On the Stanhope Temper avient. 151 



a major third, be made a very little imperfect, then we in- 

 stantly perceive a slow beating, which is a third sound 

 completely distinct from either of the two sets of beats 

 above mentioned. The beating (as every one, except 

 Mr. Farej", well knows), increases in quickness, as the im- 

 perfection increases. And it is only by means of the com- 

 parative quickness or slowness of the beatings, that the 

 exact degree of the imperftction of any musical interval can 

 be ascertained by the human ear. 



The BEATINGS which denote " equal deviations from per- 

 fection," in those intervals which are exactly similar, pos- 

 sess a distinguishing equality in their effect upon the ear, by 

 means of which, and bv means of which alone, we are ca- 

 pable of ascertaining, with the requisite precision, the equa- 

 lity of the imperfections in such corresponding intervals, 

 when carefully compared with each other merely by the ear, 

 unassisted by any vionochordical or other mechanical con- 

 trivance. 



This phaenomenon I explain as follows. Let us suppose, 

 as an example, that I wish to compare the tri-eqiial quint 

 DA in the first bass seplave, with the tri-equal quint DA 

 in the middle septavc, of a piano forte. If those quints be 

 exactly what they ought to be, if the octaves be tuned per- 

 fect, and if the lower D A be struck alone, there will be 

 heard three sounds; viz. the beat of the first bass D, and 

 the BEAT of the first bass A, and also a third sound which 

 is the BEATING of the tri-equal quint DA in the first bass 

 septave. In like maimer, if the upper DA mentioned above 

 be struck alone, there will also be heard three sounds ; vij5, 

 the BEAT of the middle D, and the beat of the middle A ; 

 and likewise a third sound, which is the beating of the 

 tri-equal quint DA in the middle scptave. Now, lit those 

 two DAs be struck together, we shall then have four 

 BEATS, and also those two beatings above specified, which 

 two beatings will have no beating whatsoever between 

 them. But, let either of the two DAs be made cither a 

 little more or a little less perfect than a true tri-equal quint; 

 then, the two beatings above specified will produce a very 

 striking third sound, which might be denominated " the 

 K 4 bkating 



