- 国立民族学博物館研究報告 = Bulletin of the National Museum of Ethnology (ISSN:0385180X)
- vol.14, no.3, pp.519-670, 1990-02-28
Numeral systems of Middle American Indian languagesshow an enormous variety of ways of forming number words.But fundamental methods of counting are quinary, decimal andvigesimal. There may, however, exist no language having a purevigesimal system, which would require nineteen different numerals.So-called vigesimal systems generally have a decimal undertwenty, and very few languages possess only one system throughout.Therefore, terms such as quinary and decimal should beused under twenty and that of vigesimal over twenty. Thatis, I discuss separately numeral systems below ten, from ten totwenty, and above twenty. In this paper I limit myself to ananalysis of structural features, although I am interested incomparing each vocabulary.As a rule, numeral words are formed from combinations ofD and U, such as D x U+D, U x D+D, D+D x U, D+U x D.In this expression, the symbols U and D denote the numeralscorresponding to the unit- or base-word and the digit or minornumbers, respectively. For example, the number 33 is writtenas 3 x 10+3, of which 3 is D and 10 is U.Under 10, we have two systems, quinary and decimal.Quinary systems are observed in Southern Uto-Aztecan,Tarascan, Northern Otomanguean, Mixe-Zoquean, Sumu andCabecar-Chiripo (Fig. 2). But subtraction occurs in the case ofnine, and multiplicative or duplicative method in numbers 4and 8 in northern part of Middle America. Mixe-Zoquean showa quinary system, but the formation from 7 to 9 seems irregular,except in Tlahuitoltepec and Classical Mixe. Misquito hasalso rare system based on 6, for the numbers from 6 to 9.From 10 to 20, additive constructions with a base of 10 arecommon, but both orders of D+U and U+D are attested. Theformer is seen in Mayan, and the latter in other languages. ButHuastec, a Mayan language, has U+D order. This must havebeen obtained from neighboring languages, such as Totonacan orOtomian. The difference in formation of the number words11 and 12 divides the Mayan into Lowlands and Highlands.Numeral systems of the Southern Otomanguean are purelydecimal below 10, but follow the quinary method from 10 to 20and counting by twenties from 20 to 100. But NorthernOtomanguean possess some trace of the quinary method under10. The Tlapanec number sequence from 11 through 19follows the Southern Otomanguean pattern, although thegenetically related language, Subtiaba shows decimal under 20.Therefore, the quinary system mixed with decimal in Tlapanecmight have been borrowed from neighboring languages (Fig. 3).Thorough decimal systems are found in Seri, Northern Uto-Aztecan languages, and some Chibchan languages. Otherlanguages show vigesimal systems, of which additive constructionswith a preceeding unit (undercounting) are common, andadditive constructions with a succeeding unit (overcounting) areconfined to Lowland Mayan (including some Highland Mayan)and Yatzachi Zapotec (Fig. 4). Classical Zapotec uses asubtractive method for the five numbers below the next unit.From 20 up, Mayan languages show an interesting formation.Undercounting and overcounting are distinguished geographically(Fig. 6). Unit words for twenties, such as *k'a l, *winaq,*tah- or *may are used differently (Figs. 7-11). Although thevigesimal system is predominant throughout Middle America,the center is Mesoamerica and the system of the southernlanguages beyond Mesoamerica is different, that is, the coefficientsfollow the units (U x D).As shown above in the case of Huastec, borrowings are amongthe best witnesses to past contacts and relationships between oramong various languages. Many languages have borrowed theword for 100 from Spanish, but conserve their own words in thecoefficients, just like xun-sye:nta (1ˑ100) in Tzutujil. Even theword for 100 is formed from 5 x 20 in some languages, accordingto its system, and interval numbers between the hundreds areconserved (Fig. 12). That is, only a counting method byhundreds is borrowed. This indicates that only the formationprinciple can be borrowed, although borrowing is generallyexpected in lexical items.From 20 up, the modern Cakchiquel numeral sequencefollows undercounting, whereas Classical Cakchiquel conservedan overcounting system. Many languages of highland Mayahave a special word, mue' or mue for 80. This is utilized from80 to 99 in Modern Cakchiquel, but Classical Cakchiquel used itfor the numbers from 61 to 80, as indicated below;Modern Cakchiquel 60 os-k' al 61 os-k' al xun 80 xu-mue 90 xu-muc' laxuxClassical Cakchiquel os-k' al xun ru-xu-muc' xu-mueThis is another excellent example of borrowing of the principleof formation of words. In other words, only media, but notcontents, are borrowed. That is, structural or formal borrowingdoes occur.The diversity and uniformity of the numeral systems areshown plainly in the accompanying maps. On the one hand,diversity is attributed to different methods, such as decimalvigesimal,quinary-vigesimal, decimal-quinary-vigesimal, andthorough decimal. On the other, similar counting methodsextended beyond language boundaries are the result of borrowing,as mentioned above.