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XIX. On the Stanhope Temperament of the Musical Scale. 

 By jM/\ John Farey. 



To Mr. Tilloch. 



HSIR, 

 AviNG undertaken to elucidate the Stanhope scale of 

 musical intervals by every means in my power, I beg here 

 to resume the tables, pages 195 to 197 of" your last volume, 

 for the purpose of staling the Stanhope intervals, &c. in 

 two other modes of notation : the first of which, or that by 

 tone major T {^g), tone minor i {-^%), and liemiione H. {\^) , 

 is already well known, and was omitted on the above occa- 

 sion merely for want of room. Kespccting the second mode, 



or that by ihc Schisma ~ ( V^j \.\\e lesser Fractio?ii (—^^-^j , 



and the most Minute m (^g,- ), I wish to remark, that the 



interval S I have been long acquainted with, as the lesser 

 Diesis of Mr. Maxwell, and it is the flat temperament of the 

 fifths in my equal-temperament, mentioned in your 'last 

 number, p. 05 : the interval m, is the wolf or difference 

 between 12 fifths tempered as there directed and 7 octaves : 

 the other interval f I obtained, from a valuable set of manu- 

 scripts by the late Mr. Marmaduke Over end, organist of 

 Islewortli, in Middlesex, now in the possession of Dr. Call- 

 cott, w'ho obligingly lent them to me for perusal, since I 

 had completed n)y equal temperament. The intervals m 

 and fare the two smallest intervals which Mr. Overend was 

 able to deduce, from an almost endless subtraction of the 

 ratios expressing musical intervals from each other, in all 

 their forms of combination; their smallness, compared 

 even with S, si.emed to me to render them fit to be used 

 therewith in expressing musical intervals; and so I have 

 found them, in an extensive reduction of Mr. Overe?id's 

 scales of intervals into this notation, and also in Lord Stan- 

 hope's intervals, shown in columns 6 and 7 of Table I, and 

 columns 4 and 3 of Table II. folio vving. 



Table 



