Why is a Cracked Shofar Disqualified?
The mishna (Rosh Hashana 27a) mentions several disqualifications regarding the structure of the shofar. Several of these rules seem self-evident. For example, the mishna disqualifies a shofar made from broken pieces pasted together. As the Rishonim explain, the Torah wants us to blow an integrated shofar, not an item composed of multiple shofarot (Rosh Hashana 26a: "God said 'shofar' and not two or three shofarot"). Another issue relates to a shofar with a hole in it which was repaired. In this instance, a foreign element contributes to the sound and the shofar should logically be disqualified. Indeed, there is some debate as to whether any filler would invalidate the shofar, or only a foreign substance. However, the basic conceptual model is understandable. The mishna, however, lists an additional disqualification whose basis seems unclear: splits in the body of the shofar. Why should these splits invalidate the shofar?
The first type of split mentioned in the mishna (27a) relates to a shofar split along its entire length. Rashi claims that this shofar would be invalid because, like one composed of multiple shofar fragments, it, too, is considered "two or three shofarot." Tosafot infer from Rashi that the horizontal split caused the two pieces to separate physically. They then ask the inevitable question: if so, then this case and the one of someone who pieced together shofar fragments are redundant. In each instance, a person attaches shofar parts and in each case the disqualification is based upon the rule that the Torah requested one integrated shofar and not a hybrid.
One possible way to explain Rashi is to dispute Tosafot's inference. Maybe Rashi claimed that the mishna referred to a horizontal split which did not cause actual separation into two halves. Hence, the mishna provides a new case here: even if the shofar is still physically joined, it may be considered "logically split" and would be invalid because of the multiple shofar rule. Hence, the mishna stated both cases - where multiple shofars are a product of actual separate fragments and one in which the fragments are still joined at the hip.
Tosafot themselves, as well as most Chachmei Sefarad (Ramban, Rashba, and Ritva), offered a different reading of this halakha of "nisdak le-orko" (a horizontal split). Assuming the shofar is split along its entire length, then even if the split has not caused separation into two halves, the basic structure of the shofar has been dismantled. Any further attempt at reconstruction would be an attempt to build a shofar with material which is not identified as a shofar. Many Rishonim (Tosafot, for example) appear to apply this rule only when the split has appeared along the entire rim. Others (such as the Ritva) apply it even when only most of the shofar is cracked. In either instance, the same rule is applied: a shofar with a split has lost the basic identity of shofar.
A third position appears in Rabbenu Yonatan of Lunel (cited by the Rosh and Ran). Even a small split on the surface of the shofar is sufficient to disqualify it. This marks the most extreme position and also the most stringent. Interestingly enough, the Shulchan Arukh cites this position (and afterwards cites the position of Tosafot). Rabbenu Yonatan explains that, given enough time, any split along the shofar is likely to expand to its entirety. The blowing action and general handling of the shofar will ensure such a split.
There are two ways to understand this position. The Ritva reasons that oftentimes the gemara recognizes an inevitable occurrence as having already occurred. This is known as the principle of "kol ha-omed." For example, anything destined to be burned is considered already burnt (and cannot become impure – see Menachot 102b). Similarly, according to Rabbenu Yonatan (the Ritva suggests), a miniature split is likely to grow into a larger one. The Mishna Berura (586:39) provides this explanation as well. This application, however, is questionable, since we generally do not rule based on this "kol ha-omed" principle.
A different explanation of Rabbenu Yonatan might be that any split, however small, would constitute a disqualification. What the basis for such a disqualification would be is a different story. Rashi (dealing with an almost total and possibly physical split) invoked the multiple shofar issue. Tosafot, dealing with a split along the shofar's entirety, viewed it as an item no longer defined as a shofar. What would be the nature of the disqualification according to Rabbenu Yonatan?
A possible explanation would center upon the notion of "mum," an idea familiar to us from the realm of living beings. For example, an animal with a physical imperfection possesses a "mum" and cannot be sacrificed, even though it is still defined as an animal. It is merely a deformed animal. Along similar lines, a kohen who possesses a deformity cannot serve in the Temple.
Generally, this concept applies only to living things. However, when the gemara in Sukka disqualifies a lulav whose leaves grow on only one side of the spine, many explain that such an item is invalid because it possesses a mum. Here, according to some, Halakha applies the mum concept to inanimate objects. Alternatively, the lulav can be viewed as a living organism (as evidenced by the fact that a dry lulav is invalid).
Could the same principle be applied to a shofar? Would a shofar with a small split be disqualified because it possesses a mum, even though its basic structure is intact?
The Ran cites the Ra'avad, who agrees in principle with Rabbenu Yonatan that even a minor split disqualifies the shofar. However, he suggests a way of repairing the shofar: by tying the split very tightly with string, a person can ensure that the split will not widen. Upon first glance, this position evokes the Ritva's. We consider the inevitable split as having already occurred, but by tying the shofar, such an assumption (and the consequent disqualification) would not apply. However, even if we viewed the halakha as based upon mum, we might be able to adopt the Ra'avad's idea.
The mum of a shofar is not measured in purely structural terms. A split is considered a mum because it will ultimately prevent the shofar from functioning properly (due to its eventual widening along its entire length). The shofar has already contracted an ailment which will ultimately render it useless for its task. Hence, the mum exists in the present, even without applying the questionable principle of "kol ha-omed." Although the split hasn't yet occurred, the prospect of its occurrence constitutes a present mum. If, by tying the shofar, a person can prevent the spread and, in effect, correct the malformation, then no mum exists.
The Kolbo, however, adds an idea which almost surely forces us to think in terms of the "mum" approach to Rabbenu Yonatan's position. He claims that if, after tying the shofar, there does not remain enough surface (i.e. a tefach, or handsbreadth) which is not split, then the shofar is disqualified. When the Rema cites this halakha, the Magen Avraham questions the need for this measurement, and most Acharonim reject the Kolbo's ruling (see Mishna Berura 586:41). According to the Ritva's explanation, the entire disqualification was based on the notion that the shofar would ultimately fall apart. Preventing this scenario would be sufficient, and the entire shofar should be considered valid even without a tefach of unsplit shofar. What motivates the Kolbo's ruling?
It is possible that the Kolbo felt that a split is considered a mum – an inherent deformity of the shofar. Tying it is insufficient because the inherent mum still exists and hasn't been physically rectified. Hence, there must remain a complete measurement of shofar independent of the split, for the area with the split does not count.