Halacha

הלכה א
דָבָר אָסוּר שֶׁנִּתְעָרֵב בְּדָבָר מֻתָּר מִין בְּשֶׁאֵינוֹ מִינוֹ בְּנוֹתֵן טַעַם. וּמִין בְּמִינוֹ שֶׁאִי אֶפְשָׁר לַעֲמֹד עַל טַעֲמוֹ יִבָּטֵל בְּרֹב:
כסף משנה
1.
When a forbidden substance becomes mixed with a permitted substance of another type, [it causes it to become forbidden] if its flavor can be detected. When [a forbidden substance becomes mixed with a permitted substance of] the same type and it is impossible to detect [the forbidden substance] by its flavor,1Because it tastes the same as the permitted substance. its presence becomes nullified if there is a majority [of the permitted substance].2According to Scriptural Law. As stated in Halachot 4-5, the Rabbis enforced more stringent requirements.

הלכה ב
כֵּיצַד. חֵלֶב הַכְּלָיוֹת שֶׁנָּפַל לְתוֹךְ הַגְּרִיסִין וְנִמּוֹחַ הַכּל. טוֹעֲמִין אֶת הַגְּרִיסִין. אִם לֹא נִמְצָא בָּהֶן טַעַם חֵלֶב הֲרֵי אֵלּוּ מֻתָּרִין. וְאִם נִמְצָא בָּהֶם טַעַם חֵלֶב וְהָיָה בָּהֶן מַמָּשׁוֹ הֲרֵי אֵלּוּ אֲסוּרִין מִן הַתּוֹרָה. נִמְצָא בָּהֶן טַעֲמוֹ וְלֹא הָיָה בָּהֶן מַמָּשׁוֹ הֲרֵי אֵלּוּ אֲסוּרִין מִדִּבְרֵי סוֹפְרִים:
כסף משנה
2.
What is implied? When the fat of the kidneys3Which is forbidden (Chapter 7, Halachah 5). falls into beans and becomes dissolved, the beans should be tasted.4By a gentile (see the notes to Halachah 30 and Chapter 9, Halachah 8) for a discussion of why the gentile's word is accepted. If the taste of fat cannot be detected, they are permitted. If [not only] the taste, [but also] the substance of the fat is present, they are forbidden according to Scriptural Law. If the flavor could be detected, but there is no substance, they are forbidden by Rabbinic Law.5See Tosafot (Chullin 98b) which mentions a difference of opinion among the Rabbis if the principle "the flavor of an entity is equivalent to its substance" is of Rabbinic or Scriptural origin.

הלכה ג
כֵּיצַד הוּא מַמָּשׁוֹ. כְּגוֹן שֶׁהָיָה מִן הַחֵלֶב כְּזַיִת בְּכָל שָׁלֹשׁ בֵּיצִים מִן הַתַּעֲרֹבֶת. אִם אָכַל מִן הַגְּרִיסִין הָאֵלּוּ כְּשָׁלֹשׁ בֵּיצִים הוֹאִיל וְיֵשׁ בָּהֶן כְּזַיִת מִן הַחֵלֶב לוֹקֶה שֶׁהֲרֵי טַעַם הָאִסּוּר וּמַמָּשׁוֹ קַיָּם. אֲבָל פָּחוֹת מִשָּׁלֹשׁ בֵּיצִים מַכִּין אוֹתוֹ מַכַּת מַרְדּוּת מִדִּבְרֵיהֶם. וְכֵן אִם לֹא הָיָה בַּתַּעֲרֹבֶת כְּזַיִת בְּכָל שָׁלֹשׁ בֵּיצִים אַף עַל פִּי שֶׁיֵּשׁ בָּהֶן טַעַם חֵלֶב וְאָכַל כָּל הַקְּדֵרָה אֵינוֹ לוֹקֶה אֶלָּא מַכַּת מַרְדּוּת:
כסף משנה
3.
What is meant by its substance? For example, there was enough forbidden fat for there to be an olive-sized portion [of fat] in each portion the size of three eggs from the mixture. If a person eats a portion of beans the size of three eggs, he is liable for lashes for they contain an olive-sized portion of forbidden fat, for [not only] the flavor, [but also] the substance of [the forbidden fat] is present.6The Rambam shares the perspective of Tosafot (Avodah Zarah 67b) who maintains that if there is more than an olive-sized portion of fat in a portion of food k'dei achilat p'ras (the size of three eggs), its substance is considered as present even though it is dissolved and not discernable. Rashi differs and maintains that as long as the fat is dissolved, it is considered as if the substance of the forbidden entity is not present. If one eats less than a portion the size of three eggs [of the mixture], one is liable for stripes for rebellious conduct as prescribed by Rabbinic Law.
Similarly, if there was less than an olive-sized portion of [forbidden] fat in every portion the size of three eggs, even if the flavor of fat is detectable and he eats the entire pot, he is not liable for lashes7Even though he may eat an olive-sized portion of forbidden fat, he will not have eaten it in the required time (the time it takes to eat three eggs, as stated in Chapter 14, Halachah 8) for one to be held liable. The concentration of the forbidden fat is too small for that to happen. [as prescribed by Scriptural Law], only stripes for rebellious conduct.

הלכה ד
נָפַל חֵלֶב כְּלָיוֹת לְחֵלֶב הָאַלְיָה וְנִמּוֹחַ הַכּל. אִם הָיָה חֵלֶב הָאַלְיָה כִּשְׁנַיִם בְּחֵלֶב הַכְּלָיוֹת הֲרֵי הַכּל מֻתָּר מִן הַתּוֹרָה. אֲפִלּוּ חֲתִיכַת נְבֵלָה שֶׁנִּתְעָרְבָה בִּשְׁתֵּי חֲתִיכוֹת שֶׁל שְׁחוּטָה הַכּל מֻתָּר מִן הַתּוֹרָה. אֲבָל מִדִּבְרֵי סוֹפְרִים הַכּל אָסוּר עַד שֶׁיְּאַבֵּד דָּבָר הָאָסוּר מֵעֹצֶם מִעוּטוֹ וְלֹא יִהְיֶה דָּבָר חָשׁוּב שֶׁעֵינוֹ עוֹמֶדֶת כְּמוֹ שֶׁיִּתְבָּאֵר:
כסף משנה
4.
[The following laws apply when] the fat of the kidneys8Which is forbidden (Chapter 7, Halachah 5). falls into the fat from the fat tail9Which is permitted. and the entire [mixture] becomes dissolved.10Since both are fat, the mixture is considered as being of the same substance. If there is twice as much fat from the fat tail as fat of the kidneys, the entire mixture is permitted according to Scriptural Law.11For according to Scriptural Law, as long as the majority is kosher, the mixture may be eaten. Indeed, there is no need for there to be twice as much kosher fat as non-kosher fat. A simple majority is sufficient. Even when a piece of [meat from] a nevelah becomes mixed with two pieces of [meat from] a ritually slaughter animal, everything is permitted according to Scriptural Law.12With regard to the mixture of fat, there is greater reason for leniency, for there is no longer any non-kosher fat that exists as an independent entity, it is all mixed together with the kosher fat. In this instance, the meat from the nevelah exists as an independent entity, it is just that we have no way of detecting which of the pieces it is (Radbaz). Nevertheless, according to Rabbinic Law, everything13In all instances when forbidden substances are mixed with kosher substances. See Shulchan Aruch (Yoreh De'ah 109:1) which rules leniently and allows one to rely on Scriptural Law in certain situations. See the notes to Halachah 20. is forbidden until the forbidden substance will be nullified because of the tiny proportion [of the entire mixture it represents] to the extent that it is not significant and it is as if it does not exist, as will be explained.14In the following halachot.

הלכה ה
וּבְכַמָּה יִתְעָרֵב דָּבָר הָאָסוּר וִיאַבֵּד בְּעֹצֶם מִעוּטוֹ. כַּשִּׁעוּר שֶׁנָּתְנוּ בּוֹ חֲכָמִים. יֵשׁ דָּבָר שֶׁשִּׁעוּרוֹ בְּשִׁשִּׁים. וְיֵשׁ שֶׁשִּׁעוּרוֹ בְּמֵאָה. וְיֵשׁ שֶׁשִּׁעוּרוֹ בְּמָאתַיִם:
כסף משנה
5.
Into what quantity [of a permitted substance] must a forbidden substance be mixed for it to be considered nullified because of its tiny proportion? [Each forbidden substance according to] the measure the Sages specified for it. There are substances that are nullified in a mixture 60 times its size, others in a mixture 100 times its size, and still others in a mixture 200 times its size.

