Tonal system

Nystrom's "Tonal Watch, or Clock-dial". Note the use of his invented digits for hex values 9-F. Also note that midnight (0) is at the bottom, rather than the top of the clockface.

The Tonal system is a base 16 system of notation (predating hexadecimal), arithmetic, and metrology proposed in 1859 by John W. Nystrom.^[1] 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). Nystrom advocated his system thus:

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.^[2]

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 9 with his own invented characters (shown on his clockface above) and changed the value of 9 to ten. Later, the hexadecimal notation overcame 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.

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.

Although Nystrom did not propose a language for tonal fractions, his nomenclature for units of measure does provide one: the name of a power of sixteen before the base unit's name multiplies it by that number, but a power of sixteen after the base unit's name divides it by that number. Thus, de timtons means ⅛ tim.

Geography

Nystrom's hexadecimal compass

For latitudes he put 0 at the North Pole, 4 at the equator and 8 at the South Pole. The units were called tims. They are the same as the colatitudes measured in turns times 16.

Music

A page in the tonal system book

In his book he made a reference to music notation, where binary division is already in use for time. He also discussed the problem of pitch inflation, which he proposed to solve by setting the A below middle C to a frequency of san per timmill (194 Hz).

References