Gemara

(R. Chanina): One who is commanded and observes is greater than one who is not commanded and observes.

Eruvin 96a (Beraisa): Michal (Sha'ul's daughter, David's wife) used to wear Tefilin, and the wife of Yonah ha'Navi was Olah l'Regel (came to Yerushalayim for the festivals). Chachamim did not protest against either of them.

The Tana holds like R. Yosi, who says that Nashim Somchos Reshus (women may lean on a Korban before Shechitah, or do other Mitzvos Aseh sheha'Zman Gerama (Mitzvos that apply only at certain times).

Rosh Hashanah 33a (Mishnah): We do not stop children from blowing a Shofar on Rosh Hashanah.

Inference: We stop women from blowing.

Contradiction (Beraisa): We do not stop women or children from blowing on Yom Tov.

Answer (Abaye): Our Mishnah is like R. Yehudah. The Beraisa is like R. Yosi and R. Shimon;

(Beraisa - R. Yehudah): "Benei Yisrael" do Semichah, but Benos Yisrael do not;

R. Yosi and R. Shimon say, Semichah is optional for women.

Rishonim

Rambam (Hilchos Tzitzis 3:9): A woman is exempt from Tzitzis. If she wants to wear Tzitzis without a Berachah, she may. Similarly, if she performs any Mitzvah from which she is exempt without a Berachah, we do not protest.

Hagahos Maimoniyos (30): Chachamim did not object to women who fulfilled Mitzvos from which they are exempt (Eruvin 96a). Michal wore Tefilin and Yonah's wife was Olah l'Regel. The Yerushalmi says that Chachamim objected. I heard from a Gadol that we protest only where there is concern for transgression, e.g. Chulin ba'Azarah, Ervah (her hair might show), or blowing a Shofar on Rosh Hashanah, which is Shevus (if it is not a Mitzvah). Where there is no concern, such as Sukah and Lulav, we do not protest.

Ran (Rosh Hashanah 9b DH ul'Inyan Halachah): Even though the Stam Mishnah forbids women to blow (or do Semichah), we find that Chachamim did not object to Michal and Yonah's wife. We rely on what was done in practice. Women may blow a Shofar; we are not concerned for Shevus or Bal Tosif

Shiltei ha'Giborim (Rosh Hashanah 9b 3): We stop women from blowing the Shofar, even on Yom Tov. Mori says that this is only if they bless, for then they intend for the Mitzvah and transgress Bal Tosif. The same applies to Tefilin and every Mitzvah they are exempt from. I proved that they do not transgress, for a man does not transgress (Bal Tosif) for putting them on in the wrong place, and a Yisrael does not transgress for giving Birkas Kohanim, since he is not commanded. Women may not blow on Rosh Hashanah, just like men may not blow on any other Shabbos or Yom Tov, or even move a Shofar. Women may not wear Tefilin even without a Berachah, for this is like deviators who expound verses unlike Chachamim do.

Rashi (Rosh Hashanah 33a DH Ha): The Gemara says that we stop women from blowing the Shofar. They are exempt from Mitzvas Aseh sheha'Zman Gerama. If they blow, Bal Tosif applies.

Question (Maharsha): Bal Tosif applies only to doing a Mitzvah, and adding! Rashi should have said that mid'Rabanan, women may not blow not for the sake of a Mitzvah. R. Yehudah says that women may not do Semichah, for this is using Kodshim not for the sake of a Mitzvah. He did not say that it is Bal Tosif!

Tosfos (Eruvin 96a DH Michal): The Ri disagrees. R. Yehudah agrees that Hilni sat in a Sukah (Sukah 2b)! However, perhaps she sat to be with her children, so it does not look like Bal Tosif. Alternatively, Rava taught that not at the time of the Mitzvah, one transgresses Bal Tosif only with intent. A woman is exempt, so it is as if it is not the time for the Mitzvah. This is difficult. Rather, the one who forbids women holds that Tefilin requires a clean body, and they are not zealous enough. If a woman would bring Olas Re'iyah (the obligatory Korban for Olei Regalim), it would look like Chulin b'Azarah. Alternatively, women may enter the Azarah only for a need. Blowing a Shofar is a Melachah mid'Rabanan. Semichah looks like unnecessary use of a Korban, even if it is done lightly.

