This time is the third halachic hour of the day, by when people of luxury would arise in the morning. The תנאים (Tanaic Sages) codified this time to have one completely read קריאת שמע (Kriat Shema) before then (R’ Yehoshua in Mishnah Berakhoth 1:2, Shemuel in Talmud Bavli 10b), based on the word ובקומך (as one rises).

To calculate this time, one would need to know how long a seasonal hour is and when to start counting from (the time you start measuring the length of a seasonal hour will also determine when the seasonal hour starts). A majority of Poskim understand the day’s seasonal hour length to be determined by dividing the length of time between sunrise and sunset into 12 timeframes (called “seasonal hours”), of which include the Rambam (Kriat Shema 1:11), Rav Sa’adia Gaon (Siddur, page 12) and the Vilna Gaon (reflected in Biur HaGra on Oraḥ Ḥayim, 459:2).

However, some are stringent to measure the day’s seasonal hour length by dividing the length of time from Alot Hashachar until Tzet Ha’Kokhavim into 12 timeframes (called “seasonal hours”), of which include the Ḥida (Shu”t Ḥayim Sha-al II 38:70), Ben Ish Ḥai (Rav Pa’alim 2:2 & BI”Ḥ Vayakhel 4), Kaf Hachaim (58:4) & Terumat Hadeshen. To calculate as such in a symmetric fashion (so that the midpoint of both sunrise->sunset + alot->tzet line up), one would need to measure Tzet Ha’Kokhavim by Rabbenu Tam’s time; otherwise, there is a missing 58.5 minutes between the time of the Geonic Tzet Ha’Kokhavim and Rabbenu Tam’s (counterpoint would be the Ben Ish Ḥai’s calculations, which are indeed shifted by that time).

• As per the rule of Halichot Olam (v. 1 Vaera 3), one should be stringent by this opinion since this is a matter of a Biblical commandment, especially when the Maghen Avraham (58:1) interprets even the earlier Poskim quoted above to hold by this time when it comes to Shema. However, one who did not manage to fulfil this stringency in time should still aim to say Kriat Shema by the time of the “Vilna Gaon”.

Within the seasonal hour, there are two time periods; the beginning of the hour or the end of the hour. Although the Geonic era of Poskim hold by the beginning of the third hour (Machzor Vitri I pg 7; Siddur Rav Amram 1:15-16), the Shulḥan Arukh (Oraḥ Ḥayim, 58:6) held like the Rambam (ibid) as well as other Rishonim (Chinuch 420; Tosafoth Avodah Zara 4b s.v. Betelat) who instead calculate it by the end of the third hour.

This time is the third halachic hour of the day, by when people of luxury would arise in the morning. The תנאים (Tanaic Sages) codified this time to have one completely read קריאת שמע (Kriat Shema) before then (R’ Yehoshua in Mishnah Berakhoth 1:2, Shemuel in Talmud Bavli 10b), based on the word ובקומך (as one rises).

To calculate this time, one would need to know how long a seasonal hour is and when to start counting from (the time you start measuring the length of a seasonal hour will also determine when the seasonal hour starts). A majority of Poskim understand the day’s seasonal hour length to be determined by dividing the length of time between sunrise and sunset into 12 timeframes (called “seasonal hours”), of which include the Rambam (Kriat Shema 1:11), Rav Sa’adia Gaon (Siddur, page 12) and the Vilna Gaon (reflected in Biur HaGra on Oraḥ Ḥayim, 459:2).

However, some are stringent to measure the day’s seasonal hour length by dividing the length of time from Alot Hashachar until Tzet Ha’Kokhavim into 12 timeframes (called “seasonal hours”), of which include the Ḥida (Shu”t Ḥayim Sha-al II 38:70), Ben Ish Ḥai (Rav Pa’alim 2:2 & BI”Ḥ Vayakhel 4), Kaf Hachaim (58:4) & Terumat Hadeshen. To calculate as such in a symmetric fashion (so that the midpoint of both sunrise->sunset + alot->tzet line up), one would need to measure Tzet Ha’Kokhavim by Rabbenu Tam’s time; otherwise, there is a missing 58.5 minutes between the time of the Geonic Tzet Ha’Kokhavim and Rabbenu Tam’s (counterpoint would be the Ben Ish Ḥai’s calculations, which are indeed shifted by that time).

