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N16 in the Archaic Texts

Salvatore F. Monaco < >
UPE, Monterotondo, Italy

proto-cuneiform, accounting, numeric values, metrology

§1. The sign N16 is scarcely attested in the archaic texts, limited to only the Uruk III/JN period. Until recently, only three attestations were available,[1] all in tablets coming from Uruk and in fragmentary contexts. A few more tablets in which the sign occurs are now available and in much better preserved condition, albeit of uncertain provenance. The scope of the following analysis is to deduce and assess the meaning of this sign.

§2.1. A text that has recently been made available,[2] an almost complete but damaged tablet with an account of barley destined as food (GU7), includes the sign N16 in a partially broken context. The transliteration of the relevant section is provided in the following.[3]

  O0105a ˹6N14˺ 3N1 3N39a ˹1N24 1N28˺ [...]
  O0105b1 ˹6N14˺ 1N24 1N28 ˹ŠU˺ UR5a
  O0105b2 ˹3N1˺ 1N16 TARa

§2.2. Case O0105a registers the total of the quantity of barley listed in case O0105b1, qualified as ŠU UR5a, and the quantity reported in case O0105b2, qualified as “tribute” (TARa). Such “tribute” is usually equivalent to 10% of the value of the relevant transaction (case O0105b1). In terms of N1 = “barig,”[4] we have the following equivalence:

39.75 (total)   = 36.15 (˹ŠU˺ UR5a) + 3 +1N16 (TARa)

which, by calculation, would provide for 1N16 the value 0.6 (= 39.75 - (36.15 + 3)). Since such a quantity is always written 3N39a, as in case O0105a, we have to assume a scribal error in case O0105b2, which should be corrected to:

˹3N1˺ <3N39a> 1N16 TARa,

i.e., in terms of barig, equivalent to 3.6+1N16.

§2.3. Considering that 10% of the quantity in case O0105b1 is

  1/10 × (˹6N14˺ 1N24 1N28)
    = 1/10 × 36.15
    = 3.615 (barig),

it would follow that

  1N16 = 0.015 (barig)

§2.4. As a consequence, the total reported in case O0105a should be restored as

˹6N14˺ 3N1 3N39a ˹1N24 1N28˺ [1N16].

Such calculations will be reviewed below by taking into account the correct value of N16, as resulting from the following textual analysis.

§3.1. CUNES 50-06-203,[5] a well preserved tablet with an account of beer for five months, registers the results of calculations similar to those recorded in the tablet MS 4499. The transliteration of the obverse (the reverse is uninscribed) reads as follows:

 O01011N28 ŠEa U4.1N57 KAŠ
 O0102a1N1 3N39a 1N29a 1N16 U4x1N1 KAŠ
 O0102b11N1 2N39a 1N24 U4x1N1
 O0102b21N24 1N29a 1N16 TARa
 O01031N14 2N1 1N39a 1N24 U4x5N1 KAŠ
 O0104 ABa KAŠ

§3.2. The quantity recorded in case O0101 is a daily ration of beer equivalent to 1/20 (barig) of barley, which is calculated in case O0102b1 over a period of one month (U4x1N1)[6]:

 1N1 2N39a 1N24= 30 (days) × 1N28
  = 30 × 0.05 (barig)
  = 1.5 (barig)

§3.3. Case O0102b2 records the “tribute” (TARa), equivalent to 10% of the quantity registered in the preceding case O0102b1:

 1/10 × (1N1 2N39a 1N24)
  = 1/10 × 1.5
  = 0.15 (barig)
  = 1N24 1N29a 1N16
  = 0.1 + 0.04 + 0.01
  = 1/10 + 1/25 + 1/100

§3.4. It follows that 1N16 has the value 1/100 “barig.” Consequently, the quantity reported in case O0102a, being the sum of the quantities in cases O0102b1 and O0102b2, results, in terms of barig, in

1N1 3N39a 1N29a 1N16 = 1.65 (barig)

§3.5. Obviously, such a numerical value for the sign 1N16 is much more suitable than the value (0.015) calculated in the previous paragraph, and consequently it shall be assumed that in tablet MS 4499 the value of the “tribute” was rounded off to 3.61 (barig). It follows that the total quantity reported in case O0105a should read

 ˹6N14˺ 3N1 3N39a ˹1N24 1N28˺ [1N16]
  = 36 + 3 + 0.6 + 0.1 + 0.04 + [0.01]
  = 39.75 (barig)

§4.1. The sign N16 occurs in two other archaic tablets of the Cornell University Collection, one of which (CUNES 50-06-217) brings additional evidence for the value of N16 (1/100) obtained above. The other tablet, CUNES 51-10-007,[7] an account of grain groats, registers in case O0102 an amount of groats (1N1 1N24 ˹1N16? HIgunûa˺ ERIN E2a UR2), with the possible occurrence of the sign N16,[8] the value of which, however, cannot be determined from the context.

§4.2. CUNES 50-06-217,[9] a damaged tablet with a mixed account of cereal producs (bread and beer), records a quantity (of bread?), measured in the numerical notation N51, together with the corresponding amount of grain groats. The relevant section reads as follows:

  R0302a 2N51 [...] 1N16
  R0302b ˹2N1 2N39a˺ HIgunûa,

where 1N16 in case R0302a is to be regarded as the reference value for the accounted product.[10] The following equivalences confirm the value 1/100 for the sign 1N16, which represents the equivalent amount of grain groats for a single unit of a small cereal product, probably bread.[11] Thus

  (R0302a) 2N51 [...] 1N16
    = 240 [breads ?] × 1/100 (barig each)

which, in terms of barig, gives

  (R0302b) ˹2N1 2N39a˺ HIgunûa
    = 2.4 (barig of) grain groats

§5. In conclusion, there is sufficient textual evidence available to demonstrate the numerical value of the sign N16, representing the smallest fraction (1/100) of the unity of capacity barig currently known. With such considerations in mind, it is surely of interest to analyze in greater detail the text W 21208,8+. The tablet is a lexical list dealing with cereal products that registers in sequence several kinds of bread, following apparently two criteria. These are typology and size of the products. In the first column, only partially preserved, there are at least three numerical notations, which could denote the size of some standard type of bread, probably by measuring the relevant quantity of cereals needed for their production. It is noteworthy that 1N16 is followed by 1N17, for which a value of 1/200 (barig), corresponding to 1/8 of a liter, seems logically the most appropriate. Since there are presently no other occurrences of the sign N17 in the known archaic tablets, however, the proposed value must be considered hypothetical for the time being, awaiting future textual evidence for its confirmation.

Version: 3 December 2005