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The tonal system is a
''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
For latitudes he put 0 at the
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
The tonal system is a base 16
Hexadecimal (also known as base-16 or simply hex) is a positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbols, hexadecimal uses sixteen distinct symbols ...
system of notation (predating the widespread use of hexadecimal
Hexadecimal (also known as base-16 or simply hex) is a Numeral system#Positional systems in detail, positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbo ...
in computing), arithmetic
Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms.
...
, and metrology
Metrology is the scientific study of measurement. It establishes a common understanding of Unit of measurement, units, crucial in linking human activities. Modern metrology has its roots in the French Revolution's political motivation to stan ...
proposed in 1859 by John W. Nystrom.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 calendar date, date is the designation of a single and specific day within such a system. A calendar is ...
with sixteen months, a new system of coinage, and a clock
A clock or chronometer is a device that measures and displays time. The clock is one of the oldest Invention, human inventions, meeting the need to measure intervals of time shorter than the natural units such as the day, the lunar month, a ...
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. (Unicode approximation: β¬―πίΆΖ·α·5678π9κΉπ£πκ―β³ ) 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 rotation, Earth's axis of rotation meets its surface. It is called the True North Pole to distingu ...
, 4 at the equator
The equator is the circle of latitude that divides Earth into the Northern Hemisphere, Northern and Southern Hemisphere, Southern Hemispheres of Earth, hemispheres. It is an imaginary line located at 0 degrees latitude, about in circumferen ...
and 8 at the South Pole
The South Pole, also known as the Geographic South Pole or Terrestrial South Pole, is the point in the Southern Hemisphere where the Earth's rotation, Earth's axis of rotation meets its surface. It is called the True South Pole to distinguish ...
. 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. In geography, Southern latitudes are defined to be negative, and as a result the colatitude ...
s measured in turn
To turn is to rotate, either continuously like a wheel turns on its axle, or in a finite motion changing an object's orientation. Turn may also refer to:
Sports and games
* Turn (game), a segment of a game
* Turn (poker), the fourth of five co ...
s 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 time. The ISO defines international standard pitch as A440, ...
, which he proposed to solve by setting the A below middle C to a frequency of san per timmill (194 Hz).
See also
*Earthly branches
The Earthly Branches (also called the Terrestrial Branches or the 12-cycle) are a system of twelve ordered symbols used throughout East Asia. They are indigenous to China, and are themselves Chinese characters, corresponding to words with no co ...
References
{{reflist Hexadecimal numeral system