to what Exlenl, and how most readily attainable?" 185 



<3escribe an arch which will pass through B and H. Let a si- 

 milar arch passing through B and G be also described. Then 

 if we divide the arches BG and BH into seven equal parf^^*. and 

 let fall perpendiculars upon the line AC, we shall not only I'.is- 

 cover in the length of every line or string, what should properly 

 be termed the " natural scale," but also the probable origin of 

 *he Grecian " disdiapason," the line HG as well as the line FH 

 being equal to one-fourth of the original line AC. 



All music then is contained within the isosceles right-angled 

 triangle ABC ; and in proportion as we extend the edifice or 

 system beyond the boundary of the disdiapason, as thus 



so shall we deviate more and more widely from that beautiful 

 and perfect order which the great Architect of nature appears to 

 have established. 



You will now permit me to offer some remarks on that pass- 

 age of my former paper which glanced at the proportion of our 

 common chords; — the accusation of " heterogeneous mixture" 

 applied by some persons to those chords, as I mentioned in that 

 passage, not having received my altogether imqualified assent. 



That certain proportions do actually exist within these chords 

 is undeniable ; but that these proportions do not approximate, 

 in the remotest degree, to that superior species called ^' Har- 

 monic," must be confessed. Simple arithmetical progression is 

 indeed obvious in the chord minor (the natural third =4^, not 

 the tempered third = -^ being employed) : thus 

 Base, suppose 60"^ 

 3d Minor = ^ . . 50 I p . ., , , ^ 



Fifth = I .. 40>P'^ogress.on3.4.5.6. 



Octave = \ . . 30 J 

 But in our chord major even this species of proportion is de- 

 stroyed; viz. 



Base 60 



3d Major = -^ . . . . 48 



Fifth = .... 40 



Octave = . . . , 30 



• A division into 45 equal parts, delineated on a very extensive scale, 

 will afford much gratification to the speculative musician. 



Thus 



