Mr. A. J. Ellis. Tonometrical Observations on [Nov. 20, 



Conjectural Just 



Vih 320 356 400 480 535 640 



From Tib C 182 D, 204 EI 316 G 182 A t 316 c 



Sums 182 386 702 884 1200 



Transformed sums. . 498 680 884 182 Ifs 



This was again so nearly just that I have conjectured a just resto- 

 ration, C D! EI AI c : and if this is transformed, by beginning it with 

 G, or by deducting 702 cents from each of the last sums (previously 

 adding 1200 cents where needed), we obtain the scale G 182 A l 

 316 C 182 #! 204 E l 316 ,m which the intervals are precisely the 

 same as in No. 7. 



9. Balloon Guitar or P'l-p'a. The body of the guitar was oval. 

 There were four strings, the lowest tuned to 234 vib., and them its 

 Fourth, its Fifth, and its Octave, but we did not test the accuracy of 

 these intervals, which were tuned by the same musician who tuned 

 Nos. 7 and 8. Near the nut were four large, round-backed, semi- 

 elliptical frets, joining each other at bottom. These the player 

 did not use. But on two examples of the S. K. Museum, I con- 

 jectured by measuring the strings, that they were intended to give 

 such a tetrachord as 



C 204 D 90 E\> 114 E 90 F 



204 294 408 498 



or their just or tempered forms. There were 12 frets on the body of 

 the instrument. They were high but broad at the top. We did not 

 test each, but merely took down the following pentatonic scale : 



Observed vib. . 320 348 392 465 530 638 



From vib I 145 II 206 III 296 IV 227 V 321 VI 



Sums 145 351 647 874 1195 



Tempered vib.. 320 349 392 466 538 640 



From vib I 150 II 200 III 300 IV 250 V 300 VI 



Sums 150 350 650 900 1200 



The tempered scale agrees well in all notes but V. The scale is so 

 remarkable in every way, though it did not sound amiss, that I 

 suspect the frets to have been inaccurately placed ; they were bits of 

 wood roughly glued on. 



This completes our observations with the Chinese musicians. I 

 measured also the vibrating lengths of strings in two other P'i-p'as, 

 and also two Moon Guitars or Yueh-chins in the S. K. Museum. 

 One of the latter seemed intended for equal temperament of 

 12 Semitones, and it is the only Chinese instrument which has 

 suggested this to me ; the other looked like an attempt to divide the 

 Octave into eight Three-quartertones, and had at any rate eight tones 



