Gemara

(Beraisa - R. Yehudah): The law of Koshi applies only in her (last) month;

This can be a stringency, e.g. if she saw blood amidst Koshi for the last two days of the eighth month and the first day of the ninth month. Even if she gave birth at the beginning of the ninth month, she is a Zavah.

This can be a leniency, e.g. if she saw blood amidst Koshi on the last day of the eighth month and the first two days of the ninth month, she is not a Zavah, even if she gives birth at the end of the ninth month.

Inference (Rav Ada bar Ahavah): R. Yehudah holds that the Shofar (blown to declare Rosh Chodesh) causes the law of Koshi.

Question: Shmuel taught that a woman gives birth after exactly 271, 272 or 273 days (nine full months after conception, which is on the first, second or third day) from Bi'ah!

Answer: Shmuel holds like the early Chasidim;

(Beraisa): The early Chasidim would have Bi'ah only on Tuesday night, to avoid the possibility of desecration of Shabbos (due to birth on Shabbos).

(Mar Zutra): Even according to the opinion that the nine months must be full, a seven month baby can be born at the beginning of the month. "Va'Yehi li'Sekufos ha'Yamim... va'Teled." Sekufos teaches two seasons (six months), and Yamim teaches another two days.

Yevamos 36b (Ravina citing Rava): If Reuven died, and then his only child died within 30 days of its birth, and David (a stranger) was Mekadesh the widow:

If David is a Yisrael, she must do Chalitzah. If he is a Kohen, she does not need Chalitzah.

37a (R. Hoshaya brei d'Rav Idi): Chachamim assume that a baby was viable even if he died within 30 days. Since there is no solution for a Kohen to keep his wife if she does Chalitzah, we rely on Chachamim (to be lenient).

Rishonim

Rambam (Hilchos Yibum 1:5): If a man died when his wife was pregnant, and the baby was born alive, even if he died immediately, she is exempt from Chalitzah and Yibum. Mid'Rabanan, we must know that his months were complete, and he was born at the end of nine full months.

Tosfos (38a DH Shipura): How do we infer from R. Yehudah that it depends on the Shofar? If Kishuy did not depend on Rosh Chodesh, she could not know which day begins the ninth month. Even if she knew from which Bi'ah she became pregnant, she does not know whether conception was that same day, or on one of the next two days!

Mahari Mintz (6): Tosfos holds that if a woman became pregnant on Nisan 29 and gave birth on Kislev 1, it is a viable baby even though it is not eight full months. It is only seven months and two days. Even though one opinion holds that the months of a nine-month baby must be complete it depends on the Shofar), and all the more so regarding a seven month baby), for all agree that the seven months need not be complete. If she became pregnant on Nisan 29 she can give birth on Tishrei 1 to a viable baby, even though there are only five months and two days in between.

Poskim

Rema (EH 4:14): If a woman became pregnant from her husband at the end of Sivan and gave birth at the beginning of Kislev, even though there are only five months in between, we are not concerned lest she was pregnant beforehand, for the (calendar) months determine viability.

Chelkas Mechokek (12): This is like R. Yehudah, who holds that even a nine-month baby depends on the Shofar, and all the more so a seventh month baby does, for all agree that the seven months need not be complete. Everyone asks, if a woman can give birth after five months and two days, why do we say (Kesuvos 39a) that a woman cannot give birth before becoming a Bogeres, for only six months separate Na'arus from Bagrus? This is not difficult, for also the six months of Na'arus depend on the Shofar.

Rebuttal (Beis Shmuel 37:5): The Rambam (Hilchos Ishus 2:1,2) requires six full months.

Beis Shmuel (19): Rosh Hashanah 11a connotes unlike the Rema. The Gemara asked how Sarah could give birth at Pesach if the angel informed them (before she was pregnant) at Sukos, only six months earlier, and answered that it was a leap year. This was not difficult according to the opinion that it depends on the Shofar! Perhaps in the conclusion, that the seven months can be incomplete, we need not say that it was a leap year. However, Tosfos (DH Ela) is unlike this. Even though we hold that woman can give birth after nine incomplete months, then it does not depend on the Shofar (below, 156:4). The Bach says so (there). However, Tosfos and the Agudah say that it depends on the Shofar even for a nine month baby.

Gra (34): The Ramban says that even the Rambam, who rules like Shmuel, admits (that it depends on the Shofar).

Shulchan Aruch (156:4): If a baby was born alive, even if he died immediately, his mother is exempt from Chalitzah and Yibum. Mid'Rabanan, we must know that his months were complete, and he was born at the end of nine full months.

Rema: Some say that nowadays, even if she entered only one day into the ninth month from when she became pregnant, it is a viable baby. The Gemara says that a woman does not give birth after nine incomplete months, but many were astounded at this, for we see otherwise. We must say that nature changed.

