NEW YORK — The union representing Broadway’s musicians reached a tentative labor agreement with commercial producers on Thursday, averting a potentially crippling strike that would have silenced nearly two dozen musicals.

The American Federation of Musicians Local 802 — which represents 1,200 musicians — had threatened to strike if they didn’t have a new contract by the morning, after going into mediation Wednesday.

Early Thursday, the union said it had struck a tentative deal that includes wage increases and contribution increases to the health fund.

“This three-year agreement provides meaningful wage and health benefit increases that will preserve crucial access to health care for our musicians while maintaining the strong contract protections that empower musicians to build a steady

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