104 Mr. A. J. Ellis on a Perfect Musical Scale [Jan. 21, 



as E, JC?S, XB^y &c., and below as f^b, fi^t?, &c., and then the fifths above 

 and below these tones. The names of the tones thus tuned are apparent 

 from Table V. This tuning is much simpler than any system of tem- 

 perament, and can be successfully conducted by ear only, taking care to 

 avoid all beats in the middle octave c to e^. 



Scheme for Four Concertinas. 



1. f^b Concertina. 



Manuals. . 6b, D d\^, E feb, F f/, G ^, A tab, B tSb, 

 Scales.... Z^, t^b, t-E^b, (t^b), [i^], [6b],/, c. 



2. -j-^b Concertina. 



Manuals.. C fc, D c^, -fE feb, t-F/Jf, G iff, t«b, B t^b. 

 Scales. . . .t^b, t-Bb, ^F, (tC), [G], D-, [c], ff, d. 



3. C Concertina. 



Manuals.. t4, XDd, E Xd% F G Xg%, A fa, B bb, 

 Scales. ...I, Cy G, (D), \_A\ E; lld\ e. 



4. D Concertina, 



Manuals. . C e#, i) t^, ^tf 9^, U a% B fS, 



Scales. ...G,I), fA, [fE], [^], Fp, [.], 6, 



In Table III. the first column shows the number of degrees of any tone, 

 two tones whose degrees differ by one-sixteenth being schismatic equivalents. 

 The second column contains the notes of the tones. The third column 

 contains the logarithm of the ratio of their pitch to that of c, whence the 

 ratio itself, the absolute pitch, and the length of the monochord are readily 

 found. In the fourth column marks Euler's primary, and E^ his secon- 

 dary tones ; Hi the tones on Helmholtz's lower and upper board ; T, 

 the 40 tones of General T. Perronet Thompson's Enharmonic Organ ; P, 

 the 50 tones of Mr. Poole's Enharmonic Organ; t, the 72 tones of 

 Table v., cols. III. to VIII. ; the 24 tones out of these 72 which may be 

 played as their adjoining schismatic substitutes without injuring the har- 

 mony ; 5^, the 3 tones which, if played as their schismatic equivalents, 

 would produce a sHght but sensible error ; ty not followed by either s or se, 

 the 45 tones which form the minimum number of a justly intoned or teleon 

 scale ; et, the 1 2 tones of the equally tempered scale. The seven tones of 

 the major scale of C are printed in capitals in the second column. 



