On Musical Temperament. ISl 



calculated, will be found in the 2d, 3d, and 4th columns of 

 Table VIL 



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 

 must be diminished 156-|-139, or be =4820. By thus fixing 

 the extent of one interval after anotlier, from the tempera- 

 ments of either of the different kinds of concords, as is most 

 convenient, the intervals in question will be found to have 

 the values exhibited in Table VI. 



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 

 Fitch,) 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 cseteris 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 numerical 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 

 as logarithms, must be brought back to the decimal form, 

 agreeably to Scholium 2. Prop. I. 



To find the number of beats made in a secondly 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 in a second. The 3 last columns contain the beats made 

 by each of the concords, in 10 seconds. 



