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In P'sachim (58a), Abaye frames a disagreement between Rabbi Yishma'el and Rabbi Akiva regarding the ordering of the korban musaf and the bazichin (bowls of frankincense burned when the old showbread was removed and eaten) when Erev Pesach falls on Shabbos.

According to R' Yishma'el, the musaf service was scheduled for six hours into the day, the bazichin for seven*, and the tamid slaughtering for seven and a half hours into the day. According to R' Akiva, the bazichin were scheduled for five hours into the day, the musaf for six, and the tamid was scheduled to be slaughtered six and a half hours into the day:

במוספין קודמין לבזיכין קמיפלגי רבי ישמעאל סבר מוספין קודמין לבזיכין עבד להו למוספין בשש ובזיכין בשבע ועביד ליה לתמיד בשבע ומחצה רבי עקיבא סבר בזיכין קודמין למוספין בזיכין בחמש ומוספין בשש ועביד ליה לתמיד בשש ומחצה

Seemingly, a different amount of time is scheduled for the musaf depending on whose order is followed; R' Yishma'el allots one hour for musaf, whereas R' Akiva allots only a half hour for musaf. Why?


* Rashi and Tosafos disagree regarding how long the bazichin service actually takes, but they agree that it takes at least an hour and, according to R' Yishma'el's schedule, the showbread part of the bazichin service would conclude after the tamid service. In any case, Rashi and Tosafos agree that the tamid was slaughtered seven and a half hours into the day so as not to depart from a standard Erev Pesach schedule (the other standard Erev Pesach schedule is from when Erev Pesach falls on Erev Shabbos and the tamid is slaughtered six and a half hours into the day - this is the schedule used by R' Akiva in our case).

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The discussion here is of start times. From where do we learn that the space between them is completely filled with the designated activites? Maybe there's a break and musaf only takes half an hour no matter whose scheduling you follow? –  Monica Cellio Nov 19 '13 at 18:47
    
@MonicaCellio Perhaps, but why would there need to be a space for extra activities after musaf only according to R' Yishma'el? –  Fred Nov 19 '13 at 18:56
    
It might not be about need for waiting so much as need for the services being done at the right times, even if that implies some downtime. I don't know; I'm just asking/speculating. –  Monica Cellio Nov 19 '13 at 18:59
    
@MonicaCellio As far as I can tell, there are two definite conditions: the musaf is always started at noon ("six") and the tamid is always slaughtered on a half hour (6.5, 7.5, or 8.5). Abaye's apparent inconsistency in explaining the schedules of R' Yishma'el and R' Akiva seems to belie the possibility that other conditions apply. In fact, the only other condition that I can think of to explain this would be that some half-hour activity always comes between the bazichin and the musaf (regardless of the order), but I don't see this indicated (and it would also not fit with Tosafos). –  Fred Nov 19 '13 at 19:15
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