Yan Tan Tethera - Origin and Usage

Origin and Usage

Sheep-counting systems ultimately derive from Brythonic Celtic languages, such as Cumbric, although Tim Gay writes: “They all compared very closely to 18th century Cornish and modern Welsh”. It is impossible, given the corrupted form in which they have survived, to be sure of their exact origin. The counting systems have changed considerably over time. A particularly common tendency is for certain pairs of adjacent numbers to come to resemble each other by rhyme (notably 1 and 2, 3 and 4, 6 and 7, or 8 and 9). Still, multiples of five tend to be fairly conservative; compare bumfit with Welsh pymtheg, in contrast with standard English fifteen.

Like most Celtic numbering systems, they tend to be vigesimal (based on the number twenty), but they usually lack words to describe quantities larger than twenty; though this is not a limitation of either modernised decimal Celtic counting systems or the older ones. To count a large number of sheep, a shepherd would repeatedly count to twenty, placing a mark on the ground, or move his hand to another mark on his crook, or drop a pebble into his pocket to represent each score (e.g. 5 score sheep = 100 sheep).

It is also worth noting the number theory behind the scheme. Although decimal up to 10, in most dialects the scheme then changes to counting in (sub-)base 5. It is possible to carry out limited arithmetic in base 5 on numbers up to 30 (decimal) using your fingers as a rudimentary abacus. It is pure speculation, but there may be a connection between the two facts, and the shepherds of England may have carried out limited accounting on their fingers.

In particular, the names of the numbers fit a pattern in which the index finger and forefinger each represent 0 when retracted, 1 when bent, and 2 when straight, while the other three fingers each represent 5 when extended. The rhyming transitions occur with the straightening of a finger, and the pattern repeats at intervals of 5. Thus, with two hands, a person can count up to 399. In the similar but simpler system, discernible in Roman numerals, in which the thumb is 5 and the other fingers 1 each, a person can only count up to 99 on two hands. The Yan Tan Tethera system was thus advantageous until writing made the limitation of two hands less important.

Another reason for the use of base five is suggested by the design of the shepherds crook which has grooves, nobbles, nicks or other impressions on it which enable the shepherd to note the number of fives counted on the other hand. Using base five counting in this way allows the shepherd to total as many sheep as the markings on the crook will allow, each mark representing five sheep.

Their use is also attested in a knitting song from Yorkshire.