The sefer, Harirai Kedem, suggests a different understanding behind the machlokes. He suggests that the machlokes as to whether aveilus betzina applies on Shabbos Tisha B’Av is dependent on a different point. The Ramah, who says that it applies, holds that Tisha B’Av is in essence always on the ninth day and therefore aveilus betzina applies. The Mechaber agrees to this, but holds that there can only be one day that aveilus of Tisha B’Av is observed. And since we cannot fully observe the aveilus on Shabbos, we observe it only on Sunday.
Both sides of the machlokes regarding whether there are halachos of shavua she’chal bo the week before Tisha B’Av agree that Tisha B’Av is essentially on Shabbos. However, the opinion that holds that there are no halachos of shavua she’chal bo believes that the halachos applying to the week of Tisha B’Av are connected to the aveilus of Tisha B’Av – similar to a prelude to the aveilus of Tisha B’Av. So even though the actual day of the fast is primarily on Shabbos, and since aveilus is not observed on Shabbos, the week that Shabbos falls out also does not have any halachos of aveilus.
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