Classical Kasshian numbers
Classical Kasshian used a duodecimal number system. The basic numerals, uninflected, are used for the cardinal numbers. To form ordinals, gender prefixes and appropriate number- and case-suffixes are added.
Basic Numerals
- 1 - Tā (-ta)
- 2 - Kabi (-bi)
- 3 - Flī (-fli)
- 4 - Vandu (-chi)
- 5 - Daç (-zzhi)
- 6 - Mandu
- 7 - Blanta
- 8 - Bīchi (or bichi)
- 9 - Blamfli
- 10 - Bezzhi
- 11 - Dutā (or duta)
- 12 - Nadu
1-5 have alternate forms used when suffixed in compounds, -ta and -bi also make the preceding vowel long.
Note that 4 and 6 are derived from nadu with the prefixes va- (1/3) and ma- (1/2)
Multiples of Six
Although Classical Kasshian was fundamentally base-12 in its numeral system, higher numbers mixed elements of base-6 and base-12. Most multiples of twelve are derived from the basic numerals with -ndu suffixed. Numbers six greater than multiples of twelve have the element ma- (half) compounded with the basic numerals. Other numbers greater than 12 and below 144 add the numbers 1-5 to the multiples of six. For example, decimal 21, duodecimal 19, is tamandufli (ta- = one, ma- = "half", -ndu = "twelve", -fli = "three"). Thus, 13-23 by way of example are:
- 13 Nadūta
- 14 Nadūbi
- 15 Nadufli
- 16 Naduchi
- 17 Nadozzhi
- 18 Tamandu
- 19 Tamandūta
- 20 Tamandūbi
- 21 Tamandufli
- 22 Tamanduchi
- 23 Tamandozzhi
There are several irregular multiples of six:
- 24 (20_{12}) - Kannadu
- 36 (30_{12}) - Mitala
- 48 (40_{12}) - Vasshā
- 54 (46_{12}) - Chimandu
- 72 (60_{12}) - Masshā
- 78 (66_{12}) - Bammandu
The word for 36 is a vestige of an older base-6 system, while the words for 48 and 72 are derived from saçā (144, see below) with the prefixes va- and ma-. In addition, the long vowels in tā (1) and flī (3) are shortened when used as prefixes (thus 18 is tamandu not *tāmandu and 42 is flimandu not *flīmandu) and daç (5) becomes daçi as a prefix, as a result of the regular phonetic rule that çi becomes ç after a vowel and word-final or before a voiceless consonant.
All multiples of 6 (12-136)
Majorly irregular forms bolded, italics for slight irregularities
- 12 (10_{12}) Nadu
- 18 (16_{12}) Tamandu
- 24 (20_{12}) Kannadu
- 30 (26_{12}) Kabimandu
- 36 (30_{12}) Mitala
- 42 (36_{12}) Flimandu
- 48 (40_{12}) Vasshā
- 54 (46_{12}) Chimandu
- 60 (50_{12}) Daçendu
- 66 (56_{12}) Daçimandu
- 72 (60_{12}) Masshā
- 78 (66_{12}) Blammandu
- 84 (70_{12}) Blantandu
- 90 (76_{12}) Blantamandu
- 96 (80_{12}) Bīchendu
- 102 (86_{12}) Bīchimandu
- 108 (90_{12}) Blamflendu
- 114 (96_{12}) Blamflimandu
- 120 (A0_{12}) Bezzhendu
- 126 (A6_{12}) Bezzhimandu
- 132 (B0_{12}) Dutandu
- 138 (B6_{12}) Dutāmandu
144 and Higher
The number for 144 is saçā. Multiples are formed by prefixing the basic numeral (shortened in the case of tā and flī) to saçā, which becomes -sshā when compounded. 720 (144*5) is daçesshā. Multiples of 144 do not compound with smaller numbers, e.g., 200 = 144 + 54 + 2 = saçā chimandūbi. 576 and 864 (400_{12} and 600_{12}) may be either vandosshā and mandosshā or vazanta and mazanta building on the word for 1,728
1,728 (12^{3}) is zanta, -zanchi with multipliers. 6,912 and 10,368 (4000_{12} and 6000_{12}) are usually vanduzanchi and manduzanchi, but, rarely, may also be vāpalta and māpalta. Va- and ma- are never used with higher powers.
20,736 (12^{4}) is kapalta; -palchi plus lengthening with multipliers
429,981,696 (12^{8}) is tasanna; -ssanni with multipliers. Archaically, this could also be used for 248,832 (12^{5})
Nadu, saçā and zanta can be used themselves as multipliers. For example, 247,669,456,896 (400,0000,0000 in duodecimal) would be vandosshassanni (vandu saçā tasanni)
For numbers above 12^{8}, mathematicians have devised several higher numbers, but with three different systems for their values. In the first, each number is 12^{4} times the value of the preceding number, and thus, only nadu, saçā, and zanta can be used as prefixes, while in the second, each number is 12^{8} times larger than the preceding, necessitating that kapalta be used as a prefix too. The third system is archaic, and each number in that one is 12 times the previous, being based on the value 12^{5} for tasanna. In all forms below, the final -ā becomes -aç when used in compounds, e.g., two times ītā is kabītaç, in addition, when numbers ending in -du, such as mandu are added to forms starting with vowels, the -du changed to -b, e.g., mandu + ītaç becomes mambītaç, and saçā becomes saçak-/saçaç-
Name | Value (system 1) | Value (system 2) | Value (system 3) | |
---|---|---|---|---|
ītā | 12^{12 } | 12^{16} | 12^{6} | |
askatā | 12^{16} | 12^{24} | 12^{7} | |
enkatā | 12^{20} | 12^{32} | 12^{8} | |
sheskatā | 12^{24} | 12^{40} | 12^{9} | |
alsātā | 12^{28} | 12^{48} | 12^{10} | |
meskatā | 12^{32} | 12^{56} | 12^{11} | |
vaskatā | 12^{36} | 12^{64} | 12^{12} | |
kaskatā | 12^{40} | 12^{72} | 12^{13} | |
chaltātā | 12^{44} | 12^{80} | 12^{14} | |
chaltaffūtā | 12^{48} | 12^{88} | 12^{15} | |
chaltafītā | 12^{52} | 12^{96} | 12^{16} |
This system uses numbers borrowed from Classical Sanle, translating literally as "second number" (ītā), "third number" (askatā), etc., and thus, in principle, has no limit to the words that can be formed.