1. What blessings are valid to recite, and can one make up a new blessing:

Blessings instituted post Talmudic era:[1] Some Poskim[2] rule that after the Talmudic period, which preceded the Geonic period by about half a century, it is not possible for blessings to be instituted and no one contains the power to do so. Hence only those blessings which were instituted prior to the end of the Talmudic[3] era are valid, and all those instituted pass this time are prohibited from being recited, and are considered a blessing in vein. According to this approach, even the blessings instituted by the Geonim are invalid. Other Poskim[4] however rule that it is possible to institute blessings even after the time to the Talmud, and that so is justifiably done in the times of the Geonim. Practically, we accept the institution of the Geonim and the widespread custom of reciting a blessing that was instituted in their time period. (However certainly any blessing which has not been instituted by the Geonim, or was even instituted by the Geonim but has not become the widespread custom to recite by the majority of the congregation, then such a blessing may not be said and one who recites it transgresses the saying of a blessing in vain. Thus one may not say blessings which are written after certain supplications and requests, being that they have been written after the Talmudic times and have never been enacted by the Geonim, and one is to protest against those who print these blessings.[5])

List of blessings instituted post Talmudic era and their status:

1. Hanosane Layaef Koach:[6] The blessing of Hanosane Layaef Koach was instituted by the Geonim as a result of the physical weakness which had descended to the world.[7] Some Poskim[8], however, question whether one may say this blessing as it was instituted after the Talmudic period. Practically, the blessing is to be recited.[9] [Even Sephardim are accustomed, based on the Mekubalim, to recite this blessing despite the fact that according to the Michaber it is not to be said.[10]]
2. Baruch Someich Noflim and Baruch Magbia Shefalim:[11] Some are accustomed to recite the blessings of Baruch Someich Noflim and Baruch Magbia Shefalim.[12] Practically, these blessings are forbidden to be recited as they were not instituted by the Sages of the Talmud and have not become accepted amongst majority of the Jewish people, and hence those who say it are making a mistake.[13]
3. Sheasani Kiritzono:[14] Some women are accustomed to recite the blessing of “Sheasani Keritzono/That He made me according to his will[15]” [in the place of the blessing of “Shelo Asani Isha,” and so is the widespread Ashkenazi custom[16]]. [Other Poskim[17] , however, rule that the blessing is not to be said being that it has no source in the Talmud and so is the widespread Chabad custom as explained next. Some Poskim[18] conclude that it is to be said without God’s name and so is the Sephardic custom. According to all it is completely forbidden for a woman to say Shelo Asani Isha.[19]]
4. Baruch Mikadesh Shemo Barabim:[20] Some are accustomed to recite the blessing of Baruch Mikadesh Shemo Barabim with Hashem’s name.[21] Practically, it is proper not to conclude with Hashem’s name in this blessing as this blessing is not recorded in our Talmud.[22] (Now, although this blessing is mentioned within some versions of the Jerusalem Talmud, nevertheless there are versions in the Jerusalem Talmud which do not mention this blessing, as well we do not find any institution of the Geonim to recite the blessing with G-d’s name, as they did with the blessing of Hanosein Layaoef Koach.[23]) Nevertheless, since it has become accustomed to say it, therefore they may continue with their custom.[24] Nonetheless, one who desires to avoid entering himself into a possible recital of blessing in vain, is doing a proper thing.[25] [Practically, the Chabad custom is not to recite it.[26]]
5. Shelo Asani Shifcha:[27] Some women have the custom to recite the blessing of Shelo Asani Shifcha in place of Shelo Asani Aved.[28] [This is not the widespread Chabad custom, however there are some that say it.[29]]
6. Shelo Asani Goyah: Some women have the custom to recite the blessing of Shelo Asani Goyah in place of Shelo Asani Goy.[30] [This is not the widespread Chabad custom.[31]]
7. Shelo Asani Biheima:[32] Some have the custom to recite the blessing of Shelo Asani Biheima. This is not the accepted custom.
8. Baruch Sheamar: The blessing of Baruch Sheamar is not mentioned in the Talmud.[33] Nevertheless, the Poskim[34] write that it was established by the Anshei Kneses Hagedola based on a letter that fell from heaven and they found this blessing written on it.

