The tonal system is a

base 16 In mathematics and computing, the hexadecimal (also base-16 or simply hex) numeral system is a positional numeral system that represents numbers using a radix (base) of 16. Unlike the decimal system representing numbers using 10 symbols, he ...

system of notation (predating the widespread use of

hexadecimal In mathematics and computing, the hexadecimal (also base-16 or simply hex) numeral system is a positional numeral system that represents numbers using a radix (base) of 16. Unlike the decimal system representing numbers using 10 symbols, hexa ...

in computing),

arithmetic Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th ...

, and

metrology Metrology is the scientific study of measurement. It establishes a common understanding of units, crucial in linking human activities. Modern metrology has its roots in the French Revolution's political motivation to standardise units in Fran ...

proposed in 1859 by

John W. Nystrom John Williams Nystrom ( sv, Johan Vilhelm Nyström) (1825–1885) was a Swedish born, American civil engineer, inventor, and author. He served as an assistant Secretary and Chief Engineer of the United States Navy during the American Civil War ...

.Nystrom, John W.
''Project of a New System of Arithmetic, Weight, Measure and Coins, Proposed to be Called the Tonal System, with Sixteen to the Base''
/ref> In addition to new weights and measures, his proposal included a new

calendar A calendar is a system of organizing days. This is done by giving names to periods of time, typically days, weeks, months and years. A date is the designation of a single and specific day within such a system. A calendar is also a physi ...

with sixteen months, a new system of

coinage Coinage may refer to: * Coins, standardized as currency * Neologism, coinage of a new word * ''COINage'', numismatics magazine * Tin coinage, a tax on refined tin * Protologism, coinage of a seldom used new term See also * Coining (disambiguatio ...

, and a

clock A clock or a timepiece is a device used to measure and indicate time. The clock is one of the oldest human inventions, meeting the need to measure intervals of time shorter than the natural units such as the day, the lunar month and the ...

with sixteen major divisions of the day (called tims). Nystrom advocated his system thus:

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, ''ton''al 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 ''tim''.

Geography

For latitudes he put 0 at the

North Pole The North Pole, also known as the Geographic North Pole or Terrestrial North Pole, is the point in the Northern Hemisphere where the Earth's axis of rotation meets its surface. It is called the True North Pole to distinguish from the Mag ...

, 4 at the

equator The equator is a circle of latitude, about in circumference, that divides Earth into the Northern and Southern hemispheres. It is an imaginary line located at 0 degrees latitude, halfway between the North and South poles. The term can als ...

and 8 at the

South Pole The South Pole, also known as the Geographic South Pole, Terrestrial South Pole or 90th Parallel South, is one of the two points where Earth's axis of rotation intersects its surface. It is the southernmost point on Earth and lies antipod ...

. The units were called ''tims''. They are the same as the

colatitude In a spherical coordinate system, a colatitude is the complementary angle of a given latitude, i.e. the difference between a right angle and the latitude. Here Southern latitudes are defined to be negative, and as a result the colatitude is a non- ...

s measured in turns times 16.

Music

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 Concert pitch is the pitch reference to which a group of musical instruments are tuned for a performance. Concert pitch may vary from ensemble to ensemble, and has varied widely over music history. The most common modern tuning standard uses 4 ...

, which he proposed to solve by setting the A below middle C to a frequency of san per timmill (194 Hz).

References

{{reflist Hexadecimal numeral system