Mishnah Arakhin 2:5-6

Sugya Map

• Issue: The Mishnah in Arakhin enumerates various halachot that operate within specific numerical ranges, setting minimum and maximum limits. This phenomenon, known as min u'max (minimum and maximum), appears across diverse areas of Halakha, from financial obligations to ritual purity and Temple service.
• Nafka Mina(s):
  • Understanding the underlying principle behind these numerical boundaries – is it a fixed decree, a reflection of practical necessity, or indicative of a deeper theological concept?
  • Applying this principle to potentially analogous situations not explicitly covered by the Mishnah.
  • The precise definition of what constitutes a "fulfillment" or "non-fulfillment" of an obligation when the amount falls within the specified range.
• Primary Sources:
  • Mishnah Arakhin 2:5-6 (the immediate text).
  • Tanakh (e.g., Bamidbar 10:1-10 for trumpets, Shemot 12 for Pesach).
  • Talmud Bavli (relevant discussions in Pesachim, Menachot, Shevuot, etc.).

Text Snapshot

Mishnah Arakhin 2:5:

"One cannot be charged for a valuation less than a sela, nor can one be charged more than fifty sela. How so? If one gave one sela and became wealthy, he is not required to give anything more, as he has fulfilled his obligation. If he gave less than a sela and became wealthy, he is required to give fifty sela, as he has not fulfilled his obligation."

• Dikduk/Leshon Nuance: The phrase "אין מחייבין אותו" (Ein mechayvin oto - "one is not charged") is passive, suggesting an external imposition of a rule. The repetition of the min u'max structure ("אין פוחתין... ואין מוסיפין..."), applied to diverse laws, highlights a common motif. The phrasing "כיון שנתחייב" (Kiyvon shenitchayav - "since he became obligated") implies a fixed, perhaps initial, commitment.

Mishnah Arakhin 2:6:

"No fewer than twenty-one trumpet blasts are sounded daily in the Temple... And no more than forty-eight are ever sounded on a single day... When accompanying their song with instruments, the Levites do not use fewer than two lyres and do not use more than six. When flutes are played, they do not use fewer than two flutes and do not use more than twelve."

• Dikduk/Leshon Nuance: The consistent use of "אין פוחתין" (Ein p'chatin - "there is no decrease") and "אין מוסיפין" (Ein musafin - "there is no addition") or "אין... אלא" (Ein... ela - "not... but") establishes a clear boundary. The phrase "עד לעולם" (Ad le'olam - "up to infinity") in some instances, contrasted with specific numbers elsewhere, raises questions about the nature of these limits.

Readings

Rambam on Mishnah Arakhin 2:5:1 (Lambs)

The Rambam, in his commentary on the Mishnah concerning the minimum of six lambs inspected for blemishes in the Chamber of the Lambs, connects this requirement to the concept of biduk (inspection) of lambs for the tamid (daily offering). He explains: "This Mishnah follows the opinion of Ben Bag Bag, who holds that the tamid requires preparation and inspection for blemishes four days prior to its slaughter."¹ He derives this from the verse "You shall safeguard to offer Me My offering in its appointed time" (Bamidbar 28:2), linking the tamid to the Pesach offering. The Pesach of Egypt, as stated in Shemot 12:6, was taken on the tenth of Nisan and slaughtered on the fourteenth. This four-day interval for inspection is thus applied to the tamid. The Rambam clarifies that the six lambs are not necessarily all that are needed for Shabbat and two festival days, as more would be required. Rather, it signifies that at least six lambs were already prepared, which could cover Shabbat and two festival days, leaving four more days of the week. The number six is thus a mnemonic or illustrative point.

• ¹ Rambam, Peirush HaMishnayot, Arakhin 2:5.

Tosafot Yom Tov on Mishnah Arakhin 2:5:1 (Lambs)

Tosafot Yom Tov (TYT) grapples with the Rambam's source for the four-day inspection period. TYT notes: "The Rav (Rambam) explains that this Tanna (Ben Bag Bag) holds that the lambs for the tamid require inspection for blemishes four days before their slaughter, similar to the Pesach of Egypt."² TYT then raises a significant question: "It is puzzling, for this verse is in Parshat Behaalotkha regarding the Pesach, and in Mishnah 5, Chapter 9 of Pesachim, we learn: 'What is the difference between the Pesach of Egypt and the Pesach of generations? The Pesach of Egypt was taken from the tenth [of Nisan]...'"³ TYT questions how the Pesach of Egypt can be equated with the Pesach of generations, and how the Pesach of generations itself is derived. TYT points to the Gemara in Pesachim (96a) where Ben Bag Bag's opinion is indeed found. Rashi there explains that the tamid is derived from Pesach, but TYT finds this difficult, as the Pesach of Egypt isn't necessarily included in the Pesach of generations. TYT suggests that the derivation might be from the verse "And you shall serve this service in this month" (Shemot 13:10), implying all services should be treated similarly. However, TYT concludes that the Mishnah here and in Pesachim explicitly links the tamid to the Pesach of Egypt via Ben Bag Bag. The Rambam's commentary, TYT observes, implies he follows this explicit derivation in the Gemara.