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^[1] Admur 46:6

[2] 2^nd opinion in Admur 46:6 and Stam opinion in Admur 46:10 in  parentheses; Michaber 46:6; Beis Yosef 127; Rashal 64; Iggur 87; Rosh Bechoros 8:8; Levush 46:7 in Hagah; Seder Hayom Kavanos Birchas Hashachar; Taz 46:9 regarding Mikadeish Shemo Barabim

[3] Some write that this applies only to those blessings instituted and written in the Babylonian Talmud, while those written only in the Jerusalem Talmud may not be recited. [Bach 46 regarding Mikadesih Shemo Berabim and Beis Yosef 127 regarding Modim Derabanon, brought in Taz 46:9; See also Admur 46:10 “as it is not mentioned in our Talmud”

[4] 1^st opinion in Admur 46:6; Rama 46:6; Tur 46 in name of Siddurei Ashkenaz; Semag Asei 27; Peri Eitz Chaim Shaar Habrachos 7; Shaar Hakavanos Inyan Birchas Hashachar; Taz 46:7 and 9 regarding Hanosein Layaeif Koach; Ashel Avraham of Butchach on Taz 46:9 regarding Mikadeish Shemo Barabim that there is no need for a blessing to be mentioned in the Talmud to be able to recite it, and on the contrary, the Talmud itself states [Brachos 40b] that one may enact new blessings

[5] Admur 46:6 in parentheses and Admur 46:10 in parentheses; Shelah Miseches Chulin Emek Habracha Birchas Hashachar;

[6] See Admur 46:6

^[7] 1st opinion in Admur 46:6; Rama 46:6; Tur 46 in name of Siddurei Ashkenaz; Semag Asei 27; Peri Eitz Chaim Shaar Habrachos 7; Shaar Hakavanos Inyan Birchas Hashachar; Taz 46:7 and 9 regarding Hanosein Layaeif Koach; Ashel Avraham of Butchach on Taz 46:9 regarding Mikadeish Shemo Barabim that there is no need for a blessing to be mentioned in the Talmud to be able to recite it, and on the contrary, the Talmud itself states [Brachos 40b] that one may enact new blessings

[8] 2^nd opinion in Admur 46:6; Michaber 46:6; Beis Yosef 127; Rashal 64; Iggur 87; Rosh Bechoros 8:8; Levush 46:7 in Hagah; Seder Hayom Kavanos Birchas Hashachar; Taz 46:9 regarding Mikadeish Shemo Barabim

[9] Admur 46:6; Taz 46:7 and 9

[10] Birkeiy Yosef 46:11; Sdei Chemed Mareches Brachos 2; Piskeiy Teshuvos 46 footnote 138

[11] Admur 46:6

[12] Ittur Hilchos Tzitzis 3:2; Bahag end of Brachos; Teshuvos Hageonim Hachadashos 30; Shibulei Haleket 4; Beis Yosef 46; Levush 46:7 in gloss; Taz 46:7; Elya Raba 46:11 in name of Bahag that one is to say the blessing of Magbia Shefalim each day; Shulchan Hatahor 46:7; See Mishmees Shalom 8:4

[13] Admur 46:6; Michaber 46:7; Iggur Hilchos Brachos 87; Ittur Hilchos Tzitzis 3:2; Taz 46:7

[14] Admur 46:4; Michaber 46:4; Levush 46:5; Tur 46; Abudarham Seder Shacharis Shel Chol; Taz 46:4; P”M 46 M”Z 4

[15] The reason: This blessing comes to justify the judgment of G-d upon herself which inherited her with a negative aspect. [Admur ibid; This means to say that despite the negative fact that He did not obligate them to fulfill all of His commands nevertheless they bless Him and thank Him for His judgment.]

