The other temples did not come up in that discussion--for the moment those do not fall under "involving music."
Some verses to consider next time you discuss this with the elders.
from 1 Chronicles 6:32-
"They ministered with music at the Tabernacle until Solomon built the Temple of the Lord in Jerusalem. They carried out their work, following all the regulations handed down to them."
from 1 Chronicles 9:33 -
"The musicians, all prominent Levites, lived at the Temple. They were exempt from other responsibilities since they were on duty at all hours."
They were literally living there, doing nothing but making music. seems to me like they should be musical.