NOTES

משנה א

כל סאה שיש בה רבע - There are 6 קבים in 1 סאה; thus 1/4 of a קב is 1/24 of a סאה (a ration of 1:23), which the משנה is saying is the minimum amount of a foreign species necessary for a mixture to be forbidden.  This is only where the mixture was made unintentionally, otherwise, as set forth in the previous משנה, even a single grain of wheat mixed with a single grain of barley is אסור when intentionally planted together.

ימעט - This may be accomplished by either adding more to the majority species in the mixture, making the minority mixture constitute less than the threshold amount of 1/24, or by removing some of the minority mixture to achieve the same effect.  There appears to be three different explanations as to how this משנה can permit the intentional בטול an איסור.  One approach, brought by תוי"ט is the ר"ב, who says that מן התורה a ratio of even 1:2 is בטל ברוב, and it was only due to fears of מראית עין that the חכמים prohibited anything with 1/24 or more of a different species in the mixture.  תוי"ט rejects this reasoning, as ביטול ברוב is allowed only when the two substances cannot be distinguished from each other (e.g. a drop of forbidden liquid mixed into a larger amount of permitted liquid).  However where, as here, the forbidden substance can be picked out from the permitted substance, then ביטול is cannot be employed.  Instead, תוי"ט explains that our case is one where there is no intent to plant a mixture, and as such there is no איסור דאורייתא no matter what the ratio is, and no ביטול at all is required.  However the חבמים were מתקן that one could not plant a mixture of 1/24 due to מראית עין.  At smaller fractions there is no מראית עין, and so by adding or subtracting to the mix to get below that threshold one is not intentionally being מבטל any forbidden substance, rather the problem of מראית עין is being removed.  According to both the ר"ב and תוי"ט, even if the mixture of our משנה is planted without the reduction to below 1/24, it is only an איסור דרבנן.  However the רמב"ם indicates inהלכות כלאים, פ"ב  ה"א that if a mixture of 1/24 is planted, that is an איסור דאורייתא.  One possible explanation is that the רמב"ם held that כלאי זרעים is actually an איסור of מראית עין דאורייתא, that is to say, the prohibition of the תורה is against noticeably planting a mixture of two or more varieties.  According to this פשט, when the mixture contains 1/24 or more of a foreign species, than it is apparent that there are two or varieties and it is אסור ; however when that fraction is less than 1/24, there is no such appearance and the איסור does not apply.  Thus, as in the solution of the תוי"ט, being ממעט the foreign species is not intentionally diluting a forbidden substance to an acceptable level, but is rather the removal of the איסור altogether. 

רבי יוסי אומר יבור - According to the  רע"ב, R' Yose's reason is that if one were to dilute the mixture to less than 1/24 without removing the foreign species completely, it then creates the impression that one desires the mixture.  (The משנה ראשונה raises the question of whether we can distinguish between dilution by removal of the foreign species according to R' Yose, and  dilution by adding to the larger species.  While the former is certainly forbidden, it is possible that in the latter case, where one does not manipulate the amount of foreign species in the mixture, it would not appear as if one desires it, which R' Yose might permit it.)  However, if the mixture was less than 1/24 to begin with, than even R' Yose would permit it. 

כל שהוא כלאים בסאה מצטרף לרובע - The difference between the ת"ק and the חכמים (who we פסקן like) is best illustrated by a case where a סאה of שעורים has 1/8 of a קב of שיבולת שועל (with is not כלאים when mixed with שעורים) and 1/8 of a קב of כוסמין (which is).  According to the ת"ק, it musty be diluted, while the חכמים hold that, since there is only 1/8 of a קב (or 1/48 of the סאה) of problematic grains, it is permitted to plant the mixture.