Why does the Pasuk refer to Miriam as 'Miriam ha'Nevi'ah'?
Rashi: Because she prophesied the birth of Moshe. 1
Rashbam: Because someone who rebukes or someone who sings the praises of Hashem is also called a prophet.
Why is Miriam called the sister of Aharon?
Rashi #1: Because it was when she was the sister only of Aharon, before Moshe was born, that she prophesied. 1
Rashi #2: Her name is connected to that of Aharon, who was Moser Nefesh on her behalf when she was later stricken with Tzara'as. 2
Ramban #1: Since Moshe and Miriam are mentioned in the Shirah but not Aharon, the Torah calls Miriam "Achos Aharon, in order to mentioned his name too."
Ramban #2 and Rashbam: It is the way of T'nach 3 to connect a person to his older brother (the B'chor - Rashbam). 4
Hadar Zekenim (in Pasuk 19): It is normal to attribute a woman to her older brother.
See Bamidbar 12:11.
See for example, Divrei ha'Yamim 1, 2:42 (Ramban). Refer also to Bereishis 28:9:2:2*.
And it did so in a way that was a Kavod for him, in that he was Miriam's older brother and that Miriam his sister was a prophetess, seeing as he too, was a Navi and a K'dosh Hashem (Ramban).
What is the definition of "Tupim u'Mecholos"?
Rashi (in Eruvin, 3b): 'Drums and dances'.
Targum Yonasan: 'Drums and flutes'. 1
See Na'ar Yonasan in Sh'mos 32:19.
Why did the women take musical instruments with them into the desert?
Rashi: The righteous women of that generation took musical instruments out with them in anticipation of the miracles that they were convinced Hakadosh-Baruch-Hu would perform with them.
Tiferes Yonason and Ma'ayanah shel Torah: So that the men should not hear them singing - due to the principle 'Kol be'Ishah Ervah.'