the mesopotamians seem to have utilized a heptatonic lydian scale, heptatonic meaning a scale with seven pitches. the lydian scale is the regular major scale but with a raised fourth. for example, the f-lydian scale would contain the same key signature as a c-major scale. the f-major scale has a b-flat in the key signature, however with the raised fourth in the lydian scale, the b-flat becomes a b-natural. the drawback in modern music with the lydian scale is the use of what's known today as the "devil's tritone," however, the mesopotamians don't seem to have a term for this interval, nor a term for the octave which we know they had a concept of. the use of a heptatonic scale would have eliminated any practical need for a term for the octave, as it wouldn't have the importance that is has in today's music.