Rashba (Eruvin 96a DH mide'Lo): If Bal Tosif applies to Semichah and Tefilin, it should apply also to Sukah! Rather, since men are commanded about Mitzvos, it is not Bal Tosif for women. It is a leniency to exempt them, just like (R. Yehudah holds that) a blind person is exempt from all Mitzvos, but he does not transgress Bal Tosif.

Ohr Some'ach (Hilchos Sukah 2:1 DH Hinei): Regarding Semichah, we cannot say that it is time for the Mitzvah. It is not a bodily obligation. Rather, when a man brings a Korban, he must do Semichah. Also for women it is not the time. They may not do Semichah, for it is Avodah with Kodshim. We compare this to other Mitzvos from which they are exempt, which they may not do for another reason, i.e. Bal Tosif. Rashi did not mention Bal Tosif regarding Semichah. If for women it is as if it is not the time of the Mitzvah, so Bal Tosif applies only with intent, what was the Gemara's proof from Tefilin to Semichah (which is not due to Bal Tosif)? Rather, Sukah is not a bodily Chiyuv. (After the first night.) if one does not eat a fixed meal, he need not eat in the Sukah. Tefilin is a bodily obligation, so it is the time also for women. Do not say that Michal did not intend for the Mitzvah of Tefilin, for in any case it looks like she adds. For what does she wear them?! Regarding Sukah, it looks like she is there for her children.

Pri Megadim (Petichah Koleles to Shulchan Aruch, 1:40): Rashi and Tosfos hold that when woman do an Aseh sheha'Zman Gerama and bless, they intend for a Mitzvah mid'Rabanan, not for a Torah Mitzvah. Or, Bal Tosif applies only to adding part to a Torah Mitzvah. One should tell women that they are exempt.

Tosfos Rid (Avodah Zarah 3a DH Lomar): Our Gemara teaches that one who is exempt and fulfills gets some reward. Why do we say that a Chasan who is exempt from Shma should not read? Why does it say that Chachamim did not protest against Michal for wearing Tefilin? Why should they protest?! She gets reward! A Chasan should not read, for it looks like haughtiness. There is room to protest against Michal due to Bal Tosif, i.e. like the Tana'im who forbid women to do Semichah. The Tana'im who permit them to do Semichah hold that Bal Tosif does not apply. They argue about every Mitzvas Aseh sheha'Zman Gerama from which women are exempt. Bal Tosif does not apply to Nochrim.

Me'iri (Eruvin 96a DH Kevar): Women may do any Mitzvah from which they are exempt. Likewise, Bal Tosif does not apply to anyone exempt, such as smelters and people who gather dung, who are exempt from Olas Re'iyah (for others cannot bear their smell), and one engaged in another Mitzvah.

Ohr Some'ach (DH Lachen): Even if Bal Tosif applies to women doing Mitzvos from which they are exempt, this does not apply to Talmud Torah.

Shevet ha'Levi (8:1): Sefer ha'Machri'a says that the Halachah follows R. Yosi, and he agrees that if women intend for the Mitzvah, Bal Tosif applies. If so, why did Abaye answer that our Stam Mishnah is R. Yehudah? He should have said that it is like R. Yosi, whom the Halachah follows, and it forbids when they intend for the Mitzvah!

Poskim

Shulchan Aruch (OC 589:6): Even though women are exempt, they may blow the Shofar.

Rema:

Beis Yosef (589 DH v'Af and DH v'Chosav ha'Rav): The Ran and Rosh say that just like women may do Semichah, without concern for Avodah with Kodshim, they may do any Aseh sheha'Zman Gerama, without concern for Bal Tosif or Shevus of Teki'ah. R. Yeshayah says that if a woman blesses, she shows that it is a Chiyuv, and she transgresses Bal Tosif and a Berachah l'Vatalah. Regarding Bal Tosif, this is not true.

Birkei Yosef (OC 589:2): Bal Tosif does not apply to Semichah, for even R. Yosi permits women to do Semichah only loosely. It is not proper Semichah. However, Korban Aharon says that R. Yosi permits women to do proper Semichah, so Bal Tosif could apply. The Gemara mentioned Avodah with Kodshim regarding Semichah on another's Korban in the Ezras Nashim, which was not real Semichah.