הלכה ו
נִמְצֵאתָ לָמֵד שֶׁכָּל אִסּוּרִין שֶׁבַּתּוֹרָה. בֵּין אִסּוּרֵי מַלְקוֹת. בֵּין אִסּוּרֵי כָּרֵת. בֵּין אִסּוּרֵי הֲנָיָה. שֶׁנִּתְעָרְבוּ בַּמַּאֲכָל הַמֻּתָּר מִין בְּשֶׁאֵינוֹ מִינוֹ בְּנוֹתֵן טַעַם. מִין בְּמִינוֹ שֶׁאִי אֶפְשָׁר לַעֲמֹד עַל הַטַּעַם שִׁעוּרוֹ בְּשִׁשִּׁים אוֹ בְּמֵאָה אוֹ בְּמָאתַיִם. חוּץ מִיֵּין נֶסֶךְ מִפְּנֵי חֻמְרַת עַבוֹדָה זָרָה. וְחוּץ מִטֶּבֶל שֶׁהֲרֵי אֶפְשָׁר לְתַקְּנוֹ. וּמִפְּנֵי זֶה אוֹסְרִין בְּמִינָן בְּכָל שֶׁהֵן. וְשֶׁלֹּא בְּמִינָן בְּנוֹתֵן טַעַם כִּשְׁאָר כָּל הָאִסּוּרִין:
כסף משנה
6.
Thus we learn from this that [the following laws apply] with regard to all of the prohibited substances in the Torah, whether those punishable by lashes or punishable by kerait or substances from which it is forbidden to benefit that become mixed with permitted substances. If the substances are of different types, [the mixture is forbidden] if the flavor is detectable.
If the substances are of the same type and thus it is impossible to detect the flavor [of the forbidden substance], we measure [whether there was] 60, 100, or 200 [times the amount of permitted substances]. The only exceptions are wine poured as a libation to a false deity, because of the severity [of the prohibition against] worship of a false deity15In his Commentary to the Mishnah (Avodah Zarah 5:8), the Rambam cites Deuteronomy 13:18: "No trace of the condemned should cling to your hand" as evidence that even the slightest amount is forbidden. See Chapter 16, Halachah 28, for a leniency that is granted with regard to this restriction. and tevel, because it can be corrected.16The terumot and the tithes can be separated from it, causing it to be permitted. See Halachah 10.
In his Commentary to the Mishnah (ibid.), the Rambam cites the rationale given by Avodah Zarah 73b: Just as one kernel of grain can serve as terumah and correct the entire crop; so, too, one kernel of grain from which terumah was not separated can cause an entire crop to be forbidden. The rationale given by the Rambam here has its source in the Jerusalem Talmud (Shivi'it 6:3).
For that reason, even the slightest mixture of them with a substance of their type is forbidden. If they become mixed with substances of a different type, the matter is dependent on whether their flavor is detectable.

הלכה ז
כֵּיצַד. טִפַּת יֵין נֶסֶךְ שֶׁנָּפְלוּ עָלֶיהָ כַּמָּה חָבִיּוֹת שֶׁל יַיִן הַכּל אָסוּר כְּמוֹ שֶׁיִּתְבָּאֵר. וְכֵן כּוֹס שֶׁל יֵין טֶבֶל שֶׁנִּתְעָרֵב בְּחָבִית הַכּל טֶבֶל עַד שֶׁיַּפְרִישׁ תְּרוּמוֹת וּמַעַשְׂרוֹת הָרְאוּיִין לְתַעֲרֹבֶת כְּמוֹ שֶׁיִּתְבָּאֵר בִּמְקוֹמוֹ:
כסף משנה
7.
What is implied? When several barrels of wine fell over a drop of wine that was poured as a libation, the entire mixture is forbidden, as will be explained.17Chapter 16, Halachah 28. Similarly, if a cup of wine which is tevel becomes nixed into a barrel [of wine], the entire [barrel] is considered tevel until the amount of terumah and tithes that are appropriate to be separated18I.e., the terumah and tithes that would have been required to have been separated from the tevel originally. In this context, the fact that it became mixed with other wine is not significant. are separated as will be explained in the appropriate place.19Hilchot Terumah, Chapter 13.

הלכה ח
פֵּרוֹת שְׁבִיעִית אַף עַל פִּי שֶׁאִם נִתְעָרְבוּ בְּמִינָן בְּכָל שֶׁהוּא וְשֶׁלֹּא בְּמִינָן בְּנוֹתֵן טַעַם אֵינָן בִּכְלָל אִסּוּרֵי תּוֹרָה שֶׁאֵין אוֹתָהּ הַתַּעֲרֹבֶת אֲסוּרָה. אֶלָּא חַיָּב לֶאֱכל כָּל הַתַּעֲרֹבֶת בִּקְדֻשַּׁת שְׁבִיעִית כְּמוֹ שֶׁיִּתְבָּאֵר בִּמְקוֹמוֹ:
כסף משנה
8.
[Related concepts apply with regard to] produce of the Sabbatical year.20The Rambam feels it necessary to mention this point, because his source, Avodah Zarah 73b mentions the produce of the Sabbatical year together with the two prohibited substances mentioned above. The Rambam clarifies that the comparison is not entirely correct, because the produce of the Sabbatical year is not forbidden. If [such produce] becomes mixed with [produce of] the same type, the tiniest amount [causes the mixture to be considered bound by the laws of the produce of the Sabbatical year].21The Ra'avad mentions that this concept applies only until the time it is required to destroy the produce of the Sabbatical year. After that time, that produce is forbidden to be eaten and hence, is considered like other forbidden substances. [If it becomes mixed with produce of] another type, [the ruling depends on whether] its flavor can be detected. [Nevertheless,] it is not considered as one of the substances forbidden by Scriptural Law. For this mixture is not forbidden. Instead, one is obligated to eat the entire mixture in keeping with the holiness of the produce of the Sabbatical year, as will be explained in the appropriate place.22Hilchot Shemitrah ViYovel, chs. 4-7.

הלכה ט
חָמֵץ בְּפֶסַח אַף עַל פִּי שֶׁהוּא מֵאִסּוּרֵי תּוֹרָה אֵינוֹ בִּכְלָלוֹת אֵלּוּ. לְפִי שֶׁאֵין הַתַּעֲרֹבֶת אֲסוּרָה לְעוֹלָם שֶׁהֲרֵי לְאַחַר הַפֶּסַח תִּהְיֶה כָּל הַתַּעֲרֹבֶת מֻתֶּרֶת כְּמוֹ שֶׁבֵּאַרְנוּ. לְפִיכָךְ אוֹסֵר בְּכָל שֶׁהוּא בֵּין בְּמִינוֹ בֵּין שֶׁלֹּא בְּמִינוֹ:
כסף משנה
9.
Although chametz on Pesach is forbidden by Scriptural Law, it is not governed by these general principles,23I.e., although even the tiniest amount of chametz causes an entire mixture to be forbidden, chametz was not mentioned by Avodah Zarah 73b together with wine poured as a libation and tevel. The reason is that the prohibition of the mixture of chametz is motivated by a different rationale (Kessef Mishneh). for this mixture is not forbidden forever. For after Pesach, the entire mixture will be permitted, as we explained.24See Hilchot Chametz UMatzah 1:5 which states that a mixture of chametz and another substance is permitted after the Pesach holiday. Therefore the slightest amount [of chametz] causes [a mixture] to become forbidden,25As explained in the following halachah and notes. See also Halachah 12. whether [it becomes mixed] with a substance of its own type or of another type.

