Return to Numbers & Metrology in the 2nd millennium

Middle Babylonian Nuzi

Sources

The Middle Babylonian Nuzi corpus is rich of approximately 5000 tablets mostly found during the American excavations (1925-1933) conducted in different places on the tell (Yorghan-Tepe nowadays). Cdli MB Nuzi tablets collection

The written data cover a time span of around five generations (1450-1350 B.C.E.) and stop with the site destruction due to an Assyrian campaign during the first part of king Aššur-uballiṭ I’s reign. Within this period, Nuzi was one of the provincial towns of the kingdom of Arraphe, whose eponymous capital lies beneath modern Kirkuk, about 15 km from the tell. The designation “Nuzi  tablets” also includes some hundreds of tablets found at Kirkuk and Tell al-Fahhar.

Nuzi tablets mainly consist of administrative texts accounting for economic operations, records of business activities and law documents which are connected with various agents such as the palace, very large households and smaller family units.

Scope

The MB Nuzi metrological and numerical system is broadly equivalent to the contemporary Mesopotamian systems. However, there are some characteristic features which should be highlighted. Firstly, a special system of weight is documented for wool. Moreover, most of the Arraphean populations were probably Hurrian native speakers, as shown by the textual documentation. In the linguistic sphere, Hurrian influence is discernable on Akkadian, the common language of the texts, at various levels (syntactical, grammatical and lexical levels). So it is hardly surprising that Hurrian terminology is also commonly used for measures of length and numbers as well as for the wool measurement.

Bibliography

  • Abrahami, P. (2014) Wool in the Nuzi Texts. In C. Breniquet and C. Michel, (eds), Wool Economy in the Ancient Near East and the Aegean: from the Beginnings of Sheep Husbandry to Institutional Textile Industry. Ancient Textiles Series 17. Oxford, p. 305.
  • Andrews, S. J. (1996) Duck Tales at Nuzi: A Note on the Trused-Duck Weights Excavated at Yorgan Tepa. In D. I. Owen and G. Wilhelm (eds.), Richard F. S. Starr Memorial Volume, SCCNH 8. Bethesda, p. 241-243.
  • Cross, D. (1937) Movable Property in the Nuzi Documents. AOS 10. New Haven, Connecticut, p. 9-14.
  • Friberg, J. (1987-1990) Mathematik. In Reallexikon der Assyriologie vol. 7, p. 537.
  • Gordon, C. H. (1934) Numerals in the Nuzi Tablets. RA 31, p. 53-60.
  • Grosz, K. (1988) The Archive of the Wullu Familly. CNIP 5, Copenhagen, p. 113, 118 n. 5.
  • Hallock, T. R. (1957) The Nuzi Measure of Capacity. JNES 16/3, p. 204-206.
  • Lion, B. and Sauvage, M (2005). Les Textes de Nuzi Relatifs aux Briques. In D. I. Owen and G. Wilhelm (eds.), General Studies and Excavations at Nuzi 11/1, SCCNH 15. Bethesda, p. 82 n. 71.
  • Maidman, M. P. (1994) Two Hundred Nuzi Texts from the Oriental Institute of the University of Chicago, Part I. SCCNH 6, Bethesda.
  • Mayer, W. (1978) Nuzi-Studien I. Die Archive des Palastes und die Prosopographie der Berufe. AOAT 205/1. Neukirchen-Vluyn, p. 219.
  • Pfeiffer, R. H. and Speiser E. A. (1936) One Hundred New selected Nuzi Texts. AASOR 16. New Haven, Connecticut, p. 131-135.
  • Powell, A. (1987-1990) Masse und Gewichte. In Reallexikon der Assyriologie vol. 7, p. 462, 472-473; 477 (length measures); 485-488 (surface measures); 500-501 (capacity measures); 514-515 (weight measures).
  • Richter, T. (2012) Bibliographisches Glossar des Hurritischen. Wiesbaden.
  • Starr, R. F. S.  (1937) Nuzi. Vol. 2. Plates and Plans, Cambridge, pl. 122-124.
  • Starr, R. F. S.  (1939) Nuzi. Vol. 1. Texts, Cambridge, p. 464-467.
  • Wilhelm, G. (1980) Das Archiv des Šilwa-Teššup Heft 2. Rationen Listen I. Wiesbaden, p. 27.
  • Wilhelm, G. (1984) Hurritisch nari(ya), “Fünf”. SMEA 24, p. 223-224.
  • Wilhelm, G. (1996) Nuzi Notes. 18. A New word in –arbu: kirarbu. In D. I. Owen and G. Wilhelm (eds.), Richard F. S. Starr Memorial Volume, SCCNH 8. Bethesda, p. 347-348.
  • Wilhelm, G. (1988) Zu den Wollemaßen in Nuzi. ZA 78, p. 276–283.
  • Zaccagnini, C. (1976) Tummu and par(as)-ṣehru. Note on Two Measures of Weight at Nuzi. JAOS 96, p. 273.
  • Zaccagnini, C. (1979) Notes on the Nuzi Surface Measures. UF 11, p. 849-856.
  • Zaccagnini, C. (1981) A Note on Nuzi Textiles. In M. A. Morrison and D. I. Owen (eds), Studies on the Civilization and Culture of Nuzi and the Hurrians in Honor of Ernest R. Lacheman on his Seventy-Fifth Birthday April 29, 1981. Winona Lake Indiana, p. 349-360.
  • Zaccagnini, C. (1990) The Nuzi Wool Measures Once Again. Orientalia 59, p. 312-319.
  • Zaccagnini, C. (1999-2001) The Mina of Karkemiš and Other Minas. SAAB 13, p. 39-56.

