The Chachamim established the time of the Minchah prayer to correspond to the afternoon Tamid. In principle, the time of the Tamid offering starts after six hours into the day, for that marks chatzot (midday), and the sun then begins to descend towards the west. However, the Chachamim were concerned that perhaps an incorrect estimation would be made regarding the position of the sun; therefore they established that the Tamid can only be offered half an hour later, which means that the time of Minchah starts at six-and-a-half hours into the day.
In actuality, the Tamid offering was the final offering of the day, after which it was not permissible to offer burnt offerings, peace offerings, sin offerings, or guilt offerings. Therefore, it was customary to delay bringing the afternoon Tamid offering until after nine-and-a-half hours of the day already passed.
Only when Erev Pesach fell on Erev Shabbat was the Tamid brought immediately after six-and-a-half hours into the day. The reason for this is because the time to bring the Pesach offering is after the time of the Tamid, and in order for all of Israel to succeed in bringing their Pesach offerings before Shabbat arrived, it was necessary to make the time of the Tamid offering as early as possible.
That is the basis for the division of Minchah time into two parts: “Minchah Gedolah” (large Minchah) and “Minchah Ketanah” (small Minchah). Minchah Gedolah starts from six-and-a-half hours and lasts until nine-and-a-half hours, and in principle, it is the proper time to bring the Tamid offering. However, in actuality, only in rare cases is the Tamid brought at Minchah Gedolah. Minchah Ketanah lasts from nine-and-a-half hours until the end of twelve hours, meaning, until the end of the day, within which time the Tamid of the afternoon was offered. The first Minchah period is named “Gedolah” (large) since its duration is longer – three hours; the second, whose time is two-and-a-half hours, is called “Ketanah” (small). As we already learned, these hours are proportional hours. The day is divided into twelve parts and each part is called a proportional hour. In the summer, when the day is long, the hours are long as well, and in wintertime, when the day is short, the hours are concurrently short (see earlier in this book 11:10).
Since the Tamid offering was actually brought at Minchah Ketanah, it is the opinion of the Rambam that l’chatchilah, it is necessary to recite Minchah at that time, and it is only permissible b’dieved to fulfill one’s obligation of Minchah at the time of Minchah Gedolah. That is also how the Shulchan Aruch rules (233:1). However, others maintain that since, in principle, the time of the Tamid starts six-and-a-half hours into the day, it is permissible l’chatchilah to recite Minchah at the time of Minchah Gedolah (Rif and Rosh). Some say that it is even proper l’chatchilah to pray Minchah as early as possible, for those who are expeditious perform mitzvot as soon as they can (Rasag).
In practice, it is preferable to pray at the time of Minchah Ketanah. However, in times of need, it is permissible l’chatchilah to pray Minchah Gedolah. For example, if one has two options: to pray Minchah Gedolah in a minyan, or Minchah Ketanah individually, it is preferable that he prays Minchah Gedolah in a minyan. Similarly, one who is accustomed to eating lunch after the time of Minchah Gedolah, even though he is allowed to rely on those who are lenient and permit eating before Minchah (as explained in halachah 6), nevertheless, l’chatchilah, it is better that he prays in a minyan before that, as practiced in many yeshivot.
. If one mistakenly prayed in the first half-hour after chatzot, the Acharonim disagree as to whether or not he fulfilled his obligation b’dieved. According to the Magen Avraham he did not, whereas according to the Pri Chadash he did. The Sha’ar HaTzion 233:6 indicates that this matter requires further study, and the Kaf HaChaim 2 concludes that because prayer is a rabbinic obligation, when there is doubt, we are lenient, and he does not repeat his prayer. Further, there is uncertainty with regard to that first half-hour, as to whether it is proportional or permanent. The Sha’ar HaTzion 233:8 tends to say that it is proportional.