• As per the rule of Halichot Olam (v. 1 Vaera 3), one should be stringent by this opinion since this is a matter of a Biblical commandment, especially when the Maghen Avraham (58:1) interprets even the earlier Poskim quoted above to hold by this time when it comes to Shema. However, one who did not manage to fulfil this stringency in time should still aim to say Kriat Shema by the time of the “Vilna Gaon”.

Within the seasonal hour, there are two time periods; the beginning of the hour or the end of the hour. Although the Geonic era of Poskim hold by the beginning of the third hour (Machzor Vitri I pg 7; Siddur Rav Amram 1:15-16), the Shulḥan Arukh (Oraḥ Ḥayim, 58:6) held like the Rambam (ibid) as well as other Rishonim (Chinuch 420; Tosafoth Avodah Zara 4b s.v. Betelat) who instead calculate it by the end of the third hour.

Although the Passover holiday only begins on the 15^th of Nisan for the following seven days, the Talmud (Pesaḥim Bavli 5a) includes a Biblical prohibition of חמץ during the 14^th, due to an apparant contradiction between the commandment to dispose of the חמץ on the same day that one should not own any to dispose of. This reading is supported by the verse’s (Parashat Bo, Exodus 12:15) use of the word הראשון as opposed to the simpler ראשון. With the preceding words including “אך”, we learn that this day is divided into two halves, with the first half focused on the action of תשביתו (“disposition”).

The second half (בן הערבים - starts after the end of the 6^th hour/beginning of the 7^th) is the timeframe of the Biblical prohibition, mimicking the days when the Temple stood and one would bring the relevant Korban offering (translated to time in our days when we’re unable to bring any offerings - “זְמַן שְׁחִיטָה אָמַר רַחֲמָנָא” [Pesaḥim Bavli 5b]). Once the offering is brought, it is forbidden to own or derive benefit (including eating) from חמץ, as said in Exodus 34:25 - “לֹֽא־תִשְׁחַ֥ט עַל־חָמֵ֖ץ דַּם־זִבְחִ֑י”. In specific, violating this prohibition transgresses a negative commandment, which is learned out from the Asmakhta of “וְזָבַ֥חְתָּ פֶּ֛סַח לַיהֹוָ֥ה אֱלֹהֶ֖יךָ…לֹא־תֹאכַ֤ל עָלָיו֙ חָמֵ֔ץ” (Deuteronomy 16:2-3. Ruling came from Rabbi Yehuda, Pesaḥim Bavli 28b; later codified in two foremost authorities [רמב”ם הלכות חמץ ומצה א’:ח’; רא”ש פסחים סוף ב’:ד’ - “וכן נראה לי”] and other Rishonim [רב יצחק אבן גיאת ז”ל בשם הרא”ש ומגיד משנה]).

Due to concerns about potentially mistaking this time on a cloudy day, the rabbinic safeguard introduced a new minimum of the entire 6^th hour, forbidding all activity related to חמץ for an additional hour (starting at the end of the 5^th hour). Additionally, Rabbi Yehuda further restricted eating חמץ throughout the 5^th hour (which starts at the beginning of the 4^th hour), adding a second hour on top of the original rabbinic safeguard (Mishna Pesaḥim 1:4; Pesaḥim Bavli 12b; Rambam Hilchot Hametz Umatzah 1:9).

These hours are calculated by dividing the length of the day into 12 timeframes, each portion representing a “seasonal hour”. Although the typical length of the day is measured from sunrise until sunset, the severity of חמץ demands us to be strict (unless it’s for permitting a child to eat חמץ, meaning they would be lenient to stop by the time we would normally report as “Sof Zeman Berakhot Shema”; see Ḥazon Ovadia - Pesach I pg. 60 & Yalkut Yosef on Pesach (5775 edition) pg. 652) to extend the day symmetrically to Dawn & Nightfall (Pri Ḥadash, beginning of Siman 443 & Ḥazon Ovadia II pg. 37. The Nightfall chosen is Rabbenu Tam’s, as it includes the 58.5 minutes needed for the expected symmetry), similar to the rules of “Sof Zeman Keriat Shema”.

Although the Passover holiday only begins on the 15^th of Nisan for the following seven days, the Talmud (Pesaḥim Bavli 5a) includes a Biblical prohibition of חמץ during the 14^th, due to an apparant contradiction between the commandment to dispose of the חמץ on the same day that one should not own any to dispose of. This reading is supported by the verse’s (Parashat Bo, Exodus 12:15) use of the word הראשון as opposed to the simpler ראשון. With the preceding words including “אך”, we learn that this day is divided into two halves, with the first half focused on the action of תשביתו (“disposition”).

