Mr. A. J. Ellis. Tonometrical Observation* on [Nov. 20, 



G 200 D 150 qB 150 F 200 G 150 q4 150 (, 200 C, 

 200 350 500 700 850 1000 1200 



although in the Middle Ages a different scale prevailed in Arabia, to 

 which I need not further allude. Now between Zalzal's time and this 

 mediaeval alteration the Crusaders brought the Syrian bagpipe to 

 England, and after it had passed out of fashion in England, it became 

 the national instrument of the Highlands of Scotland. 



Such an instrument, made by Macdonald, of Edinburgh, and 

 obligingly played to us by its possessor, Mr. Charles Keene, the well- 

 known artist, yielded on examination the following results : 



Highland Bagpipe. 



Vib. 395 441 494 537 587 662 722 790 882 



From vib. . . ' / 191 a' 197 i' 144 c" 154 d" 208 </' 150 f" 156 /' 191 a" 

 Sums from a'. -191 197 341 495 703 853 1009 1200 

 Tempered . . - 200 200 350 500 700 850 1000 1200 

 Notes c d qe f g qa 4|> c' 



The tempered form, therefore, coincides with the Damascus form of 

 Zalzal's scale, which I did not discover till long afterwards. The 

 theory of this scale is lost, but it is usual to make g' to a' rather 

 less than a whole tone, while the two drones, an Octave and two 

 Octaves below a', necessitate a pure Fifth, a' 702 e". Zalzal divided a 

 Pythagorean minor Third of 294 cents into 151 and 143 cents ; the 

 modern instrument divides the just minor Third 316 cents, probably, 

 into 151 and 165 parts. We thus get a possible rationalised form of 

 the bagpipe scale, the first attempted, so far as I know. As usual in 

 bagpipe music, I begin the scale on a'. I have calculated the vibra- 

 tion to the same base a 441 vib., for both tempered and rational vibra- 

 tions, to show how close they are to the observed : 



nationalisation of the Bagpipe Scale. 



Observed vib. . 441 494 537 587 662 722 790 882 



Tempered vib.. 441 495 540 687 661 721 786 882 



Rational vib... 4 U 496 541 595 662 722 794 882 



Notes a' 204 V 151 c" 165 d" 182 e" 151 /" 165 g" 182 a" 



Sums of cents . 204 355 520 702 853 1018 1200 



Ratios a / 8:96'll:12c"10:llrf"9:10"ll:12/"10:ll/'9:10 a" 



Ratio from a'. . 1 8:9 22 : 27 20 : 27 2:3 11 : 18 5:9 2 



* In these tables the line " Tib." contains the number of vibrations determined 

 by us. The line " from vib." contains the notes, in this case those usually given in 

 bagpipe music, but generally merely distinguished by Roman numerals, I, II, III, 

 &c., with the interval between them in cents. The line " sums " gives the sums of 

 these cents, interval by interval, that is, the interval between each note and the 

 lowest. The line " tempered " shows the nearest intervals on an equally tempered 

 scale of 24 Quartertones in the Octave. The " notes" sometimes added, as those due 

 to taking as r, as already explained. 



