(Ibid. 21) "And Miriam answered to them: Sing to the L–rd, for He is exalted (over all the) exalted: horse and its rider He cast into the sea": Scripture hereby apprises us that just as Moses chanted song to the men, so did Miriam chant song to the women.
Miriam Did Not Simply Repeat What Moses Sang
Mekhilta Tractate Shirah 10:17