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Yom Kippur: Atonement, Cleansing and Water

אַ֡ךְ בֶּעָשׂ֣וֹר לַחֹדֶשׁ֩ הַשְּׁבִיעִ֨י הַזֶּ֜ה י֧וֹם הַכִּפֻּרִ֣ים ה֗וּא מִֽקְרָא־קֹ֙דֶשׁ֙ יִהְיֶ֣ה לָכֶ֔ם וְעִנִּיתֶ֖ם אֶת־נַפְשֹׁתֵיכֶ֑ם וְהִקְרַבְתֶּ֥ם אִשֶּׁ֖ה לַיהוָֽה׃ וְכָל־מְלָאכָה֙ לֹ֣א תַעֲשׂ֔וּ בְּעֶ֖צֶם הַיּ֣וֹם הַזֶּ֑ה כִּ֣י י֤וֹם כִּפֻּרִים֙ ה֔וּא לְכַפֵּ֣ר עֲלֵיכֶ֔ם לִפְנֵ֖י יְהוָ֥ה אֱלֹהֵיכֶֽם׃ כִּ֤י כָל־הַנֶּ֙פֶשׁ֙ אֲשֶׁ֣ר לֹֽא־תְעֻנֶּ֔ה בְּעֶ֖צֶם הַיּ֣וֹם הַזֶּ֑ה וְנִכְרְתָ֖ה מֵֽעַמֶּֽיהָ׃ וְכָל־הַנֶּ֗פֶשׁ אֲשֶׁ֤ר תַּעֲשֶׂה֙ כָּל־מְלָאכָ֔ה בְּעֶ֖צֶם הַיּ֣וֹם הַזֶּ֑ה וְהַֽאֲבַדְתִּ֛י אֶת־הַנֶּ֥פֶשׁ הַהִ֖וא מִקֶּ֥רֶב עַמָּֽהּ׃ כָּל־מְלָאכָ֖ה לֹ֣א תַעֲשׂ֑וּ חֻקַּ֤ת עוֹלָם֙ לְדֹרֹ֣תֵיכֶ֔ם בְּכֹ֖ל מֹֽשְׁבֹֽתֵיכֶֽם׃ שַׁבַּ֨ת שַׁבָּת֥וֹן הוּא֙ לָכֶ֔ם וְעִנִּיתֶ֖ם אֶת־נַפְשֹׁתֵיכֶ֑ם בְּתִשְׁעָ֤ה לַחֹ֙דֶשׁ֙ בָּעֶ֔רֶב מֵעֶ֣רֶב עַד־עֶ֔רֶב תִּשְׁבְּת֖וּ שַׁבַּתְּכֶֽם׃ (פ)

Mark, the tenth day of this seventh month is the Day of Atonement. It shall be a sacred occasion for you: you shall practice self-denial, and you shall bring an offering by fire to the LORD; you shall do no work throughout that day. For it is a Day of Atonement, on which expiation is made on your behalf before the LORD your God. Indeed, any person who does not practice self-denial throughout that day shall be cut off from his kin; and whoever does any work throughout that day, I will cause that person to perish from among his people. Do no work whatever; it is a law for all time, throughout the ages in all your settlements. It shall be a sabbath of complete rest for you, and you shall practice self-denial; on the ninth day of the month at evening, from evening to evening, you shall observe this your sabbath.

What word normally associated with Yom Kippur does not appear in the Torah?

וְהָיְתָ֥ה לָכֶ֖ם לְחֻקַּ֣ת עוֹלָ֑ם בַּחֹ֣דֶשׁ הַ֠שְּׁבִיעִי בֶּֽעָשׂ֨וֹר לַחֹ֜דֶשׁ תְּעַנּ֣וּ אֶת־נַפְשֹֽׁתֵיכֶ֗ם וְכָל־מְלָאכָה֙ לֹ֣א תַעֲשׂ֔וּ הָֽאֶזְרָ֔ח וְהַגֵּ֖ר הַגָּ֥ר בְּתוֹכְכֶֽם׃ כִּֽי־בַיּ֥וֹם הַזֶּ֛ה יְכַפֵּ֥ר עֲלֵיכֶ֖ם לְטַהֵ֣ר אֶתְכֶ֑ם מִכֹּל֙ חַטֹּ֣אתֵיכֶ֔ם לִפְנֵ֥י יְהוָ֖ה תִּטְהָֽרוּ׃ שַׁבַּ֨ת שַׁבָּת֥וֹן הִיא֙ לָכֶ֔ם וְעִנִּיתֶ֖ם אֶת־נַפְשֹׁתֵיכֶ֑ם חֻקַּ֖ת עוֹלָֽם׃

And this shall be to you a law for all time: In the seventh month, on the tenth day of the month, you shall practice self-denial; and you shall do no manner of work, neither the citizen nor the alien who resides among you. For on this day atonement shall be made for you to cleanse you of all your sins; you shall be clean before the LORD. It shall be a sabbath of complete rest for you, and you shall practice self-denial; it is a law for all time.