The second half (בן הערבים - starts after the end of the 6^th hour/beginning of the 7^th) is the timeframe of the Biblical prohibition, mimicking the days when the Temple stood and one would bring the relevant Korban offering (translated to time in our days when we’re unable to bring any offerings - “זְמַן שְׁחִיטָה אָמַר רַחֲמָנָא” [Pesaḥim Bavli 5b]). Once the offering is brought, it is forbidden to own or derive benefit (including eating) from חמץ, as said in Exodus 34:25 - “לֹֽא־תִשְׁחַ֥ט עַל־חָמֵ֖ץ דַּם־זִבְחִ֑י”. In specific, violating this prohibition transgresses a negative commandment, which is learned out from the Asmakhta of “וְזָבַ֥חְתָּ פֶּ֛סַח לַיהֹוָ֥ה אֱלֹהֶ֖יךָ…לֹא־תֹאכַ֤ל עָלָיו֙ חָמֵ֔ץ” (Deuteronomy 16:2-3. Ruling came from Rabbi Yehuda, Pesaḥim Bavli 28b; later codified in two foremost authorities [רמב”ם הלכות חמץ ומצה א’:ח’; רא”ש פסחים סוף ב’:ד’ - “וכן נראה לי”] and other Rishonim [רב יצחק אבן גיאת ז”ל בשם הרא”ש ומגיד משנה]).

Due to concerns about potentially mistaking this time on a cloudy day, the rabbinic safeguard introduced a new minimum of the entire 6^th hour, forbidding all activity related to חמץ for an additional hour (starting at the end of the 5^th hour). Additionally, Rabbi Yehuda further restricted eating חמץ throughout the 5^th hour (which starts at the beginning of the 4^th hour), adding a second hour on top of the original rabbinic safeguard (Mishna Pesaḥim 1:4; Pesaḥim Bavli 12b; Rambam Hilchot Hametz Umatzah 1:9).

These hours are calculated by dividing the length of the day into 12 timeframes, each portion representing a “seasonal hour”. Although the typical length of the day is measured from sunrise until sunset, the severity of חמץ demands us to be strict (unless it’s for permitting a child to eat חמץ, meaning they would be lenient to stop by the time we would normally report as “Sof Zeman Berakhot Shema”; see Ḥazon Ovadia - Pesach I pg. 60 & Yalkut Yosef on Pesach (5775 edition) pg. 652) to extend the day symmetrically to Dawn & Nightfall (Pri Ḥadash, beginning of Siman 443 & Ḥazon Ovadia II pg. 37. The Nightfall chosen is Rabbenu Tam’s, as it includes the 58.5 minutes needed for the expected symmetry), similar to the rules of “Sof Zeman Keriat Shema”.

These are the times associated with Mincha, the afternoon prayer.

• Mincha Gedolah: This is half an hour after Hatzot Hayom. The measurement of half an hour is the more stringent of seasonal or fixed minutes.
• Mincha Ketanah: 9 1/2 seasonal hours after sunrise. This is the more preferable time to pray (Yalkut Yosef 233:1).

Each of those are named based on how much time you would have to pray Mincha; you have a big time at Mincha Gedolah and you have a shorter timeframe at Mincha Ketanah. Saying Korbanot is tied to these times; do not aim just to start Amidah by this time.

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These are the times associated with Mincha, the afternoon prayer.

• Mincha Gedolah: This is half an hour after Hatzot Hayom. The measurement of half an hour is the more stringent of seasonal or fixed minutes.
• Mincha Ketanah: 9 1/2 seasonal hours after sunrise. This is the more preferable time to pray (Yalkut Yosef 233:1).

Each of those are named based on how much time you would have to pray Mincha; you have a big time at Mincha Gedolah and you have a shorter timeframe at Mincha Ketanah. Saying Korbanot is tied to these times; do not aim just to start Amidah by this time.