Metrological system

Units of length
ubānu   finger  
×8? ×9? ×10? ×12?
kiṣir ammāti 1)   joint/detachment of the forearm  
?
ūṭu   fingers, handspan? 25 cm
×1.5?
kimṣu / kinṣu 2)   shin bone 37.5 cm?
×1.33?
ammatu 3) Cubit 50 cm4)
×3
gìr / purīdu foot / leg foot /  leg 1.50 m
Units of surface
mišil hararni 5)   ½ hararnu (hurrian word) 225 m2
× 2
hararnu   (hurrian word) 450 m2
× 2
kumānu   (hurrian word) 900 m2
× 2
giš.apin epinnu awiharu 6)  nuzi_gish.apin.jpg   plough plough hurrian: furrow length? plough? 1800 m2
× 10
anše (imēru)7) nuzi_anshe.jpg ass 1,8 ha
Units of capacity

The four units of the capacity system by ascending order are sila3 (), ban2 (sūtu), pi (pānu) and anše (imēru). They are used for both dry products and liquids. The commodities documented are seeds, cereals, oil, lard and beer. For the last three products, a specific unit, the tallu (DAL), a container of standard capacity is also used. Two values are attested for the tallu: eight sila3 (HSS 13 50 = AdŠ 73; HSS 13 142 = AdŠ 72 see Wilhelm 1980, p. 27) and one ban2 (HSS 15 248; HSS 15 249, see CAD T, p. 102b). The kukkubu, a small container, is also used for oil (HSS 15 291). Its capacity is of 2 sila3 and 4 sila3 in HSS 15 248 and HSS 15 249. The latter text is an account of beer. Straw was counted in šaharru, a type of net. It corresponds to the yearly ideal production of a field of one aweharu (CAD Š/1, p. 81b).

