Why not include "的" in "传统音乐"? I have found the following two sentences:

他们正在演奏传统音乐。
这是一个传统的玩具。


Why does the former not use 的 but the latter does? I know you can remove 的 if you express family's relation as stated in other question, but this is not the case here...

Is there any other rule to remove 的 in Mandarin?
The words "的" for adjectives or "地" for adverbs are optional. e.g. 快速上升 = 快速地上升 (ascend rapidly), 聪明人 = 聪明的人 (clever man). Ancient Chinese didn't have these conjunctions/sometimes used other conjunctions(e.g. 然). You might treat the version without these conjunctions as a bit more formal/written, but that's not always the case. Either version is perfectly understandable/acceptable to people.