Shirat Hayam: Whose song was it, anyway?

Exodus Rabbah 21:10, as quoted in Sefer Haagadah p.73, #85
"And the children of Israel went into the midst of the sea upon dry ground" (Exod. 14:22). [How is it possible?] If they went into the sea, why does it say, "Upon the dry ground"? And if they went "upon the dry ground," then why does it say, "Into the midst of the sea"? Hence you learn that the sea was not split for them until they stepped into it, indeed until the waters reached up to their noses. Only then did the passage become dry land.
In a discourse, R. Nehorai said: When an Israelite woman was walking through the sea, leading her son by the hand, and he began to weep, she had merely to reach out her hand, pluck an apple or a pomegranate from the sea, and give it to him, for "He led them through the depths as [He was to do later] through the wilderness." (Psalm 106:9)--as they were to lack nothing in the wilderness, so also they lacked nothing in the depths.

Yalhut, Hukkat 263, as quoted in Sefer Haagadah p.74, #90
"Then sang Moses and the children of Israel" (Exodus 15:1). Rabbi Avin the Levite said: When Israel stood up to chant the song at the sea, Moses did not let them chant it by themselves, but like a teacher who recites a portion in scripture with a child when he is young, so did Moses recite it with Israel--"then sang Moses and the children of Israel," they being like a child who repeats after his teacher. But after forty years [in the wilderness], Israel grew up and on their own proceeded to chant the Song of the Well, as is said, "Then sang Israel"(Numbers 21:17).

The Torah: A Woman's Commentary, p.386 on Exodus 14:31-15:1
...the title "Song of Miriam" that is often used by modern scholars and interpreters for v.21 might in fact be appropriate for this passage as well....The prose introduction mentions Moses, the chief human protagonist of the Exodus narrative, as the performer of the Song, along with the people. Hence it has traditionally been assumed that Moses is the author of the song. Why would a woman's composition be attibuted to a man? Perhaps the centrality of Moses to the Exodus story meant that authorship of this hymnic masterpiece accrued to him.

The Torah: A Woman's Commentary, p.392 on Exodus 15:20
Unnamed in Moses' birth narrative (2:4, 7-9), the woman mentioned in more biblical books (five) than any other female figure finally gets a name. She also gets a title, one that never appears for Moses in the book of Exodus. Miriam is the first of several biblical women--including Deborah (Judges 4:4), Huldah (2 Kings 22:14), and Noadiah (Nehemiah (6:14)-- to bear the title of prophet. The authority of prophets are conveyers of God's will to the people was gender inclusive both in the biblical world and in other parts of the ancient Near East. The 8th century B.C.E. prophet Micah acknowledges Miriam's leading role in the Exodus when he proclaims in God's name that to deliver Israel "I sent you Moses, Aaron and Miriam" (Micah 6:4). In the present verse, Miriam appears also as a singer and leader of other singing woman, a role familiar from other biblical texts and ancient cultures....
It was apparently customary in ancient Israel for women to welcome victorious armies with victory songs (see Judges 11:34; 1 Samuel 18:6-7). Accomplished female musicians would have earned the esteem of their community. Also, groups of female performers liekly would have met together to practice their instruments and compose songs for specific occasions, which would have provided occasions for female bonding and for women to exert organizational skills and mentor younger performers....dance was an integral part of this performance genre.

The Torah: A Modern Commentary, revised p. 452
In ancient Israel, as in other cultures, dancing was a normal aspect of worship. At the Reed Sea only the women are reported to have danced, but neither then nor nater was this expression of emtion confined to women only. King David showed the depth of his joy through dancing when the Ark of the Covenant was brought to Jerusalem (II Sam. 6:14).
There are, in fact, no fewer than eleven Hebrew words denoting dance, suggesting that ritual choreography was extensive and highly sophisticated. There were dances to express communal joy, and various biblical passages picture such dancing as the opposite of mourning; there is a "a time to mourn and a time to dance" says Koheleth. There were victory dances, petitional dances, dances to celebrate the harvest with gratitude, and of course dances were indigenous to wooing and wedding. It may be supposed that specific motions were customary or prescribed for these various occasions, with movements of choral and other participating groups having symbolic meaning....The dance of the women at the Reed Sea is experienced once more as a natural and even necessary expression of religious joy, a complement to the Shirah: the two belong together and complement each other in a grand and memorable celebration of God's glory.

B Sot30b-31a, P. Sot. 5:6, as explained in Sefer Haagadah p.74, #89
R. Yose the Galilean expounded: When Israel came out of the sea, they gazed upward to chant their song. But how were all of them--even the infant lying upon his mother's knees and the suckling feeding at his mother's breast--able to do so? When they saw the Presence, the infant raised his neck, the suckling let go of his mother's nipple, and all said "This is my God, and I will glorify Him" (Exodus 15:2).
It is taught that according to Rabbi Meir, even fetuses in their mothers' wombs chanted the song. But were they [being in the womb] able to see [The Presence]? Yes, said Rabbi Tanhum, the wombs became as transparent as glass, and so even the fetuses were able to see the Presence.

Kli Yakar on Exodus 15:1:1
Why did they not sing immediately after they left Egypt? Because Moshe knew that the Bnei Yisrael were hesitant in their faith - until he saw at the sea that they believed in God and his servant Moshe. Then he sang...And why is a song described as feminine? Our sages taught that all songs of this world are linguistically feminine, becuase there will be after them distress, just like women who have distress in childbirth;

Kitzur Baal Haturim on Exodus 15:1:3
The spelling is "Yod" then "Shir" - meaning there are 10 songs: Sea, Well, Haazinu, Joshua, Devorah, Hannah, Rod, Shlomoh, Hizkiyahu, and the song to come.