The Tonal system is a base 16 system of notation (predating hexadecimal), arithmetic, and metrology proposed in 1859 by John W. Nystrom. In addition to new weights and measures, his proposal included a new calendar with sixteen months, a new system of coinage, and a clock with sixteen major divisions of the day (called tims).
"I am not afraid, or do not hesitate, to advocate a binary system of arithmetic and metrology. I know I have nature on my side; if I do not succeed to impress upon you its utility and great importance to mankind, it will reflect that much less credit upon our generation, upon scientific men and philosophers."
(Quotation: John W. Nystrom, ca. 1863)
Names for the numbers
He proposed names for the digits, calling zero "noll" and counting (from one to sixteen):
"An, de, ti, go, su, by, ra, me, ni, ko, hu, vy, la, po, fy, ton." (Therefore tonal system.)
Because hexadecimal requires sixteen digits, Nystrom supplemented the existing decimal digits 0 through 8 with his own invented characters. (These can be seen on his clockface at right.) Later, the hexadecimal notation overcome this same obstacle by using the digits 0 through 9 followed by the letters A through F.
The numbers 1116 and 1216 would be said "tonan", "tonde", etc. The table below shows Nystrom's names for successive powers of 1016.
|Base 16 Number||Tonal Name||Base 10 Equivalent|
Thus, the hexadecimal number 1510,0000 would be "mill-susanton-bong". This first hexadecimal system, proposed in the 19th century, has thus far not achieved widespread usage.
|Tonal (in tims)||ISO 6709||Colatitude (in degrees)||Colatitude (in turns)|
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- The Art of Computer Programming section 4.1, Donald Knuth.