What element mentioned in Leviticus 16 is absent from Leviticus 23?

Atonement (כפרה)
חַטָּאת וְאָשָׁם וַדַּאי מְכַפְּרִין. מִיתָה וְיוֹם הַכִּפּוּרִים מְכַפְּרִין עִם הַתְּשׁוּבָה. הַתְּשׁוּבָה מְכַפֶּרֶת עַל עֲבֵרוֹת קַלּוֹת עַל עֲשֵׂה וְעַל לֹא תַעֲשֶׂה. וְעַל הַחֲמוּרוֹת הִיא תוֹלָה עַד שֶׁיָּבֹא יוֹם הַכִּפּוּרִים וִיכַפֵּר:

The sin-offering and the certain guilt-offering bring about atonement. Death and Yom HaKippurim effect atonement together with repentance. Repentance effects atonement for light transgressions: [the transgression of] positive commandments and negative commandments. And for severer transgressions [repentance] suspends [the divine punishment], until Yom HaKippurim arrives and effects atonement.

חטאת ואשם ודאי. מכפרים עם התשובה. ולא חש התנא להזכירה, דמסתמא כשהוא מביא חטאתו ואשמו כבר עשה תשובה, שאם לא היה מתחרט לא היה מביא קרבן:

The sin-offering and the certain guilt-offering bring about atonement – they atone together with repentance. The Tanna did not bother mentioning it, for obviously when he brings his sin-offering and guilt-offering, he has already repented, for if he had not felt regret he would not have brought a sacrifice.

בַּזְּמַן הַזֶּה שֶׁאֵין בֵּית הַמִּקְדָּשׁ קַיָּם וְאֵין לָנוּ מִזְבַּח כַּפָּרָה אֵין שָׁם אֶלָּא תְּשׁוּבָה. הַתְּשׁוּבָה מְכַפֶּרֶת עַל כָּל הָעֲבֵרוֹת. אֲפִלּוּ רָשָׁע כָּל יָמָיו וְעָשָׂה תְּשׁוּבָה בָּאַחֲרוֹנָה אֵין מַזְכִּירִין לוֹ שׁוּם דָּבָר מֵרִשְׁעוֹ שֶׁנֶּאֱמַר (יחזקאל לג יב) "רִשְׁעַת הָרָשָׁע לֹא יִכָּשֶׁל בָּהּ בְּיוֹם שׁוּבוֹ מֵרִשְׁעוֹ". וְעַצְמוֹ שֶׁל יוֹם הַכִּפּוּרִים מְכַפֵּר לַשָּׁבִים שֶׁנֶּאֱמַר (ויקרא טז ל) "כִּי בַיּוֹם הַזֶּה יְכַפֵּר עֲלֵיכֶם": אַף עַל פִּי שֶׁהַתְּשׁוּבָה מְכַפֶּרֶת עַל הַכּל וְעַצְמוֹ שֶׁל יוֹם הַכִּפּוּרִים מְכַפֵּר. יֵשׁ עֲבֵרוֹת שֶׁהֵן מִתְכַּפְּרִים לִשְׁעָתָן וְיֵשׁ עֲבֵרוֹת שֶׁאֵין מִתְכַּפְּרִים אֶלָּא לְאַחַר זְמַן. כֵּיצַד. עָבַר אָדָם עַל מִצְוַת עֲשֵׂה שֶׁאֵין בָּהּ כָּרֵת וְעָשָׂה תְּשׁוּבָה אֵינוֹ זָז מִשָּׁם עַד שֶׁמּוֹחֲלִין לוֹ, וּבְאֵלּוּ נֶאֱמַר (ירמיה ג כב) "שׁוּבוּ בָּנִים שׁוֹבָבִים אֶרְפָּה מְשׁוּבֹתֵיכֶם" וְגוֹ'. עָבַר עַל מִצְוַת לֹא תַּעֲשֶׂה שֶׁאֵין בָּהּ כָּרֵת וְלֹא מִיתַת בֵּית דִּין וְעָשָׂה תְּשׁוּבָה, תְּשׁוּבָה תּוֹלָה וְיוֹם הַכִּפּוּרִים מְכַפֵּר, וּבְאֵלּוּ נֶאֱמַר (ויקרא טז ל) "כִּי בַיּוֹם הַזֶּה יְכַפֵּר עֲלֵיכֶם". עָבַר עַל כְּרֵתוֹת וּמִיתוֹת בֵּית דִּין וְעָשָׂה תְּשׁוּבָה, תְּשׁוּבָה וְיוֹם הַכִּפּוּרִים תּוֹלִין וְיִסּוּרִין הַבָּאִין עָלָיו גּוֹמְרִין לוֹ הַכַּפָּרָה. וּלְעוֹלָם אֵין מִתְכַּפֵּר לוֹ כַּפָּרָה גְּמוּרָה עַד שֶׁיָּבוֹאוּ עָלָיו יִסּוּרִין, וּבְאֵלּוּ נֶאֱמַר (תהילים פט לג) "וּפָקַדְתִּי בְשֵׁבֶט פִּשְׁעָם וּבִנְגָעִים עֲוֹנָם". בַּמֶּה דְּבָרִים אֲמוּרִים בְּשֶׁלֹּא חִלֵּל אֶת הַשֵּׁם בְּשָׁעָה שֶׁעָבַר אֲבָל הַמְחַלֵּל אֶת הַשֵּׁם אַף עַל פִּי שֶׁעָשָׂה תְּשׁוּבָה וְהִגִּיעַ יוֹם הַכִּפּוּרִים וְהוּא עוֹמֵד בִּתְשׁוּבָתוֹ וּבָאוּ עָלָיו יִסּוּרִין אֵינוֹ מִתְכַּפֵּר לוֹ כַּפָּרָה גְּמוּרָה עַד שֶׁיָּמוּת. אֶלָּא תְּשׁוּבָה יוֹם הַכִּפּוּרִים וְיִסּוּרִין שְׁלָשְׁתָּן תּוֹלִין וּמִיתָה מְכַפֶּרֶת שֶׁנֶּאֱמַר (ישעיה כב יד) "וְנִגְלָה בְאָזְנָי ה' צְבָאוֹת" וְגוֹ' (ישעיה כב יד) "אִם יְכֻפַּר הֶעָוֹן הַזֶּה לָכֶם עַד תְּמֻתוּן":

