of the Musical Scale. 201 



of the li-equal third, deduced from experiment in page 301, 

 and calculated in page 311, will be found in my Table 11, 

 No. 6. 



A very radical defect in the application of the Stanhope 

 temperament to practice, as directed by his lordship, now 

 presents itself in the mistake made in the third paragraph of 

 page 301, and the third paragraph in page 302, in supposmg 

 that equal temperaments of two successive thirds, or of three 

 successive fifths, effected by means of geometric mean pro- 

 portionals interposed between the extremes in each case (as 

 mentioned at the top of page 301, and third paragraph m 

 page 302), and on which all his lordship's calculations are 

 found to be grounded (and to agree very exactly with my 

 calculations upon the same principles), produce ^^ equality 

 of the healings," by which, says his lordship, '' equal de- 

 viations from perfection may be correctly ascertained." 



For the purpose of showing the inconsistency of the two 

 methods here proposed, for obtaining equal temperaments to 

 a succession of the same conchords, I shall refer to the beau- 

 tiful theory of imperfect consonances laid down by the late 

 Dr. Robert Smith in his Harmonics, or rather to the late 

 professor Robison's popular explication of the same, in his 

 article Temperament, in the Supplement to the Encyclopcsdia 

 Brilannica, 3d edit. vol. ii. p. 656 aud 657. 



Referring to his lordship's table at page 303, vol. xxv. of 

 your Magazine, I take the last step or process of the tuning, 

 and consider, that the note C in the middle septave, according ■ 

 (o the present concert-pitch, occasions about 240 complete 

 vibrations in the air in one second of time, (see Sup. Ency. 

 Brit. ii. 649 and 651,) and, the vibrations of chords being 

 inversely as their lengths, we have 240 x \ = 120 for the 

 vibrations of the C next below; and 120 X |- = 180, the 

 viljrations of G, at bottom of the table; also 180 x \/^- 

 (the tri-c(iual quint reversed) = 26S-9j the vibrations of d; 

 also, 268*9 X yi£ =401-7, the vibrations of a; and 401*7 X 

 ylA = 600, the vibrations of E or c in one second of time : 



3 



and for proof , if we compare the vibrations of t' by considering 



it 



