It's certainly true that most traditional (i.e. 'source') singers seem to sing/have sung without accompaniment, but I'm not convinced by the argument that says that this is because they don't use fixed rhythm in their songs. In listening to the 'Voice of the People' CDs, I was quite surprised at the number of songs sung in strict rhythm - it seems to depend entirely on the song and how it works best. And Stormalong's right about choruses, even when the verse is taken freely - I noticed that with Belle Stewart, for instance, who incidentally I seem to remember singing with her husband Alex accompanying her on the pipes!

Barbara