            The value of the ban2 may have varied from place to place: it is suggested by the record of 12 anše of wheat and 45 anše of emmer measured “with the ban2 of the city of Al-ilâni” (HSS 16 119).

sila3  () ca. 0,84 l.
× 8 or × 108)
ban2 (sūtu) 9) ca. 6,7 l. or 8,4 l.
× 6
pi (pānu)10) ca. 40,4 l.
× 10 ban2
anše (imēru)   ca. 60,7 l. or 84 l.
Oil, lard, beer
sila3  ()   ca. 0,84 l.
× 811)
dal (tallu) = 1 ban2 a container ca. 6,7 l. or 8,4 l.
× 10
anše (imēru)   ca. 60,7 l.
Units of weight

The three weight measures12) are by ascending order the shekel (šiqlu, written su and not gin2), the mina (ma.na) and the talent (gun biltu).

su (šiqlu) c. 8.3 g
× 60
ma.na13)   c. 500 g
× 60
gu2.un (biltu) c. 30 kg

Wool is also measured with specific units which by ascending order are šehtunu, kuduktu and nariu (all Hurrian terms). Their value is open to debate. The question is conveniently summarized in Lion and Sauvage 2005, p. 82 n. 71 and Powell 1987-1990, p. 515 where the following relationships are given: 3600 šiqlu = 60 mina = 1 talent = 24 nariu = 40 kuduktu = 80 šehtunu.

However, the value of the kuduktu as equivalent to 80 šiqlu (and not 90 šiqlu), relies among other things, on the sequential arrangement 1:2:4 found in other systems of weight for wool in the Near East and in the Aegean (see Zaccagnini 1990, 313-315 and Zaccagnini 1999-2001, 51-54). Regular delivery of wool for work assignment, given alternatively in both systems of weight, seems to support this view (Abrahami 2014, p. 305).

Units system for wool
šehtunu 14) 40 šiqlu c. 332 g / c.
× 2
kuduktu 15) 80 šiqlu c. 664 g
× 4
nariu 160 šiqlu c. 1.3 kg

Numerical system

To count objects, a mixed decimal and sexagesimal system is used: sexagesimal values for numbers under 100 and decimal values above 100.

60 (šūši), 100, 1000, and 10,000 are expressed phonetically.

 

ilten (1-en nuzi_pi.jpg 1
  ×10
  nuzi_u.jpg   10
  × 6
šūši nuzi_pi.jpg or nuzi-shu.si.jpg   60
  swtich from sexagesimal to decimal
mât nuzi_ma-at.jpg   100
  ×10
līmu nuzi_limmu.jpg   1000
  ×10
nubi (hurrian) nuzi_nubi.jpg   10,000

Hurrian names of numbers are identified in several words and expressions; they are used especially to express the age of animals, which is formed in hurrian by a suffix –arbu.

  hurrian  
2 šin- in šinadumma epēšu: to repeat, to appeal against a verdict, šinahilu: second in command; second quality, šinahiluhli: second in rank?, šinamumma epēšu: to pay twofold, šinamuna: twice, twofold, šinamunu: substitute, šinarbu: 2 years old.
3 kig- in kigarbu: 3 years old, kikamunu: third in line?, kukumnu: 3 years old.
4 tumn- in tum(u)narbu: 4 years old, tumnātui: 4 spoked (wheel).
5 nar- in narijarbu: 5 years old.
6 šez- in šeššātu: 6 spoked (wheel).
7 šind- in šintarbu: 7 years old.
10 eman in emanamumma epēšu: to pay tenfold, emandi: group of 10 men, ematuhlu (= GAL 10), officer commanding 10 men.
Fractions:

Fractions are expressed with their nouns:

Fraction akkadian hurrian
1/2 mišlu16)  
1/3 paras-ṣerhu17) (or pár-tur)  
1/4 rebūtu tummu

