Nineteenth century laws of sound correspondence led to major advances in linguistics. Numeracy, the linguistics of numeral systems, and calculations … now represent twentieth century contributions to an understanding of the … decades. Numeral names … recall an old pre-exponential numeral system that stands between concrete counting and exponential decimal systems.
Seiler has characterized breaks in numeral formations as a “turning point between serializations” that mark the “semiotic status of the base”, while Hurford called attention to the point where a language changes methods for signaling addition as indicative of a base break. So the syntax of English ‘thir-teen … nine-teen’ (digit + base), in stating the smaller number first, differs from that of 21-29 (base + digit) with the smaller number suffixed to the base. Addition in one but multiplication in the other signals the teens / decades break.
Non-standard decade formations from 30 to 90 in French, trente, quarante, cinquante, soixante, septante, uitante /octante, nonante ‘thirty, forty, fifty, sixty, seventy, eighty, ninety’, are built on the strategy digit + a ten-valued suffix -(a)nte, parallel to the English forms with digit + ‘-ty’.
But despite French numerical reforms, standard French numerals for decade counting, like many Celtic systems, retain well-known breaks reminiscent of non-decimal systems. Major breaks in the standard system begin with 70 (soixante-dix, literally ’60-10′ to soixante-dix-neuf ’60-ten-nine’ or ’60-nineteen’) and 80 (quatre-vingt, literally ‘four-twenty’ to quatre-vingt-dix-neuf ‘four-twenty-nineteen’).
French soixante-dix and quatre-vingt have been accounted for as the result of Celtic influence. If Celtic, as a branch of IE, has inherited the PIE decimal system, however, both IE Celtic and French should share an inherited decimal system. To the extent that soixante ’60’ is 6 x 10, and 60 marks a base-like entity on which to build soixante-dix ’70’ as ’60-ten’, soixante formations recall a base value ’60’, but numerals quatre-vingt ’80’ (four-twenty), quatre-vingt-dix ’90’ (four-twenty-ten) build on 20
Breaks in the standard French decade system reflect factors [10 and 6] operating on base units 10 and 60 as far as 79 and factors [10, 2, and 5] operating on base units 10 and 20 from 80 to 99. These numeral bases and factors are not powers of any base, but pre-exponential factors reminiscent of traditional systems of measure rather than sequential counting. Decade numerals trente to soixante ’30-60′ are formed regularly from the digits 3-6 plus the decade suffix -(a)nte, and French 62-69 follows the strategy of addition: ‘sixty+2 …’ established with 22.
The first break begins with soixante-dix ’60-10′ which uses 60 as base for adding 10-19 to build 70-79. But soixante itself is otherwise not the productive base that French cent (English ‘hundred’) is. There is no soixante-vingt, for example. The second break begins with the numeral quatre-vingt that, as ‘4-20′, builds on vingt ’20’ as a base. In quatre-vingt-dix ‘4-20-10’ the addition process of 60+10 recurs.
Is French vingt part of the paradigm, trente, quarante, …, or is / was it a separate, unanalyzable base? In the system that underlies quatre-vingt, it serves as a numeral base. By a factor of 5, numeral base vingt is converted to cent ‘100’. The numeral quatre-vingt (4 vingt’s) recalls the conversion of a base 20. Phonological correspondences with Latin make it part of an older decimal paradigm, to the extent that Latin vii-gint-ii ’20’ is ‘2-10’s’. Sound correspondences relate French vingt to Latin vii-gint-ii ‘twenty’ or IE *ui-kentii (Coleman 1992:397-398 with discussion of the relation of *kent- to IE ‘ten, decade, hundred’), while subsequent decades in -(a)nte correspond to Latin *-(a)-gint-aa: quinqu-a-gint-aa, tri-ginta ‘fifty, thirty’ (Pope 1966 :127; 318). Although historically vingt is a phonological reduction from a potential ancestral ‘two decades’ (Latin vii-gint-ii ‘two gint’s), whether vi-ngt was only accentually separated from soix-ante or not), vingt and soixante have separate roles in the French system of numeration.
NUMERACY AND THE GERMANIC UPPER DECADES*by Carol F. Justus Journal of Indo-European Studies 24, 1996, 45-80
I tried to contact Carol Justus, Director, Numerals Project at the University of Texas at Austin, to request her advice on my own study. I found that she had passed away on 1 August 2007. So I tried to contact Winfred Lehmann, Director of the Linguistics Research Center, University of Texas at Austin , but found, to my astonishment, that he also died, on the very same day.