הלכה י
וְהוּא הַדִּין לִתְבוּאָה חֲדָשָׁה שֶׁנִּתְעָרְבָה בִּישָׁנָה מִלִּפְנֵי הָעֹמֶר אוֹסֶרֶת בְּכָל שֶׁהוּא. שֶׁהֲרֵי יֵשׁ לָהּ מַתִּירִין שֶׁלְּאַחַר הָעֹמֶר יֻתַּר הַכּל. וְכֵן כָּל דָּבָר שֶׁיֵּשׁ לוֹ מַתִּירִין וַאֲפִלּוּ הָיָה אִסּוּרוֹ מִדִּבְרֵיהֶם כְּגוֹן אִסּוּר מֻקְצֶה וְנוֹלָד בְּיוֹם טוֹב לֹא נָתְנוּ בּוֹ חֲכָמִים שִׁעוּר אֶלָּא אֲפִלּוּ אֶחָד בְּכַמָּה אֲלָפִים אֵינוֹ בָּטֵל. שֶׁהֲרֵי יֵשׁ דֶּרֶךְ שֶׁיֻּתַּר בָּהּ כְּגוֹן הֶקְדֵּשׁ וּמַעֲשֵׂר שֵׁנִי וְכַיּוֹצֵא בָּהֶן:
כסף משנה
10.
The same law26The Radbaz states that the comparison is to tevel and not to chametz on Pesach. For like tevel, if it becomes mixed with a different substance, it is permitted if its flavor cannot be detected. There are special stringencies applied with regard to chametz, as stated in Halachah 12 (Radbaz). applies when new grain becomes mixed with old grain before [the offering of] the omer. Even the tiniest amount causes [the entire mixture] to become forbidden. For there is a factor that will cause the substance to become permitted. For after [the offering of] the omer, the entire mixture is permitted.27See Chapter 10, Halachah 2.
Similarly, whenever there is a factor that will cause the substance to become permitted, e.g., consecrated entities,28For they can be redeemed (Radbaz). the second tithe,29For they can be eaten in Jerusalem or their holiness can be transferred to money (Radbaz). or the like,30E.g., Bikkurim; see the Rambam's Commentary to the Mishnah (Bkkurim 2:2). our Sages did not mention a measure [in which it could be nullified]. Instead, even if one [of the forbidden substance] becomes mixed with several thousand31Our Sages (Beitzah 3b) state it is not nullified when mixed with 1000 times the amount of kosher substances. The Rambam's wording clarifies that 1000 is not an upper limit. No matter how many times more of the permitted substance there is, the mixture is forbidden. [times that amount of a permitted substance], it is not nullified. [The rationale is that] there is a way that the prohibition can be released.32Hence, this option should be taken rather than relying on the nullification of the forbidden substance. [This principle applies] even when the prohibition stems from Rabbinic decree, e.g., an article set aside or born on a festival.33As explained in Hilchot Sh'vitat Yom Tov 1:19 that when a person sets an object aside before the holiday with the intent that he will not use it on the holiday, he may not change his mind and use it on the holiday. This prohibition is referred to as muktzeh.
Halachah 1:20 states that an egg laid on a holiday following the Sabbath was prepared on the Sabbath, as it were. Therefore it may not be used on the holiday. This prohibition is referred to as nolad. Both of these prohibitions are of Rabbinic origin. Halachah 1:21 states that if such an egg becomes mixed with other eggs, they are all forbidden.

הלכה יא
אֲבָל הָעָרְלָה וְכִלְאֵי הַכֶּרֶם וְחֵלֶב וְדָם וְכַיּוֹצֵא בָּהֶן וְכֵן תְּרוּמוֹת נָתְנוּ חֲכָמִים בָּהֶן שִׁעוּר שֶׁאֵין בָּהֶן דֶּרֶךְ הֶתֵּר לְכָל אָדָם:
כסף משנה
11.
With regard to orlah, mixed species grown in a vineyard, fat, blood, and the like, our Sages fixed a measure [that would enable mixtures to be nullified]. Similarly, our Sages fixed a measure with regard to terumot, for there is no way it can be permitted for all people.34I.e., a mixture of terumah could be eaten in a permitted manner by a priest. Nevertheless, since there is no way it could be permitted to an ordinary person, our Sages were not stringent (Kessef Mishneh).
Both the Kessef Mishneh and the Radbaz ask: It is possible to have to have terumah permitted by making a statement of regret concerning its separation before a wise man. If so, seemingly, it should be considered as an object that could be eaten in a permitted manner. The Radbaz explains that a wise man who can nullify the separation of terumah may not always be found. The Kessef Mishneh states that since this is not the common practice, a substance may not be considered as an object that could be eaten in a permitted manner for this reason.

הלכה יב
יֵרָאֶה לִי שֶׁאֲפִלּוּ דָּבָר שֶׁיֵּשׁ לוֹ מַתִּירִין אִם נִתְעָרֵב בְּשֶׁאֵינוֹ מִינוֹ וְלֹא נָתַן טַעַם מֻתָּר. לֹא יִהְיֶה זֶה שֶׁיֵּשׁ לוֹ מַתִּירִין חָמוּר מִטֶּבֶל שֶׁהֲרֵי אֶפְשָׁר לְתַקְּנוֹ וְאַף עַל פִּי כֵּן שֶׁלֹּא בְּמִינוֹ בְּנוֹתֵן טַעַם כְּמוֹ שֶׁבֵּאַרְנוּ. וְאַל תִּתְמַהּ עַל חָמֵץ בְּפֶסַח שֶׁהַתּוֹרָה אָמְרָה (שמות יב כ) "כָּל מַחְמֶצֶת לֹא תֹאכֵלוּ" לְפִיכָךְ הֶחְמִירוּ בּוֹ כְּמוֹ שֶׁבֵּאַרְנוּ:
כסף משנה
12.
It appears to me35This term indicates a conclusion deduced by the Rambam without an explicit prior Rabbinic source. There are others, including Rav Yitzchak Alfasi and Rav Moshe HaCohen, who differ and maintain that since the mixture could be eaten in a permitted manner, the above stringencies apply. The Ra'avad, however, states that this concept is explicitly stated in the Mishnah. He does not, however, mention which mishnah. The Radbaz and the Kessef Mishneh offer different hypotheses as to the Ra'avad's intent and why the Rambam did not accept it. that even there is a factor that will cause a substance to become permitted, if that substance becomes mixed with a substance of a different type and its flavor is not detectable, it is permitted. The fact that there is a factor that will cause the substance to become permitted does not [cause the prohibition to be] more severe than tevel. [For tevel] can be corrected,36By separating the appropriate terumot and tithes. and yet when it [becomes mixed with a substance] of a different type, [it is permitted if] its flavor cannot be detected, as explained.37Halachah 6. One should not raise a question with regard to chametz on Pesach [where such leniency is not granted. A distinction can be made.] For with regard to chametz, the Torah [Exodus 12:20] states: "Do not eat any leavened substance." For this reason, [our Sages] were stringent with regard to it, as we explained.38Halachah 9.

הלכה יג
וְאֵלּוּ הֵן הַשִּׁעוּרִין שֶׁנָּתְנוּ חֲכָמִים. הַתְּרוּמָה וּתְרוּמַת מַעֲשֵׂר וְהַחַלָּה וְהַבִּכּוּרִים עוֹלִין בְּאֶחָד וּמֵאָה וְצָרִיךְ לְהָרִים וּמִצְטָרְפִין זֶה עִם זֶה. וְכֵן פְּרוּסָה שֶׁל לֶחֶם הַפָּנִים לְתוֹךְ פְּרוּסוֹת שֶׁל חֻלִּין עוֹלִין בְּאֶחָד וּמֵאָה. כֵּיצַד. סְאָה קֶמַח מֵאֶחָד מֵאֵלּוּ. אוֹ סְאָה מִכֻּלָּם שֶׁנָּפְלָה לְמֵאָה סְאָה קֶמַח שֶׁל חֻלִּין וְנִתְעָרֵב הַכּל. מֵרִים מִן הַכּל סְאָה אַחַת כְּנֶגֶד סְאָה שֶׁנָּפְלָה וְהַשְּׁאָר מֻתָּר לְכָל אָדָם. נָפְלָה לְפָחוֹת מִמֵּאָה נַעֲשֶׂה הַכּל מְדֻמָּע:
כסף משנה
13.
These are the measures which the Sages established: Terumah, terumat ma'aser39The terumah which the Levites offer from the tithes they are given. challah, and bikkurim become nullified [when the mixture is] 101 times the [original] amount. [In addition,] one must separate [a portion and give it to a priest].40Although the prohibition is negated, we are still concerned with the fact that property due the priest is not given to him, as stated in Halachah 15. [All of these sacred foods] are combined one with the other.41I.e., as stated in the conclusion of the halachah, if two of these substances fall into the same accumulation of permitted substances, it is necessary to have 100 times their combined size. Similarly, a slice of the showbread becomes nullified when mixed with slices of ordinary bread [if] the mixture is 101 times the original amount.42The Kessef Mishneh notes that the Rambam's ruling here appears to contradict his ruling in Hilchot Pesulei HaMukdashim 6:24 where he states that the showbread is not nullified. He explains that in Hilchot Pesulei HaMukdashim, the Rambam is speaking about pieces of the showbread that are ritually pure. Hence the entire mixture should be eaten by the priests. (Note the Radbaz who questions how the priests could eat the mixture.) Here, by contrast, we are speaking about pieces of the showbread that are impure. If the showbread was a significant part of the mixture, the entire mixture would have to be burnt. Since it is not significant, we considered its existence negated.
What is implied? When a se'ah of flour from one of the above43Terumah, terumat ma'aser challah, or bikkurim.- or one se'ah from all of them [combined] - falls into 100 se'ah of ordinary [flour] and [the flour] became mixed together,44If, however, the sacred substances are distinct, they must be separated from the ordinary substances. one should separate one se'ah from the mixture for the se'ah that fell in originally. The remainder is permitted to all people.45It does not have to eaten with attention to the laws of terumah. If it fell into less than 100 se'ah, the entire mixture is meduma.46This term refers to a mixture of terumah or other sacred substances with ordinary substances. The mixture must be sold to priests (at the price of terumah) with the exception of the original sacred amount (Hilchot Terumah 13:2).

