ABSTRACT
DISCUSSION
OF THE FIVE PHASES & FIVE TONES
The theory of the Five Phases (‘Wu Xing’ 五行, also known as Five Elements) is deep-rooted
in Chinese medicine. However, there
exist inconsistency and limitation in the application of the theory to medicine
(Notes 1 and 2). This paper is to review
the history of the Five Phases theory, examine its limitation, and provide
additional insight by analyzing the closely-correlated Five Tones (‘Wu
Yin’ 五音) theory, namely five notes in the pentatonic scale.
FIVE PHASES
o
The earliest reference to the Five Phases
appeared in the ‘Great Plan’ section of the ‘Book of Documents’ (Shu Jing, c. 4th
century BC). It states:
‘Of the five phases, the first is WATER
水;
the second FIRE 火; the third, WOOD 木; the
fourth, METAL 金; and the fifth, EARTH 土.’
This is known as the ‘Cosmogonic
sequence’.
o
The Five Phases were also called Five Abilities, Talents or Materials (材, pronounced 'cai').
One book in the Warring States period (476-221 BC) says,
‘Heaven sends five abilities (talents or materials) and the people use them’.
The five tones that correlates to the five phases are:
Figure 1 Earliest
Five Phases and Five Tones
·
It is not coincidental that, in the Bible, creation begins with
water:
Genesis 1:2 ‘The earth was without
form, and void; and darkness was on the face of the deep. And the Spirit of God was hovering over the
face of the waters.’
Book of Changes 易經 says 'Heaven one bears water'. （天一生水。）
Guodian Chu Slips 郭店楚簡 (300 BC) unearthed in 1993 says The Great One
Generates Water （太一生水。） Chinese classics such as Lao-tzu 老子 and
Huai-nan Tsu 淮南子 also recorded the creation story (note 3).
·
The order of the phases (1 for Water, 2 for Fire
… 5 for Earth) coincides mysteriously with that of the pitch of corresponding five
notes
in the pentatonic scale: D# (La) the highest, C# (So) the 2
nd, A# (Mi) the 3
rd,
G# (Re) the 2
nd lowest and F# (Do) the lowest.
This is a movement down the pentatonic scale
and it signifies creation descends from the highest frequency – that of Water to
the lowest – that of Earth, like rain precipitating downward from heaven.
The Five Notes
in the pentatonic scale is believed by some
people to be the natural precursor of the Five Phases.
o
The Five Phases theory was systemized by Zou Yan
(305-240 B.C.) when he proposed a ‘Five Virtue Cyclic Sequences of Ends and Beginning’, i.e., the controlling
sequence of the Five Phases:
Figure
2 The Controlling Sequence of the Five Phases
o
Liu Xiang (77-6 BCE) and his son Liu Xin
advocated a generating sequence of the Five Phases:
Figure
3 The Generating Sequence of the Five Phases
· The controlling sequence Five Phases theory was criticized for its absurdness by the respectable scientist and scholar Wang Ch'ung 王充 (27-97 AD) of the Han
dynasty (note 1). There is inconsistencies in the generating sequence Five Phases theory, too. Water generates Wood, Fire generates Earth
and Earth generates Metal, which are all seemingly natural phenomena. Wood, however, does not readily catch Fire. Wood needs to be drilled to generate fire or
to be ignited by thunder, for example. Metal will only melt into liquid under a high temperature and high pressure
condition. Nevertheless, the Five Phases theory has a wide application in Chinese medicine.
FIVE NOTES
o
The Yellow Emperor’s pentatonic scale consists
of musical notes related by perfect fifths (the most harmonious of all musical
intervals) which confers health and tranquility on all beings coming in contact
with it (Note 3).
When arranged in a
circle of ascending fifths to fashion the ‘Five Virtue
Cyclic Sequences of Ends and Beginning’, the Five Pentatonic Notes
are in the following order:
·
Inconsistency becomes apparent in above circle
of fifths because the end fails to meet the beginning. The interval between notes
A# and F# is not a perfect fifth, rather it is an augmented fifth, i.e., a fifth
plus half a step or one semitone.
