to what Extent, and how most readily attainable f" 1 S3 



Although the major 4th is certainly inferior to the preceding 

 jTumbers called concords : yet, if this mode of calculation be just, 

 it is by far superior to the proper discords, as will appear by the 

 succeeding analysis. 



Analysis of Discords — [Base, as before counted, 12.) 



7lh Minor=:6-3- i.e. t^ or — — I shall call it 6f, for I am in- 

 clined to consider 6 1- an aberra- 

 tion, the latter number not be- 

 ing divisible into the extremes, 

 so as to produce any acknow- 

 Generated by ledged interval. 



Octave =61., C-, 

 and 6thMinor = 7|/^^'^"^' 

 In ratio as 4 to 5. 



Second =10-*- or ^ (properly called Tone major). 



Base =12 

 xby Octave = G 

 H-by7th Minor = 6|-) 72(1 Of. 



Semitone = 11 1 . . . . or -f^ 



and New Number* =10i/^^*" ^^* 

 Ratio 7 to S. 



* iOy is generated 



byBase=12\j,j ,^r 

 and Fourth = gj^^^^ean IW,- 



7lh Major =64- ... .or J- 

 Base =12 

 xby Octave = 6 

 -^by Semitone = 1 li)72(6|-. 



Such is the result of those uniform operations which I have 

 adopted in the analysis of our musical numbers; and by those 

 operations may be instantly discovered the superiority of the 

 intervals called concords; — all the discordant intervals, com- 

 mencing with the major 4th, being generated by means, whose 

 originating extremes have descended from the ratio of 3 to 4, 

 to that of 7 to 8. Intervals so basely constituted as the latter 

 can lay no claim whatsoever to proportion. Even our 3ds and 

 6ths, as originating from extremes in the ratio of 2 to 3, can 

 merit no other than the ancient appellation of discords, when 

 compared with the more perfect 5th, and its still purer gene- 

 rator the 4th. 



A subject perhaps still more desirable than all our calculations 



comes next in order, viz, the construction of a musical diagram, 



the relative length of whose lines or strings shall not only accord 



M 4 with 