At this time, when the Temple is not established and, therefore, no altar to atone for us, there is nothing else left for us but repentance. Repentance atones for all sins. Even one who was an evildoer all his life but repented in the end, not a thing of the wickedness is held out against him, even as it is said: "As for the wickedness of the wicked, he shall not fall thereby in the day that he turneth from his wickedness" (Ez. 33.12). Even the Day of Atonement itself atones only for those who did repent, even as it is said: "For on that day shall the priest make an atonement for you" (Lev. 16.30). Even on the presumption that repentance atones for all sins, and the Day of Atonement as such, too, atones, there are yet certain sins which are wiped off at the time, and certain other sins which are are not wiped off but after a lapse of time. For example? If a man violated a mandatory commandment which does not carry the guilt of excision and did repent, he moves not from the place of prayer before he is forgiven. Of such it is said: "Return, ye backsliding children and I will heal your back-slidings" (Jer. 3.22). If he violated a prohibitive commandment which carries neither excision nor death by a tribunal, and did repent, the repentance suspends punishment, whereafter the Day of Atonement wipes out the sin. Of such it is said: "For on that day shall the priest make an atonement for you" (Lev. 16. 30). If he sinned in matters which carry excisions and deaths by a tribunal and did repent, repentance and the Day of Atonement suspend punishment, and the pain which he suffers thereafter complete the atonement for him. Forsooth, no complete atonement ever comes to the penitent before he has a visitation of suffering. Of such it is said: "Then will I visit their transgression with the rod, and their iniquity with strokes'" (Ps. 89.32). That saying is concerning a sinner who did not blaspheme the Name in connnection with his transgression, but whosoever blasphemes the Name even he did repent, and the Day of Atonement did come and he still be a penitent, and sufferings did visit him, no complete atonement is granted to him till his death, for, repentance, the Day of Atonement and sufferings suspend punishment, and only death atones for him, even as it is said: "And it was revealed in mine ears by the Lord of hosts. Surely this iniquity shall not be purged from you till ye die" (Is. 22.14).