[16] Likkutei Maharich [although arites to say Baruch Sheim afterwards]; Halichos Bas Yisrael 2:5

[17] Peri Chadash 46:4; Mateh Yehuda 46:10; Shalmei Tzibur p. 54; Makor Chaim [Chavos Yair] 46:4; Radbaz in Metzudos David Mitzvah 74

[18] Chida in Kesher Gudal 5:23; Siddur Beis Oveid 13; Siddur Yaavetz; Ben Ish Chaiy Vayeishev 10; Od Yosef Chaiy Vayeishev 9; Aruch Hashulchan 46:11; Kaf Hachaim 46:41; Yechaveh Daas 4:4; Chazon Ovadia 1:38; Halacha Berurah [Yosef] 46:10 footnote 38

[19] Pashut; Koveitz Zalman Shimon p. 28; Maaneh of Rebbe “it is obvious that women cannot say the blessing of Shelo Asani Isha”

[20] Admur 46:10 in parentheses; See Piskeiy Teshuvos 46:18

[21] Custom brought in Admur 46:10 in parentheses; Taz 46:9; Tur 46; Tana Divei Eliyahu Raba 21; Tosafus Brachos 46a; Pesachim 104b; Seder Rav Amram Gaon 7; Semag Asei 27; Rokeiach 302; Implication of Teshuvas Rashal 64; Implication of Beis Yosef 46, brought in Taz ibid; Gr”a; Ashel Avraham of Butchach on Taz 46:9 that the Minhag is valid; Siddur Tzelusa Diavraham; Rav SZ”A, brought in Halichos Shlomo 6 footnote 20; Minhag of Rav Nethonson; Minhag of Chazon Ish; See Piskeiy Teshuvos 46:18 footnote 191

[22] Admur ibid; Siddur Admur; Taz 46:9; Bach 46; Seder Hayom Kavanos Kerias Shema; Nussach of Rambam Seder Hatefila; Nussach of Siddur Arizal, Siddur Admur; Derech Pikudecha Mitzvah 30; Shulchan Hatahor 48:10 in name of Arizal and Besht who did not say Hashem’s name in the blessing; Minhagei Chasam Sofer; See Mishmeres Shalom 13:3; Ashel Avraham of Butchach 46;

[23] See Tur 46; Ravayah Brachos 146; Yalkut Shimoni Vaeschanon Remez 837 in name of Yerushalmi Perek Haroeh; Rambam Seder Hatefila

[24] Admur ibid; Taz ibid

[25] Admur ibid; Siddur Admur; See M”A 46:8

[26] Siddur Admur

[27] The Rebbe was addressed the question of whether women are to recite this blessing and replied that it is dependent on the custom of the community. [Likkutei Sichos 24 p. 410]

[28] Chida in Kesher Gudal 5:22 in name of Achronim; Ashel Avraham Butchach writes that he has not seen in any Sefer that women should say the blessing of Shelo Asani Shifcha instead of Aved. The Yaavetz in his Siddur writes women are to say this blessing without Hashem’s name.

[29] See Koveitz Zalman Shimon p. 28 that mentions this custom [although not amongst Chabad women].

[30] Chida in Kesher Gudal 5:22 in name of Achronim; The Yaavetz in his Siddur writes women are to say this blessing without Hashem’s name.

[31] See Koveitz Zalman Shimon p. 28 that mentions this custom [although not amongst Chabad women].

[32] The mother of the Terumas Hadeshen was accustomed to say “Shelo Asani Biheima”. [Koveitz Zalman Shimon p. 28]

[33] See Admur 51:3

[34] Admur 51:2; Tur 51; Menoras Hamaor in name of Sefer Heichalos; Rokeiach 320; Tashbeitz 218; Tolas Yakov in name of Or Zarua; Bach 53; Taz 51:1; Levush 51