The notice requirement would be 15 days for a month-to-month periodic tenancy.
The landlord will charge rent for each day up to the end of the current periodic tenancy, not pro-rate the rent.
If rent is due on the first, the landlord will have to send a letter so that the tenant has fifteen days of notice before the first of the month.
If rent is due on the sixteenth of the month, the landlord will have to send a letter so that the tenant has fifteen days of notice before the sixteenth of the month.