Cleansing (טהרה)

הָאוֹמֵר, אֶחֱטָא וְאָשׁוּב, אֶחֱטָא וְאָשׁוּב, אֵין מַסְפִּיקִין בְּיָדוֹ לַעֲשׂוֹת תְּשׁוּבָה. אֶחֱטָא וְיוֹם הַכִּפּוּרִים מְכַפֵּר, אֵין יוֹם הַכִּפּוּרִים מְכַפֵּר. עֲבֵרוֹת שֶׁבֵּין אָדָם לַמָּקוֹם, יוֹם הַכִּפּוּרִים מְכַפֵּר. עֲבֵרוֹת שֶׁבֵּין אָדָם לַחֲבֵרוֹ, אֵין יוֹם הַכִּפּוּרִים מְכַפֵּר, עַד שֶׁיְּרַצֶּה אֶת חֲבֵרוֹ. אֶת זוֹ דָּרַשׁ רַבִּי אֶלְעָזָר בֶּן עֲזַרְיָה, מִכֹּל חַטֹּאתֵיכֶם לִפְנֵי יְיָ תִּטְהָרוּ (ויקרא טז), עֲבֵרוֹת שֶׁבֵּין אָדָם לַמָּקוֹם, יוֹם הַכִּפּוּרִים מְכַפֵּר. עֲבֵרוֹת שֶׁבֵּין אָדָם לַחֲבֵרוֹ, אֵין יוֹם הַכִּפּוּרִים מְכַפֵּר, עַד שֶׁיְּרַצֶּה אֶת חֲבֵרוֹ. אָמַר רַבִּי עֲקִיבָא, אַשְׁרֵיכֶם יִשְׂרָאֵל, לִפְנֵי מִי אַתֶּם מִטַּהֲרִין, וּמִי מְטַהֵר אֶתְכֶם, אֲבִיכֶם שֶׁבַּשָּׁמַיִם, שֶׁנֶּאֱמַר (יחזקאל לו), וְזָרַקְתִּי עֲלֵיכֶם מַיִם טְהוֹרִים וּטְהַרְתֶּם. וְאוֹמֵר (ירמיה יז), מִקְוֵה יִשְׂרָאֵל יְיָ, מַה מִּקְוֶה מְטַהֵר אֶת הַטְּמֵאִים, אַף הַקָּדוֹשׁ בָּרוּךְ הוּא מְטַהֵר אֶת יִשְׂרָאֵל:

One who says: I shall sin and repent, sin and repent, they do not afford him the opportunity to repent. [If one says]: I shall sin and Yom HaKippurim will atone for me, Yom HaKippurim does not effect atonement. For transgressions between man and God Yom HaKippurim effects atonement, but for transgressions between man and his fellow Yom HaKippurim does not effect atonement, until he has pacified his fellow. This was expounded by Rabbi Elazar b. Azariah: “From all your sins before the Lord you shall be clean” (Leviticus 16:30) for transgressions between man and God Yom HaKippurim effects atonement, but for transgressions between man and his fellow Yom HaKippurim does not effect atonement, until he has pacified his fellow.. Rabbi Akiva said: Happy are you, Israel! Who is it before whom you become pure? And who is it that purifies you? Your Father who is in heaven, as it is said: “And I will sprinkle clean water upon you and you shall be clean” (Ezekiel 36:25). And it further says: “O hope (mikveh) of Israel, O Lord” (Jeremiah 17:1--just as a mikveh purifies the unclean, so too does he Holy One, blessed be He, purify Israel.

האומר אחטא ואשוב אחטא ואשוב כו':
האומר אחטא ויום הכפורים מכפר אין יום הכפורים מכפר כמו אמרם אין מספיקין בידו לעשות תשובה ולפיכך לא יעזרהו השם שיעשה בצום כיפור מה שראוי לו לעשות כדי שיתכפרו לו עונותיו באותו היום ושעיר המשתלח אינו מכפר עבירות שבין אדם לחבירו.

"One who says I shall sin and repent etc." One who says I will sent and Yom Kippur will atone for my sins, Yom Kippur will not atone for his sins. As they said: he is not afforded the opportunity to repent, and therefor God will not assist him to do on Yom Kippur what is needed for his sins to be atoned for on that day. And the scapegoat does not atone for sins between fellow people.

