6 L-Y-R-
Are you sure about the Y?
I have been thinking along the track of leger lines, the little lines for notes that are above or below the staff.
Legers then could be defined as the things put on scales.
Hi kookaburra
the clue giving me the Y is...In the convent it gives preferential treatment...my answer is PRIORITY
The clue giving me the R is...Just the place to find amusement...my answer is FAIR
How about looking at it this way - layers - they put things on, and scales - could be a layer on something, such as deposit in a kettle, tartar on teeth, etc, etc.
Chambers gives the following for scale:
a thin plate on a fish, reptile.., overlapping in armour.
verb : to peel off in thin layers
And more similar, I've broken my arm so typing isn't easy!