100 Mr. A. J. Ellis on a Perfect Musical Scale [Jan. 31, 



tones in Table V., lines 1 to 8, throughout all the columns are exactly 

 one schisma flatter than the corresponding tones in lines 10 to 17. Hence 

 we only require the tones in lines 5 to 13 in order to reproduce the whole 

 Table, with the help of schismatic substitution. It is, however, more con- 

 venient to use columns III., IV., lines 14 to 17, in place of columns I. and 

 II., lines 5 to 8 ; and columns VII., VIII., lines 1 to 4, in place of columns 

 IX. and X., Unes 10 to 13. In this case only 48 tones vrill be required. 

 If the schismatic substitution of %/> cb for efl, g^, were allowed, 

 which would introduce three schismatic errors of no great importance, the 

 number of tones would be reduced to 45, which is the lowest possible 

 number of tones by which a complete scale can be played. All these tones 

 are enumerated in Table III. 



There are several ways of realizing such a scale in whole or in part*. 

 The following appears to be the most feasible, as it would render the mere 

 mechanism of playing a perfect scale on an organ or harmonium easier than 

 that of playing the tempered scale on the same instruments. 



On a board of manuals similar to that now in use for the organ, intro- 

 duce two additional red manuals (of the same shape as the black, but with 

 a serrated front edge to be recognizable by blind and colour-blind per- 

 formers, as in some cases on General Perronet Thompson's organ) in the 

 two gaps between B and C, and between E and Fy so as to make 14 ma- 

 nuals in all. Let there be 16 stops worked as pedals with the foot, as in 

 Mr. Poole's Enharmonic Organ (loc. cit. p. 209). Let one of these stops 

 give the equally tempered tones to the manuals, so that any piece could be 

 played in the tempered scale, and thus compared with the same piece when 

 played with just intervals. Let the 15 other stops give the tones required 

 for the 15 keys ^Ob to ■\C^, as shown in Table II., and be numbered 7 b, 



6 b . . • 1 b, natural, 1 # 7 ft* When any pedal is put down, let the seven 



white manuals give the seven tones of the primary major scale of the cor- 

 responding key, and the seven coloured manuals give seven out of the nine 

 other tones required to complete the key, omitting the acute fourth (which 

 would be found in the key of the dominant) and the grave seventh (which 

 would be found in the key of the subdominant). To the right of each 

 white manual let there be its conjugate coloured manual, of such a value 

 that, if the seven tones of the major scale be indicated by the numbers 1 to 

 7, the tones corresponding to the manuals in any key may be 



Coloured,. tljf ^2 fSb t5fl t<3b t^b 



WTiite..,. 1 2 3 4 5 6 7. 



Table II. shows the tones associated with the manuals in each stop ; 

 capital letters indicate white manuals, small letters black, and small 



* Singers and performers on bowed instruments and trombones can produce 

 any scale whatever. Other instruments are more limited in range and would 

 requhe special treatment, similai' to the crooks " of the horns and the various 

 clarinets. 



