Japanese writer Akira Asada wrote and said repeatedly that pure music reaches a certain limit with John Cage. This is parallel to his other assertions, such as that literature reaches a limit with Joyce, dance reaches a limit with Forsythe, or film with Godard. Therefore, when talking about artists coming after these figures in each of their respective genres, Asada praises those aspects of their work which relate to pleasure, but not to their contribution to the historical progress of fine art.
In an overwhelming majority of cases, Asada's stance seems to be the most fruitful. It helps one avoid the trap of assuming that what comes later is necessarily more progressive.
In a very important sense, at least for me personally, it is largely thanks to Asada that Björk's music comes as such a shock. I am not an expert on contemporary music, so I cannot say this for sure, but it seems quite plausible to interpret Björk as someone who (indirectly and accidentally) successfully took the baton from Cage and ran ahead.
The basic dilemma that plagued Cage is the fact that any sound can be listened to as music if the listener puts him or her self into the right kind of situation. Cage struggled to explore the various ways in which people can be put into such situations. Björk also begins from this dilemma: this is how one can listen to the songs of KUKL. They are not really songs, but rather a kind of ritual in which Björk and the others try to elevate sound to music.
The next step comes with the Sugarcubes and the early Björk up to Post. Einar and Björk both say that the Sugarcubes was meant as a joke. It is a very well-done joke, a pleasant joke. It makes fun of much of what goes by the name of pop music - from rock and role to blues and country to jazz. Making fun of genres can be easy; making fun of them seriously and well is difficult. Björk continues with this parodying style in Debut and Post too - e.g. "I Go Humble" is an ambiguous homage to Michael Jackson's "Bad" (the contrast between "I'm bad!" and "I go humble!") The trace of this homage-parody mood stays with songs in Homogenic too - "All is Full of Love" is an answer to John Lennon's "All You Need is Love." Whereas the listener to Lennon's song is in need of love, listeners to Björk's song is called to find love that is already there.
The third big step is when the parody mode is replaced by a fusion of Cage-like experiments and pop. This is what I absolute love about Björk's music, that it fuses experiment with pop. The element of pop is the element of universality. Unusual time signatures and beats in Homogenic, domestic sounds and complex beats in Vespertine, the human voice as such in Médúlla, the patterns of nature in Biophilia, all are elevated not only to music, but to pop music.
As only a Dubliner would really understand the finer details of Ulysses, so it seems that only an Icelander would really get the subtle humor of Björk's music, but nonetheless, as an outsider, instead of reading into the music any excessive speculation of mine, I can simply sit back and listen and feel thoroughly replenished.