23 



On Musical Temperament, 



TABLE III. 



The chance of occurrence for any chord varies as the fre- 

 quency of the key to which it belongs, and as the number be- 

 longing to the place which it holds, as referred to the tonic, in 

 Table II, jointly. Hence the chance of its occurrence in all 

 the keys in which it is found, is as the sum of the products of 

 the numbers in Table III., each into such a number of Table 

 II. as corresponds to its place in that key. To give a speci- 

 men of the manner in which this calculation is to be conducted, 

 the numbers belonging to the major mode in the three first 

 divisions of Table II, are first to be multiplied throughout by 

 176, which expresses the relativefrequency of the major mode 

 of the natural key. They are then to be multiplied through- 

 out by 322, which expresses the frequency of the key of one 

 sharp. But the first product, which expresses the frequency 

 of the Vth on the tonic, now becomes GD, and must be added, 

 not to the first, but to the fifth, in the last row of products. 

 The product into 59, expressing the frequency of the Vth on 

 the mediant, becomes BF^, an interval not found among the 

 essential chords of the natural key. In general, the products 

 of the numbers in Table III, into those in Table II. are to be 

 considered as belonging, not to the letters against which these 

 multipliers stand, bnt to those which have the same position 



