Years ago I shared here that there was one category of Jewish music that had no parallel in goyish music: The atonal serial music of Arnold Schoenberg.
Schoenberg actually composed a setting of Kol Nidre — commissioned by a Reform Rabbi — but it is unsuitable for use in our shuls as it uses musical instruments (including an organ). And interestingly it is not atonal even though it was written in the late 1930s.