1884.] some existing Non-liarmonic Musical Scales. 371 



14 cents, and major Sixths too sharp by 16 cents, while of course the 

 minor Sixths are 14 cts. too flat, and the minor Thirds 16 cts. too flat. 

 That is to say, these would be the errors if the tuning were perfect. 

 The practice, as I have determined by actual measurement, is neces- 

 sarily far from being restricted to these limits. Hence the results 

 here given have to be compared with many other results from other 

 instruments of the same kind, tuned by different tuners before the 

 intended intervals could be, if they ever can be, satisfactorily deter- 

 mined. In the meantime we know that native ears have actually 

 been satisfied by the intervals here given. 



It must also be remembered that as the tones heard were often 

 exceedingly brief (as from wood harmonicons), or very impure, being 

 mixed with inharmonic proper tones (as from metal harmonicons, 

 kettles, gongs, &c.), it was generally impossible to count beats, and 

 often even exceedingly difficult to tell within what pair of forks 

 the note heard really lay, so that there is a possible error of two 

 vibrations occasionally, but, thanks to the acuteness of Mr. Hipkins's 

 ear, it is not probable that the error at any time exceeds one vibration 

 in a second. The number determined is therefore purposely given 

 only to the nearest integer. 



I. ARABIA AND SYRIA. 



The theoretical account of Arabic scales is admirably given in 

 Professor Land's " Gamme Arabe." It there appears that one 

 Zalzal, more than a thousand years ago, being dissatisfied with the 

 ordinary division of the Fourth, as 



C 204 D 90 E\> 114 E 90 F 

 204 294 408 498 



(where the figures between give the number of cents from note to 

 note, and the figures below give the number of cents from the lowest 

 note), introduced a division, which, carried out to the Octave, 

 amounted to 



G 204 D 151 qE 143 F 204 G 151 qA 143 B\> 204 C, 

 204 355 498 702 853 996 1200 



where qE and qA mean about a quarter of a tone less than (or before 

 coming to) E and A, and in the same way Eq, Aq would mean a 

 quarter of a tone beyond E and A. (In musical notes q will become 

 <j, a turned |>.) 



In later periods this was tempered to a division of the Octave into 

 24 equal Quartertones, as we learn from Eli Smith, an American 

 missionary at Damascus, who translated Meshaqah's treatise in 

 the " Journal of the American Oriental Society," 1849, vol. i, pp. 171- 

 '217. The scale therefore becomes 



