There are some early records of map makers, adventurers and other relatively lone travelers who did not remain in the area to teach or convert but did document some aspects of the culture in a "by the way" or more observant manner.
Early field recordings and drawings/photographs of ethnic groups people can be compared with later recordings and drawings/photographs/videos.
Also there have been more isolated West African ethnic groups whose music and religion and other indices of their culture has been studied and documented after more "popular" ethnic groups such as the Ashanti and the Yoruba. ..
Furthermore one can ask people was things were like before. We use interviews with informants to find out information about other folk cultural offerings. Why not African music?
The West African musican class {called by the French word 'griot' but also known by the name/title "Jali"} are trained for years to accurately remember generations after generations of their ancestors=both their names and the deeds that they are known for. Jalis are historians/singers/musicians..and the Jali tradition lives on in Senegal and other West African nations [not to mention their practice of creating 'insult' songs lives on in Calypso and Rap music]
Furthermore, I believe that traditional African societies {like other traditional societies} had a different attitude towards and more respect & appreciation for the past than, say, most people in modern day USA do. I believe that certain customs and practices can be documented to have lived on in those societies because the some of the people [maybe fewer than before] want them to take pains for them to. Studying these traditions would also provide information about cultural continuity and change.
One other thought-anthropologist can also study the societies created by Maroons {runaway slaves} in Jamaica, Brazil and more isolated African American peoples like the Gullah people of the Sea Isles of Georgia to get an idea of what music, religion, and other cultural practices were like in West Africa.
Here is one example of cultural continuity from Colin M. Turnballs's 1966 book Tradition and Change in African Tribal Life {Avon Pubishing}
"The first boy born to a Bushman family is named for his father's father, and the first girl is neamed for her father's mother. The next children are named after their mother's parents, and then, ift he family grows still further, names are taken form the children's various uncles and aunts. This is quite a widespread custom, although the details are different from tribe to tribe. It is all part of a pattern that creates a special bond between old and young people..But it is more than juet a mark of affection, it is part of the whole tribal system. It is the belief that somehow the tribe that is living today is a reflection of the past, and will also extend into the future. Past, present, and future all fuse into one. That is why some important rituals are performed exactly, to the smallest detail, as they are believed to have been performed by the original ancestors. The coronation of the Kabaka, or king, of BaGanda is a fine example of this, he has actually to retrace the footsteps of his ancestor, the founder of the kingdom, and go through the various events that befell him". {pp. 44-45}
end of quote.. {It should be noted that this is the page that the book opened to when I went to see what I could find on your question}...
BTW, Torctgyd-"natives" and "African bush" are loaded terms which can be more than a bit off-putting..But that's the way society generally refers to African societies. I have seldom heard these terms being used to refer to persons born in rural areas of, say, England or Germany...