North Lanarkshire Council has set its budget for 2020/21 and voted to increase domestic rates by almost 5%.
The local authority's leader admitted it faced a "difficult task" to reduce spending by £31m.
The council tax rise of 4.84% equates to an equivalent of £1.08 per week for a Band D house.
Councillors rejected options which would have wound up music groups, including the world champion North Lanarkshire Schools pipe band.
Additional funding of £2m was approved for adult health care and community alarm charges were set at the national average of £3.40 per week.
Cllr Jim Logue, leader of North Lanarkshire Council, said: "We were faced with choices that no councillor wished to take.
"The fact is that local government revenue grant from the Scottish government falls far short of the money required to continue to fund council services at current levels.
"No councillor enters local government to make these kinds of cuts. However, the council has approved a budget which does its very best to protect the most vulnerable people in North Lanarkshire."
Last week Scotland's two biggest councils voted to increase taxes by nearly 5%.
The budgets for Glasgow and Edinburgh were published after local government body Cosla warned Scottish councils need an extra £300m of funding just to "stand still".