CHINESE MUSIC. 11

The question has been raised as to whether the iiis 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

the sound will vary in pitch accordmg to the degi-ee of pressure of the air. The different

notes so produced are called harmonics. The longer and narrower the tube, the more harmonics

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.

1

"^-Z -.i 456789 etc.

A tube closed at one end \vill give only the harmonics marked with odd numbers, with

this important peculiarity, that to produce the same note this tube requires only half the length

of an open tube.

m ^ ¥^

e-1

1 1 etc.

The Hrst Inumg-chang tube measured only i foot. An open tube of that size would

scarcely give any sound, whereas a corked tube i foot long gives the same note as 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 lils the Chinese added two new series, one lower and one higher.

The lils were used merely to regulate the instruments and give a uniform pitch to the

music. The diameter of all the las must be the same.' Meng K'ang (^ ^) says that the

<;-ircumfGrence of all tubes diminislies according to their length, but this is explicitly contra-

dicted by Ts'Ai Tzu (^ ^), who quotes Cheng Ivang-ch'eng (% )^ ^) and Ts'ai Yung (^ g,)(two gi-eat wine-bibbers and famous writers on music), and he flatly declares that Meng K'ang

and his adherents know nothing about music.'^ The tubes were all of tlie same thickness,

circumference, and diameter; only the length varied according to the sounds. HaarKj-chv/ny,

or the first tube, was i foot 'in length in reality, but that foot was considered as being only 9inches, because 9 is perfectly divisible by 3, whereas 10 is not.'*

•^''^ W)^J^n^li.^ ^'"ch «vys: A ft § 1 :ft- ^. 11 E ^•