A periodic lease includes the same contractual terms that the original tenancy did, but the period of the tenancy is determined by the rent cycle. For instance, if you paid rent monthly, your periodic lease become a monthly agreement. 

The start date of the periodic lease is determined by the the end date of the original tenancy - not the date the rent is paid on. The landlord is legally unable to make any changes to the tenancy agreement by changing the date of the rental payment. 

If you are a tenant wondering how to end your periodic lease:  you should give at least a month’s notice in writing.  The notice to leave should state the last day of the tenancy and the reasons for terminating the agreement. 

The same rule applies to the landlord. The landlord must issue a written termination notice to vacate to the tenant, stating that they wish to terminate the tenancy. The notice should also include the reason you wish to terminate the tenancy and the last day of the tenancy. 

However, you should note that the number of days given depends on the reason for the termination and the state you are in.  According to Consumer Affairs Victoria, the advance notice needed for ending a periodic lease in VIC has a minimum requirement of 28 days, except in certain cases. Similarly, ending a periodic lease in NSW would differ from a periodic lease in QLD.