i'4 



NA TURE 



[August 2, 1894 



it should be firmly fixed to something with a consider- 

 able moment of inertia, and then placed on its cushion. 

 Any fairly regular motion of the case is fatal to good 

 going. And as to astronomical clocks, they should be 

 fixed to stone piers with the same sort of care as is 

 bestowed on transit instruments. 



Another paper, " On a New Astronomical Clock," notes 

 the defects of Graham's dead-beat escapement, and 

 suggests a new one, wherein the escapement wheel is 

 carried by a loose friction collar at a rate a trifle faster 

 than the proper rate, so that its pellets engage the pen- 

 dulum only occasionally, receiving the necessary check 

 and maintaining the motion of the pendulum sufficiently, 

 even though they only touch once a minute or so. 



In a paper " Cn Beats of Imperfect Harmonies," of date 

 1878, Lord Kelvin virtually lends his support to the view 

 advocated by Koenig, that in the appreciation of har- 

 mony the ear detects phase-difl^erences and is not limited 

 to analysis of a complex note into simple harmonic con- 

 stituents. For instance, a harmony of even and odd 

 vibration numbers (like 2 : 3) will have one kind of 

 phase relation, while a harmony of two odd numbers will 

 have another kind, the most obvious feature of these 

 phase relations being the way successive maxima and 

 minima coincide or oppose. In general the shape of the 

 curve representing the composition of two notes varies in 

 appearance, as is well known, according to the phase in 

 which they are compounded. If one of the constituents is 

 out of tune there will be a gradual transition from one 

 of these phase-relations to another. " In favourable cir- 

 cumstances ... a variation of the sound recurring 

 periodically in the successive cycles is distinctly heard. 

 ... It is this variation which is called the 'beat' on the 

 imperfect harmony.'' 



Lord Kelvin has made experiments on pure tuning-fork 

 tones, and his experience is " that in every case the ear 

 does distinguish the two halves of the period of each 

 beat. . . . The ear distinguishes the quality of the sound 

 represented by the sharp-topped and tlat-hoUowed curve 

 from that represented by the flat-topped and sharp- 

 hollowed curve. In the one case the pressure of air 

 close to the ear rises very suddenly to, and falls very 

 suddenly from, its maximum, and (as in cases of tides in 

 which there is a long hanging on low water) there is a 

 comparatively slow variation of pressure for a few ten- 

 thousandths of a second on each side of the instant of 

 minimum pressure ; in the opposite phase-relation there 

 is a slow change before and after the time of maximum 

 pressure, and a rapid change before and after the time of 

 minimum pressure." 



The car is thus found able to distinguish between a 

 push and pull on the tympanum ; or the receiving ap- 

 paratus is not symmetrical on either side of zero. This 

 is equivalent to saymg that second order of small quan- 

 tities must affect the sound as heard, and on this can be 

 based the usual theory of the difference and summition 

 tones of Hclmhollz. 



But the mode of expression adopted by Lord Kelvin is 

 not that of interference of any resultant simple tones; he 

 prefers to ihmk of the actual phase changes as directly 

 detected by the ear, and says that " a. revolving character 

 which I perceive in the beat is to me certainly distinct 

 N J. 1 292, VOL. 50J 



enough to prove that the ear does distinguish between 

 these configurations, which are one of them the same as 

 the other taken in the reverse order of time." 



According to his experiments it is singular how very 

 faint is the disturbance necessary to bring out these beat 

 tones : much less than would appear to be necessary on 

 HelmhoUz' theory of difference tones, whose amplitude is 

 proportional to the product of the constituent amplitudes. 

 Thus, " if when the approximate harmony C E is being 

 sounded, with the E slightly out of tune and the beats 

 on it heard, the faintest sound of G is produced by a 

 very gentle excitation of the fork by the bow, instantly a 

 loud beat at half speed is heard. ... It is marvellous how 

 small an intensity of the sound G is required to give a 

 smooth unbroken loud beat in the double period.'' This 

 practical method of tuning a major third, by addition of 

 the minor third above it, completing the common chord, 

 is of course well known ; but the ordinary Helmholtz 

 explanation, of beats between the C E difference tone 

 and the E G difference tone, scarcely seems to fit the 

 above observed facts. 



Again, if the notes C E G are sounded and one of the 

 notes (say C) is flattened, the beats are not only very 

 audible but " the sound dies beating, the beats being dis- 

 tinctly heard all over a large room as long as the faintest 

 breath of sound is perceptible. The smooth melodious 

 periodic moaning of the beat is particularly beautiful when 

 the beat is slow (at the rate, for instance, of one beat in 

 two seconds or thereabouts), being, in fact, sometimes the 

 very last sound heard when the intensities of the three 

 notes chance at the end to be suitably proportioned." 



Incidentally an inconvenient usage of musical nomen- 

 clature is mentioned in a note. The word " tone," 

 which is now coming to be used to mean a pure sine 

 curve disturbance or simple note, means in music the 

 interval of the major or minor or tempered second. 



Those who have to do with acoustics must have often 

 experienced the inconvenience of the ordinary childish 

 nomenclature of intervals — a fourth, a third, a seventh, and 

 soon — especially when these intervals are being numeri- 

 cally expressed at the same time. To call the interval 

 2: 3 a fifth, 3/4 a fourth, and f25 a third, is often con- 

 fusing. Might I suggest that these intervals, when true, 

 might be named readily and intelligibly as respectively a 

 do-sol, a sol-do, or if preferred a do-fa, and a do-mi ; 

 similarly a minor third would be a mi-sol ; a major and a 

 minor tone would be a do-re and a re mi respectively ; 

 and so on. 



It might be convenient to drop the /in sol, so as to make 

 all the syllables of two letters ; and th en the flattening 

 or sharpening of notes might be indicated readily by 

 a final a or c; thus a flattened major tone would be a 

 do-rea (the same as a re-mi), and a sharpened one a 

 doree. 



On the tempered scale the intervals could be called 

 cg,gc, cc, eg, Ike, with perfect ease. 



Again, the ordinary musical notation, with its various 

 clefs, if it were not hallowed by usage, would seem a 

 barbarous piece of stupidity. Undoubtedly a couple of 

 lines should have been understood as missing between 

 the bass and treble clefs, instead of only one ; so that 

 the V label could be aflixed to the top line of the bass 