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Pelag Ha’Minḥa is defined as the latter half of the time span between מנחה קטנה until the end of the day (ערב), occurring at 10¾ hours into the day (Berakhot Bavli 26b). Since מנחה קטנה begins at 9½ hours into the day, this leaves only 1¼ seasonal hours from the start of this half until the end of the מנחה. It is during this time that one may start performing a select few commandments of the night, such as accepting Shabbat early (Shulḥan Arukh O”Ḥ, 273:4), lighting Ḥanukah candles early (footnotes of Ḥazon Ovadia Ḥanukah pg. 89) or praying תפילת ערבית when one (preferably) already prayed Minḥa (Berakhoth 26a, Rabbi Yehuda).

The Gemara’s central inquiry concerns whether the “half” is measured from מנחה גדולה or מנחה קטנה; once the beraita clarifies it is the latter, the Gemara proceeds to calculate the day’s span assuming a 12-hour daytime period, and פלג המנחה happening within those 12-hours. It identifies that מנחה קטנה is the 9½’th hour of the day, then leaving this “half” (פלג המנחה) to start at “11 minus a quarter hours”. This implies that the two halves of מנחה קטנה are equal, placing ערב at the 12th hour—after both halves have elapsed. However, the Gemara does not explicitly define ערב, leaving it to the Rishonim to associate it either with sunset or nightfall.

The calculation of seasonal hours from sunrise to sunset aligns with the sacrificial schedule, particularly the כבש של בין הערבים (afternoon lamb offering), which parallels the מנחה prayer. This is per the proof of Rabbenu Ḥananel (citing R’ Yehuda’s parallel’s between the rules of the שתי תמידים and when one can pray the two daytime prayers). Thus, פלג המנחה is placed 1¼ seasonal hours before sunset (as held by Talmideh Rabbenu Yonah, Berakhoth Bavli 26a; Rambam, Laws of Prayer, 3:4; Shilteh Hagiborim on the Mordekhi; R’ Yitzḥak Yisraeli’s explanation of the Meiri - Yoseh Binah pg. 105).

However, other authorities defined the day as starting from Dawn and ending by Nightfall, thus defining ערב (being the end-time of מנחה) as Nightfall (as writes the Rosh on Berakhot 1:1 & 4:6; Tosafot Ha’Rosh on Berakhot 27a; Rashba on Berakhot 2a). The questions on the specific implementations comes from the origin of said definition (Pesaḥim Bavli 94a) and how it’s structured there:

• The Gemara in Pesaḥim extended the day proportionally, where the same 4 mil that was used to start the day is the same 4 mil that was used to end the day. One approach is to assume the seasonal hours get extended to match this new length (as ruled by the Terumat Ha’Deshen; see siman 1), thus keeping halachic midday corresponding with the sun’s midpoint in its traversal (as explicitly outlined by Shu”t Divreh Yosef Shwartz pg. 58 & R’ Tukachinsky in the Sefer “Ben Hashmashot”, pg. 98). Nevertheless, Pelag Ha’Minḥa is independent from proportionality (as discussed in Pri Ḥadash, Kuntress Debei Shimsha, end of ספר מים חיים), hence allowing either one of those rules to be broken. This opened the door for two preceding interpretations:
• By ignoring the extended length of a seasonal hour but still keeping a proportionate Nightfall (thus being 72 minutes in both directions), the S”A & Ramban (in addition to Ra’ah, Berakhoth 26b; Ritva, Berakhoth 27b; Rabbi Yaakov Emden, Prozdor Bayit 41, paragraph 28 explicitly linking this to Shabbat’s Candle Lighting) created a time for פלג המנחה that was close enough to sunset to make both terms used interchangeably (see the Ramban, Pesaḥim 54b; as for the S”A, see O”Ḥ 233 for Nightfall being the end time of מנחה as well as O”Ḥ 261 describing what Nightfall is, and the connection between sunset for Tosefet Shabbat to פלג המנחה, as the Rama implicitly outlines).
• Contemporary authorities, however, extended the length of each seasonal hour but defined Nightfall using the 13.5 seasonal minutes measurements, disproportionate to the 72 seasonal minutes added for Dawn (see the Ben Ish Ḥai, Year I, Vayakhel VIII; see also Ohr Letzion vol. 2 pg. 147 & the responsas of the Ma’amar Mordechai vol. 4 siman 12). This meant that the 6^th seasonal hour no longer corresponded to the midpoint of the sun’s traversal.