• ² Tosafot Yom Tov, Arakhin 2:5.
• ³ Ibid.
• ⁴ Pesachim 96a.

Tosafot Yom Tov on Mishnah Arakhin 2:5:2 (Sacred Festivals)

Regarding the minimum of six lambs being sufficient for Shabbat and two festival days of Rosh HaShanah, TYT offers a practical insight: "If Shabbat and two Yom Tov days of Rosh HaShanah coincide, one would need to prepare the lambs for the third day in advance."⁵ This suggests that the min of six is calculated based on the potential for consecutive festival days, necessitating preparedness beyond the immediate need.

• ⁵ Tosafot Yom Tov, Arakhin 2:5.

Tosafot Yom Tov on Mishnah Arakhin 2:5:3 (Trumpets)

Concerning the minimum of two trumpets, TYT notes: "The reason is not explicitly explained. Perhaps it is derived from the verse 'Make for yourself two trumpets' (Bamidbar 10:2), implying two are the basic unit."⁶ This suggests a possible biblical basis for the minimum, mirroring the instruments Moses was commanded to make.

• ⁶ Tosafot Yom Tov, Arakhin 2:5.

Tosafot Yom Tov on Mishnah Arakhin 2:5:4 (Trumpets)

On the statement that trumpets can be added "up to infinity," TYT cites the Gemara's explanation: "The Gemara explains 'up to 120,' as it is stated 'and with them the priests for 120 horn players' (Bamidbar 10:4)."⁷ This indicates that while the principle might be one of expansion, there's a specific, albeit large, limit derived from a biblical passage. TYT also considers the practical aspect: "Otherwise, if they added more, it would cause confusion of sounds." The Rambam, in a later Mishnah, also limits the trumpets to 120, while other instruments can be added indefinitely.

• ⁷ Tosafot Yom Tov, Arakhin 2:5.
• ⁸ Ibid.

Tosafot Yom Tov on Mishnah Arakhin 2:5:5 (Lyres)

Regarding the minimum of nine harps, TYT states: "The reason is not explicitly explained. Rashi provides no further explanation."⁹ This leaves the basis for this specific minimum open to interpretation, possibly a fixed decree or tradition.

• ⁹ Tosafot Yom Tov, Arakhin 2:5.

Tosafot Yom Tov on Mishnah Arakhin 2:5:6 (Cymbal)

On the cymbal being played alone, TYT refers to the Rav's commentary and Rashi: "The Rav explains in Chapter 7 of Tmidin, Mishnah 3, and in Chapter 1 of Shekalim... Rashi also writes this. The cymbal is described as two pieces of copper that are struck together."¹⁰ The description of the cymbal as a singular instrument, even when composed of two parts, explains why no additions are made to it.

• ¹⁰ Tosafot Yom Tov, Arakhin 2:5.

Rashash on Mishnah Arakhin 2:5:1 (Lambs)

Rashash questions TYT's observation about the Pesach of Egypt not being included in the Pesach of generations. He argues: "How could one think so? It is mentioned there [in Shemot] the sprinkling of blood on the lintel... in haste... and their leavening all day. All these were practiced for the Pesach of Egypt!"¹¹ Rashash implies that the uniqueness of the Egyptian Pesach was not in its observance of these details, but in its specific historical context and immediate departure from Egypt. This challenges TYT's premise about the distinctiveness of the Pesach of Egypt from general Pesach observances, lending support to the idea that lessons learned from the Egyptian Pesach could apply more broadly.

• ¹¹ Rashash, Arakhin 2:5.

Friction

The most salient friction point within this sugya lies in the principle underlying the min u'max regulations. The Mishnah presents a series of seemingly disparate laws – financial valuations, ritual purity periods, Temple service instrumentations, and even the timing of circumcisions – all bound by numerical constraints. The immediate question is: what unifies these boundaries?

One might initially assume these are purely practical. For instance, a sela is the smallest practical unit for a significant financial transaction, and fifty sela might represent a substantial, yet manageable, sum for a vow. Similarly, the durations for purity or quarantine likely reflect observable biological realities or practical waiting periods. The number of instruments or blasts could be tied to achieving a certain acoustic effect or fulfilling a prescribed ritual.

However, the explicitness of the numbers, and their often seemingly arbitrary nature (why precisely six lambs, or nine harps?), suggests something deeper. The Rambam's explanation for the six lambs, linking it to Ben Bag Bag's derivation from Pesach Mitzrayim, points towards a tradition-based, possibly allegorical, rationale. The Tosafot Yom Tov’s struggle with this derivation underscores the challenge of pinpointing a single, consistent source for all these min u'max rules. Are they divinely ordained limits? Are they reflections of an ideal, divinely sanctioned proportion or measure?

A significant tension arises when considering the intent of the law versus the literal fulfillment. In the case of the arakhin, if one vows a large sum and has only a small amount, becoming wealthy later requires fulfilling the entire vow, up to fifty sela. If they gave less than a sela initially, they must pay the full fifty sela upon wealth, indicating the initial payment was insufficient and the obligation remained open. This suggests the min is not just a floor for any payment, but a threshold for initial fulfillment. If the initial fulfillment is sub-par, the max becomes the new target. This dynamic implies the limits are not merely descriptive, but prescriptive, shaping the very nature of obligation and fulfillment.