Figure 5 ‘san fen sun yi fa’ 三分损益法
‘the Technique of Adding and Subtracting One Third’
As shown in the following, twelve Lu 律 tones (notes) were generated from Yellow Bell 黄钟using
‘san fen sun yi fa’:
Yellow Bell黄钟∶eight cun ten fen one八寸十分一、81
fen分
(note 4);
林钟∶81 * 2/3 = 54；
太簇∶54 * 4/3 = 72；
南吕∶72 * 2/3 = 48；
姑洗∶48 * 4/3 = 64；
应钟∶64 * 2/3 = 42.6667；
蕤宾∶42.6667 * 4/3 = 56.8889；
大吕∶56.8889 * 4/3 = 75.8519；
夷则∶75.8519 * 2/3 = 50.5679；
夹钟∶50.5679 * 4/3 = 67.4239；
无射∶67.4239 * 2/3 = 44.9492；
仲吕∶44.9492
* 4/3 = 59.9323；
Clean Yellow Bell清黄钟 (one
octave above Yellow Bell 黄钟)∶59.9323 * 2/3 = 39.9549
Please note that Clean Yellow
Bell 39.9546 still deviates a little from 40.5 half of Yellow Bell. This means Yellow Bell cannot be
regenerated. In other word, Yellow Bell
cannot come back to itself.
If Yellow Bell designated as 1 (Do), notes derived from
Yellow Bell using ‘san fen sun yi fa’ will be 5 (Sol) for林钟, fifth
above Yellow Bell 1 (Do), 2 (Re) for太簇, fourth down from林钟5
(Sol), 6 (La) for南吕, fifth above太簇2 (Re), and so forth. Clean Yellow Bell 清黄钟will
be 7# (Si/Ti Sharp). 7# has a pipe
length of 39.9546 that is slight off from one octave above Yellow Bell 1 (Do),
which has a pipe length of 40.5. The
following figure gives another presentation of 12 lu 律 tones
(notes) obtained from Yellow Bell using ‘san fen sun yi fa’.
Figure 6 Twelve Lu 律 Tones (Notes)
Derived from Yellow Bell using ‘san fen sun yi fa’
F.
Figure 4 Five notes in the pentatonic scale in ascending perfect fifths
Figure 5 Guan Zi管子地員篇san fen sun yi fa三分損益法
v
‘Five Virtue Cyclic Sequences of Ends and
Beginning’ will be very ingenious if five tones which correlate closely to five virtues
can be connected in a circle.
However,
the circle of (perfect) fifths that begins with F#, estimated to be approximately the frequency of
Yellow Bell (note 3), end in F (Figure 4).
Ascending additional 7 perfect fifths above F, one arrives at an F#, 12 perfect fifths above Yellow Bell F#, which is very close to (but not the same as) an F# of 7 octaves above Yellow Bell F# (Figure 5).
Pythagorean Comma is well-known for identifying the difference between twelve just perfect fifths and seven octaves. The difference is expressed as the ratio of (3/2)**12 over (2)**7, which is 1.01364.
The ratio of half of Yellow Bell pipe length 40.5 (an octave above Yellow Bell) over Clean Yellow Bell pipe length 39.9546
is 1.0136505. This ratio which deviates from unity shows Yellow Bell can not come back to itself. Both Pythagorean
Comma and Chinese historical record both essentially explains the same fact. Thus, it becomes clear that, in a rigorous fashion, five tones cannot be connected in a circle.
Figure 5 Five
Pentatonic Notes in a Circle of Fifths showing 12 perfect fifths between ending
F# and base F#.
(Note: ending F# is nearly 7 octaves above base F#)
The inconsistency, however, may only be a
superficial observation.
An in-depth
analysis from this work has revealed that an F# lies 8 (perfect) fifths above
A#.
This F# is 7 octaves above the
beginning F# in the circle of fifths.
Figure 5 depicts a brand new presentation of the circle of fifths for
the Five Pentatonic Notes:
Figure 6 Five Pentatonic Notes in a Circle of Fifths
where the interval between A# and the ending F# is 8 perfect fifths.