This is all a build up to the opinions of Yabi’a Omer (handwritten notes on Yabi’a Omer I O”Ḥ 43:20) and his two sons - R’ Avraham Yosef in his Parashat Terumah 5779 shiur min 3:55 as well as R Yitzḥak Yosef in multiple shiurim (Motzei Shabbat Pesach 5779 shiur min 37, Motzei Shabbat Bo 5778 shiur min 25) & his Yalkut Yosef (new edition, siman 271, pages 139 & 144-147) - to use the Geonic Nightfall as an offset for Pelag, in both stringencies (such as by blessings in vain regarding ערבית and הדלקת נרות), but also in its leniencies (such as the last time to eat Seudat Shelishit on Erev Pesaḥ - see Ḥ”‘O Pesaḥ pg. 67 & pg. 199). This is also reflected in later writings of Maran zt’l himself (Ḥazon ‘Ovadia Ta’anit pg. 94; Halikhot ‘Olam vol. 1 pg. 223), even if he’s not made mention of it by earlier sections of how seasonal hours work (Halikhot Olam, vol. 1 pg. 248). The questions on this position do not come from its specifications in the books, since the Sefarim were vague in terms of a resulting time; rather, the questions come from the implementation in the Ohr Hachaim calendar, which fills in blanks that the sefarim did not specify (often times from the direction of Hakham Ovadia himself). In that calendar, they ignore both the proportionality of the day when defining Nightfall and the use of those extended seasonal minutes. Furthermore, this calculation is isolated to פלג המנחה; other zemanim in the calendar are all consistent with the time range from sunrise to sunset. Nevertheless, we’ve used the implementation of the Ohr Hachaim calendar when representing the “Yalkut Yosef” opinion, due to its authoritative status in representing the calculations from the sefarim.

In contrast, R’ David Yosef (אוצרות יוסף תשובה ז בסוף הלכה ברורה חלק י”ד) advocates restoring פלג המנחה’s definition as 1¼ seasonal hours before sunset, as per the original Sepharadic tradition. In addition to the questions raised on the Yabi’a Omer’s position above, there is no concern about going against the stricter ruling for matters of blessings (effectively being everything that can be done from פלג המנחה), since precedents in a blessing override concerns about them (source: מנחת כהן, מעמר ב, בסוף פרק ט. This is also applicable for the latest time to say the blessings of קריאת שמע, where we are not concerned for the MG”A seasonal hour calculation). However, the Halacha Berura also allows praying מנחה after sunset; although this would be fine if it was reserved as a בדיעבד ruling, the Halacha Berura relies on this time enough that one should prefer this time for minyan instead of praying alone before sunset, even though he wouldn’t use it as a reliability for the calculation of פלג המנחה.

Each of the differing opinions introduce its stringencies, but also leniencies. Combining that reason with a general concern of either adhering to the text or intellectual honesty with the structure for the day (both brothers respectively) introduces the two opinions without any room for compromising (irrespective of Halacha Berurah Siman 233 pg. 75 saying the Yalkut Yosef opinion). Therefore, we’ve presented both opinions with equal weight. However, by knowing the stringencies, one can adhere to both opinions, especially by restricting Biblical obligations with its blessings (such as קידוש בליל שבת or הבדלה מוקדם ביום שבת) to the stricter/later פלג המנחה, based on the Halikhot ‘Olam (vol. 1 pg. 248) who attributed Biblical matters to the extended seasonal hours.

• There are opinions that would argue that ערבית, what they assert as the first prayer of “the day”, would fulfill the Biblical obligation to prayer and thus be subject to the same recommendation. Nevertheless, the Kaf Ha’Ḥayyim (O”Ḥ 233:7) asserts that we are lenient regarding prayer to use the time represented in our calendar as the Halacha Berura time (which we can thus extend to anything needing a blessing - the “stringency” of this ruling - based the position of the מנחת כהן), even if he rules in other cases would indicate that פלג המנחה should be based on Nightfall (O”Ḥ 692:29). As for the second concern, there are others who assume שחרית is the Biblically-mandated prayer (ראה בפרי מגדים סי’ ד’ מש”ז ס”ק טס), especially in light of the opinion that ערבית is a תפילת רשות in the Gemara’s perspective.
• The “later time” for the Rabbinic/Biblical divide above would depend on whether you demand proportionality (as the Halacha Berura does) or don’t (as the Yalkut Yosef does). However, interesting to note that the only authority that considered the Nightfall position (the Yalkut Yosef) is also the one that doesn’t demand proportionality. Thus, one could use the ילקוט יוסף time above to be exempt according to both opinions; should it prove to be too strict (which may happen in northern countries), one should calculate the seasonal hours from Dawn to the Geonic Nightfall and use the 10.75^th hour instead of our listed time, which should result in a time closer to the Halacha Berura time. As for the difference of “צאת הכוכבים” between this implementation of the MG”A hours and the morning ones (those being by קריאת שמע and both times for חמץ בערב פסח), perhaps we’re not concerned about proportionality since this form of calculation is already a stringency for us, and the proportionate time would increase the stringency on the assumption (that Nightfall is 72 minutes) we do not rule by.