אֵין הַתְּשׁוּבָה וְלֹא יוֹם הַכִּפּוּרִים מְכַפְּרִין אֶלָּא עַל עֲבֵרוֹת שֶׁבֵּין אָדָם לַמָּקוֹם כְּגוֹן מִי שֶׁאָכַל דָּבָר אָסוּר אוֹ בָּעַל בְּעִילָה אֲסוּרָה וְכַיּוֹצֵא בָּהֶן. אֲבָל עֲבֵרוֹת שֶׁבֵּין אָדָם לַחֲבֵרוֹ כְּגוֹן הַחוֹבֵל אֶת חֲבֵרוֹ אוֹ הַמְקַלֵּל חֲבֵרוֹ אוֹ גּוֹזְלוֹ וְכַיּוֹצֵא בָּהֶן אֵינוֹ נִמְחַל לוֹ לְעוֹלָם עַד שֶׁיִּתֵּן לַחֲבֵרוֹ מַה שֶּׁהוּא חַיָּב לוֹ וִירַצֵּהוּ. אַף עַל פִּי שֶׁהֶחֱזִיר לוֹ מָמוֹן שֶׁהוּא חַיָּב לוֹ צָרִיךְ לְרַצּוֹתוֹ וְלִשְׁאל מִמֶּנּוּ שֶׁיִּמְחל לוֹ. אֲפִלּוּ לֹא הִקְנִיט אֶת חֲבֵרוֹ אֶלָּא בִּדְבָרִים צָרִיךְ לְפַיְּסוֹ וְלִפְגֹּעַ בּוֹ עַד שֶׁיִּמְחל לוֹ. לֹא רָצָה חֲבֵרוֹ לִמְחל לוֹ מֵבִיא לוֹ שׁוּרָה שֶׁל שְׁלֹשָׁה בְּנֵי אָדָם מֵרֵעָיו וּפוֹגְעִין בּוֹ וּמְבַקְּשִׁין מִמֶּנּוּ. לֹא נִתְרַצָּה לָהֶן מֵבִיא לוֹ שְׁנִיָּה וּשְׁלִישִׁית. לֹא רָצָה מְנִיחוֹ וְהוֹלֵךְ לוֹ וְזֶה שֶׁלֹּא מָחַל הוּא הַחוֹטֵא. וְאִם הָיָה רַבּוֹ הוֹלֵךְ וּבָא אֲפִלּוּ אֶלֶף פְּעָמִים עַד שֶׁיִּמְחל לוֹ: אָסוּר לָאָדָם לִהְיוֹת אַכְזָרִי וְלֹא יִתְפַּיֵּס אֶלָּא יְהֵא נוֹחַ לִרְצוֹת וְקָשֶׁה לִכְעֹס וּבְשָׁעָה שֶׁמְּבַקֵּשׁ מִמֶּנּוּ הַחוֹטֵא לִמְחל מוֹחֵל בְּלֵב שָׁלֵם וּבְנֶפֶשׁ חֲפֵצָה. וַאֲפִלּוּ הֵצֵר לוֹ וְחָטָא לוֹ הַרְבֵּה לֹא יִקֹּם וְלֹא יִטֹּר. וְזֶהוּ דַּרְכָּם שֶׁל זֶרַע יִשְׂרָאֵל וְלִבָּם הַנָּכוֹן. אֲבָל הָעוֹבְדֵי כּוֹכָבִים עַרְלֵי לֵב אֵינָן כֵּן אֶלָּא (וְעֶבְרָתָן) [וְעֶבְרָתוֹ] שְׁמָרָה נֶצַח. וְכֵן הוּא אוֹמֵר עַל הַגִּבְעוֹנִים לְפִי שֶׁלֹּא מָחֲלוּ וְלֹא נִתְפַּיְּסוּ וְהַגִּבְעֹנִים לֹא מִבְּנֵי יִשְׂרָאֵל הֵמָּה:

Neither repentance nor the Day of Atonement atone for any save for sins committed between man and God, for instance, one who ate forbidden food, or had forbidden coition and the like; but sins between man and man, for instance, one injures his neighbor, or curses his neighbor or plunders him, or offends him in like matters, is ever not absolved unless he makes restitution of what he owes and begs the forgiveness of his neighbor. And, although he make restitution of the monetory debt, he is obliged to pacify him and to beg his forgiveness. Even he offended not his neighbor in aught save in words, he is obliged to appease him and implore him till he be forgiven by him. If his neighbor refuses a committee of three friends to forgive him, he should bring to implore and beg of him; if he still refuses he should bring a second, even a third committee, and if he remains obstinate, he may leave him to himself and pass on, for the sin then rests upon him who refuses forgiveness. But if it happened to be his master, he should go and come to him for forgiveness even a thousand times until he does forgive him. It is forbidden for man to be ill-natured and unforgiving, for he must be easily appeased but unwidely to wrath; and when a sinner implores him for pardon, he should grant him pardon wholeheartedly and soulfully. Even if one persecuted him and sinned against him exceedingly he should not be vengeful and grudge-bearing, for such is the path of the seed of Israel and of their excellent heart. Only the idolaters are not so, they are of uncircumcised heart, and their wrath is ever-watchful; and, because the Gibonites were unforgiving and unappeasing, that of them it is said: "Now the Gibonites were not of the children of Israel" (II. Samuel, 21.2).

