79 On Music. 
4 
_ fifth below » G are directed to be tuned perfect; but why 
these anomalies in the system are introduced I am at a loss to 
guess, especially as » G is thereby made 1c the worse by it. 
It isto be lamented by those who study the philosophy 
of musical sounds, that among the various ways in which 
musical intervals can be expressed, no one mode has yet 
been generally adopted by the writers on this subject, parti- 
cularly by those who treat on the temperament, or deviation 
from truth and nature, which is necessary for adapting the 
harmonic intervals to our imperfect instruments and com- 
mon notation of music, wherein only 12 intervals of sound 
are admitted in an octave; and this occasions the necessity 
to the student, on the appearance of every new scheme of 
temperament, for reducing the intervals resulting therefrom 
to some one standard or measure, before he can compare or 
judge of its merits and defects. Among the several ways of 
expressing these intervals, none is so general, or convenient, 
as the logarithms of their corresponding ratios ; and, in order 
to save the readers of Mr. Hawkes’s Treatise, and of your 
Magazine, a repetition of the trouble which I took in 1798, 
as also to compare this with the Stanhope temperament, 
described in your October number, and with Dr. Thomas 
Young’s progressive temperament: Phil. Trans. 1800; Sup- 
plement to Ency. Brit. 3d edit. ii, 663; or Young’s Sylla— 
bus, p. 95, I beg to present 
A Table 
eS 
