On Musical Temperament. 181 
-ealculated, will be found in the 2d, 3d, and 4th columns of 
Table VIL. 7 
Having ascertained the temperaments, the value of the 
diatonic and chromatic intervals may be found. The Vth CG 
being flattened 156, and the Vth FC 139, the major tone FG 
q  mnust be diminished 1564139, or be =4820. By thus fixing 
pe the extent of one interval after another, from the temperaments 
7 = of either of the different kinds of concords, as is most convenient, 
the intervals in question will be found to have the values ex- 
hibited in Table VI. a 
Let the numbers in this table be added successively, begin- 
ning at the bottom, to the log. of 240, the number of vibra- 
tions per second of the tenor C, (see Rees’s Cyc. Art. Concert 
Pitch,) and the numbers corresponding to these logarithms 
- will be the vibrations in a second, of a string sounding the 
| several degrees of the scale. They are shown in col. 6, 
| Table VII. . 
Since the length of a string ceteris paribus is inversely as 
its number of vibrations, the lengths in col. 5 may be deduced 
from the vibrations in col. 6; or more expeditiously, by sub- 
tracting the numertial distances from C of the several degrees 
in Table VI. from O, and taking the corresponding numbers, 
from the table of logarithms. These numbers, when used 
4s logarithms, must be brought back to the decimal form, 
agreeable to Scholium 2. Prop. I. 
To find the number of beats made in a second by any con- 
cord, it is only necessary to take from col. 5 the numbers 
belonging to the degrees which terminate that concord, and to 
multiply them crosswise into the terms of its perfect ratio. 
The difference of the products will be the number of beats made 
inasecond. The $ last columns contain the beats made by 
each of the concords, in 10 seconds. 
. 
' 
' 
: 
| 
