Just purchased a 1890 end terrace, musty smell in downstairs room and bedroom directly above when rooms have been shut up all day, both rooms share sandstone gable wall, no signs of dampness on internall walls.
A musty smell is more often than not a reliable sign of rot and decomposition; it is the odour of fungi or mildew spores in the air, the source of which can’t always be readily spotted, or unearthed.
Generally, a thoroughly good drying out and airing of the infected area is usually just about the only cure that is needed.
I think youv'e answered your own question (when its been closed up all day).
This time of year condensation is a problem and if rooms aren't properly heated and ventilated then musty smells can appear along with mould etc.
Its quite possible however that you have also inherited musty smell from previous owners lifestyle. If you are out all day and without compromising the properties sercurity, then try leaveing a window open and internal doors etc. Also ensure external walls are not obstructed as this cuts off air movement!
Also try opening windows front and back first thing before you leave house as this will sweep out moist air and replace with dry.