Types of numerals; bases in natlangs.

http://scholar.google.com/scholar?q=author:"Hammarstrom"%20intitle:"Number%
20Bases,%20Frequencies%20and%20Lengths%20Cross-Linguistically"

and

[PS] Number Bases, Frequencies and Lengths Cross-Linguistically Harald ...
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2.2 Less Common Bases Frequency data on other numeral systems tends to be
very
... a frequency curve not much different from its base-10 neighbour
languages ...
www.cs.chalmers.se/~harald2/numericals.ps - Similar pages

[PDF] Number Bases, Frequencies and Lengths Cross-Linguistically
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systems is now lost forever. The different-natured body-tally counting
systems of
... Chepang: A sino-tibetan language with a duodecimal numeral. base? ...
www.cs.chalmers.se/~harald2/utrechtabs.pdf - Similar pages

discuss base-and-place systems in the world's languages, among other topics.

He mentions the existence of, and provides references to find out about,
natlang systems that are (or, in some cases, were) binary, ternary,
quaternary, octal, base-six, base-five, base-ten, base-twenty, and base-
twelve.

He says: "The different-natured body-tally counting systems of Papua New
Guinea can have cycles of sizes from eighteen to seventy-four, with twenty-
seven the commonest; but it is not clear in what sense they should be
equated with 'bases'..."

He looks at the "commonest numbers" in several languages (specifically, the
frequency of numbers from zero to one-hundred in corpora from 100 different
languages).  Low numbers and round numbers (powers of bases, and low-number-
multiples of powers of bases) tend to be used with greater frequency in
every language.

He also looks at the "length" (in segments) of number-words in these
languages to test his hypothesis that the more frequent numbers tend to be
shorter than the less frequent numbers.  He looks more closely at a decimal
language (English) and a vigesimal language (Danish).

Interestingly, he reports that, among the numbers between eleven and
nineteen, the most frequently used numbers in seven languages (English,
French, Japanese, Kannada, Dutch, Catalan, and Spanish) are twelve and
fifteen.  Twelve is a "round number" in bases two, three, four, six, and of
course twelve; but not in bases five, eight, ten, or twenty.  Fifteen is
a "round number" in bases three and five; but not in bases two, four, six,
eight, ten, twelve, or twenty.

I do not know the number systems of any of those languages except English
and French (and I or may not remember that much Spanish), so I don't know
what bases they use.  English is decimal, and French is vigesimal from
seventy up to ninety-nine, decimal otherwise.  Hints in the manuscript seem
to indicate that the other five languages are also each mostly-decimal, at
least for most of the range from zero to one-hundred.

If a language does not have base three or base five, why is "fifteen" a
common numeral?  If a language has base five or base eight or base ten or
base twenty, why is "twelve" a common numeral?

-----

Extant, as opposed to extinct, base-four and base-eight languages, are
(says the author) hard to get corpora for; as is the only "bona-fide base-
six system" he knows about.  He says all of the base-five systems he knows
about convert to base-ten or base-twenty for numbers above twenty.  He
mentions some base-twelve systems that stay base-twelve up to twelve-cubed
(1728).

ObConLang; Human natlang multiplication-and-addition based numeral systems,
seem to have bases of seventy-four or less.  Would a conlang for a non-
human language work well with a base of eight-four, ninety, ninety-six, one-
hundred-eight, one-hundred-twenty, or one-hundred-sixty-eight?  What sort
of rationale would make this plausible?

-----

Tom H.C. in MI

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