, his Principles for Tuning Instruments, &c. 299 



the new notation vol. xxviii. p. 142, would at once discover, 

 that 35.4J S 4- 7 f + S0| m, and 207-^ S + 4f + 18ra, 

 represent the triequal quint and biequal third respectively, 

 and that the difference of these, or 146-j;- £ + 3 f + 12$ m, 

 admits of an immediate comparison with all the various in- 

 tervals in the tab'e in plate V. of the same volume. One 

 simple subtraction would further show it to be, a minor 

 third flattened 14 * 2 -f 1 V m, or 2£ 2 + ± m more than the 

 diaschisma orqnint-wolf of our noble author: and hundreds 

 of instances might be shown, wherein this notation gives 

 still greater facility to the comparison of intervals with very 

 complex ratios, than it does in the above case ; but can His 

 Lordship show a single instance (except the well-known and 

 useful process of reducing large numbers of pence to pounds, 

 shillings, and pence, for some purposes be considered such,) 

 wherein his ingenious notation by scores, dozens, and odd 

 would possess any advantage over decimal arithmetic? ana- 

 logous to the conversion of simple ratios by the new notation 

 into three elementary ratios (or two in some cases) which 

 I have effected for the general comparisons of intervals ? or, 

 can his sapient approvers make out, similar advantages to 

 result from their " cubit " and i( measuring rod of Ezekiel," 

 for expressing the Lapland degree ? 



I have not dropped my design of entering at some future 

 time on a comparison of His Lordship's monochord and 

 equal-beating systems, with the systems of other writers, 

 particularly those which His Lordship has in so summarv a 

 way condemned, as I originally proposed, by the help of a 

 table of the temperaments and beats of every concord which 

 can arise in each system respectively; and as I am kindly 

 assisted in the labour of these calculations, by a gentleman 

 of more leisure than myself, with whom His Lordship is well 

 acquainted, he has in the mean time the opportunity through 

 him, of himself anticipating my intended comparisons, and 

 of giving, any further support to his systems, which such 

 comparative evidence will warrant. 



I am, sir, your obedient bumble servant, 



John Farey. 



,12, Upper Crown Street. Westmii 

 March 14, 1609, 



LIIL On 



