58
THE CHINA REVIEW.
line in that trigram; and likewise every single broken line (in the trigram for Earth) stands for Six."
Nevertheless there is such an amount of exact scientific knowledge of the theory of musis and such an acquaintance with Chi- nese music and the Yih King philosophy here combined and brought to bear on the doubtful question whence the ancient philo- sophy of the Chinese arose, that we venture to say no student of the Yib King should leave Dr. Wagener's essay neglected. Want of space compels us to confine ourselves here to noting some of the more important results of Dr. Wagener's investigations.
1. The characteristic features of ancient Chinese music appear to consist in this, that the Chinese seala did not originally progress according to pure fifths, that the con- sonance of the octave exercised an ira- portant influence from the very begin- ning, and that, as a matter of logical necessity, the number of tones was first cou- fined to five and then afterwards extended to twelve. Dr. Wagener starts on the correct supposition that the originators of Chinese music operated upon bamboo tubes, closed at the bottom, of uniform diameter and varying lengths, and that they constructed their scala on the basis of a tube measuring 9 grains along the inner periphery, 81 grains in length and therefore 1200 grains in cubie vohane. This being so, the Chinese musicians found that tube, besides supplying the primary tono (81), made also, when more effort was used in blowing, an upper tone apparent, viz. the duodecima. Endeavouring to obtain the latter by a separate tube the Chinese inventors of music found that they had to ent a shorter tube of the length of the primary tube. Cutting off then from a tube of the original length, they had al- together three tubes supplying the tones 81, 27, and 54. Comparing the tones thus furnished they must have recognized the consonance of the octave and of the fifth, as also the rule that in the one case the length of the tube is and in the other less by i
than the original tube, whence followed the recognition of the octave of the ground tone, 40%. The tube furnishing that new tone, 54, being treated like the original tube ie. having of the length cut off, they obtained two tubes furnishing respectively tones 36 and 72. The latter tube (72) being also treated according to the rule thus evolved viz. of alternately adding or dednoting of the length, furnished two further tubes giving tones 64 and 32. Then again ent- ting off they obtained tone 42§, having now altogether two octaves each of which contain- ed five tones. But now it was found that this last tone differed so imperceptibly from the octave 40% that the then comparatively un- practised ear of ancient musicians identified the two, and thus the series of tones was therefore considered finally conoluded. In this manuer two series of tubes had been obtained:--
83. 72. 64. 54. 48. 40. 36. 32. 27. 24.
Of these two series of tones, the toues 81, 403, 72, and 36 were found to differ from the tones 27, 54, 24 and 48, the former being naturally ascribed to the male prin- ciple (Yang), the others to the female prin- ciple (Yin), whilst the tones 64 and 32 stood midways and became the basis of the sub- sequent development of the Chinese scale into twelve tones.
2. We cannot quite follow Dr. Wagener in his attempt to deduce the system of the eight diagrams and thereby the whole Yih King philosophy from this theory of rausie. He becomes somewhat obscnre here and The very rather difficult to understand.
first link of connection between the two systems, seems clear enough, but more ingenious than plausible. With reference to the construction of the eight trigrams by Fuli Dr. Wagener says:—
"The first object was to represent the two principles Yin and Yang by symbols, and whereas in music the male tone (e.g. 81) was directly derived from the primary tube, whilst the corresponding female tone was pro-
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duced only by duplicating the upper tone 27, which latter strictly considered belonged to a tube of in length, Fuhi accordingly formed his symbols, representing Yang by a long line, and Yin by two short lines This derivation affords the eimplest explaus- tion of the reason why the unbroken lines in the trigrams and hexagrams are designated "first nine" () "second nine" () and so forth, and why the broken lines are referred to as "first six" ( A), "second aix" and so forth. For the length of the primary tube was, from tho beginning, assumed as equal to 9 inches, and the length of the first tube furnishing a female tone was obtained by duplicating one third, the length of it being therefore 2 X 3-6 inches."
Plansible as this may seem, we cannot agree with Dr. Wagener, because our own study and a historical analysis of the Yik King convinced us that the really ancient part of the Yil King was constructed with- out any regard to the Yin and Yang prin- ciples, which, we believe, were introduced into the Yih King philosophy centuries after the 8 trigramas and 64 hexagrams had been in practical use for purposes of divination.
59
Nevertheless we are quite ready to believe that the early study of music, and the laws and properties of numbers thence derived, had some influence on the early develop- ment of Wen Wang's and Chow Kung's systems of philosophy. But it remains yet to be shewn what that influence amounted to.
Dr. Wagener gives yet another explanation of the genesis of the eight trigrams, entirely unconnected with music, and based on the analogy of vegetable growth. This theory, which Dr. Wagener derived from a Japanese scholar, is very poetical, but a mere play of fancy, entirely unsupported by the Yih King itself or any ancient commentary.
3. The scala of modern Chinese music, with its twelve tones, appears to have been formed on the same principle as the old scals of five tones, viz. by alternately de- ducting or adding 1/3 of the length of a primary tube (Grundtonpfeife). In other words the twelve tones of the Chinese scala are obtained by proceeding from a primary tone (Grundton) and alternately elevating the fifth and depressing the fourth, The subjoined tables are constructed by Dr. Wagener in illustration of his subject.
Series of Tubes.
Series of Times.
Intervals,
ARA
Comparison with European Seala (German Notution.)
L 81
J.
1. 81
Ꮔ
IL 54
VIII. 2.
75, 85 *
9/8
h
II.
72
IIL 3. 72
1,0679
IV. 48
X.
9/8 16/15--1,0667
4. 67, 42*
V.
64
V.
5. 64
9/8
9/8
VI
42, 67
XII.
6. 69, 93 *
l
VII. 56, 89
VII.
7. 56, 89
1,1099
10/9-1,1111
VIII. 97, 93*
II.
8. 54
IX, 50, 67
IX.
9. 50, 57
I.
1,0679
33, 71*
IV.
16/15=1,0637
10. 48
f'
XI. 44, 95
XI.
11. 44, 95
XII. 29, 97*
40, 50
VI.
12. 42, 67 10, 50
9/8
1,1099.
B
9/8 a' 10/9 1,1111
Dr. Wagener observes that this Chinese scala of twelve tomes, with a distinction of male and female tones, based as the latter distinction is on the idea that the odd num- bers are male and related to Heaven, the
*
even numbers female and rolated to Earth, is identical with the scala of Pythagoras. As according to Origines' Philosophumena Pythagoras is asserted to have learned these theories in the East, from the Chal-
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