62 On Musical Temperament. 
TABLE III. 
Signatures. | Major Mode. Minor Mode. 
2 yee weitiak 6 Pico st | 
Sis. eT so ee 
b= . 322 72 
} oe ¢ 176 ° . 121 
Say . 180 7 
Qhs . 70 77 
Sbs ‘ 116 8 
Abs. 0 8 
Ratio of their sums 1201: 399 
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 relative frequency 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 I, are to be 
considered as belonging, not to the letters against which these 
multipliers stand, but to those which have the same position 
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