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CHINESE MUSIC. 11 The question has been raised as to whether the lus were open at both ends or not. Those acquainted with the theory of the vibration of tubes will readily admit that they were stopped at one end, for the following reasons. Sound in a tube, open or not, is produced by the vibrating movement of the air, and t·he sound will vary in pitch according to the degTee of pressme of the air. The different notes so produced are called ha?·rnonics. . The longer and narrower the tube, the more harmonic it will give. A long tube open at both ends will give the· following harmonics, which are marked I , 2 , 3, etc , according to their place in the succession of sounds. 0 <2 i ~o t) 0 0 0 -0- 2 3 4 5 6 7 8 9 etc. A tube closed at one end will o-ive onlv the harmonics marked with odd numbers, with t, " this important peculiarity, that to produce the same note this tube requires only half the length nf an open tube. @= t2 & 0 ~e 0 -9 3 5 7 9 1l etc. The first huu/rtg-claing tube measured only 1 foot. Au open tube of that ize would scarcely give any sound, whereas a corked tube 1 foot long gives the same note a · an open tube 2 feet long. Moreover, the tubes of the Pandean pipe, which was a collection of bamboos made on the principle of the lus, were closed at the lower end. To their series of 12 lus the 'hinese added two new series, one lower and one higher. 'The lus were used merely to regulate the instn{rnents and gi ve a uniform pitch to the music. The cliameter of all the lus must be the same. 1 MENG K'ANG (~ 1,l) sn.ys that the circumference of all tubes diminishes according to their length , but this is explicitly contra– licted by Ts'AI Tzu (~ ,J- ), who quotes CHENG K'ANG-CH'ENG (~ Bre »x.) and Ts'Al Y UNG (~ ~) (two great wine-bibbers and famous writers on music), and he flatly declares that MENG K 'AKG and his adherents know nothing about music. 2 The tubes were all of the ·ame thickne · ·, t; iTcumference, and diameter; only the length varied according to the som1ds. Huang-chvn.fJ, 4 ir the first tube, was I foot in length in Teality, bnt thli),t foot was considered as being only 9 iuchos, because 9 is perfectly divisible by 3, whereas 10 is not. 3 ' See ~ bit nx J:J 1t tt' wbicb [LYS : }L fft ~ Iii -Jr.. ~ , ~ =~– • Sec ~ T : Bre lffl ~ ;r. ~ ff: g · , Jlt j{ ii .½. u ~ -Ii + ~ Iii JfJ z -Jr.. tl ~ +. 2