I play flute and, whilst I guess experiments are required, I would be surprised if - for slow tunes at least - the effect is not similar. I think I have read someone drawing parallels between wind instruments and 'calming breath' exercises. Are you deliberately avoiding ‘calming’ as an alternative word because it already has wide usage for something similar?

I was wondering about dance tunes, where the aim is usually for a more rhythmic effect and to provide ‘lift’ for the dancers. So your mention of “Rocky Road to Dublin” is interesting. Others here will correct me if I am wrong but I am fairly sure it is a dance tune to which words have been added. The different breathing strategies in it of a singer or, say, a whistle player are interesting but, I suspect, not very relevant to your study. (I was as the first guest who posted but thought it too soon to bring in wind intruments)