504 On the Stanhope Temperament 



The values of all the intervals in his lordship's tahle, page 

 311, some of which have been already mentioned, will be 

 found in my Table II. 



Twelve successions of four major sixths each, may (as iu 

 the case of the Til, before rnentioned) be carried on upwards 

 in tuning, and compared with the third octave ; miothcr 

 wolf is thus produced, which we call the sixieme wolf. 

 No. 13 in Table II, and is so considerable an interval as 

 nearlv to equal three commas ! 



I beg here to remark, that Nos. 13, 14, and 15,, besides 

 representing, in the two last columns, the diffeTcnces between 

 the sixieme, tierce, and quint wolfs, and the key-note re- 

 spectively ; represent also. No. 13, the minor third iiolf, or 

 VIII— 4 3ds, and likewise the VI and 3d wolf, or VI— sSds : 

 No. 14 represents the minor sixth ivolf or 2 VIII — aSths ; 

 and likewise the &t.h and III U'olf or 2 III — 6th : and 

 No. 15 represents the minor fojirth wolf, or 1 24ihs — 5VIII, 

 and likewise the V and 4 th wolf, or 7 4lhs — 5V. 



Thus nine out of the tuentij-one ivolves which may arise, 

 by comparing together ei'er?/ two of the seven conchords, viz. 

 3d, III, 4th, V, 6th, VI, and VIII, (including all of those 

 with VIII), have been examined, and produce only three 

 diflcrent intervals : the remaining twelve wolves I have not 

 'leisure at present to examine, but the mode of doing so is 

 sufficiently evident from these tables, and also of comparing 

 all the otker combinations of the seven conchords ; from a 

 complete table of which, a clearer insight into the natural 

 scale of music would be obtained than has, perhaps, yet been 

 had. 



- I recommend to the reader of lord Stanhope's mode of 

 tuninor, pages 300 to 302, to lay my Table I. before him, 

 and to con)pare the tuneable intervah in colunm 5 with each 

 step of his lordship's process, as he goes along, by which 

 the reason for each step will the belter appear. 



On the whole, I would not be considered as now giving 

 an opinion on the merits of the Stanhope temper mnent, com- 

 pared with those of M. Kirnberger (p. 302), Dr. Young, 

 Mr. Hawkcs (xxvi. 171), &c, Sec, but rather as anxious to 



assist 



