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CHINESE MUSIC. 21 Thus, when the flute-player is warned by the heading of his music that chia-chung is to be considered as tonic or lciing, he knows that the five-note gamut of those three instru– ments will be- Chia-chiing, chung-li;,, lin-chung, ying-chung, pei ying-chung, Kung, shu,ng, chiao, chih, yu, and he will play accordingly. In their music the Chinese carefully avoid the pien or half tones. Therefore the note creat,ing half tones are named in the heading, that they may be excluded. OF THE DIATONIC GAMUT. In Westem music we call t:;he diatonic gamut a scale of seven degrees · (eight with the ·octave), containing five full tones and two half tones. In the major scale the semitones are found between the third and fourth deQ"rees and between the seventh and eighth. In the . 0 minor scale they are between the second and third and between the fifth and sixth degrees. The Chinese gamut also contains eight degrees, but these being a series of perfect fifths brought within the compass of an octave, without having undergone any temperament, they form irregular intervals incompatible with our tempered instruments. - Experience teaches us, and it is proved mathematically, that if the following series of perfect fifths, C, G, D, A, E, is not tempered, the E last obtained will be found too shci1-p to form a true maj or third to the. note C. Indeed, the third thus obtained is so sharp as to be absolutely offensive to the ear. If we continue the above series we shall find defects in all the other intervals. To exemplify this assertion, let us suppose that t he absolute length of a tube necessary to sound. the note C or hiiang-chung is V,1\? parts of an inch, and let us take from the comparative table on p. 12 the notes necessary to form a diatonic scale ; we shall have the following table :- Required Lenath Required Length Comparison by Height of 'l'ubes to rend~r the of Tubes to render the of Line-. NAMES OP No·1'ES. Chine. e Notes,- Foreign Notes,- stated in r2oth parts stated in 1 20th parts of an Inch. of a.n Inch. Chinese. _ For~~ . - - - -- - - -- H i1,ang-chung .... Li11, ...,_ C /\ 526.237 540 Ying-chwng . ....... Fan J{. B 559.2 576 Nan-lii. ... .......... K 1ung I A 636 645.3 Lin-chitng .... ..... (Jh'ih R G 720 720 Chi ing-lu ........... Shang _t F 789.888 810 Ki~-hsi.. ............ Yi ~ E 852 864 I T'ai-ts'u .. ........ .. Ssil mi D 960 963.99 Huang-chimg ... . Ho 1t C 1080 H 1080 I