הלכה יד
הָעָרְלָה וְכִלְאֵי הַכֶּרֶם עוֹלִין בְּאֶחָד וּמָאתַיִם וּמִצְטָרְפִין זֶה עִם זֶה וְאֵינוֹ צָרִיךְ לְהָרִים. כֵּיצַד. רְבִיעִית שֶׁל יֵין עָרְלָה אוֹ כִּלְאֵי הַכֶּרֶם אוֹ שֶׁהָיְתָה הָרְבִיעִית מִצְטָרֶפֶת מִשְּׁנֵיהֶם שֶׁנָּפְלָה לְתוֹךְ מָאתַיִם רְבִיעִיּוֹת שֶׁל יַיִן הַכּל מֻתָּר וְאֵינוֹ צָרִיךְ לְהָרִים כְּלוּם. נָפְלָה לְפָחוֹת מִמָּאתַיִם הַכּל אָסוּר בַּהֲנָיָה:
כסף משנה
14.
Orlah and mixed species grown in a vineyard become nullified [when the mixture is] 201 times the [original] amount. The [two prohibitions] are combined one with the other,47Although they are separate and unrelated prohibitions, since it is forbidden to benefit from both of them and we derive the laws pertaining to one from the laws pertaining to the other, we rule that they may be combined (Orlah 2:1). and it is not necessary to separate any thing.48As explained in the following halachah, in this instance, one is not causing the priests a loss.
What is implied? When a revi'it of wine which is orlah or which [came from grapes] grown together with mixed species in a vineyard - or one revi'it was combined from both prohibited substances - falls into 200 revi'iot of wine, the entire mixture is permitted. It is not necessary to separate anything. If it falls into less than 200, it is forbidden to benefit from the entire [mixture].49The Ra'avad questions the Rambam's ruling, objecting to the decision that it is forbidden to benefit from the mixture. (He maintains that although partaking of the mixture is forbidden, one should be able to sell it to a gentile with the exception of the value of the forbidden substance. For, he maintains, it is never forbidden to benefit from a mixture that is not inherently forbidden.) The Radbaz justifies the Rambam's view.

הלכה טו
וְלָמָּה צָרִיךְ לְהָרִים הַתְּרוּמָה וְלֹא יָרִים עָרְלָה וְכִלְאֵי הַכֶּרֶם. שֶׁהַתְּרוּמָה מָמוֹן כֹּהֲנִים. לְפִיכָךְ כָּל תְּרוּמָה שֶׁאֵין הַכֹּהֲנִים מַקְפִּידִין עָלֶיהָ כְּגוֹן תְּרוּמַת הַכְּלִיסִין וְהַחֲרוּבִין וּשְׂעוֹרִין שֶׁבֶּאֱדוֹם אֵינוֹ צָרִיךְ לְהָרִים:
כסף משנה
15.
Why is it necessary to separate [a measure of] terumah and not a measure of orlah or mixed species from a vineyard? Because terumah is the property of the priests. Accordingly, any terumah which the priests are not concerned with, e.g., terumah from [low-grade] figs,50Our translation is based on the Rambam's Commentary to the Mishnah (Terumot 11:4). carobs, and Edomite barley, need not be separated.51For the priests will not be concerned about its loss.

הלכה טז
וְלָמָּה כָּפְלוּ שִׁעוּר עָרְלָה וְכִלְאֵי הַכֶּרֶם מִפְּנֵי שֶׁהֵן אֲסוּרִין בַּהֲנָיָה. וְלָמָּה סָמְכוּ עַל שִׁעוּר מֵאָה בִּתְרוּמוֹת שֶׁהֲרֵי תְּרוּמַת מַעֲשֵׂר אֶחָד מִמֵּאָה וּמְקַדֵּשׁ הַכּל שֶׁנֶּאֱמַר (במדבר יח כט) "אֶת מִקְדְּשׁוֹ מִמֶּנּוּ" אָמְרוּ חֲכָמִים דָּבָר שֶׁאַתָּה מֵרִים מִמֶּנּוּ אִם חָזַר לְתוֹכוֹ מְקַדְּשׁוֹ:
כסף משנה
16.
Why was the measure doubled for orlah and mixed species grown in a vineyard? Because it is forbidden to benefit from them.52Therefore they were treated more stringently. The Radbaz emphasizes that they are compared to terumah and not to other forbidden substances for the root kodesh is used with regard to them.
Why did [the Sages] choose the figure of 100 for terumot? For terumat ma'aser is one hundredth of the entire crop,53For it is one tenth of a tenth. and yet it causes the entire crop to be "sanctified,"54I.e., "forbidden." as [Numbers 18:29] states: "its sacred part."55As the Rambam continues to explain, the Jerusalem Talmud (Orlah 2:1) offers a non-literal interpretation of this phrase, understanding it as meaning "the one who sanctifies it." Our Sages said: "An entity which must be separated from it sanctifies it if it returns to it.

הלכה יז
שְׁאָר אִסּוּרִין שֶׁבַּתּוֹרָה כֻּלָּן כְּגוֹן בְּשַׂר שְׁקָצִים וּרְמָשִׂים וְחֵלֶב וְדָם וְכַיּוֹצֵא בָּהֶן שִׁעוּרָן בְּשִׁשִּׁים. כֵּיצַד. כְּזַיִת חֵלֶב כְּלָיוֹת שֶׁנָּפַל לְתוֹךְ שִׁשִּׁים כְּזַיִת מֵחֵלֶב הָאַלְיָה הַכּל מֻתָּר. נָפַל לְפָחוֹת מִשִּׁשִּׁים הַכּל אָסוּר. וְכֵן אִם נָפַל כִּשְׂעוֹרָה חֵלֶב צָרִיךְ שֶׁיִּהְיֶה שָׁם כְּמוֹ שִׁשִּׁים שְׂעוֹרָה. וְכֵן בִּשְׁאָר אִסּוּרִין. וְכֵן שֻׁמָּן שֶׁל גִּיד הַנָּשֶׁה שֶׁנָּפַל לִקְדֵרָה שֶׁל בָּשָׂר מְשַׁעֲרִין אוֹתוֹ בְּשִׁשִּׁים. וְאֵין שֻׁמַּן הַגִּיד מִן הַמִּנְיָן. וְאַף עַל פִּי שֶׁשֻּׁמַּן גִּיד הַנָּשֶׁה מִדִּבְרֵיהֶם כְּמוֹ שֶׁבֵּאַרְנוּ. הוֹאִיל וְגִיד הַנָּשֶׁה בְּרִיָּה בִּפְנֵי עַצְמָהּ הֶחְמִירוּ בּוֹ בְּאִסּוּרֵי תּוֹרָה. וְהַגִּיד עַצְמוֹ אֵין מְשַׁעֲרִין בּוֹ וְאֵינוֹ אוֹסֵר שֶׁאֵין בַּגִּידִים בְּנוֹתֵן טַעַם:
כסף משנה
17.
The measure for all of the other prohibitions of the Torah,56With this wording, the Rambam also eliminates those prohibitions of Rabbinic origin, which have a smaller measure as stated in the following halachah. e.g., the meat of crawling animals, teeming animals, fat, blood, and the like is sixty times [the original amount].
What is implied? When an olive-sized portion of the fat of the kidneys falls into sixty times the size of an olive of the fat from the fat tail, the entire mixture is permitted. If it falls into less than sixty [that amount], the entire mixture is forbidden. Similarly, if a portion of forbidden fat the size of a barley-corn, [the mixture] must contain permitted substances the size of sixty barley-corns.57Although there is not enough of the forbidden substance for a person to be liable for lashes according to Scriptural Law, unless there is 60 times the amount of forbidden fat, the mixture is forbidden according to Scriptural Law (see Chulin 98a). Similar [laws apply] with regard to other prohibitions.
Similarly, if the fat of the gid hanesheh falls into a pot of meat,58The prohibitions are considered of the same type, because the taste of the fat is not distinct from that of the meat (Rabbenu Yitzchak Alfasi to Chulin 98a). we require sixty times its amount. The fat of the gid itself is included in this sum.59As is the law with regard to Rabbinic prohibitions as stated in the following halachah. Although the fat of the gid is prohibited [only] by Rabbinic Law, as we explained,60Chapter 8, Halachah 1. since the gid hanesheh is considered a creation in its own right,61As our Sages ruled [Chulin 100a; Chapter 16, Halachah 6; quoted by Shulchan Aruch (Yoreh De'ah 100:1)], a forbidden being which is a creation in its own right is never forbidden. Therefore they ruled more stringently. In this instance, the gid hanesheh itself will be removed. Hence the full stringency of our Sages' ruling is not applied, nevertheless, in recognition of the serious of the prohibition involved, this stringency is applied. [our Sages] ruled stringently concerning it as if it was forbidden by Scriptural Law. The gid itself is not measured and it does not cause other substances to be forbidden, because the gid does not impart flavor.62See Chapter 8, Halachah 6.

