But that might be part of the question (or answer). Kagel has always been a figure of contradiction, the greatest contradiction, perhaps, is that his music may appeal more to a literary-based public than a musical one, although a music-based public that is steeped in Mahler should surely be attracted to a music that arguably springs from a similar source.
Kagel, a Jew, was born in Argentina on Christmas Eve, 1931. Unlike most Jews post-war, he chose to live in Germany. He has based himself in Cologne since 1957.
The London Sinfonietta, in two concerts, has offered a small retrospective, the first conducted by Oliver Knussen, the second concert, directed by the Dutch conductor, Reinbert de Leeuw, a long-term advocate of Kagel's music.
Kagel's music is informed by Jewish sensibilities: subtleties of contradiction; ambivalence, perception, deception, provocation. His music is political, disturbing and funny.
On Tuesday at the Queen Elizabeth Hall, London, De Leeuw took us through Kagel's magical travelogue, The Compass Rose, for salon orchestra. The eight movements visit the geographical areas of the North, South, East, West, South-West, North-East etc, but not necessarily from the point of view of the Northern Hemisphere.
Flirting with forgotten or imaginary evocations of folk and popular music, the whole cycle is teasingly economic. The same instrumentation is used throughout - clarinet, piano, harmonium, two violins, viola, cello and double bass - with only the percussionist changing instruments from piece to piece.
For a composer so steeped in film and theatre, it comes as no surprise that each "point" is so visual, music in search of a silent film with all the necessary plots, excursions, evocative moods and contrasts. Kagel's journey which has no pre-ordained order, spans the planet from "somewhere between Trans-Carpathia and the Gulf of Finland".
Kagel's ear for colour is extraordinary - water poured from a jug, the breaking of polystyrene, the rustling of a branch, the chopping of an axe, attention drawn to the sound rather than the gesture. Whimsical it is not. Bitter-sweet it is.
The clarinettist, Mark van de Wiel and percussionist, David Hockings were remarkable. A small audience loved it.