@article{oai:minpaku.repo.nii.ac.jp:00004305,
 author = {八杉, 佳穂 and Yasugi, Yoshiho},
 issue = {3},
 journal = {国立民族学博物館研究報告, Bulletin of the National Museum of Ethnology},
 month = {Feb},
 note = {Numeral systems of Middle American Indian languages
show an enormous variety of ways of forming number words.
But fundamental methods of counting are quinary, decimal and
vigesimal. There may, however, exist no language having a pure
vigesimal system, which would require nineteen different numerals.
So-called vigesimal systems generally have a decimal under
twenty, and very few languages possess only one system throughout.
Therefore, terms such as quinary and decimal should be
used under twenty and that of vigesimal over twenty. That
is, I discuss separately numeral systems below ten, from ten to
twenty, and above twenty. In this paper I limit myself to an
analysis of structural features, although I am interested in
comparing each vocabulary.
As a rule, numeral words are formed from combinations of
D 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 numerals
corresponding to the unit- or base-word and the digit or minor
numbers, respectively. For example, the number 33 is written
as 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 and
Cabecar-Chiripo (Fig. 2). But subtraction occurs in the case of
nine, and multiplicative or duplicative method in numbers 4
and 8 in northern part of Middle America. Mixe-Zoquean show
a quinary system, but the formation from 7 to 9 seems irregular,
except in Tlahuitoltepec and Classical Mixe. Misquito has
also rare system based on 6, for the numbers from 6 to 9.
From 10 to 20, additive constructions with a base of 10 are
common, but both orders of D+U and U+D are attested. The
former is seen in Mayan, and the latter in other languages. But
Huastec, a Mayan language, has U+D order. This must have
been obtained from neighboring languages, such as Totonacan or
Otomian. The difference in formation of the number words
11 and 12 divides the Mayan into Lowlands and Highlands.
Numeral systems of the Southern Otomanguean are purely
decimal below 10, but follow the quinary method from 10 to 20
and counting by twenties from 20 to 100. But Northern
Otomanguean possess some trace of the quinary method under
10. The Tlapanec number sequence from 11 through 19
follows the Southern Otomanguean pattern, although the
genetically related language, Subtiaba shows decimal under 20.
Therefore, the quinary system mixed with decimal in Tlapanec
might have been borrowed from neighboring languages (Fig. 3).
Thorough decimal systems are found in Seri, Northern Uto-
Aztecan languages, and some Chibchan languages. Other
languages show vigesimal systems, of which additive constructions
with a preceeding unit (undercounting) are common, and
additive constructions with a succeeding unit (overcounting) are
confined to Lowland Mayan (including some Highland Mayan)
and Yatzachi Zapotec (Fig. 4). Classical Zapotec uses a
subtractive 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 the
vigesimal system is predominant throughout Middle America,
the center is Mesoamerica and the system of the southern
languages beyond Mesoamerica is different, that is, the coefficients
follow the units (U x D).
As shown above in the case of Huastec, borrowings are among
the best witnesses to past contacts and relationships between or
among various languages. Many languages have borrowed the
word for 100 from Spanish, but conserve their own words in the
coefficients, just like xun-sye:nta (1ˑ100) in Tzutujil. Even the
word for 100 is formed from 5 x 20 in some languages, according
to its system, and interval numbers between the hundreds are
conserved (Fig. 12). That is, only a counting method by
hundreds is borrowed. This indicates that only the formation
principle can be borrowed, although borrowing is generally
expected in lexical items.
From 20 up, the modern Cakchiquel numeral sequence
follows undercounting, whereas Classical Cakchiquel conserved
an overcounting system. Many languages of highland Maya
have a special word, mue' or mue for 80. This is utilized from
80 to 99 in Modern Cakchiquel, but Classical Cakchiquel used it
for 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' laxux
Classical Cakchiquel
 os-k' al
 xun ru-xu-muc'
 xu-mue
This is another excellent example of borrowing of the principle
of formation of words. In other words, only media, but not
contents, are borrowed. That is, structural or formal borrowing
does occur.
The diversity and uniformity of the numeral systems are
shown plainly in the accompanying maps. On the one hand,
diversity is attributed to different methods, such as decimalvigesimal,
quinary-vigesimal, decimal-quinary-vigesimal, and
thorough decimal. On the other, similar counting methods
extended beyond language boundaries are the result of borrowing,
as mentioned above.},
 pages = {519--670},
 title = {中米諸語の数体系},
 volume = {14},
 year = {1990},
 yomi = {ヤスギ, ヨシホ}
}