3U8 Mr. A. J. Ellie. Tonometrical (Jbsewations on [Nov. 20, 



1 1. " Tonometrical Observations on some existing Non-harmonic 

 Musical Scales." By ALEXANDER J. ELLIS, B.A., F.R.S., 

 assisted by ALFRED J. HIPKINS (of John Broadwood and 

 Sons). Received October 30, 1884. 



Musical Scales are said to be Harmonic or Non-harmonic according 

 as they are or ape not adapted for playing in harmony. 



Most accounts of non-harmonic scales, such as the Greek, Arabic, 

 nnd Persian, either (1) are derived from native theoreticians, who 

 give the comparative lengths of the strings for the several notes, 

 whence, on the assumption that the numbers of vibrations are inversely 

 proportional to the lengths (which is only approximately correct in 

 practice), the intervals from note to note are inferred ; or (2) are 

 attempts to express the effects of the intervals by the European equally 

 tempered scale. The former when reduced, as in Professor J. P. N. 

 Land's " Gamme Arabe," 1884, is the best that can be done without 

 hearing the scales themselves. The latter is utterly delusive and mis- 

 leading. 



Having about 100 tuning-forks, the pitch of each of which has been 

 determined by Scheibler's forks (see " Proc. Roy. Soc.," June, 1880, 

 vol. 30, p. 525), and having had an opportunity of hearing the notes 

 themselves produced on various instruments, and* having had the great 

 advantage of being assisted by Mr. A. J. Hipkins's musical ear, which 

 is wonderfully acute to detect and estimate minute differences of 

 pitch, and without which I could have done little,* I have been able, 

 I believe for the first time, to take down the actual pitch of the notes 

 in various existing non-harmonic scales far better than it was possible 

 to do with the siren or the monochord, which are not only difficult to 

 manipulate and to carry about, but at the best are very apt to mis- 

 lead. Where it was impossible actually to hear the sounds, I carefully 

 measured the comparative vibrating lengths of the strings producing 

 the notes on fretted instruments, whence, with by no means the same 

 certainty, the scales could be inferred. But I have not here noted 

 these measurements or their results, unless I could contrast them with 

 the intervals obtained by measuring the actual pitch of the notes pro- 

 duced on the instruments themselves, as in the cases of India and 

 Japan. 



But the mere statement of the numbers of vibrations, or of the 

 vibrating lengths of the strings producing a scale, conveys no musical 

 notion whatever to a musician. He wants to know how many equally 



* Throughout this paper, " we " and " us " relate to Mr. Hipkins and myself 

 jointly, and all measurements of numbers of vibrations made by us rest on the 

 judgment of Mr. Hipkins's ear with respect to the position of the note heard 

 between two forks, of which I had previously determined the pitch, or their Octaves. 