הלכה יח
אֲבָל כְּחַל שֶׁנִתְבַּשֵּׁל עִם הַבָּשָׂר בְּשִׁשִּׁים וּכְחַל מִן הַמִּנְיָן. הוֹאִיל וְהַכְּחַל מִדִּבְרֵיהֶם כְּמוֹ שֶׁבֵּאַרְנוּ הֵקֵלּוּ בְּשִׁעוּרוֹ:
כסף משנה
18.
When, by contrast, an udder is cooked with meat, we require sixty times its amount and the udder is considered as part of the sum.63Thus instead of requiring 61 times the forbidden substance (60 plus the substance itself) all that is required is 60 (59 and the substance itself). [The rationale is that] since [the prohibition against] the udder is Rabbinic in origin, [our Sages] were lenient in establishing a measure.64See Chapter 9, Halachot 12-13. As explained in the notes there, the Ra'avad and the Rashba offer a different rationale for this ruling, explaining that since the meat of the udder is acceptable, we include it in the reckoning of 60. Thus in contrast to other instances where 60 times the amount of the forbidden substance is required, here, we require only 59. According to his view, we cannot extrapolate from this ruling to other Rabbinic prohibitions.

הלכה יט
בֵּיצָה שֶׁנִּמְצָא בָּהּ אֶפְרוֹחַ שֶׁנִּשְׁלְקָה עִם בֵּיצִים הַמֻּתָּרוֹת אִם הָיְתָה עִם שִׁשִּׁים וְאַחַת וְהִיא הֲרֵי הֵן מֻתָּרוֹת. הָיְתָה עִם שִׁשִּׁים בִּלְבַד נֶאֶסְרוּ הַכּל מִפְּנֵי שֶׁהִיא בְּרִיָּה בִּפְנֵי עַצְמָהּ עָשׂוּ הֶכֵּר בָּהּ וְהוֹסִיפוּ בְּשִׁעוּרָהּ:
כסף משנה
19.
[The following laws apply when] an egg in which a chick is found65Such an egg is forbidden to be eaten (see Chapter 3, Halachah 8). is cooked together with eggs that are permitted. If there are 61 and it,66I.e., a total of 62. they are permitted. If, however, there are only sixty [permitted eggs], the entire mixture is forbidden. [The rationale is that the chick] is a creation in its own right,67As stated in the notes to the previous halachah, in this instance, the forbidden substance itself will be removed. Hence the full stringency of our Sages' ruling concerning an entity that is a creation in its own right is not applied. Nevertheless, in recognition of the serious of the prohibition involved, this stringency is applied. See the notes to the following halachah where a rationale cited by other authorities is mentioned. [our Sages] made a distinction and added to its [required] measure.

הלכה כ
אֲבָל בֵּיצַת עוֹף טָמֵא שֶׁנִּשְׁלְקָה עִם בֵּיצֵי עוֹף טָהוֹר לֹא אָסְרָה אוֹתָם. וְאִם טָרַף אֵלּוּ עִם אֵלּוּ. אוֹ שֶׁנִּתְעָרְבָה בֵּיצַת עוֹף טָמֵא אוֹ בֵּיצַת טְרֵפָה עִם בֵּיצִים אֲחֵרוֹת שִׁעוּרָן בְּשִׁשִּׁים:
כסף משנה
20.
If, however, the egg of an non-kosher fowl was cooked together with the eggs of kosher fowl, it does not cause them to become forbidden.68Here we are talking about eggs that are cooked in their shells. When an egg contains a chick, the chick will impart its flavor to the entire pot. When, by contrast, eggs are cooked in their shells, they do not impart flavor (Chulin 97b). The non-kosher egg must be removed from the mixture. This, however, can sometimes be done, because the appearance of non-kosher eggs may differ from that of kosher eggs (Chapter 3, Halachah 18).
The Rama (Yoreh De'ah 86:6) differs and states that if a substantial loss will not be caused, we should be stringent and follow the same ruling with regard to all eggs. If, however, there will be a substantial loss, even he counsels to rely on the more lenient views.

If [the eggs were opened and] mixed together or the egg of a non-kosher fowl or the egg of a fowl that is trefe become mixed with other eggs,69For, at times, non-kosher eggs are not distinguishable from kosher eggs (ibid.). the required measure is 60.70I.e., the mixture is judged as an ordinary instance in which kosher food becomes mixed with non-kosher food. According to the Rambam, the non-kosher egg is not a creation that is forbidden in its own right.
The Shulchan Aruch (Yoreh De'ah 86:5) differs and rules that we require 61 kosher eggs in this instance as well. The Ramban explains that the reason is that not all eggs are the same size and by adding an extra egg, we make certain that we have the necessary amount. (He uses this rationale to explain the law stated in the previous halachah as well.) The Siftei Cohen 86:15 offers a different rationale, stating that an egg itself is considered a creation in its own right.
The Kessef Mishneh notes that there are some who would rule that 60 eggs are not necessary, for there are opinions [see Shulchan Aruch (Yoreh De'ah 109:1)] that when kosher and non-kosher entities are intermingled in a dry mixture, we rely on Scriptural Law and require only a simple majority of the kosher substances. As obvious from this ruling, the Rambam does not accept this leniency.

הלכה כא
וּמִנַּיִן סָמְכוּ חֲכָמִים עַל שִׁעוּר שִׁשִּׁים. שֶׁהֲרֵי הַמּוּרָם מֵאֵיל נָזִיר וְהִיא הַזְּרוֹעַ אֶחָד מִשִּׁשִּׁים מִשְּׁאָר הָאַיִל וְהִיא מִתְבַּשֶּׁלֶת עִמּוֹ וְאֵינָהּ אוֹסֶרֶת אוֹתוֹ שֶׁנֶּאֱמַר (במדבר ו יט) "וְלָקַח הַכֹּהֵן אֶת הַזְּרֹעַ בְּשֵׁלָה מִן הָאַיִל":
כסף משנה
21.
What is the source because of which the Sages relied on the measure of 60? For the portion given [to the priest] from the ram brought by a Nazirite,71When a Nazirite completes the days of his Nazirite vow, he brings several sacrifices. Among them is a ram brought as a peace offering. The foreleg from this offering is given to the priest and may not be eaten by an ordinary Israelite (Chulin 98a; Hilchot Nazirut 8:1-4).i.e., the foreleg, is one sixtieth of the remainder of the ram. It is cooked together with it and does not cause it to be forbidden,72I.e., although this portion which is forbidden to an Israelite is cooked together with the entire ram, the Israelite is permitted to partake of the remainder of the ram. Accordingly, our Sages inferred that a similar ratio may be used when other prohibited substances are cooked with permitted substances. as [Numbers 6:19] states: "And the priest shall take the cooked foreleg from the ram."