Three prophetic images of forgiveness and water
וְלָקַחְתִּ֤י אֶתְכֶם֙ מִן־הַגּוֹיִ֔ם וְקִבַּצְתִּ֥י אֶתְכֶ֖ם מִכָּל־הָאֲרָצ֑וֹת וְהֵבֵאתִ֥י אֶתְכֶ֖ם אֶל־אַדְמַתְכֶֽם׃ וְזָרַקְתִּ֧י עֲלֵיכֶ֛ם מַ֥יִם טְהוֹרִ֖ים וּטְהַרְתֶּ֑ם מִכֹּ֧ל טֻמְאוֹתֵיכֶ֛ם וּמִכָּל־גִּלּ֥וּלֵיכֶ֖ם אֲטַהֵ֥ר אֶתְכֶֽם׃ וְנָתַתִּ֤י לָכֶם֙ לֵ֣ב חָדָ֔שׁ וְר֥וּחַ חֲדָשָׁ֖ה אֶתֵּ֣ן בְּקִרְבְּכֶ֑ם וַהֲסִ֨רֹתִ֜י אֶת־לֵ֤ב הָאֶ֙בֶן֙ מִבְּשַׂרְכֶ֔ם וְנָתַתִּ֥י לָכֶ֖ם לֵ֥ב בָּשָֽׂר׃

I will take you from among the nations and gather you from all the countries, and I will bring you back to your own land. I will sprinkle clean water upon you, and you shall be clean: I will cleanse you from all your uncleanness and from all your fetishes. And I will give you a new heart and put a new spirit into you: I will remove the heart of stone from your body and give you a heart of flesh.

וְלָֽקְחוּ֙ לַטָּמֵ֔א מֵעֲפַ֖ר שְׂרֵפַ֣ת הַֽחַטָּ֑את וְנָתַ֥ן עָלָ֛יו מַ֥יִם חַיִּ֖ים אֶל־כֶּֽלִי׃ וְלָקַ֨ח אֵז֜וֹב וְטָבַ֣ל בַּמַּיִם֮ אִ֣ישׁ טָהוֹר֒ וְהִזָּ֤ה עַל־הָאֹ֙הֶל֙ וְעַל־כָּל־הַכֵּלִ֔ים וְעַל־הַנְּפָשׁ֖וֹת אֲשֶׁ֣ר הָֽיוּ־שָׁ֑ם וְעַל־הַנֹּגֵ֗עַ בַּעֶ֙צֶם֙ א֣וֹ בֶֽחָלָ֔ל א֥וֹ בַמֵּ֖ת א֥וֹ בַקָּֽבֶר׃ וְהִזָּ֤ה הַטָּהֹר֙ עַל־הַטָּמֵ֔א בַּיּ֥וֹם הַשְּׁלִישִׁ֖י וּבַיּ֣וֹם הַשְּׁבִיעִ֑י וְחִטְּאוֹ֙ בַּיּ֣וֹם הַשְּׁבִיעִ֔י וְכִבֶּ֧ס בְּגָדָ֛יו וְרָחַ֥ץ בַּמַּ֖יִם וְטָהֵ֥ר בָּעָֽרֶב׃ וְאִ֤ישׁ אֲשֶׁר־יִטְמָא֙ וְלֹ֣א יִתְחַטָּ֔א וְנִכְרְתָ֛ה הַנֶּ֥פֶשׁ הַהִ֖וא מִתּ֣וֹךְ הַקָּהָ֑ל כִּי֩ אֶת־מִקְדַּ֨שׁ יְהוָ֜ה טִמֵּ֗א מֵ֥י נִדָּ֛ה לֹא־זֹרַ֥ק עָלָ֖יו טָמֵ֥א הֽוּא׃

Some of the ashes from the fire of cleansing shall be taken for the unclean person, and fresh water shall be added to them in a vessel. A person who is clean shall take hyssop, dip it in the water, and sprinkle on the tent and on all the vessels and people who were there, or on him who touched the bones or the person who was killed or died naturally or the grave. The clean person shall sprinkle it upon the unclean person on the third day and on the seventh day, thus cleansing him by the seventh day. He shall then wash his clothes and bathe in water, and at nightfall he shall be clean. If anyone who has become unclean fails to cleanse himself, that person shall be cut off from the congregation, for he has defiled the LORD’s sanctuary. The water of lustration (מי נידה) was not dashed on him: he is unclean.

