interval between that C and the G next above a perfect quint. And then, in 

 like manner, let us tune all the following intervals by perfect quints, until we get 

 to C again. We shall then have twelve perfect quints, in the following order, 

 which will bring us to the upper C of this second instrument, viz. 



C, G ; — G, D ; — D, A ; — A, E ; — E, B ; — B, F sharp, which is the 

 same key as G flat f ; — G flat, D flat ; — D flat, A flat ; — A flat, E flat ; — 

 E flat, B flat ; — B flat, F ; — F, C. 



Now, let us suppose that the pitch of the upper C in the first instrument be 

 carefully compared with the pitch of the upper C in the second instrument, and 

 it will be found that those two C s are not in unison. For, the upper C in the 

 second instrument, which was pitched by means of the twelve perfect quints, will 

 be found to yield a more acute sound than the upper C in the first instrument, 

 which was pitched by means of the seven perfect octaves. Or, hi other words, 

 the C twelfth quint in the second instrument will be sharper than the C seventh 

 octave in the first instrument. 



The difference of pitch between those two high Cs will be rendered far 

 more perceptible to the ear, by transferring that difference to the lower octaves. 

 Therefore, let us suppose that the third instrument be tuned in the following 

 manner, viz. Let us begin by tuning the upper C in this third instrument to the 

 same pitch exactly as the G 'twelfth quint, or upper C, Jii thie second instrument. 

 And then, beginning froin the upper C in this third instrument, let us tune all 

 the other Cs in it successive perfect octaves descending. 



Now, if we strike one of the C s in this third instrument, about the middle 

 octave, or lower down, and if at the same time we strike the corresponding C 

 in the first instrument, then the C in the third instrument, which was derived 

 from the C twelfth quint in the second instrument, will yield a more acute sound 

 than the corresponding C in the first instrument which was derived from the 

 octaves. A beating will be heard between them ; and a kind of disagreeable 

 sound will be produced, not very unlike the howling of a wolf at a distance. 

 Now, the difference of pilch, between the C derived from the quints and the 

 corresponding C derived from the octaves, is what is technically called, by 

 tuners, THE WOLF. 



Musicians and tuners are in the habit of talking of the wolf in the 

 singular number. I shall, however, shew in the sequel that there are as many 

 as FIVE WOLVES, in the quints and major thirds taken together, in all those 

 instruments which have exactly twelve fixed keys, or exactly twelve fixed tones, 

 in each septave. Now, in order to distinguish these five from each other, the 

 difference of pitch, between the C derived from the quints and the corresponding 

 ( derived from the octaves, (which is, by tuners, commonly termed the wolf,) 

 fa what /shall call THE QUINT WOLF. See the following table. 



t Whenever I say that F sharp is the same key as G flat, or that G sharp is the same key 

 as A fl:it \c. I always mean that it is so in a keyed instrument which has exactly twelve 

 fixed ><>s in each septave. 



( 5 ) 



