On RYTHMICAL MEASURES. 69 



These oppofite operations of divifion and combination faci- 

 litate and Amplify the procefs of rythmical perception, and, at 

 the fame time, enable us to take in a much wider range of 

 proportion, than could be done if we proceeded only in one di- 

 rection. As the unit is commonly fome intermediate time be- 

 twixt the longed and the Ihorteft which occurs in the fucceflion, 

 it bears no very diftant proportion to either of them. We 

 frequently meet with femibreves and femiquavers in the fame 

 piece of mufic ; notes which are to one another in the proportion 

 of one to fixteen. This proportion is too great to be conceived 

 and felt by a fingle operation of the mind. When, however, 

 the crotchet is accounted the unit, we are enabled to eftimate, 

 and accurately to exprefs, thefe diftant times, without going 

 beyond the fimple and familiar proportion of four to one, on 

 either hand. 



The ancients indeed accounted their fm ailed time as the 

 unit or ftandard of rythmical movement. This fmalleft time, 

 however, was not lefs than that of a fhort fyllable in pronun- 

 ciation, and they had no founds in their fuccefTions, which 

 they confidered as bearing to this a greater proportion than that 

 of two to one. It may alfo be of importance to remark, that 

 as their arithmetic was very imperfect, compared with that of 

 the moderns, it is very probable that they had not the fame 

 ideas of fractional divifion, which we now have. In treating 

 upon any fubject, therefore, in which number is concerned, 

 they would naturally take for their unit the fmalleft of the kind 

 which they were examining, fbmething that was either naturally 

 indivifible, or that they did not expect to be under the neceflity 

 of dividing. Thus Aristides Quintilianus calls the fingle 

 time of rythmical movement o-ripeiov ; a term by which, as he 

 tells us, geometricians exprefted that which has no parts. This 

 time, he adds, being without parts, holds, in fome degree, 

 the place of unity *. The moderns, on the other hand, being 



able 



* Page 32, 33. Edit. Meib*- 



