As a trainee perfumer in the latter part of the Sixties, I was once given 2 perfumes to match with the unlikely names of MAKWAKWAFA and ALPIDAHUDA. I remember the names more clearly than the odours but one was an early example of overdosing, in that case Aldehydes C8 and C12L. Not only were good matches required but the copies had to be soluble in both mineral oil and odourless kerosene, the latter then being the cheapest solvent/carrier available. The client was Nigerian and he was selling mostly to Muslims who bought such perfumes along with Bint for use not just as pleasant smells but as Attahs.
From Morocco to Indonesia, where you find Muslims, you will normally but not always find an Attah market. This is because, according to a good Muslim friend, there are varying traditions within Islam and while many use the Attahs as part of the cleansing ritual before the five times daily prayers or just to ward off evil spirits, others have no use for Attahs. I suppose it is a bit like Methodists and Baptists, the differences are in the detail. But why use them at all, again my friend says that in Koran it says that God holds only two things dear, Women and Perfume. Certainly not a full answer but a useful one.
Attah, Attarr, Atrah Arttre and many more names possibly derived from Otto, which means oil or spice. Certainly they began in the middle east and spread across the world with the spread of Islam and to a lesser extent with Christianity, though the latter is now mostly reduced to the use of Incense in High Church services only.
Early Attahs were probably mixtures of ground herbs, spices and flowers, etc together with resins (Myrrh and Frankinsence were available but pricey), all of which were macerated with a vegetable oil, probably olive. Then matured for a while before being bottled and sold. Some were sold as highly coloured powders and had a makeup element to them.