ואת חקתי תשמרו. דְּבָרִים שֶׁהֵן גְּזֵרַת הַמֶּלֶךְ, שֶׁיֵּצֶר הָרַע מֵשִׁיב עֲלֵיהֶם לָמָּה לָנוּ לְשָׁמְרָן? וְאֻמּוֹת הָעוֹלָם מְשִׁיבִין עֲלֵיהֶם, כְּגוֹן אֲכִילַת חֲזִיר וּלְבִישַׁת שַׁעַטְנֵז וְטָהֳרַת מֵי חַטָּאת, לְכָךְ נֶאֱמַר אני ה', גָּזַרְתִּי עֲלֵיכֶם, אֵי אַתָּה רַשַּׁאי לִפָּטֵר (יומא ס"ז):

ואת חקתי תשמרו AND KEEP MINE ORDINANCES — matters which are decrees of the King (promulgated without any reason being stated) against which the evil inclination raises objections: "Why should we observe them? and against which also the nations of the world raise objections, as e. g., the prohibition of eating swine’s flesh, of wearing clothes of a mixture of wool and linen, the purgatory power of "water mingled with the ashes of the Red Heifer" (טהרת מי חטאת) — therefore it is stated: "I", the Lord, have enacted this for you — you are not at liberty to evade the obligation (Yoma 67b).

מִקְוֵ֤ה יִשְׂרָאֵל֙ יְהוָ֔ה כָּל־עֹזְבֶ֖יךָ יֵבֹ֑שׁוּ יסורי [וְסוּרַי֙] בָּאָ֣רֶץ יִכָּתֵ֔בוּ כִּ֥י עָזְב֛וּ מְק֥וֹר מַֽיִם־חַיִּ֖ים אֶת־יְהוָֽה׃
O Hope of Israel! O LORD! All who forsake You shall be put to shame, Those in the land who turn from You Shall be doomed men, For they have forsaken the LORD, The Fount of living waters.

What is the midrash on the word mikveh מקוה?

מקוה ישראל ה'. אפשר לרמוז כי ברוב חסדיו הגם שהוא אל קנ"א מטהר את ישראל כמשז"ל ובמקום קנא נעשה מקוה וכן קנ"א גימטריא מקו"ה:

Rabbi Chaim Yossef David Azulai (Jerusalem, 1724-1806)

There may be an allusion here that although he is a jealous God (אל קנא) he purifies Israel, and instead of Kana he becomes a mikveh as the numeric value of the word קנא equals that of the word מקוה.

מִי־אֵ֣ל כָּמ֗וֹךָ נֹשֵׂ֤א עָוֺן֙ וְעֹבֵ֣ר עַל־פֶּ֔שַׁע לִשְׁאֵרִ֖ית נַחֲלָת֑וֹ לֹא־הֶחֱזִ֤יק לָעַד֙ אַפּ֔וֹ כִּֽי־חָפֵ֥ץ חֶ֖סֶד הֽוּא׃ יָשׁ֣וּב יְרַֽחֲמֵ֔נוּ יִכְבֹּ֖שׁ עֲוֺֽנֹתֵ֑ינוּ וְתַשְׁלִ֛יךְ בִּמְצֻל֥וֹת יָ֖ם כָּל־חַטֹּאותָֽם׃

Who is a God like You, Forgiving iniquity And remitting transgression; Who has not maintained His wrath forever Against the remnant of His own people, Because He loves graciousness! He will take us back in love; He will cover up our iniquities, You will hurl all our sins into the depths of the sea.

ואמר) ר' יוסי בר חנינא כל המבקש מטו מחבירו אל יבקש ממנו יותר משלש פעמים שנאמר (בראשית נ, יז) אנא שא נא ועתה שא נא ואם מת מביא עשרה בני אדם ומעמידן על קברו ואומר חטאתי לה' אלהי ישראל ולפלוני שחבלתי בו ר' ירמיה הוה ליה מילתא לר' אבא בהדיה אזל איתיב אדשא דר' אבא בהדי דשדיא אמתיה מיא מטא זרזיפי דמיא ארישא אמר עשאוני כאשפה קרא אנפשיה (תהלים קיג, ז) מאשפות ירים אביון שמע ר' אבא ונפיק לאפיה אמר ליה השתא צריכנא למיפק אדעתך דכתיב לך התרפס ורהב רעיך.

