598 A Reply to Earl Stanhope, on Ids Defence of 



the heatings," and of course so acute an observer as His 

 Lordship cannot fail of perceiving them : and will be ne- 

 cessitated to " beat" a retreat, out of the labyrinth of error 

 into which he has with temerity advanced, instead of think- 

 ing to " beat" his pretended " facts" and " important mu- 

 sical truths" into me, or any one else who has the least pre- 

 tensions to mathematical knowledge. 



VI. — I have here to complain of the same superficial view 

 of the subject, as His Lordship took when commenting on 

 decimally divided monochords : the object of any general 

 notation of musical intervals cannot be to represent the per- 

 fect concords, as j i-, -f , 4 £, &c, more simply than they 

 are already expressed, but for comparing inconcinnous inter- 

 vals, such as His Lordship's biequal third for instance, with 

 any other intervals : if we examine the i( important musical 

 truths" in Stereotype with this view, what do we findj more 

 than that the biequal third has an approximate ratio of 



2,371,708.245 +,„„,,,,„„ 

 3,000,000,000 



(page 23) ? If we wish to compare this with 



the triequal quint for instance, whose ratio is stated in the 



. 3,008,298,850+ , . ' . 



same page, viz. 3-^,55^555-, and are desirous to learn 



their difference or the interval remaining after the former is 

 taken from the latter; in vain do we search the records of 

 " musical truths" for the mode of accomplishing this. A 

 novice, misled by the term " difference" in the last column 

 of this page, might think his work easy, and attempt to 

 give us the difference of these fractions, already reduced to a 

 common denominator j for the purpose; but on discovering 

 that the least interval had the largest numerator, here our 

 tyro's exertions would probably end. One a little more ex- 

 perienced would discover, that it is a ratio which is to be 

 deducted, and recollecting his school rule for the division of 

 fractions, would proceed to multiply the denominators and 

 numerators together reciprocally, when after proper reduction, 



.2,009,298,8.504- ! . VI- „ , „ , 



• 0.7! n ci* oirj. would appear as the ultimate " truth to be 

 come at. 

 Now those who have done me the honour, of attending to 

 2 the 



