of the Musical Scale, 203 



quoted (published in 1801), contains a calculation and ex- 

 periment on the leats made by a succession of equally tem- 

 pered fifths, and mentions, that each fifth in ascending 

 leats half as fast again as the preceding one ; which is also 

 the result of my calculations above: and the same follows 

 immediately from Dr, Smith's original theorem. 



Instead of the three Jifths, Gd, da, and aS, each flat- 

 tened hy ^ of a coimna (as is done by his lordship in his cal- 

 culations and table, p. 309), producing eqziality of the beat- 

 ings, I find by a calculation (not direct, but approximating) 

 that the Jifih Gd must be flattened about -^^ of a comma j 

 the ff'th da, about -j-Vo- of a comma; and the fifth ae, about 

 -jSqL- of a comma, in order to make these successive fifths 

 leat equally quick, the rate of which will be found about 

 3-16 times per second in each case; the note d making about 

 268*4, and the note a about 401 '0 vibrations per second, 

 when thus tempered. 



The value of the tri-equal quint, deduced by experiment 

 in page 302 of his lordship's treatise, and calculated at 

 page 311, is shown in No. 5 of my Table II. 



In pages 304, 303, &c., where perfect thirds or thirds are 

 mentioned by his lordship, the major, or III, is to be un- 

 derstood. 



From the first experiment, in page 304, the tierce wolf 

 results : see No. 14 in Table II. 



The value of a major third in the scale of Hqual tempera- 

 ment, third experiment, page 304, is shown No. 8 in the same 

 table ; and where No. 4 exhibits ihe fifth of that scale, hav- 

 ing a temperament only -j^pths of that of a tri-equal quint I 



The minor thirds (3d), and resulting major sixths (VI), 

 appear to me to have been too slightly passed over by his 

 lordship in the note at page 305, and not to have had their 

 temperaments in the Stanhope scale sufficiently examined 

 and considered ; especially as the VI must, in full harmony, 

 continually be used with the III, on which so much stress 

 has been laid. The values of the 3d, 6th, and VI, with 

 their principal relations to other conchords, will be found 

 Nos. 12, C, and 1, in my Table II. 



The 



