Usually leases have language that creates a "holdover" month-to-month tenancy after the lease expires, and that's the law even if it doesn't say so. Your tenancy term is the same term as your payment, and you paid rent every 30 days. Perhaps your lease says something about termination?
As with any contract question, since all contracts are unique and there's no such thing as a "standard" contract, you're best off having someone review your particular contract to see what's been agreed to.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.