How to get the counts for different cities in a certain period.

I want to determine how many letters were send per city each period of the year (kwartal, half year etc. )

Sheet 1
Column H contains different cities (about 10-12 differtent cities). In this column a certain city can appear more than once.
Column Q contains different dates on which letters were send. The dates varie over the year.

Sheet 2
A1 contains the start date of the period.
B1 contains the end date of the period

In this sheet 2 I want to count the letters that were send to each city in each period of the year, depending on data and refering to that data in cells A1 and B1 so that I can report the amount of letters send. With the cells A1 and B1 I want the get the results I want.
I tried to do this with the countif function and sumproduct though without succes.

The data is constantly changing and a pivot table doesn't update I've heard.