While we are at it....
For your viewing pleasure:
1, M/48 "hjelmbind" - in white.
When on manoeuvres, and in need of "enemies", you would have one team with white helmet bands.
The "design" originated from the helmet band used, for the same reasons, with the M23 helmet.
I suspect, that the brass fittings are from the M23 helmet band. The white cotton band has obviously been changed during the past 50+ years.