Which tenancy is established when lease payment intervals are specified, but the duration of the lease is not?

The correct choice is periodic tenancy, which is characterized by lease agreements that specify payment intervals—such as monthly or yearly rents—without detailing a fixed term for the lease's duration. This means that while tenants must pay rent at regular intervals, the lease does not have a predetermined end date. Instead, it continues until either party provides notice to terminate.

In a periodic tenancy, the lease automatically renews at the end of each rental period until a notice of termination is given, which effectively provides flexibility for both the landlord and tenant. This type of arrangement is common in residential leases, where tenants may want the option to move without a long-term commitment.

In contrast, a tenancy for years has a fixed beginning and ending date; a tenancy at will allows tenancy that can be terminated at any time by either party, and leasehold tenancy is a broader category that encompasses various forms of tenant agreements, including periodic and tenancy for years. Thus, periodic tenancy is the most fitting answer for the question posed regarding intervals for lease payments without a defined duration.