(Note: the ending F# is 7 octaves above the
beginning F#)
In such an arrangement, the Five Pentatonic
Notes, which are closely connected to the Five Phases, fit the model of Zou
Yan’s ‘Five Virtue Cyclic Sequences
of Ends and Beginning’. Interestingly, 8
is the number of ‘new beginning’, therefore, the ending F#, 8 perfect fifths above
A#, can be a new beginning F# of the next cycle. Also, 7 is the number of ‘completion’. Since the ending F# is 7 octaves above the
beginning F#, this means the completion of a cycle.
DISCUSSIONS
1. Shen Gua (Song Dynasty) explained the proceeding order of Five Notes (Tones) (note 5). The sequence is Metal (Re), Fire (So), Wood (Mi) and Water (La), ending wiht Earth (Do). The Five Note generation sequences based on san fen sun yi fa 三分損益法 is Earth (Do), Fire (So), Metal (Re), Water (La), ending with Wood (Mi).
CONCLUDING REMARKS
·
The Five Phases and the Five Tones theory are not flawless.
However, they are not unscientific superstition, either. The theory should be applied with discretion to
medicine. A mechanical fit of the theory
to reality should be avoided.
Note 1: Ted
J. Kaptchuk, “The Web That Has No Weaver”, Criticism of Five Phases Theory, p.
351. Following two short excerpts are from 王充Wang Cong's work:
"The body of a man harbors the Qi of the Five Phases, and therefore (so it is said) he practices the Five virtues, which are the Tao (Way) of the Phases. So long as he has the five inner Organs within his body, the Qi of the five Phases are in order. Yet according to the theory, animals prey upon and destroy one another because they embody the several Qi of the five Phases; therefore the body of a man with the five inner Organs within it ought to be the scene of internecine strife, and the heart of a man living a righteous life be lacerated with discord. But where is there any proof that the Phases do fight and harm each other, or that animals overcome one another in accordance with this?" p. 352.
"The horse is connected with the sign wu (Fire), the rat with the sign zi (Water). If Water really controls Fire, (it would be more convincing if) rats normally attacked horses and drove them away." p. 352.
Note 2:
Giovanni Maciocia, “The Foundations of Chinese Medicine”, The System of
Correspondences in 5-Element Physiology, p. 25.
Note 3: Lao-tzu
老子 （Tao Te
Ching
道德經，6th
century BC
） said, 'The Way (Truth) gave birth to unity, Unity gave
birth to duality, Duality gave birth to trinity, Trinity gave birth to the
myriad creatures.
（道 生一 ， 一
生 二 ， 二 生 三 ， 三 生 萬 物。 ） Huai-nan Tsu
淮南子 （卷 三 天 文 訓，2nd century BC
） states truth (way) named natural law
begins in one. Since one cannot multiply, it splits into yin and yang. When yin
and yang reach the state of harmony (can also be when yin marries with yang),
all things are born.
Note 4: “Acutone,
A New System of Healing Based on the Ancient Science of Sound”, Dean Lloyd,
John Pirog, P. 6-11. The ‘Book of Master
Guan’ (Guan Zhi, c. 4th century B.C.) said that the Yellow Emperor’s
pentatonic scale was created by a process called ‘generation by the fifth’ from
the fundamental note ‘Gong’. The
frequency of Gong is the Yellow Bell (Huang Zhong) pitch, the fundamental
frequency of the earth, which comes from a pitch-pipe of 81 fen long and
corresponds to F# to G# in the modern scale.
Note 5: Shen Gua of Song dynasty 宋朝沈括 said, "One LU (music law) (one fifth) has five notes (tones), so twelve LUs contain 60 notes. Seasons begin with East(Wood) and proceed counterclockwise. Sound begins with West (Metal) and proceeds clockwise. Yin and Yang intertwine and changes occur. That Chi begins with East explains four seasons begin with Wood and Wood passes on to Fire, Fire to Earth, Earth to Metal, Metal to Water and so forth in a clockwise fashion. That sound begins with West explains Five Notes (Tones) begin with Metal and Metal passes on to Fire, Fire to Wood, Wood to Water, Water to Earth and so forth in a counterclockwise fashion. 一律含五音，十二律纳六十音也、尾氣始于東方而左行。音起于西方而右行，阴阳根错而生变化、所谓气始于东方者。四時始于木，右行傳于火，火傳于土，土傳于金，金傳于水，所謂音始于西方者，五音始于金，左旋傳于火，火傳于木，木傳于水，水傳于土。"