Fun fact: Under Biblical Hebrew rules of “קטל”, the proper pronunciation of פלג המנחה should transliterate to “Peleg Ha’Minḥa”. Nevertheless, we’ve kept it “Pelag” to adhere to Hakham Ovadia’s pronunciation style.

Pelag Ha’Minḥa is defined as the latter half of the time span between מנחה קטנה until the end of the day (ערב), occurring at 10¾ hours into the day (Berakhot Bavli 26b). Since מנחה קטנה begins at 9½ hours into the day, this leaves only 1¼ seasonal hours from the start of this half until the end of the מנחה. It is during this time that one may start performing a select few commandments of the night, such as accepting Shabbat early (Shulḥan Arukh O”Ḥ, 273:4), lighting Ḥanukah candles early (footnotes of Ḥazon Ovadia Ḥanukah pg. 89) or praying תפילת ערבית when one (preferably) already prayed Minḥa (Berakhoth 26a, Rabbi Yehuda).

The Gemara’s central inquiry concerns whether the “half” is measured from מנחה גדולה or מנחה קטנה; once the beraita clarifies it is the latter, the Gemara proceeds to calculate the day’s span assuming a 12-hour daytime period, and פלג המנחה happening within those 12-hours. It identifies that מנחה קטנה is the 9½’th hour of the day, then leaving this “half” (פלג המנחה) to start at “11 minus a quarter hours”. This implies that the two halves of מנחה קטנה are equal, placing ערב at the 12th hour—after both halves have elapsed. However, the Gemara does not explicitly define ערב, leaving it to the Rishonim to associate it either with sunset or nightfall.

The calculation of seasonal hours from sunrise to sunset aligns with the sacrificial schedule, particularly the כבש של בין הערבים (afternoon lamb offering), which parallels the מנחה prayer. This is per the proof of Rabbenu Ḥananel (citing R’ Yehuda’s parallel’s between the rules of the שתי תמידים and when one can pray the two daytime prayers). Thus, פלג המנחה is placed 1¼ seasonal hours before sunset (as held by Talmideh Rabbenu Yonah, Berakhoth Bavli 26a; Rambam, Laws of Prayer, 3:4; Shilteh Hagiborim on the Mordekhi; R’ Yitzḥak Yisraeli’s explanation of the Meiri - Yoseh Binah pg. 105).

However, other authorities defined the day as starting from Dawn and ending by Nightfall, thus defining ערב (being the end-time of מנחה) as Nightfall (as writes the Rosh on Berakhot 1:1 & 4:6; Tosafot Ha’Rosh on Berakhot 27a; Rashba on Berakhot 2a). The questions on the specific implementations comes from the origin of said definition (Pesaḥim Bavli 94a) and how it’s structured there:

• The Gemara in Pesaḥim extended the day proportionally, where the same 4 mil that was used to start the day is the same 4 mil that was used to end the day. One approach is to assume the seasonal hours get extended to match this new length (as ruled by the Terumat Ha’Deshen; see siman 1), thus keeping halachic midday corresponding with the sun’s midpoint in its traversal (as explicitly outlined by Shu”t Divreh Yosef Shwartz pg. 58 & R’ Tukachinsky in the Sefer “Ben Hashmashot”, pg. 98). Nevertheless, Pelag Ha’Minḥa is independent from proportionality (as discussed in Pri Ḥadash, Kuntress Debei Shimsha, end of ספר מים חיים), hence allowing either one of those rules to be broken. This opened the door for two preceding interpretations:
• By ignoring the extended length of a seasonal hour but still keeping a proportionate Nightfall (thus being 72 minutes in both directions), the S”A & Ramban (in addition to Ra’ah, Berakhoth 26b; Ritva, Berakhoth 27b; Rabbi Yaakov Emden, Prozdor Bayit 41, paragraph 28 explicitly linking this to Shabbat’s Candle Lighting) created a time for פלג המנחה that was close enough to sunset to make both terms used interchangeably (see the Ramban, Pesaḥim 54b; as for the S”A, see O”Ḥ 233 for Nightfall being the end time of מנחה as well as O”Ḥ 261 describing what Nightfall is, and the connection between sunset for Tosefet Shabbat to פלג המנחה, as the Rama implicitly outlines).
• Contemporary authorities, however, extended the length of each seasonal hour but defined Nightfall using the 13.5 seasonal minutes measurements, disproportionate to the 72 seasonal minutes added for Dawn (see the Ben Ish Ḥai, Year I, Vayakhel VIII; see also Ohr Letzion vol. 2 pg. 147 & the responsas of the Ma’amar Mordechai vol. 4 siman 12). This meant that the 6^th seasonal hour no longer corresponded to the midpoint of the sun’s traversal.

