GENERAL MEETING. 27 
Mr. M. H. DoouirrLe made a communication on 
MUSIC AND THE CHEMICAL ELEMENTS. 
[Abstract. ] 
The mathematical theory of music requires the satisfaction of 
: Sane, sag 
the equation 2* = (5) nearly ; in which, for equal temperament, 
x = the number of equal intervals in the octave, and y = the 
number of these intervals that correspond to a nearly perfect fifth ; 
and, for untempered music, x = the number of approximately 
equal intervals in the octave, and y = the number corresponding 
to a perfect fifth. 
The above equation gives 
log 3 
Ey _ 176091 Type 
| art bg a nearly = 301080 7 ly; 
and by the method of continued fractions we obtain the succession 
7 24 31 
f i ti Ta coe Spr bee 
GF approximations > 5 777) pa" ) dio. 
For scales appropriate to major thirds, but disregarding fifths, 
we may substitute 2 for S in the above equations, and obtain 
HOE ts WO ae 
th t >) ==» oy 
Py OPPPOREMBORE ia). 5a! ea 
vibration ratio 7 : 4 (called by Ellis the subminor seventh), we may 
&c. For the chord having the 
Paes ; : Abi 
obtain in like manner the approximations % oF &e. 
Ue ahaa: : ; 
Since Cham Cy the first two series of approximate fractions 
include a common scale of twelve intervals to the octave, of which 
seven intervals give the fifth, and four give the major third. The 
first and the third of these series include a scale of five intervals 
to the octave, of which three constitute the major third, and four 
constitute the subminor seventh. There is some reason to believe 
that this is the scale of Japanese music, with the intervals 
Tea Ole ueeiney: We ; S : 
ca a c CAM aids a Five-tone scales have universally prevailed 
in early music; but it is questionable whether the vibration ratios 
