Reference for Moed Katan 3:5
הַקּוֹבֵר אֶת מֵתוֹ שְׁלֹשָׁה יָמִים קֹדֶם לָרֶגֶל, בָּטְלָה הֵימֶנּוּ גְּזֵרַת שִׁבְעָה. שְׁמֹנָה, בָּטְלָה הֵימֶנּוּ גְּזֵרַת שְׁלֹשִׁים, מִפְּנֵי שֶׁאָמְרוּ, שַׁבָּת עוֹלָה וְאֵינָהּ מַפְסֶקֶת, רְגָלִים מַפְסִיקִין וְאֵינָן עוֹלִין:
If one buries his dead one three days before the festival [i.e., If one of his kin died before the festival, and he observed mourning three days before the festival, the decree of shivah ("the seven days") falls off, [but not that of shloshim ("the thirty days"), i.e., the interdict of cutting his hair, so that after the festival he counts (until) thirty days including the three that he had already observed. The halachah is that if one buries his dead one even one moment before the festival, the decree of shivah falls off.] (If he buries him) eight [days before the festival], the decree of shloshim falls off. [Since one of the days of (interdicted) shaving (of the shloshim) preceded the festival, the festival comes and cancels the others entirely.] For they said: Shabbath is included [The Shabbath within the days of his mourning is included in the seven (of shivah)] and does not interrupt [It does not cancel the rest, but he sits in mourning after Shabbath.]; festivals interrupt and are not included. [If he observed mourning before the festival, the festival interrupts and cancels the decree of shloshim. And if he did not observe mourning before the festival, but began his mourning on the festival, the days of the festival are not included in the shivah, but they are included in the shloshim. The reason that Shabbath is included in the shivah is that "private" mourning obtains therein, such as the interdict against cohabitation and against uncovering the head (i.e., taking off the mourner's wrap) and bathing in warm water, these being forbidden on Shabbath. But on the festival no laws of mourning obtain, for which reason it interrupts it entirely. And if no mourning at all began before the festival, as when he buried his dead one in the midst of the festival, it is not included in the shivah, and he begins to count shivah after the festival.]