Singing Of Women

Why does the Torah emphasize that the woman sang as well? Why is it Devorah that sings the song of thanks in the haftorah? The passuk says ותען להם מרים - the mefarshim ask it should have said ותען להן for she was encouraging the women and what is ןתען, who is she answering to? The Riva cites a Midrash that the angles complained they should be able to sing shira after the men and Miraim answered them we (the women) will sing and only after that you can sing. Why is the singing of the women that allows the malachim to sing? 

The Kli Yakar addresses the word להם and he says the woman reached the level of prophesy of the men so it uses the word for men, להם and he concludes his comment וכן לעתיד נאמר (ירמיהו ל״א:כ״ב) נקיבה תסובב גבר. What is the connection between the times of the future and the shira?  

The Meor VaShemesh says the מחולות that the women did is reflective of the מחול שעתיד הקב"ה לעשות לצדיקים (end of Taanis) for it is now that there are different levels but when everyone fixes their portion, is מעלה  the ניצוצות that they need, then everyone is equal. The women are representative of the כלים of acceptance while men are representative of the כלים of giving. In the current construct the givers are above the recipients, in the sefirah order ז"א is higher than מלכות but in the future the recipients will be elevated. He says that is נקיבה תסובב גבר, the giver and recipient, will be equal. Under the great light of the circle there is no male and female, all are equal. This was the light that Miriam was tapping into with the מחול, the circle above division. Moshe said אז ישיר in the future, he wasn't able to bring down that experience at that time but Miriam was so she said שירו לה in the present. (This may answer a question meforshim ask about קול אשה for at this time the boundaries of אשה ואיש were not present.) 

Hashem tells Avraham to listen to Sarah, כל אשר תאמר שרה שמע בקולה. The Bear Mayim Chayim (on the change on name from Sarai to Sarah) says that the letter yud, the first letter of Hashem's name represents the masculine quality of giving forth was changed to a ה which is comprised of a ד and י where the ד comes first, referring to דל, the poor recipient. Sarah was at the level of the future where the feminine force comes first, where the recipient precedes the giver and hence Avraham was told to listen to her.

Any time there is a spark of geulah, a spark of the ultimate geulah present, then the woman's singing carries more weight. Song is an expression of coming full circle. שירה is like the word שיר as in בעלי שיר יוצאין בשיר, it is the recognition of the full circle. When all things are a circle. When what is down becomes equal and elevated to that which is above. That is why it is woman who are more active in the shira.