If you want to hear free improvisational singing Scots Gaelic free church of Scotland psalm singing will give you an education each member of the congration is free to choose any note they want and they all harmonise together in reply to the precentor who gives them the melodic idea to reply to.

Jazz though is imo the crowning achievment of American artistic endeavour and who can argue that the majority of the major innovators were black bebop itself was a revolution within a revolution.As for the comparisons between Jazz and Irish music it should be remembered that Irish traditional music is very conservative and resistant to innovation and although there are fields within the tradition that are very improvisational in nature ,mostly people want to hear the tune they remember and not a personally reharmonised version of it.

Embellishment and interpration is valued but complete transformation is generally rejected in Celtic traditional music.