Why does the word "al-ma'azif" in the noble Hadith not refer to places of singing, but rather to its instruments, even though the Messenger of Allah, peace and blessings be upon him, permitted the use of the tambourine (daf)?

Al-ma'azif refers to forbidden amusements, as indicated by the Hadith. The Prophet, peace and blessings be upon him, approved of A'isha listening to the daff (tambourine), so it is specifically permitted for women on appropriate occasions. Scholars have explicitly stated the permissibility of the daff and the prohibition of all other types of drums.