Rabbi Yosei bar Ḥanina said: Anyone who asks forgiveness of his friend should not ask more than three times, as it is stated: “Please, please forgive the transgression of your brothers and their sin, for they did evil to you. And now, please forgive” (Genesis 50:17). The verse uses the word please three times, which shows that one need not ask more than three times, after which the insulted friend must be appeased and forgive. And if the insulted friend dies before he can be appeased, one brings ten people, and stands them at the grave of the insulted friend, and says in front of them: I have sinned against the Lord, the God of Israel, and against so-and-so whom I wounded. The Gemara relates that Rabbi Yirmeya insulted Rabbi Abba, causing the latter to have a complaint against him. Rabbi Yirmeya went and sat at the threshold of Rabbi Abba’s house to beg him for forgiveness. When Rabbi Abba’s maid poured out the dirty water from the house, the stream of water landed on Rabbi Yirmeya’s head. He said about himself: They have made me into a trash heap, as they are pouring dirty water on me. He recited this verse about himself: “Who lifts up the needy out of the trash heap” (Psalms 113:7). Rabbi Abba heard what happened and went out to greet him. Rabbi Abba said to him: Now I must go out to appease you for this insult, as it is written: “Go, humble yourself [hitrapes] and urge your neighbor” (Proverbs 6:3).
A happy or a sad day?

יוֹם הַכִּפּוּרִים אָסוּר בַּאֲכִילָה וּבִשְׁתִיָּה וּבִרְחִיצָה וּבְסִיכָה וּבִנְעִילַת הַסַּנְדָּל וּבְתַשְׁמִישׁ הַמִּטָּה. וְהַמֶּלֶךְ וְהַכַּלָּה יִרְחֲצוּ אֶת פְּנֵיהֶם, וְהֶחָיָה תִנְעֹל אֶת הַסַּנְדָּל, דִּבְרֵי רַבִּי אֱלִיעֶזֶר, וַחֲכָמִים אוֹסְרִין:

[On] Yom HaKippurim it is forbidden to eat, to drink, to wash, to anoint oneself, to put on sandals, or to have intercourse. A king or bride may wash their face, and a woman after childbirth may put on sandals, the words of Rabbi Eliezer. But the sages forbid it.

אָמַר רַבָּן שִׁמְעוֹן בֶּן גַּמְלִיאֵל, לֹא הָיוּ יָמִים טוֹבִים לְיִשְׂרָאֵל כַּחֲמִשָּׁה עָשָׂר בְּאָב וּכְיוֹם הַכִּפּוּרִים, שֶׁבָּהֶן בְּנוֹת יְרוּשָׁלַיִם יוֹצְאוֹת בִּכְלֵי לָבָן שְׁאוּלִין, שֶׁלֹּא לְבַיֵּשׁ אֶת מִי שֶׁאֵין לוֹ. כָּל הַכֵּלִים טְעוּנִין טְבִילָה. וּבְנוֹת יְרוּשָׁלַיִם יוֹצְאוֹת וְחוֹלוֹת בַּכְּרָמִים.

Section one: Rabbi Shimon ben Gamaliel said: There were no days of joy in Israel greater than the fifteenth of Av and Yom Kippur. Section two: On these days the daughters of Jerusalem would go out in borrowed white garments in order not to shame any one who had none. All these garments required immersion. The daughters of Jerusalem come out and dance in the vineyards.

ויוה״כ. שבו נתנו לוחות האחרונות, והוא יום מחילה וסליחה:

Rabbi Ovadia Bartenura (Italy, 1445-1515)

"And Yom Kippur" since on this day the second tablets were given (to Moses), and it is a day of forgiveness and pardoning.

פּוּרִים אִתְקְרִיאַת עַל שֵׁם יוֹם הַכִּפּוּרִים, דַּעֲתִידִין לְאִתְעַנְגָא בֵּיהּ, וּלְשַׁנּוּיֵי לֵיהּ מֵעִנּוּי לְעֹנֶג, וּמַה דְּאִיהִי שְׁכִינְתָּא אָסוּר בֵּיהּ נְעִילַת הַסַּנְדָל, בְּהַהוּא זִמְנָא אִתְּמַר בָּהּ (שיר ז ב) מַה יָּפוּ פְעָמַיִךְ בַּנְּעָלִים בַּת נָדִיב, וְעִנּוּגָא וְחֶדְוָה וְכַמָּה טָבִין מְזוּמָנִין לְגַבָּהּ, וְדָא יְהֵא בְזִמְנָא דְפוּרְקָנָא בַעֲגָלָא.

Purim is named after Yom Ha-Kippurim [which can be read as “the day that is like Purim”], for in the future people will rejoice on Yom Kippur and will transform its required afflictions to delight. Although the Divine Presence forbade the wearing of shoes on Yom Kippur, at that time the verse, “How beautiful are your footsteps in sandals, O prince’s daughter” (Song of Songs 7:2) will apply. Pleasure, joy, and much good will happen on that day – this will be the case in the time of the coming Redemption.