Tibetan numerals
1
Morphological analysis
It is not immediately obvious where the morpheme boundaries fall in the data. However, it
is not necessary to determine the exact location of the morpheme boundary in the morphologically
complex numerals in order to observe that the order of morphemes in the numerals designating
teens (10 + X) must be /‘10’-‘X’/, whereas the order of morphemes in the numerals referring to
multiples of tens (10 x X) must be /‘X’-‘10’/, as seen in (1):
(1)
Order of morphemes in morphologically complex numbers
/10-X/ (teens):
[ǰubši] (lit. 10-4) ‘14’
[ǰurgu] ‘19’
/X-10/ (tens):
[šibǰu] (lit. 4-10) ‘40’
[gubǰu] ‘90’
[ǰuŋa] ‘15’
[ŋabǰu] ‘50’
This is because the sequence [ǰu] occurs in two places in these words. The sequence [ǰu] therefore
must be part (if not all) of the morpheme ‘10’. Certain strings which must be part of the numbers
‘1’ to ‘9’ occur to either side of the part that must mean ‘10’.
Forms containing ‘10’
At issue is the morphological affiliation of the consonants in between [ǰu] and the other
number. Arranging the morphologically complex words in columns, as shown in (2), a pattern
emerges which suggests the location of the morpheme boundary.
2
(2)
Words containing the morpheme ‘10’
ǰu
ǰuŋa
ǰugǰig
ǰubši
ǰurgu
gubǰu
šibǰu
ŋabǰu
‘10’
‘10-5’ (‘15’)
‘10-1’ (‘11’)
‘10-4’ (‘14’)
‘10-9’ (‘19’)
‘9-10’ (‘90’)
‘4-10’ (‘40’)
‘5-10’ (‘50’)
As mentioned above, the morpheme ‘10’ minimally contains the sequence [ǰu]. A following
consonant appears when [ǰu] precedes another morpheme, but the consonant is unpredictable ([ŋ],
[g], [b] or [r]). Forms in which ‘10’ is not word-initial all contain a [b] before the sequence [ǰu].
Let us consider the phonological consequences of some possible morphological analyses of the last
three forms in (2).
[ŋab-ǰu]: It is not likely that the [b] belongs to the preceding morpheme, for two reasons.
(1) It would be an unexplained coincidence that all of these different morphemes end in /b/. (2) The
final [b] would have to be deleted in unsuffixed forms, but the surface final consonant in [ǰig] ‘1’
suggests that there is no general process of word-final consonant deletion in Tibetan.
[ŋa-bǰu]: If the [b] is part of the morpheme ‘10’, then this morpheme has two alternants,
[ǰu] and [bǰu], which occur in word-initial and non-word-initial positions, respectively.
1
[ŋa-b-ǰu]: The [b] could be an independent morpheme, perhaps signalling the arithmetic
operation of multiplication. However, this does not extend to the number compounds where ‘10’
comes first and ‘10’ is added to the following morpheme. There are a variety of consonants as the
first member of the cluster [g b r], and sometimes no cluster.
[ŋa-ǰu]: The [b] could be a purely epenthetic segment. But why would [b] be inserted
before [ǰ]? And the phonology does not seem like it could be easily generalized to the other
number compounds, with medial sequences of [gj], [bš], and [rg].
It seems most promising to pursue the analysis in which the alternants of ‘10’ are [ǰu] and
[bǰu], with UR /bǰu/ and word-initial consonant cluster simplification.
3
Alternants of morphemes other than ‘10’
The /CC/ analysis of ‘10’ outlined in §2 also suggests an analysis of the other numbers
along similar lines. Alternants of remaining morphemes in the data are shown in (3)-(6):
(3)
(4)
(5)
(6)
Words containing the morpheme ‘1’
ǰig
ǰug ǰig
‘1’
’10-1’ (‘11’)
Words containing the morpheme ‘4’
ši
šibǰu
ǰub ši
‘4’
‘4-10’ (‘40’)
’10-4’ (‘14’)
Words containing the morpheme ‘5’
ŋa
ŋabǰu
ǰu ŋa
‘5’
‘5-10’ (‘50’)
’10-5’ (‘15’)
Words containing the morpheme ‘9’
gu
ǰur gu
gubǰu
‘9’
’10-9’ (‘19’)
‘9-10’ (‘90’)
The data in (3)-(6) suggest that all morphemes but ‘5’ have two positionally-determined alternants:
(7)
Morpheme alternants, by position within word
word-initial alternant
non-word-initial alternant
[ǰig]
[gǰig]
[ši]
[bši]
[gu]
[rgu]
[ǰu]
[bǰu]
‘1’
‘4’
‘9’
‘10’
2
4
Phonology: deletion or epenthesis?
Most of the forms exhibit a regular alternation between 0 and a consonant. This sort of
alternation can be accounted for in one of two ways, via a deletion rule (C --> 0) or an insertion
rule (0 --> C). We have already seen that positing an underlying morpheme-initial consonant
cluster, simplified to a single C word-initially, makes the most sense for ‘10’. Let us make this
explicit for all the number morphemes in the data.
4.1
Deletion
According to the deletion analysis, the URs of the number morphemes are those shown in
(8). Notice that in Tibetan, some numbers begin with a consonant cluster underlying and some
numbers begin with a single consonant.
(8)
/gǰig/
/bši/
/ŋa/
/rgu/
/bǰu/
‘1’
‘4’
‘5’
‘9’
‘10’
When a cluster-initial number morpheme is word-initial, it undergoes the rule of Consonant cluster
simplification, which neutralizes the difference between CC- and C-initial number morphemes.
(9)
Consonant cluster simplification
C --> 0 / # ___ C
When numbers beginning with a cluster occur as the second member of a compound, the cluster is
preceded by a vowel and Consonant Cluster Simplification cannot apply.
)
URs of number compounds
/bǰu-gǰig/
‘11’
/bǰu-bši/
‘14’
/bǰu-ŋa/
‘15’
/bǰu-rgu/
‘19’
/bši-bǰu/
‘40’
/ŋa-bǰu/
‘50’
/rgu-bǰu/
‘90’
4.2
Epenthesis
According to an epenthesis analysis, the URs of the number morphemes would begin with
single Cs, as shown in ):
3
)
Number URs
/ǰig/ ‘1’
/ši/ ‘4’
/ŋa/ ‘5’
/gu/ ‘9’
/ǰu/ ’10’
According to this analysis, the URs of the number compounds would be those given in ):
)
URs of number compounds
/ǰu-ǰig/ ‘11’
/ǰu-ši/ ‘14’
/ǰu-gu/ ‘19’
/gu-ǰu/ ‘90’
/ši-ǰu/ ‘40’
The problem with the insertion analysis is that the phonetic character of the inserted consonant is
not predictable from the shape of the following morpheme. A fairly complicated set of rules,
something like those in (10), would be needed:
(10)
Epenthesis
0  g / V - ___ ǰi
0  b / V- ___ š
0  r / V- ___ g
0  b / V- ___ ǰu
The rules in ) lack phonetic motivation or parallelism with phonological rules known in other
languages. Given the variety of consonants that would be inserted, it is more likely that they are
part of the UR.
5
Summary
Given the complexity of the epenthesis analysis relative to the simplicity of the deletion
analysis, the best analysis of the Tibetan number morphemes is that some number morphemes
begin with a cluster, some with a single consonant underlyingly. Word-initial consonant clusters
are simplified to single consonants in this language.
4