A Shofar with a Hole
The mishna in Rosh Hashana which lists the various physical deformities disqualifying a shofar includes the problem of a shofar which has a hole in the side. The mishna maintains that if the sound is affected by the hole, then the shofar is invalid, while if the sound is unaffected, the shofar remains kosher. The Rishonim differ as to the meaning of this condition, the relationship between this condition and an independent one stipulated by the gemara, as well as the overall nature of the halakha.
Though the mishna focuses on the hole's impact upon the shofar's sound, the gemara raises a completely different concern: what was used to repair the shofar? According to the Chakhamim, the shofar is rendered invalid even if it is repaired with shofar material. Rabbi Natan disagrees, allowing a shofar with a hole to be repaired with shofar material, but not with foreign substances.
The Rishonim differ as to the relationship between the impact factor (discussed by the mishna) and the dispute between Rabbi Natan and the Chakhamim regarding the materials used to patch the shofar.
The Ra'avad (in his derasha to Rosh Hashana, in the sefer Katuv Sham, as well as in his hassagot to the Rambam) claims that the condition of the mishna refers to the state before the hole was filled. Everyone would agree that since the hole has affected the sound, the shofar is rendered invalid by any subsequent repair. By fusing an additional element which contributes to the sound, the shofar has become invalid. The dispute between Rabbi Natan and the Chakhamim surrounds the case of a hole that did not affect the sound. Rabbi Natan claims that the repair, in and of itself, should not disqualify, provided that shofar material is used for the repair. After all, the new addition did not contribute significantly to the sound, as the sound was not previously affected by the hole. If, however, foreign substances were used to plug the hole, the shofar would be invalid. The Chakhamim would then adopt an even more extreme position: any repair of ANY hole, regardless of the filler material and regardless of the significance of the hole, invalidates the shofar. Evidently, a shofar must be purely natural, not having undergone any human repair or manufacture. If the shofar develops a hole and is not repaired, even the Chakhamim would agree that it is still valid (the Yerushalmi states this explicitly). Repair, however, even of a minor hole, would disqualify the shofar.
Most Rishonim reject the Ra'avad's position, since it forces the Chakhamim into a radical position. By assuming that Rabbi Natan and the Chakhamim argue in a case where the sound was not impeded, the Chakhamim are interpreted as invalidating any and every repair. Instead, most Rishonim reinterpret the mishna's clause about the hole's impact upon the shofar. The mishna invalidates a hole which still impacts the shofar's sound AFTER the repair. If it does not affect the sound after the repair, then the addition becomes fully integrated into the shofar and is less problematic.
Even within this camp of Rishonim, there exist two different strains. The Ramban claims that Rabbi Natan and the Chakhamim were disputing a situation in which the final repair does not affect the sound. In this instance, if shofar fillers are used, the shofar is valid, since it doesn't contain any extra or foreign element. If the repair is not smooth, as evidenced by the sound which continues to be affected, the plug would not be seen as integral and would entail an ADDITION, rather than a plug. The shofar would thus be rendered invalid because it contains an adulteration. The same rule would apply to a shofar which was successfully and smoothly repaired with a foreign alloy, for this shofar, as well, contains artificial elements. Only by fully repairing a shofar with indigenous materials can the validity be maintained. By contrast, the Chakhamim invalidate any and every plug, regardless of how integral and independent of the filler material, so long as the original hole impeded the sound. Though Rabbi Natan might be correct that the filler is now integral to the shofar, the sound is still a product of two different sources. What is the real problem with a shofar possessing additions: the shofar being a hybrid, or the sound being produced by multiple sources? It is possible that this is the subject of the disagreement between Rabbi Natan and the Chakhamim.
However, according to the Ramban, even the Chakhamim would agree that a hole which did not affect the sound is not considered a defect (the repair of which would disqualify the shofar). By establishing the dispute between Rabbi Natan and Chakhamim in a case in which a significant, sound-altering hole was plugged, the Ramban allows the Chakhamim to validate the repair of non-altering holes and thus avoid the extremism of the Ra'avad's position.
The Rosh, in basic agreement with the Ramban about the clause of the mishna, argues with his perspective of the disagreement between Rabbi Natan and the Chakhamim. Whereas according to the Ramban they dispute a situation where the repair was "smooth" and no longer affected the sound, according to the Rosh they argue about an instance where the repair was not flush and continued to affect the sound. Even in this situation, Rabbi Natan allowed homogeneous repairs. The Rosh drives the dispute in a manner which results in a tremendous leniency, allowing the use of a repaired shofar even if the filler was not absolutely level. Conversely, if the repair were level, Rabbi Natan would validate even a repair with a foreign substance (since his conditioning of the repair upon indigenous substances referred exclusively to the case of a non-flush repair). Hence, Rabbi Natan would allow either scenario flush repairs with foreign substances or jagged repairs with natural ones.
The Rosh does not fully explain his view of Rabbi Natan, but the following logic might be suggested. The Ramban envisioned an invalidation based on adding ANYTHING non-integral to the body of the shofar. Hence, for the filler to be valid, it would have to be shofar material smoothly inserted into the original. In the absence of these two conditions, the filler would be seen as separate and would disqualify the shofar. The Rosh read Rabbi Natan slightly differently: two instruments cannot produce one sound. Non-integral additions will not disqualify a shofar unless they constitute a second instrument contributing to the sound of the shofar. We define the filler as a separate instrument only if it is both a different substance AS WELL as something which is not smoothly inserted into the shofar. Otherwise, we consider the insert merely an addition to the shofar, rather than a separate instrument, and it therefore does not disqualify the shofar.
Interestingly, this reading is a more literal interpretation of the gemara's derivation. The gemara does not provide any logic for this disqualification of a shofar with a hole. Ultimately, both the Ramban and the Rosh import the logic from the gemara (26a) which cites the position of the Chakhamim invalidating the shofar of a cow because the horn is structured as overlapping layers of shofar. This horn is invalid because "shofar echad amar rachmana ve-lo bet ve-gimmel shofarot" the Torah ordered the use of one shofar and not two or three. The Rosh inferred from this gemara a problem of two shofarot or two instruments producing one sound. Hence, if the filler (at least according to Rabbi Natan) is smooth even if it is non-shofar material it is not considered two shofarot. By contrast, the Ramban expanded this gemara to include any addition to shofar even if the addition itself is not considered an instrument. Hence, he disqualified any addition which doesn't become integral (non-smooth OR foreign substances).