wire must be reduced to fifteen inches. The perfect octave is generally called 

 the octave, for the sake of conciseness. 



If the wire be reduced, not to one half, but to two thirds of its or.g.nal 

 length, namely, in the supposed case, to twenty inches ; then, the sound produced 

 by those two thirds will be that sound which is termed a perfect fifth, or a 



perfect quint. . 



If the wire be reduced to three fourths of its original length, namely, m 

 the supposed case, to twenty two inches and a half; those three fourths wdl 

 vield the sound which is termed a perfect fourth. 



And if the wire be reduced to four fifths of its original length, namely, m 

 the supposed case, to twenty four inches; those four fifths will yield the sound 

 which is termed a perfect third f. 



In like manner, any pitch whatsoever within the compass of the monochord 

 may be obtained, by regulating the length of the wire to the exact degree that 

 is requisite for that purpose. 



Havin- stated precisely what I mean by the expresses perfect octave, 

 perfect auill, perfect fourth, and perfect third, I will now shew that there is, 

 fn every musical instrument which has exactly twelve fixed keys, or exactly 

 twelve 'fixed tones, in each septave, a most curious circumstance which is 

 universal and unalterable. In order clearly to explain what I allude to let u 

 suppose a keyed instrument, the lowest key of which is C, to have exactly e.ght 

 Cs Let us also suppose that there be placed, in the same room, a second, 

 and also a third instrument; each of which is similar to the former in every 

 respect, except as to the method of tuning. 



Let us suppose that the first instrument be tuned in the following manner 

 Let us begin by tuning the lowest C to any given pitch. Then let us make all 

 the successive octaves, CC, CC, fct quite perfect. We shall then have seven 

 successive octaves, which will bring us to the upper C of this hist rument. 



Now, let us suppose that the second instrument be tuned as follows. Let us 

 begin, as in the former case, by tuning the lowest C ; and let us give it precisely 

 the same pitch as the lowest C of the first inrt rume^ The n let us make the 



t Thirds are divided into major third, and minor thirds. A major third is composed of 

 four inputs (or fit half-tones! as they are commonly called,) and a mmor third is com- 



^Th^rtwo species of ma.or thirds; namely, ^^J^f H 

 And the imperfect thirds are also of two species; viz. sharp th.rds, and flat thirds 

 ^17 if in a tuning instrument which has two wires of emial tmcWnes, the en^ 

 of some C wire be 300, and if the length of the corresponding E w re, under the* 

 leTeJL, be 240; then, CE will be a perfect tod. If the E wire be shorter ,| 

 uch » X> then CE will be a sharp third; that is fc l?f -. |*«* *JJ H 

 £ perfect third. But, if the E wire be longer, (such as 24!,) then C E wdl be a 

 flat third- Uiat is to say, a third flatter than the perfect third. ■ 



thirds) of two species also; viz. sharp minor thirds, and flat minor Surds. 



C * ) 



