121 



480, or by less than & of a 'comma. If this error be 

 imagined to be divided up into eight eqijal parts in tuning 

 the successive fifths the amount of temperament in one 

 fifth would be about ^ of a comma. This is far within 

 the limits within which vibrations are said to draw into 

 harmony. As a matter of practical tuning it is not to be 

 taken into account at all. The best tuner would be as 

 likely to come out with his Cj, a little sharp of b as a little 

 flat. This equalization is very useful because it gives the 

 tuner a check by which to test the correctness of his key- 

 notes both up and down. For if C[, = b, then by similar 

 reasoning, D b = c#, E b = d#, F = e#, Fj, = e, Gj, = 

 f #, A|, = g#, B|j = a# ; which gives a test for the key- 

 notes C[>, D|>, etc., and also saves the strings or resonators 

 for b, c#, etc., as they may be made to sound the same 

 strings or resonators as C[>, D^, etc. 



Again, since D|, = c#, and c = if D|,, and b$ = f| c#, 

 then c = &, d = ex, e^ = d$, f = e%> g =/x, a = gx, 

 a b === ff$> ^b = a #> thus saving extra sound producers 

 for eight tones of series 4 in every octave. 



By this practically inappreciable temperament the num- 

 ber of sound producers is reduced to forty-six in the 

 octave. 



The method of tuning the key-board is first to tune the 

 key-notes by fifths ; then a major third from each key- 

 note, and a major third from each of the last-named series. 

 The prime sevenths, though not familiar to most tuners, 

 are very easily tuned, especially when the third is sounded 

 with its tonic. 



There have been other* key-boards invented with the 

 same purpose as Prof. Poole's, and it is proper to say a 

 few words in regard to his labors in the cause of just 

 intonation. 



In an article published in the "American Journal of 