The friction is thus between a potential hermeneutic of practicality and a hermeneutic of symbolic or divinely mandated proportion. Are these numbers echoes of a celestial blueprint, or the pragmatic concessions of a humanly-administered legal system? The difficulty lies in reconciling the specific biblical derivations (like the two trumpets from Bamidbar) with those that seem to lack such clear textual anchors.

A potential terutz (resolution) could be that the min u'max represents the "ideal space" for a given mitzvah or halachic concept. Below the minimum, the act is insufficient; above the maximum, it is excessive or potentially disruptive. The specific number is not arbitrary but represents the point where the mitzvah is perfectly actualized, or where its integrity is compromised. The derivation from Pesach Mitzrayim for the lambs, for instance, could be teaching that the tamid requires the same degree of careful preparation and foresight as the foundational act of the Exodus itself. The trumpets, the instruments, the blasts – all contribute to the sanctity and grandeur of the Temple service, and these numbers ensure that grandeur is neither diminished nor overwhelming. The system, therefore, reflects a divinely-informed aesthetic and functional balance.

Intertext

Tanakh: Bamidbar 10:1-10 (Trumpets)

The Mishnah's detailed discussion of trumpet blasts in the Temple finds its direct antecedent in the Torah's instructions for the use of trumpets (Hebrew: chatzotzrot). Bamidbar 10:1-10 commands Moses to make two trumpets, not for one, but for "the calling of the assembly, and for the journeying of the camps."¹¹ The Torah specifies different signals for different occasions: one blast to gather the princes, two to assemble the entire community, and a continuous blowing to signal departure. It also mentions that on days of gladness, during your festivals, and at the beginnings of your months, you shall sound the trumpets over your burnt offerings and over your peace offerings. This biblical passage establishes the fundamental role of trumpets in signaling, assembly, and enhancing divine service, providing the foundational context for the Mishnah's elaboration on their specific usage in the Temple. The Mishnah's min u'max for trumpet blasts directly builds upon this biblical framework, quantifying the frequency and duration of these sacred sounds.

• ¹¹ Bamidbar 10:2.

Shulchan Aruch: Orach Chayim 551:1 (Circumcision)

The Mishnah's mention of circumcision not being performed before the eighth day and not after the twelfth (Arakhin 2:6) resonates with the established Halakha regarding brit milah. The Shulchan Aruch codifies this principle: "A male infant is circumcised on the eighth day, as it is stated 'And he that is eight days old shall be circumcised' (Bereishit 17:12)."¹² The text further elaborates on complexities similar to those hinted at in the Mishnah, such as when the eighth day falls on Shabbat or a festival, and how to determine the precise day in cases of doubt (e.g., born at twilight). While the Mishnah offers a max of twelve days, the primary obligation is the eighth day. The inclusion of the twelfth day as a limit suggests a pragmatic allowance for circumstances that prevent timely observance, but it underscores the normative expectation of the eighth day. This intertextual connection highlights how min u'max principles can regulate fundamental mitzvot, reflecting a balance between ideal observance and practical accommodation.

• ¹² Shulchan Aruch, Orach Chayim 551:1.

Psak/Practice

The min u'max structure, while prominent in the Mishnah, doesn't always translate into direct, prescriptive psak in contemporary Halakha, especially in areas not directly tied to Temple service. However, the underlying principle of establishing boundaries for observance, efficacy, and appropriateness remains relevant.

• Arakhin: The laws of arakhin themselves are largely dormant, as the Temple is not standing. The specific numerical limits for valuations are thus not practically applied.
• Circumcision: The psak regarding circumcision is firmly established on the eighth day, with practical considerations for Shabbat and other situations. The Mishnah's mention of the twelfth day serves as a background reminder of potential delays but does not alter the primary halacha of the eighth day.
• Temple Service: The detailed regulations concerning trumpet blasts, instruments, and Levite numbers are purely historical and theological, relevant for understanding the Temple's operations and for prayer and study.
• Meta-Heuristic: The most significant takeaway for psak practice is the heuristic that Halakha often operates within defined parameters. These limits can reflect:
  • Biblical Mandate: Explicit textual sources.
  • Practical Necessity: What is observable, achievable, or prevents chaos.
  • Ideal Proportionality: The "right" amount or duration for a sacred act.

When encountering a novel situation, one might ask: "What is the minimum required for this act to be considered valid? What is the maximum before it becomes excessive or invalid?" This analytical framework, derived from the min u'max motif, helps in dissecting and understanding halachic requirements.

Takeaway

The Mishnah in Arakhin demonstrates that Halakha frequently operates within defined numerical boundaries, reflecting a balance between minimal observance and maximal appropriateness. Understanding the source and rationale behind these min u'max regulations – whether practical, textual, or symbolic – is crucial for grasping the meticulous structure of Jewish law.