Hear the Tunings
The best way to understand what "tunings" are, is to listen to some. So here are the seven Mesopotamian tunings, plus the standard Equal Temperament tuning we use here in the West.
Each of the seven tunings play the same "notes," that is, the same sequence of piano keys is played each time. The difference in sound results from the different spacing between each pitch; the intervals are different in each of the tunings, which accounts for the differences you hear.
For comparision, the standard Equal Temperament tuning is also included. Each of the selections on Memories of Home is played in one of the Mesopotamian tunings.