Beis Yosef (DH Kasuv bi'Teshuvos): The Rashbash (513) discusses a case in which Ploni died on Elul 8. His wife was pregnant, and on Iyar 1 she gave birth to a baby with finished Simanim (hair and fingernails). The baby died after eight days. Ploni had a brother overseas. He permitted Ploni's wife (without Chalitzah, for surely the baby was born during the ninth month). Ploni had left his house on Tamuz 26, and said that he thinks that his wife is pregnant, for she missed a period. He did not return until Tish'ah b'Av, and from then he was very sick until he died. He left his wife b'Chezkas Tehorah. Even if she saw blood immediately after he left, she could not have become Tehorah before he returned in less than two weeks (and surely they did not have Bi'ah when he was so sick). We rely on Ploni's words that his wife is pregnant, for he knows about her, and he is believed to say that he has a son. Also, the baby had finished Simanim. His wife says that she immersed on Av 22, but even if she conceived then, there were eight months and nine days until she gave birth. The months of pregnancy must be of 30 days each. We deduct five days, for five of the months in between had only 29 days each, but still the pregnancy was eight month and four days. If the pregnancy enters even one day into the ninth month, it is a proper baby even if the Simanim are not finished and he died before 30 days. Even though the Gemara says that a woman does not give birth after nine incomplete months, many were astounded at this, for we see otherwise. Tosfos (Avodah Zarah 24b DH Parah, Chulin 47a DH Kol) says that nature changed. The Gemara (Bechoros 20a) says that cows and donkeys do not give birth before three years, and nowadays they gave birth after two.

Rivash (446, cited in Beis Yosef EH 156 DH uvi'Teshuvos ha'Rivash): A case occurred in which a woman immersed from Nidah, was with her husband, and he died three days later. Immediately she suspected that she is pregnant. She gave birth after eight months and 22 days. The baby had finished Simanim, and died after 29 days. If birth in the middle of the ninth month is not called complete months, finished Simanim do not remove the Safek Nefel, for we hold like R. Shimon ben Gamliel, who says that any baby that survived 30 days is not a Nefel. This connotes if it did not survive 30 days, it is a Safek Nefel. If in such a case she became Mekudeshes (before doing Chalitzah) to a Yisrael, she does Chalitzah. If a Kohen (who cannot marry a Chalutzah) was Mekadesh her, she relies on Rabanan, who say that it is a proper child even if he did not delay 30 days. This does not discuss when we know that the months of pregnancy were complete, for then even R. Shimon ben Gamliel agrees (Nidah 44b). We cannot say that they argue about a Vadai Ben Shemoneh, e.g. he had Bi'ah and separated (and the baby was born between seven months and eight months afterwards). Rabanan would not call it a proper child even if he did not live 30 days! Just the contrary, they say that even if he lived 30 days, he is a Nefel! Rather, they discuss a Stam child. It is not known when she became pregnant. It is a Safek Ben Shemoneh, Safek Ben Tishah, and his Simanim were finished.

Rivash: Our question depends on whether or not eight months and 22 days is considered complete months. If it is, all agree that the baby was viable, even if he did not live 30 days. The Rambam connotes that we require complete months, and so do Semag (286) and Rashi (Shabbos 136a DH Lo). They rely on Shmuel (Nidah 38a). Yevamos 42a connotes like this. However, the Ramban says that we mourn over a baby even if the ninth month was not complete. Here, he would hold that she does not need Chalitzah at all. This is not explicit in the Gemara, and the Rishonim argue about it, and even if the months were incomplete, there is not a real Safek that obligates Chalitzah. It is a mere stringency mid'Rabanan, for we are lenient for a Kohen's wife. One may rely on the Ramban to permit her without Chalitzah, especially if it is pressed circumstances, e.g. the Yavam is a minor or he is overseas. One who is stringent to obligate Chalitzah l'Chatchilah, he will be blessed.

Beis Shmuel (5): The Rambam requires nine full months of 30 days. The Shofar does not affect matters. The Ramban holds that it depends on the Shofar. If she became pregnant at the end of the month, and gave birth at the beginning of the ninth month, the baby will be viable, even though the pregnancy was only seven months and two days. The Rashbatz holds that the Shofar does not affect matters, but he does not require the ninth month to be full.

Gra (13): The Mechaber requires months of 30 days, like the Rema says below. This is like Shmuel and the early Chasidim, and Yevamos 42a. The Rambam rules like R. Yehudah, that it depends on the Shofar. Also Tosfos says so, and the Rema (4:14).

Rema: The months of pregnancy are each 30 days. We do not calculate them based on (the months of) the year.