to read a score, but it does require the ability to hear sounds in relation to those that precede them.

The dominance of western music reflects its ability to combine melody and harmony, and thereby produce a discourse. A musical composition is above all an argument that appeals to the emotions. The work of Stockhausen is not like that. It is not music so much as a series of sonic events, which at its worst feels both pretentiously mystical and interminable (though his opera cycle Licht in fact lasts only for 30 hours). It evinces - in the phrase of the critic Robin Holloway - "neo-Wagnerian ambitions unmatched by the necessary talent." I once heard Maurizio Pollini play Stockhausen's Klavierstuck X, which is one note played repeatedly for about 10 minutes at different lengths. It wasn’t music, it was sound. But it was utterly mesmerising, and was one of the most awesome pieces of pianism I have ever heard (although I am not usually a fan of Pollini).

But I have heard a fair bit of other Stockhausen and he was, I would suggest, one of the great cultural frauds of the twentieth century. This judgement has nothing to do with the somewhat tedious tonal v atonal debate or adherence to the pentatonic scale - plenty of other composers whose music I don't properly appreciate, such as Boulez, for instance, do not write music in the traditional classical idiom but are clearly worthy of study and a hearing - but is based on the simple fact that Stockhausen had no discernible talent even on his own (spurious) terms; nor did he evince any rigour in the composition of his pieces.

I actually think Oliver is being too kind in his assesment that His was not a movement but a cultural moment. What Stockhausen bequeaths to modern music comprises largely misconceived ideas and sounds of surpassing ugliness.
They were not ideas. They were cons.