P. Abrahami et B. Lion.

1)
ki-iṣ-ra-am-ma-ti: hapax at Nuzi, in HSS 19 188: 8.
2)
kim/nṣu: attested only in Nuzi. Powell, 1987-1990 p. 472: “perhaps ¾ cubit”.
3)
“The cubit of the city gate” is mentionned in HSS 5 89: 3 (am-ma-ti ša a-bu-ul-li). “The copper cubit of the city gate of Al-ilāni” (= Arraphe) is mentionned in AASOR 16 21: 18 (am-ma-tu3 ša urudu ša a-bu-ul-li ša uru.dingir) and AASOR 16 22: 11-12 (am-[ma]-ti ša urudu ša i-na ka2.gal ša uru.[dingir]); both tablets are written by the same scribe Sîn-iqīša.
4)
The length of the cubit may have varied: rich persons had their own standard as in JEN 588: 8-10, a contract concerning a house acquired by Tehip-Tilla: 45 i+na am-ma-ti mu-ra-ak-šu-nuù 40 i+na am-ma-ti ru-pu-u[s-sú-nu] i+na mi-in-dá-ti ša te-hi-ip-[til-la], «45 cubits long, and 40 cubits wide, according to the measure of Tehip-Tilla». Cf. also YBC 5143: 5 (published in SCCNH 1 p. 383-384 and 411), a tablet from Arraphe: the height of a slave should be measured i-na am-ma-at Iwu-ul-lu “according to the cubit of Wullu”.
5)
mi-ši-il ha-ra-ar-ni, ½ hararnu, is the smallest unit of surface attested in the Nuzi texts (AASOR 16 21: 4).
6)
JEN 526:1-7, the computation of the surface of a field suggests an equivalence of 1 kumānu + 1 hararnu = 1 awiharu. With the above mentioned values, il would be an approximation: 1 kumānu + 1 hararnu = 3/4 awiharu. Zaggagnini 1979, p. 849-850, proposes that 1 kumānu = 2/3 awiharu and 1 hararnu = 1/2 awiharu; so that 1 kumānu + 1 hararnu = 1 + 1/6 awiharu (and not 5/6 awiharu: correct. For the values of hararnu, kumānu and awiharu, see Maidman 1994 : 328.
7)
Zaggagnini 1979, p. 851-853, quotes several texts that give the value of 1 anše = 100 gir3 × 80 gir3. If the value of 1 gir3 corresponds to 1.50 m, 1 anše is then equal to 18 000 m2. Zaggagnini 1979, p. 853-856, suggests that the seed: surface ratio in Nuzi is 1 anše (of seed): 1 anše (of land); he proposes a value of about 11 000 m2 for the anše, 1100 m2 for the awiharu, 732 m2 for the kumānu considered as 2/3 of an awiharu, and 732 m2 for the hararnu considered as 1/2 awiharu; and thus the value of the cubit would be 40 cm.
8)
A ban2 corresponding to 10 sila3 is occasionally used. It is sometimes referred to as against the eight-sila3 ban2 in the same texts, suggesting that the latter corresponds to the common ban2 (cf Hallock 1957 and for textual references cf. CAD S, p. 422a and AHw 1064b). The anše might also therefore be equivalent to 100 sila3.
9)
2 ban2 , 3 ban2 , 4 ban2 , 5 ban2 . Note the unusual way of writing 4 ban2 in JEN 705 : 8 with four vertical wedges before the ban2 sign, see Maidman 1994 : 123
10)
The pi is only attested as a single unit.
11)
Against the CAD T, p. 102b, there is no indication of a tallu of 10 sila3 in HSS 13 50.
12)
For weights found at Nuzi, cf. Starr 1937, pl. 122-124; Starr 1939, p. 464-467; Powel 1987-1990, p. 514-515 with discussion in Andrew 1996.
13)
A non-standard mina equivalent to 100 šiqlu is mentioned in Yale 5 for weighing wool (Grosz 1988, p. 113; p. 118 n. 5).
14)
šehtunu is probably a Hurrian word for half  but perhaps not weight-specific according to Powell 1987-1990 p. 515 and CAD Š/2 p. 263-264.
15)
kuduktu and nariu, cf. Richter 2012, p. 233 and 267 for full bibliography.
16)
mišlu is used as fraction of the kumānu (length measure),  but also refers to “one half” of anything else (price, irrigation water, etc).
17)
paras-ṣerhu (HSS 15 228 and 229), rebūtu (HSS 15 229) and tummu (HSS 15 228: 1) are used as units of weight and represent respectively 1/3 and 1/4 of shekel.
nuzi.txt · Last modified: 2016/03/16 19:54 by gombert
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