Definition: The word tolfraedic refers to a measure of 120 as denoted in a duodecimal system.
Tolfraedic is comprised of two Icelandic words- tólf (twelve) and ráða (to speak). It was analogous to the baker’s dozen, referring to a hundred that was composed of 120 items instead of 100. It was a result of the duodecimal system being used simultaneously alongside the decimal system (a system based in the number twelve alongside a system based in ten). It was distinguished from a regular hundred (100) by being referred to as a tolfraedic hundred, or sometimes as a long hundred or small gross. The addition of the word tolfraed meant not ten times ten but ten times twelve, or one hundred and twenty.
From the word tolfred we obtain the English word twelve. Also, from the tradition of counting by twelve we have the French word douzain, the Swedish word dusin, and the English word dozen.
Why this word?
While base ten may currently be the most widely used base system, that was clearly not always the case. I find it fascinating that another number system once had more sway over day to day numerical operations. The effect that such a discrepancy may have had on, for instance, commerce is intriguing. It was reputedly common for nails to be sold in a tolfraedic hundred as a standard unit, but pins or other similar items were not.
Effects were seen in other areas as well. For instance, the medieval Anglo-Saxon Chronicle reported that the length of the year was 305 days, while we believe it to be 365. The reference to 300 referred to 3 tolfraedic hundreds, plus the remaining five. Therefore 3 multiplied by 120 would give us 360, plus 5, for the length of the year we currently recognize yet denoted by a different methodology.
I also find the remnants in our language of such operations to be interesting- for instance, the derivation of the words dozen, twelve, and gross.
How to use the word tolfraedic?
“The Army was operating under the tolfraedic system, but the Navy was operating under a base ten system. The resulting miscommunication led to fewer ships arriving than they had been expecting.”