Universal #1360

Legacy number: 1360

 Number  1356
 Original  All the bases of systems are divisible by the fundamental base.
 Standardized  All the bases of numeral systems are divisible by the fundamental base.
 Keywords  numeral
 Domain  word formation
 Type  unconditional
 Status  achronic
 Quality  statistical
 Basis  56 languages mentioned in Greenberg 1978a
 Source  Greenberg 1978a: 270 (#21a)

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Discussion
Counterexamples
Coahuilteco (Hokan), with 3 and 20 as base, and Sora (Munda) with 12 and 20.
Notes
A serialized multiplicand is a base. Since both multiplication and addition are involved in this definition, a system without these operations cannot have a base. There can be, however, and commonly is, more than one base, e.g. 10, 100, 1000, 1 000 000 in English. The smallest base will be called the fundamental base. If all the bases are powers of the fundamental base, the system will be called ‘perfect’. There are only four numbers which figure as fundamental bases in perfect numeral systems of the world in order of frequency: 10, 20, 4 and 12. Most systems with 20 as a fundamental base have 100 as the next highest base rather than 400 = 20 x 20.
Comment
Frans Plank · 3 Aug 2006
A serialized multiplicand is a base. Since both multiplication and addition are involved in this definition, a system without these operations cannot have a base. There can be, however, and commonly is, more than one base, e.g. 10, 100, 1000, 1 000 000 in English. The smallest base will be called the fundamental base. If all the bases are powers of the fundamental base, the system will be called 'perfect'. There are only four numbers which figure as fundamental bases in perfect numeral systems of the world in order of frequency: 10, 20, 4 and 12. Most systems with 20 as a fundamental base have 100 as the next highest base rather than 400 = 20 x 20.