104 Oil the Stanhope Temperament 



columns 5 and 3 of the Tables, first reducing the fractions to 

 a common denominator, and attending carefully to the 



V 4- 4 + III 



signs : thus, if the Stanhope 6th, C b A, or — » 



were required to be deducted from the octave c, or V + 4 j 

 we have, when reduced to a common denominator, the 



„ . V + 4 + III ,2V + 24 ,, c J 



tractions and ■ ^, and the former de- 



2 2 ' 



, , ^ ^ , 2 V + c4 - V - 4 - III 

 ducted from the latter gives , or 



V + 4-III , -, -,^,- VIII -III. . 



— —-^ ; or, because V + 4 = VIII, is the 



2 2 



interval required, and appears to be his lordship's li-equal 



third.. See No. 6 in Table II. 



As an example of the meaning and uses of column 1 in 



Table Ij we might have incjuired what is the value of this 



, VIII -III . , ,c , , cc 1 • 



interval in aal/ notes or number or nnger-key m- 



lervals : thus, the VIII containing 12, and the III 4 half 



notes, we have , equal to four half notes, which is 



found to answer in the table to E or the III ; but is in this 

 case a li-equal third instead of a diatonic III, the minute 

 difference of which intervals, is not taken into account when 

 we speak of, or estimate by, the half notes of music writers 

 and instrument makers. 



It is only when musical intervals are supposed perfectly 

 equal among themselves (each -jL- of a lineal octave) that they 

 can be added together, and treated as we have last done ; and 

 the arithmetical differences of the lengths of strings, or evei^ 

 of the fractions expressing those lengths, cannot, as before 

 observed, represent " the value" of intervals, or even of 

 the error or difference between two intervals, as they are 

 said to do by our noble author, at the bottoms of pages 294 

 and 296, last paragraph but one in page 301, fourth para- 

 graph page 302, and in all the instanftes in the last columa 

 of the table at page 311 ; mistakes, of which the student 

 should be particularly aware. 



Table 



