Jing Fang
Encyclopedia
Jing Fang born Li Fang (李房), courtesy name Junming (君明), was a Chinese
music theorist
, mathematician
and astrologer
. Born in present-day Puyang, Henan
during the Han Dynasty
(202 BC – 220 AD), he was the first to notice how closely a succession of 53 just fifths approximates 31 octave
s. This observation would much later lead to the discovery of 53 equal temperament
in the seventeenth century. He was also an advocate of the theory that the light emanating from the spherical Moon
(as seen from Earth
) was merely a reflection
of sunlight
.
(r. 48–33 BC). The historian Ban Gu
(32–92 AD) wrote that Jing Fang was an expert at making predictions from the hexagrams of the ancient Yijing. It is recorded that he was executed by beheading in the marketplace in 37 BC under the Emperor's orders after he allegedly slung false accusations at a high official for infringing upon the law.
between 12 fifths and 7 octaves (this had been published ca. 122 BC in the Huainanzi
, a book written for the prince
of Huainan
), and extended this method fivefold to a scale composed of 60 fifths, finding that after 53 new values became incredibly close to tones already calculated.
He accomplished this calculation by beginning with a suitable large starting value (
) that could be divided by three easily, and proceeded to calculate the relative values of successive tones by the following method:
To produce an exact calculation, some 26 digits of accuracy would have been required. Instead, by rounding to about 6 digits, his calculations are within 0.0145 cents
of exactness, which is a difference much finer than is usually perceptible. The final value he gave for the ratio between this 53rd fifth and the original was
.
This value would later be calculated precisely by Nicholas Mercator
in the seventeenth century (see: history of 53 equal temperament).
(27–97 AD), yet embraced by the mathematician, inventor and scientist Zhang Heng
(78–139 AD).
Jing Fang stated:
Chinese people
The term Chinese people may refer to any of the following:*People with Han Chinese ethnicity ....
music theorist
Music theory
Music theory is the study of how music works. It examines the language and notation of music. It seeks to identify patterns and structures in composers' techniques across or within genres, styles, or historical periods...
, mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and astrologer
Astrologer
An astrologer practices one or more forms of astrology. Typically an astrologer draws a horoscope for the time of an event, such as a person's birth, and interprets celestial points and their placements at the time of the event to better understand someone, determine the auspiciousness of an...
. Born in present-day Puyang, Henan
Puyang
Puyang is a prefecture-level city in northeastern Henan province, China. Located on the northern shore of the Yellow River, it borders Anyang in the west, Xinxiang in the southwest, and the provinces of Shandong and Hebei in the east and north respectively....
during the Han Dynasty
Han Dynasty
The Han Dynasty was the second imperial dynasty of China, preceded by the Qin Dynasty and succeeded by the Three Kingdoms . It was founded by the rebel leader Liu Bang, known posthumously as Emperor Gaozu of Han. It was briefly interrupted by the Xin Dynasty of the former regent Wang Mang...
(202 BC – 220 AD), he was the first to notice how closely a succession of 53 just fifths approximates 31 octave
Octave
In music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...
s. This observation would much later lead to the discovery of 53 equal temperament
53 equal temperament
In music, 53 equal temperament, called 53-TET, 53-EDO, or 53-ET, is the tempered scale derived by dividing the octave into 53 equal steps . Each step represents a frequency ratio of 21/53, or 22.6415 cents , an interval sometimes called the Holdrian comma.- History :Theoretical interest in this...
in the seventeenth century. He was also an advocate of the theory that the light emanating from the spherical Moon
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...
(as seen from Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
) was merely a reflection
Reflection (physics)
Reflection is the change in direction of a wavefront at an interface between two differentmedia so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves...
of sunlight
Sunlight
Sunlight, in the broad sense, is the total frequency spectrum of electromagnetic radiation given off by the Sun. On Earth, sunlight is filtered through the Earth's atmosphere, and solar radiation is obvious as daylight when the Sun is above the horizon.When the direct solar radiation is not blocked...
.
Life and career
According to the 3rd century historian Sima Biao, Jing Fang received an appointment as an official in the Bureau of Music under Emperor Yuan of HanEmperor Yuan of Han
Emperor Yuan of Han was an emperor of the Chinese Han Dynasty. He reigned from 48 BC to 33 BC. Emperor Yuan was remembered for the promotion of Confucianism as the official creed of Chinese government. He appointed Confucius adherents to important government posts...