This is all a build up to the opinions of Yabi’a Omer (handwritten notes on Yabi’a Omer I O”Ḥ 43:20) and his two sons - R’ Avraham Yosef in his Parashat Terumah 5779 shiur min 3:55 as well as R Yitzḥak Yosef in multiple shiurim (Motzei Shabbat Pesach 5779 shiur min 37, Motzei Shabbat Bo 5778 shiur min 25) & his Yalkut Yosef (new edition, siman 271, pages 139 & 144-147) - to use the Geonic Nightfall as an offset for Pelag, in both stringencies (such as by blessings in vain regarding ערבית and הדלקת נרות), but also in its leniencies (such as the last time to eat Seudat Shelishit on Erev Pesaḥ - see Ḥ”‘O Pesaḥ pg. 67 & pg. 199). This is also reflected in later writings of Maran zt’l himself (Ḥazon ‘Ovadia Ta’anit pg. 94; Halikhot ‘Olam vol. 1 pg. 223), even if he’s not made mention of it by earlier sections of how seasonal hours work (Halikhot Olam, vol. 1 pg. 248). The questions on this position do not come from its specifications in the books, since the Sefarim were vague in terms of a resulting time; rather, the questions come from the implementation in the Ohr Hachaim calendar, which fills in blanks that the sefarim did not specify (often times from the direction of Hakham Ovadia himself). In that calendar, they ignore both the proportionality of the day when defining Nightfall and the use of those extended seasonal minutes. Furthermore, this calculation is isolated to פלג המנחה; other zemanim in the calendar are all consistent with the time range from sunrise to sunset. Nevertheless, we’ve used the implementation of the Ohr Hachaim calendar when representing the “Yalkut Yosef” opinion, due to its authoritative status in representing the calculations from the sefarim.

In contrast, R’ David Yosef (אוצרות יוסף תשובה ז בסוף הלכה ברורה חלק י”ד) advocates restoring פלג המנחה’s definition as 1¼ seasonal hours before sunset, as per the original Sepharadic tradition. In addition to the questions raised on the Yabi’a Omer’s position above, there is no concern about going against the stricter ruling for matters of blessings (effectively being everything that can be done from פלג המנחה), since precedents in a blessing override concerns about them (source: מנחת כהן, מעמר ב, בסוף פרק ט. This is also applicable for the latest time to say the blessings of קריאת שמע, where we are not concerned for the MG”A seasonal hour calculation). However, the Halacha Berura also allows praying מנחה after sunset; although this would be fine if it was reserved as a בדיעבד ruling, the Halacha Berura relies on this time enough that one should prefer this time for minyan instead of praying alone before sunset, even though he wouldn’t use it as a reliability for the calculation of פלג המנחה.

Each of the differing opinions introduce its stringencies, but also leniencies. Combining that reason with a general concern of either adhering to the text or intellectual honesty with the structure for the day (both brothers respectively) introduces the two opinions without any room for compromising (irrespective of Halacha Berurah Siman 233 pg. 75 saying the Yalkut Yosef opinion). Therefore, we’ve presented both opinions with equal weight. However, by knowing the stringencies, one can adhere to both opinions, especially by restricting Biblical obligations with its blessings (such as קידוש בליל שבת or הבדלה מוקדם ביום שבת) to the stricter/later פלג המנחה, based on the Halikhot ‘Olam (vol. 1 pg. 248) who attributed Biblical matters to the extended seasonal hours.

• There are opinions that would argue that ערבית, what they assert as the first prayer of “the day”, would fulfill the Biblical obligation to prayer and thus be subject to the same recommendation. Nevertheless, the Kaf Ha’Ḥayyim (O”Ḥ 233:7) asserts that we are lenient regarding prayer to use the time represented in our calendar as the Halacha Berura time (which we can thus extend to anything needing a blessing - the “stringency” of this ruling - based the position of the מנחת כהן), even if he rules in other cases would indicate that פלג המנחה should be based on Nightfall (O”Ḥ 692:29). As for the second concern, there are others who assume שחרית is the Biblically-mandated prayer (ראה בפרי מגדים סי’ ד’ מש”ז ס”ק טס), especially in light of the opinion that ערבית is a תפילת רשות in the Gemara’s perspective.
• The “later time” for the Rabbinic/Biblical divide above would depend on whether you demand proportionality (as the Halacha Berura does) or don’t (as the Yalkut Yosef does). However, interesting to note that the only authority that considered the Nightfall position (the Yalkut Yosef) is also the one that doesn’t demand proportionality. Thus, one could use the ילקוט יוסף time above to be exempt according to both opinions; should it prove to be too strict (which may happen in northern countries), one should calculate the seasonal hours from Dawn to the Geonic Nightfall and use the 10.75^th hour instead of our listed time, which should result in a time closer to the Halacha Berura time. As for the difference of “צאת הכוכבים” between this implementation of the MG”A hours and the morning ones (those being by קריאת שמע and both times for חמץ בערב פסח), perhaps we’re not concerned about proportionality since this form of calculation is already a stringency for us, and the proportionate time would increase the stringency on the assumption (that Nightfall is 72 minutes) we do not rule by.

Fun fact: Under Biblical Hebrew rules of “קטל”, the proper pronunciation of פלג המנחה should transliterate to “Peleg Ha’Minḥa”. Nevertheless, we’ve kept it “Pelag” to adhere to Hakham Ovadia’s pronunciation style.

Tzet/Nightfall is the time when the next halachic day starts after Bein Hashmashot/twilight finishes.

This is the latest time a person can start praying Minḥa according to Rav Ovadia Yosef Z"TL. Although he previously ruled one should only do so if he could pray the majority of the Tefila before this time (matching the BI"Ḥ - Vayakhel IX), he uses the sefer "Bateh Knessiot" (siman 89) to permit one to start even if the above condition won't be met (Yabia Omer VII Siman 34).

This time is calculated as 13 and a half zmaniyot/seasonal minutes after sunset (elevation included). For stringent matters (brit milot, end of fasts), we use 20 zemaniyot/seasonal minutes after sunset. The GR\"A calculates a zemaniyot/seasonal hour by taking the time between sunrise and sunset (elevation included) and divides it into 12 equal parts. Then we divide one of those 12 parts into 60 to get a zemaniyot/seasonal minute.

Outside Eretz Yisrael, these numbers ("13.5" & "20") are measured in the form of degrees below the horizon (thus being converted to 3.7 & 5.075 degrees respectively) to be then applied on the equinox day, thus giving us a new number to make seasonal that reflects the local astronomy.

Tzet/Nightfall is the time when the next halachic day starts after Bein Hashmashot/twilight finishes.

This is the latest time a person can start praying Minḥa according to Rav Ovadia Yosef Z"TL. Although he previously ruled one should only do so if he could pray the majority of the Tefila before this time (matching the BI"Ḥ - Vayakhel IX), he uses the sefer "Bateh Knessiot" (siman 89) to permit one to start even if the above condition won't be met (Yabia Omer VII Siman 34).

This time is calculated as 13 and a half zmaniyot/seasonal minutes after sunset (elevation included). For stringent matters (brit milot, end of fasts), we use 20 zemaniyot/seasonal minutes after sunset. The GR\"A calculates a zemaniyot/seasonal hour by taking the time between sunrise and sunset (elevation included) and divides it into 12 equal parts. Then we divide one of those 12 parts into 60 to get a zemaniyot/seasonal minute.

Outside Eretz Yisrael, these numbers ("13.5" & "20") are measured in the form of degrees below the horizon (thus being converted to 3.7 & 5.075 degrees respectively) to be then applied on the equinox day, thus giving us a new number to make seasonal that reflects the local astronomy.