The history of music is a particularly rich and complex subject, mainly because of its characteristics: the difficulty lies first on all in the antiquity of music, a universal phenomenon dating back to Prehistory, which gave rise to the formation of traditions that have developed separately around the world over millennia. So there is a multitude of very long stories of music according to cultures and civilizations. Western music (classical music or pop-rock in the very broad sense) taking the 16th century international reference, and still very partially.
The difficulty also comes from the diversity of musical forms within the same civilization: scholarly music, elite music, official music, religious music, popular music. It ranges from very elaborate forms to popular forms like lullabies. A cultural heritage of a particularly wide diversity, unlike other arts practiced in a more restricted or elitist way (literature, theater …). Finally, with music, the art of the moment, the particular question of sources arises: the absence of a notation system of a part of the world music, prevents to really know the extent of the music of the past time, tradition has probably saved only a limited number.
The realization of a universal synthesis appears very difficult because a lot of History of the music deal essentially with the History of Western music. It is generally only possible to refer to books and articles specialized by civilization or by genre of music.