הלכה כב
מִין בְּמִינוֹ וְדָבָר אַחֵר שֶׁנִּתְעָרְבוּ כְּגוֹן קְדֵרָה שֶׁהָיָה בָּהּ חֵלֶב אַלְיָה וּגְרִיסִין וְנָפַל לְתוֹכָהּ חֵלֶב הַכְּלָיוֹת וְנִמְחָה הַכּל וְנַעֲשָׂה גּוּף אֶחָד. רוֹאִין אֶת חֵלֶב הָאַלְיָה וְאֶת הַגְּרִיסִין כְּאִלּוּ הֵן גּוּף אֶחָד וּמְשַׁעֲרִין חֵלֶב הַכְּלָיוֹת כִּגְרִיסִין וּכְאַלְיָּה. אִם הָיָה אֶחָד מִשִּׁשִּׁים מֻתָּר. שֶׁהֲרֵי אִי אֶפְשָׁר כָּאן לַעֲמֹד עַל הַטַּעַם:
כסף משנה
22.
[The following rules apply when] two substances of the same type, [one permitted and one forbidden,] and a [third] entity become mixed together, e.g., there was a pot with fat from the fat tail and beans and fat from the kidneys fell into it. The entire [mixture] dissolved and became a single entity. We view the fat from the fat tail and the beans as a single entity and we measure the fat from the kidneys against it. If the ratio was one to sixty, it is permitted. For it is impossible to detect the taste.73Because there is no significant difference between the taste of fat from the fat tail and fat from the kidneys, as indicated by Halachah 4.

הלכה כג
וְהוּא הַדִּין לַתְּרוּמוֹת שֶׁנִּתְעָרְבוּ לְשַׁעֲרָן בְּמֵאָה. וְכִלְאֵי הַכֶּרֶם אוֹ עָרְלָה לְשַׁעֵר אוֹתָן בְּמָאתַיִם:
כסף משנה
23.
The same principle applies when terumot are mixed together [with other substances, some of the same type and some of a different type], their measure is 100. And the measure of mixed species from a vineyard and orlah is 200.

הלכה כד
כְּשֶׁמְּשַׁעֲרִין בְּכָל הָאִסּוּרִין בֵּין בְּשִׁשִּׁים בֵּין בְּמֵאָה בֵּין בְּמָאתַיִם. מְשַׁעֲרִין בַּמָּרָק וּבַתַּבְלִין וּבְכָל שֶׁיֵּשׁ בַּקְּדֵרָה וּבְמַה שֶּׁבָּלְעָה קְדֵרָה מֵאַחַר שֶׁנָּפַל הָאִסּוּר לְפִי אֹמֶד הַדַּעַת. שֶׁהֲרֵי אִי אֶפְשָׁר לַעֲמֹד עַל מַה שֶּׁבָּלְעָה בְּצִמְצוּם:
כסף משנה
24.
When we calculate the measure of permitted substances with regard to all prohibitions, whether the measure is 60, 100, or 200, we include the soup, the spices, everything that is in the pot, and what the pot has absorbed after the prohibited substance fell according to our estimation.74I.e., at that time, it absorbed both the permitted substances and the prohibited substance (Radbaz).
In his Kessef Mishneh and in his Shulchan Aruch (Yoreh De'ah 99:4), Rav Yosef Caro follows the view of Rashi and the Tur who maintain that we should measure the prohibited substance and the permitted substances as they are at present, for there is no way of knowing how much the pot absorbed. This stringency applies, however, only with regard to forbidden substances mixed with permitted substances of a different type. (For then the prohibition stems from Scriptural Law.) If they are of the same type (when a simple majority is required according to Scriptural Law), the Shulchan Aruch rules more leniently and accepts the Rambam's ruling.
For it is impossible to know the exact amount which the pot absorbed.

הלכה כה
אָסוּר לְבַטֵּל אִסּוּרִין שֶׁל תּוֹרָה לְכַתְּחִלָּה. וְאִם בִּטֵּל הֲרֵי זֶה מֻתָּר. וְאַף עַל פִּי כֵן קָנְסוּ אוֹתוֹ חֲכָמִים וְאָסְרוּ הַכּל. וְיֵרָאֶה לִי שֶׁכֵּיוָן שֶׁהוּא קְנָס אֵין אוֹסְרִין תַּעֲרֹבֶת זוֹ אֶלָּא עַל זֶה הָעוֹבֵר שֶׁבִּטֵּל הָאִסּוּר. אֲבָל לַאֲחֵרִים הַכּל מֻתָּר:
כסף משנה
25.
It is forbidden to nullify a substance75I.e., after a forbidden substance fell into a mixture, one may not add enough permitted substances that there will 60, 100, or 200 times the amount of the forbidden substance. forbidden by Scriptural76If, however, a substance forbidden by Rabbinic Law accidentally fell into a mixture, one may add enough permitted substances to nullify the prohibition, as stated in Halachah 26. Law as an initial and preferred measure. If, however, one nullified it, the mixture is permitted.77Because in fact the presence of the forbidden substance has been nullified. Nevertheless, our Sages penalized such a person and forbade the entire mixture.78The Siftei Cohen 99:11 explains the reason for this penalty. If we would permit him to benefit from it, we fear that if, in the future, such a situation would recur, he would instruct his servants to nullify the prohibited substances for him. It appears to me that since this is a penalty, we forbid this mixture only to the person79Or the person whom he intended to serve after nullifying the forbidden substance. Were this not the case, he would benefit from his undesirable act (Kessef Mishneh). who transgressed and nullified the prohibited substance.80The Rambam's wording implies that the penalty was imposed only when he willfully nullified the existence of the forbidden substance. If he did so accidentally or inadvertently, no prohibition applies, for our Sages did not impose penalties in such situations [Kessef Mishneh; Shulchan Aruch (Yoreh De'ah 99:5)]. For others, however, the entire mixture is permitted.

הלכה כו
כֵּיצַד. הֲרֵי שֶׁנָּפְלָה סְאָה שֶׁל עָרְלָה לְתוֹךְ מֵאָה סְאָה שֶׁהֲרֵי נֶאֱסַר הַכּל. לֹא יָבִיא מֵאָה סְאָה אֲחֵרוֹת וִיצָרֵף כְּדֵי שֶׁתַּעֲלֶה בְּאֶחָד וּמָאתַיִם. וְאִם עָבַר וְעָשָׂה כֵּן הַכּל מֻתָּר. אֲבָל בְּאִסּוּר שֶׁל דִּבְרֵיהֶם מְבַטְּלִין הָאִסּוּר לְכַתְּחִלָּה:
כסף משנה
26.
What is implied? If a se'ah of orlah falls into 100 se'ah [of permitted produce], the entire [mixture] is forbidden. One should not bring another 100 se'ah and join [the entire quantity] together so that [the forbidden substance] will be nullified because of the presence of 201 times the original amount. If, however, he transgressed and did so, the entire [mixture] is permitted.
With regard to a prohibition forbidden by Rabbinic decree,81This point was not accepted by all authorities. The Ashkenazic authorities (as reflected by the ruling of Rabbenu Asher) maintain that even a Rabbinic prohibition should not be nullified as an initial and preferred measure. The Radbaz proposes an intermediate position: that the stringency should be applied only to Rabbinic prohibitions that have a source in Scriptural Law, e.g., milk and fowl, but not those enacted by the Rabbis entirely on their own initiative. This compromise, however, was not accepted. The Shulchan Aruch (Yoreh De'ah 99:6) adopts the Rambam's position, while the Tur and the Rama follow that of Rabbenu Asher. we do nullify a prohibition as an initial and preferred measure.

הלכה כז
כֵּיצַד. חָלָב שֶׁנָּפַל לִקְדֵרָה שֶׁיֵּשׁ בָּהּ בְּשַׂר עוֹף וְנָתַן טַעַם בַּקְּדֵרָה מַרְבֶּה עָלָיו בְּשַׂר עוֹף אַחֵר עַד שֶׁיִּבָּטֵל הַטַּעַם. וְכֵן כָּל כַּיּוֹצֵא בָּזֶה:
כסף משנה
27.
What is implied? If milk fell into a pot that contains fowl and imparted its flavor to the food, one may add other fowl to the pot until the flavor [of the milk] is no longer discernable. Similar laws apply in all analogous situations.