(r. 48–33 BC). The historian Ban Gu
Ban Gu
Ban Gu , courtesy name Mengjian , was a 1st century Chinese historian and poet best known for his part in compiling the Book of Han. He also wrote in the main poetic genre of the Han era, a kind of poetry interspersed with prose called fu. Some are anthologized by Xiao Tong in his Selections of...
(32–92 AD) wrote that Jing Fang was an expert at making predictions from the hexagrams of the ancient Yijing. It is recorded that he was executed by beheading in the marketplace in 37 BC under the Emperor's orders after he allegedly slung false accusations at a high official for infringing upon the law.
Music theory
Jing Fang came upon his observation after learning to calculate the pythagorean commaPythagorean comma
In musical tuning, the Pythagorean comma , named after the ancient mathematician and philosopher Pythagoras, is the small interval existing in Pythagorean tuning between two enharmonically equivalent notes such as C and B , or D and C...
between 12 fifths and 7 octaves (this had been published ca. 122 BC in the Huainanzi
Huainanzi
The Huáinánzǐ is a 2nd century BCE Chinese philosophical classic from the Han dynasty that blends Daoist, Confucianist, and Legalist concepts, including theories such as Yin-Yang and the Five Phases. It was written under the patronage of Liu An, Prince of Huainan, a legendarily prodigious author...
, a book written for the prince
Liu An
Líu Ān was a Chinese prince and advisor to his nephew, Emperor Wu of Han of the Han Dynasty in China and the legendary inventor of t'ai chi...
of Huainan
Huainan
Huainan is a prefecture-level city with 2,334,000 inhabitants in central Anhui Province, People’s Republic of China. It borders the provincial capital of Hefei to the south, Lu’an to the southwest, Fuyang to the west, Bozhou to the northwest, Bengbu to the northeast and Chuzhou to the east.Its...
), and extended this method fivefold to a scale composed of 60 fifths, finding that after 53 new values became incredibly close to tones already calculated.
He accomplished this calculation by beginning with a suitable large starting value (
) that could be divided by three easily, and proceeded to calculate the relative values of successive tones by the following method:- Divide the value by three.
- Add this value to the original.
- The new value is now equal to
of the original, or a perfect fourthPerfect fourthIn classical music from Western culture, a fourth is a musical interval encompassing four staff positions , and the perfect fourth is a fourth spanning five semitones. For example, the ascending interval from C to the next F is a perfect fourth, as the note F lies five semitones above C, and there...
, which is equivalent to a perfect fifth inverted at the octave. (Alternatively he would subtract
from the interval, equivalent to a perfect fifth down, in order to keep all of the values greater than 177147, or less than 354294, its double, effectively transposing them all into the range of a single octave.) - Proceed now from this new value to generate the next tone; repeat until all tones have been generated.
To produce an exact calculation, some 26 digits of accuracy would have been required. Instead, by rounding to about 6 digits, his calculations are within 0.0145 cents
Cent (music)
The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each...
of exactness, which is a difference much finer than is usually perceptible. The final value he gave for the ratio between this 53rd fifth and the original was
.This value would later be calculated precisely by Nicholas Mercator
Nicholas Mercator
Nicholas Mercator , also known by his Germanic name Kauffmann, was a 17th-century mathematician....
in the seventeenth century (see: history of 53 equal temperament).
Astronomy
Jing Fang was a proponent of the 'radiating influence' theory in ancient China, which stated that the light of the moon was merely the light reflected from the sun, and that the celestial bodies were spherical. This accurate theory was dismissed by the philosopher Wang ChongWang Chong
Wang Chong , courtesy name Zhongren , was a Chinese philosopher active during the Han Dynasty. He developed a rational, secular, naturalistic and mechanistic account of the world and of human beings and gave a materialistic explanation of the origin of the universe. His main work was the Lùnhéng...
(27–97 AD), yet embraced by the mathematician, inventor and scientist Zhang Heng
Zhang Heng
Zhang Heng was a Chinese astronomer, mathematician, inventor, geographer, cartographer, artist, poet, statesman, and literary scholar from Nanyang, Henan. He lived during the Eastern Han Dynasty of China. He was educated in the capital cities of Luoyang and Chang'an, and began his career as a...
(78–139 AD).
Jing Fang stated: