The series of the three major thirds, G, B ; — B, D sharp, which is the 

 same key as E flat ; — and E flat, G, forms a second column. 



The series of the three major thirds, D, F sharp, which is the same key as 

 G flat; — G flat, B flat; — and B flat, D, forms a third column. 



And, in like manner, the series of the remaining three major thirds, A, C 

 sharp, which is the same key as D flat ; — D flat, F ; — and F, A, forms a 

 fourth column. 



In order to distinguish these four columns from each other, I shall name 

 them from the lowest key in each column respectively ; thus, we shall have, 

 1st, The C column, which consists of C, E, and A flat. 

 2dly, The G column, which consists of G, B, and E flat. 

 3dly, The D column, which consists of D, G flat, and B flat. 

 4thly, The A column, which consists of A, D flat, and F. 

 Now, it is a very curious fact, that each of these four columns of major 

 thirds has its own distinct wolf, exclusively of the quint wolf, which, 

 as we have already seen, affects all the twelve keys without exception. 



If, in the C column, for example, the three successive major thirds, C, E ; — 



E, G sharp, which is the same key as A flat ; — and A flat, C, be all made quite 



perfect; then, CC, which is thus produced by means of those three perfect 



thirds, will not be a perfect octave, but it will be flatter than the perfect octave 



CC would be. The difference of pitch, between the C derived from the major 



thirds and the C octave corresponding to it, is what I shall call THE 



C WOLFf. I shall denominate it thus, because it belongs to the C column 



There will be found an exactly similar wolf in each of the other three columns 



These FOUR wolves may very properly be distinguished by the names of the 



four columns to which they respectively belong ; thus, we shall have, 



1st, In the C column, THE C WOLF. 



2dly, In the G column, THE G WOLF. 



3dly, In the D column, THE D WOLF. 



4thly, In the A column, THE A WOLF. 



t If, for example, the length of the wire which would yield 

 the sound of the first bass Cbe 



Then, the lengths of the same wire, under the same tension, 

 which would respectively jield the sounds of the three successive 

 perfect major thirds, would be as follows, viz. 



First bass E. 



First bass G sharp, which is the same key as the first bass A flat. 



The middle C which is thus derived from the major thirds. 



(Those numbers are found by taking four fifths successively.) 



Now, the length of that wire which would yield the sound of 

 the true middle C ; namely, the sound of the perfect octave above 

 the first bass C, would be only 



Consequently, the difference between those two last mentioned 

 lengths shews the value of the corresponding C WOLF. 



( 8 ) 



Quarters 

 of an 

 inch. 



120 



96 

 76 

 61 



60 

 1 



Hundredths 



of one quarter 



of an inch. 



SO 

 44 



44 