הלכה כח
כְּבָר בֵּאַרְנוּ שֶׁאִם נָתַן דָּבָר הָאָסוּר טַעֲמוֹ בְּדָבָר הַמֻּתָּר נֶאֱסַר הַכּל. בַּמֶּה דְּבָרִים אֲמוּרִים בְּשֶׁהִשְׁבִּיחוֹ. אֲבָל אִם פָּגַם זֶה הָאָסוּר לַמֻּתָּר וְהִפְסִיד טַעֲמוֹ הֲרֵי זֶה מֻתָּר. וְהוּא שֶׁיִּהְיֶה פּוֹגֵם מִתְּחִלָּה וְעַד סוֹף. אֲבָל אִם פָּגַם בַּתְּחִלָּה וְסוֹפוֹ לְהַשְׁבִּיחַ. אוֹ הִשְׁבִּיחַ בַּתְּחִלָּה אַף עַל פִּי שֶׁסּוֹפוֹ לִפְגֹּם הֲרֵי זֶה אָסוּר:
כסף משנה
28.
We already explained82Halachah 1. that if a forbidden substance imparts its flavor to a permitted substance, the entire mixture is not permitted. When does the above apply? [When the flavor imparted] improves [the flavor of the permitted food]. If, however, the forbidden substance detracts from the flavor of the permitted substance and impairs it, it is permitted.83Avodah Zarah 66a derives this concept from the statements of Deuteronomy 14:21 concerning the meat of an animal that died without slaughter: "Give it to the stranger in your gate and he will partake of it." Implied is that the prohibition applies only to meat that is fit for a non-Jew to partake of. If it is not fit for the non-Jew to eat, it cannot cause a Jew's food to be forbidden.
See also Shulchan Aruch (Yoreh De'ah 103:2) which states: "The impairment of the food's flavor does not have to be complete to the extent that one would be disgusted to eat it. Instead, even if it slightly detracts [from its flavor], it does not cause the mixture to become forbidden."

[This applies] provided it detracts from its flavor from the beginning until the end. If, however, it detracted from its flavor at the outset, but ultimately improved it or improved it initially, even though it will ultimately detract from it, [the mixture] is forbidden.84Avodah Zarah, loc. cit. states that if initially, the flavor of a substance is improved by the addition of the forbidden substance, it becomes forbidden. The fact that ultimately the addition detracts from the flavor of the permitted substance is not sufficient to cause it to become permitted again. The Rambam draws the conclusion that ultimately if the flavor of the substance will be improved, it is also prohibited (Kessef Mishneh).
Note, however, the Siftei Cohen 103:7 who states that it is permitted to partake of a mixture after the flavor of the permitted substance was impaired, before it improved, even though one knows that ultimately, it will improve. Based on the wording of the following halachah, however, it is questionable if the Rambam would accept this conclusion.

הלכה כט
וּמִי יִטְעֹם אֶת הַתַּעֲרֹבֶת. אִם הָיָה הַמְעֹרָב תְּרוּמוֹת עִם הַחֻלִּין טוֹעֵם אוֹתָן הַכֹּהֵן. אִם הָיָה טַעַם הַתְּרוּמָה נִכָּר הַכּל מְדֻמָּע. וּבְהִלְכוֹת תְּרוּמוֹת יִתְבָּאֵר דִּין הַמְדֻמָּע:
כסף משנה
29.
Who will taste the mixture?85I.e., since there is a question whether the mixture is forbidden or not. If terumot were mixed with ordinary crops, a priest should taste the mixture.86For he is permitted to partake of terumot. If the flavor of the terumah is discernible, the entire mixture is considered as miduma. In Hilchot Terumot,87Chs. 13 and 14. the laws pertaining to [produce that is] miduma will be explained.

הלכה ל
וְאִם הָיָה בָּשָׂר בְּחָלָב אוֹ יֵין נֶסֶךְ וְיֵין עָרְלָה וְכִלְאֵי הַכֶּרֶם שֶׁנָּפְלוּ לִדְבַשׁ. אוֹ בְּשַׂר שְׁקָצִים וּרְמָשִׂים שֶׁנִּתְבַּשֵּׁל עִם הָיָּרָק וְכַיּוֹצֵא בָּהֶן. טוֹעֵם אוֹתָן הָעַכּוּ''ם וְסוֹמְכִין עַל פִּיו. אִם אָמַר אֵין בּוֹ טַעַם אוֹ שֶׁאָמַר יֵשׁ בּוֹ טַעַם וּמִטַּעַם רַע הוּא וַהֲרֵי פְּגָמוֹ הַכּל מֻתָּר. וְהוּא שֶׁלֹּא יִהְיֶה סוֹפוֹ לְהַשְׁבִּיחַ כְּמוֹ שֶׁבֵּאַרְנוּ. וְאִם אֵין שָׁם עַכּוּ''ם לִטְעֹם מְשַׁעֲרִין אוֹתוֹ בְּשִׁעוּרוֹ בְּשִׁשִּׁים אוֹ בַּמֵּאָה אוֹ בְּמָאתַיִם:
כסף משנה
30.
If [the mixture involved] meat and milk, wine poured as a libation, wine that was orlah, or [made from grapes that grew together with] mixed species in a vineyard that fell into honey, or the meat of crawling animals or teeming animals that were cooked with vegetables and the like, a gentile should taste [the mixture].
We rely on his word.88There is a difficulty with the Rambam's statements, for generally, we do not rely on the word of a gentile with regard to ritual matters. The Shulchan Aruch (Yoreh De'ah 98:1) relies on the opinion of the Rashba quoted by the Tur, that this refers to a situation where the gentile does not know that we are relying on him, but instead makes his statements as a matter of course (masiach lifi tomo).
See also the Turei Zahav 98:2 and the Siftei Cohen 98:2 who quote views which state that an ordinary gentile is not sufficient, but instead, the intent is a gentile chef who is an expert on recognizing flavors. According to some, however, this interpretation leads to a leniency. For since he is a professional, he will not risk his professional reputation by lying to mislead a Jew. Hence, according to these views, his statements can be accepted even if they are made in response to direct questions and not as a matter of course. There are, nevertheless, authorities who differ and require even a chef to make his statements as a matter of course. Moreover, there are authorities (among them, the Radbaz and the Rama) who never accept the statements of a gentile with regard to these matters.
The Rama (Yoreh De'ah 98:1) states that in the present age, we do not rely on the statements of a non-Jew who tasted food to determine whether it is kosher or not.
If he says: "It does not have the flavor [of the forbidden substance]," or he says: "It [imparted] its flavor, but that flavor is bad and it detracts [from the flavor of the permitted substance," the entire [mixture] is permitted, provided it will not ultimately improve it, as we explained.89Halachah 28. If there is no gentile to taste it, we rely on the measures of 60,90For it is an accepted principle that the taste of a forbidden substance will be nullified in more than 60 times its volume. 100, or 200.91This refers to mixtures of terumot, orlah, and mixed species in a vineyard. The ruling is, however, problematic. For if we are speaking about a mixture of these substances together with different substances, then 60 times their volume will be sufficient. For the taste of all substances except spices is nullified in 60 times their volume as stated in the previous note. And if we are speaking about a mixture of substances with their own kind, the taste of the forbidden substance will not be detectable.

הלכה לא
עַכְבָּר שֶׁנָּפַל לְשֵׁכָר אוֹ לְחֹמֶץ מְשַׁעֲרִין אוֹתוֹ בְּשִׁשִּׁים. שֶׁאָנוּ חוֹשְׁשִׁין שֶׁמָּא טַעֲמוֹ בַּשֵּׁכָר וּבַחֹמֶץ מַשְׁבִּיחַ. אֲבָל אִם נָפַל לְיַיִן אוֹ לְשֶׁמֶן אוֹ לִדְבַשׁ מֻתָּר וַאֲפִלּוּ נָתַן טַעַם מִפְּנֵי שֶׁטַּעֲמוֹ פּוֹגֵם. שֶׁכָּל אֵלּוּ צְרִיכִין לִהְיוֹתָן מְבֻשָּׂמִים וְזֶה מַסְרִיחָן וּמַפְסִיד טַעֲמָן:
כסף משנה
31.
When a rat falls into beer or vinegar, we require a measure of 60, for we suspect that it imparted its flavor to the beer or the vinegar and it improves it.92Avodah Zarah 68b leaves unresolved the question whether the rat's flavor detracts from the flavor of beer and vinegar. Hence we rule stringently.When, however, it falls into wine, oil, or honey,93These substances are not mentioned by the Talmud, loc. cit., but it is common knowledge that the rat's flavor will detract from their own, as the Rambam explains (Kessef Mishneh). it is permitted, even if it imparts its flavor, for the [rat's] flavor detracts [from the flavor of these substances]. For [these substances] must all have a pleasant fragrance and rat meat spoils their aroma and detracts from their flavor.

