1884.] some existing Non-harmonic Musical Scales. 381 



I 738 VII, the complete compass, is exactly the 49th harmonic 

 reduced to the same Octave, which is of course only 

 a curious coincidence. 



6. Dulcimer or Yang-chin, exactly like the ordinary dulcimer 

 (see figure in Grove's " Dictionary of Music," i, 469), with four 

 wires to each note forming two Octaves, the longer wires passing 

 under the bridge which limits the shorter. It is struck with elastic 

 hammers. The instrument being out of tune was tuned for us by the 

 musician who played No. 7, according to the Chinese names of the 

 scale in Dr. William's Middle Kingdom, which are there interpi'eted 

 as the major scale of E\>. If the conjectural just scale be correct, this 

 would be the scale of J3[> major, beginning on its second note C, and 

 is therefore comparable to the Japanese Ritsusen, which is the scale 

 of major begun on its second D.* 



Chinese names... Ho sz' i chang che" knng fan liu. 



Vib 205 226 240 2?2 300 340 364 409 



Fromvib I 169 II 105 III 217 IV 170 V 217 VI 118 VII 202 I 



Sums 169 274 491 661 878 996 1U8 



Conjectured Just 



Vib 205 228 24& 273 304 342 364 410 



Fromvib C 182 Z>, 112 E\> 204 F 182 G 1 204 A^ 112 B\> 204 c 



Sums 182 294 498 680 884 996 1200 



Pentatonic form. C 182 J) 1 316 ... F 182 S 1 204 A 1 316 ... c 



The tuner had great difficulty in tuning the semitones II 105 III 

 and VI 118 VII, that is, in tuning the notes III and VII. He 

 accomplished the second more easily than the first. The Pentatonic 

 form consists of two disjunct tetrachords, CF, Gc, each divided into 

 a Tone and a minor Third. 



8. Tamboura or Sien-tsu, a three-stringed guitar with circular body 

 aud long neck without frets. The strings were tuned to 239, 266, 

 'and 400 vib., making the intervals 185 and 706 cents, meant for 182 

 the minor tone, between the first and second, and for 702, a Fifth, 

 between the Second and Third, -very fairly tuned indeed. The strings 

 were plucked with bone plectrums, attached to the first joint of 

 thumb and forefinger, and projecting like claws. The tone was good 

 and very like a banjo. Only the following pentatonic scale was 

 played to us : 



Vib 320 357 400 480 536 .642 



From vib I 189 II 197 III 316 IV 191 V 312 I' 



Sums 189 386 702 893 1200 



* In writing tones in Pythagorean intonation formed by a succession of just Fifths 

 or Fourths from C, the ordinary letters are kept unchanged ; but for just intonation 

 it is necessary to have a series a comma lower. These have a subscript 1, as JDj, so 

 that, in vibrations, Dj : D = 80 : 81. Similarly another series would be a comma 

 sharper, and be written with a superior 1, as E'y, so that, in vibrations, j&(j : E ll y 

 80 : 81. 



2c2 