הלכה לב
גְּדִי שֶׁצְּלָאוֹ בְּחֶלְבּוֹ אָסוּר לֶאֱכל אֲפִלּוּ מִקְצֵה אָזְנוֹ. שֶׁהָחֵלֶב נִבְלָע בְּאֵיבָרָיו וְהוּא מַשְׁבִּיחוֹ וְנוֹתֵן בּוֹ טַעַם. לְפִיכָךְ אִם הָיָה כָּחוּשׁ וְלֹא הָיָה בּוֹ חֵלֶב כְּלָיוֹת וְלֹא חֵלֶב קֶרֶב אֶלָּא מְעַט כְּאֶחָד מִשִּׁשִּׁים קוֹלֵף וְאוֹכֵל עַד שֶׁמַּגִּיעַ לַחֵלֶב. וְכֵן יָרֵךְ שֶׁצְּלָאָהּ בְּגִיד הַנָּשֶׁה שֶׁבָּהּ קוֹלֵף וְאוֹכֵל עַד שֶׁהוּא מַגִּיעַ לַגִּיד וּמַשְׁלִיכוֹ. וְכֵן בְּהֵמָה שֶׁצְּלָאָהּ שְׁלֵמָה וְלֹא הֵסִיר לֹא חוּטִין וְלֹא קְרוּמוֹת הָאֲסוּרוֹת קוֹלֵף וְאוֹכֵל. וְכֵיוָן שֶׁיַּגִּיעַ לְדָבָר אָסוּר חוֹתְכוֹ וּמַשְׁלִיכוֹ שֶׁאֵין בַּגִּידִים בְּנוֹתֵן טַעַם כְּדֵי לְשַׁעֵר בָּהֶן:
כסף משנה
32.
When a goat is roasted in its fat, it is forbidden to eat from even the tip of its ear. [The rationale is that] the fat permeates through all its limbs, improves [their taste], and imparts flavor. Accordingly, if [a goat] is lean and possessed only a meager amount of fat on its kidneys and digestive organs,94These are prohibited by Scriptural Law. i.e., one in sixty-one [of the entire animal], one may cut away [the meat] and eat it95In his Kessef Mishneh, Rav Yosef Caro states that, according to the Rambam, one may partake of the meat as it is. He need not scrape off or cut away its surface (kelipah or netilah). In his Shulchan Aruch (Yoreh De'ah 105:5), however, he rules according to the perspective of Rabbenu Asher, the Rashba, the Ran, and the Tur who maintain that the outer layer of the meat next to the fat itself must be cut away.
See also the ruling of the Rama (Yoreh De'ah, loc. cit.) that at present, we are not capable of differentiating which fat is considered succulent and which is considered lean. Hence, we require 60 times the amount of forbidden fat in all instances.
until he reaches the fat.
Similarly, when the thigh [of an animal] is roasted96The Kessef Mishneh emphasizes that the leniency mentioned by the Rambam applies only when the animal is roasted with its gid or with the forbidden tissues. If it is cooked, more stringent rules apply. together with the gid hanesheh, one may cut away [the meat] and eat it until he reaches the gid [hanesheh].97Although the fat of the gid hanesheh is prohibited, there is not enough fat to cause the other limbs of the animal to become prohibited (Kessef Mishneh). Nevertheless, one must cut away the outer layer of the meat next to the gid. [This], he should cast away. Similarly, if an animal was roasted whole without removing the forbidden strands of tissue and membranes, one may cut away [the meat] and eat it.98In this instance as well, there is not a significant enough quantity of fat to cause the meat to become forbidden. When he reaches a forbidden substance, he should cast it away. There is no need to calculate the ratio [of this forbidden tissue to the meat,] for this [forbidden] tissue does not impart flavor.

הלכה לג
אֵין צוֹלִין בְּשַׂר שְׁחוּטָה עִם בְּשַׂר נְבֵלָה אוֹ בְּהֵמָה טְמֵאָה בְּתַנּוּר אֶחָד. וְאַף עַל פִּי שֶׁאֵין נוֹגְעִין זֶה בָּזֶה. וְאִם צְלָאָן הֲרֵי זֶה מֻתָּר. וַאֲפִלּוּ הָיְתָה הָאֲסוּרָה שְׁמֵנָה הַרְבֵּה וְהַמֻּתֶּרֶת רָזָה שֶׁהָרֵיחַ אֵינוֹ אוֹסֵר. וְאֵינוֹ אוֹסֵר אֶלָּא טַעֲמוֹ שֶׁל אִסּוּר:
כסף משנה
33.
One should not roast ritually slaughtered meat with the meat of a nevelah or the meat of a non-kosher species in one oven, even though they do not touch each other.99The Shulchan Aruch (Yoreh De'ah 108:1) quotes the Rambam's ruling forbidding roasting the two in the same oven, but allows for certain leniencies, e.g., the oven is very large or the substances are covered. If one roasted them together, [the kosher meat] is permitted. [This applies] even if the forbidden meat was very succulent and the permitted meat was lean. For an aroma does not cause a substance to become forbidden; only the flavor of a forbidden substance does.

הלכה לד
בְּשַׂר נְבֵלָה מָלִיחַ שֶׁנִּבְלַל עִמּוֹ בְּשַׂר שְׁחוּטָה הֲרֵי זֶה נֶאֱסַר. מִפְּנֵי שֶׁתַּמְצִית הַנְּבֵלָה נִבְלַעַת בְּגוּף בְּשַׂר הַשְּׁחוּטָה וְאִי אֶפְשָׁר לַעֲמֹד כָּאן לֹא עַל הַטַּעַם וְלֹא עַל הַשִּׁעוּר. וְכֵן בְּשַׂר דָּג טָמֵא מָלִיחַ שֶׁנִּבְלַל עִמּוֹ דָּג תָּפֵל טָהוֹר נֶאֱסַר מִפְּנֵי צִירוֹ. אֲבָל אִם הָיָה הַמָּלִיחַ טָהוֹר וְהַתָּפֵל דָּג טָמֵא לֹא נֶאֱסַר הַמָּלִיחַ [אַף עַל פִּי] שֶׁהַתָּפֵל בּוֹלֵעַ מִן הַמָּלִיחַ [ אֵינוֹ בּוֹלֵעַ כָּל כָּךְ שֶׁיַּחְזֹר וְיִפְלֹט]. דָּג טָמֵא שֶׁכְּבָשׁוֹ עִם דָּג טָהוֹר הַכּל אָסוּר אֶלָּא אִם כֵּן הָיָה הַטָּמֵא אֶחָד מִמָּאתַיִם מִן הַטָּהוֹר:
כסף משנה
34.
When the meat of a ritually slaughtered animal100It appears that the kosher meat was unsalted. If, however, it were salted, it would not absorb the juices of the non-kosher meat, as indicated by the principle: "One that is involved in discharging its own juices does not absorb from another" (Radbaz). was mixed together101The commentaries note an apparent contradiction to the Rambam's rulings in Chapter 7, Halachot 17-19. The Radbaz explains that there, both the forbidden and the kosher substances were salted, while here the kosher meat was not. The Kessef Mishneh explains that here the two pieces of meat are mixed together, while there the substances were merely near each other. with the meat of a nevelah that was salted, the [kosher] meat becomes prohibited,102In this halachah, the Rambam is communicating the principle stated by Chulin 111b et al that meat which is salted is considered as if it is burning hot. It emits concentrated juices which are absorbed by other meat. for the concentrated [juices] of the nevelah are absorbed in the kosher meat. It is impossible to detect their flavor or to calculate the quantity of the forbidden substance.103I.e., no matter what the ration of the kosher meat to the non-kosher meat, the mixture is forbidden (Kessef Mishneh).
The Tur and the Shulchan Aruch (Yoreh De'ah 70:3-4) follows the more lenient views of Rabbenu Asher, the Rashba, and the Ran who maintain that only the external surface of the kosher meat becomes forbidden. Once it is peeled off, the meat is permitted.

When the meat of a unsalted species of kosher fish was mixed together with the meat of a species of unkosher fish that was salted, the [kosher] fish becomes prohibited because of the [non-kosher] brine. If, however, it was the kosher fish that was salted and the non-kosher fish was unsalted, the salted fish does not become forbidden. For even though the unsalted [fish] absorbs [the brine] of the salted one, it does not absorb it to the degree that it will cause it to discharge [its own brine].
When a non-kosher fish was pickled with a kosher fish, the entire mixture is forbidden unless the ratio of kosher fish to non-kosher is 200:1.104For pickling is considered equivalent to cooking. Fish brine is considered as very powerful. Hence it requires a much larger measure than ordinary non-kosher substances. See Rav Kapach's notes to the Rambam's Commentary on the Mishnah (Terumot 10:8) where he writes that the Rambam changed his mind three times on this issue, twice stating more stringent views than the one stated here, before writing this view as his final conclusion.

קדושה הלכות מאכלות אסורות פרק טו
Kedushah Ma`akhalos Assuros Chapter 15