5H 



THE POPULAR SCIENCE MONTHLY. 



After exploring the whole known field of harmony, and cal- 

 culating the elevations and depressions consequent on using more 

 elaborate chords, it is asserted that the exact pitch could not be re- 

 gained. 



The formulated results need not be stated here ; it is sufiicient to 

 give the conclusions to which they point. But assuming that the 

 composer could succeed in so planning his chords that the second half 

 of this melody would so correct the eccentricities of the key-note in 

 the first half that at its completion the composition would be rounded 

 off at the true pitch, it is easy to see that if the first strain were re- 

 peated, and the second left unrepeated, or any such ordinary change 

 made, all his elaborate calculations would be of no avail. 



Mr. Ellis, who proposes a system with 117 notes within the octave, 

 is thus shown that an infinite number of notes is required, for there is 

 no synonymity in any system when the key-note moves. At each change 

 of pitch the whole series is changed. Mr. Bosanquet, with 53 notes to 

 the octave, offers to provide musicians with materials for 84 scales ; 

 and thus we are more reminded of the musical formulse of the ancient 

 Hindoos — their 16,000 keys — than informed how the above simple 

 melody may be correctly rendered. 



It is somewhat amusing to find Mr, Ellis seriously proposing to 

 employ three harmoniums, the three players having to touch the notes 

 that happen to fall to their respective instruments, not only because, 

 as shown above, the music would still be out of tune, but because no 

 performer would play a complete melody by himself, but a note here, 

 another there, unconnectedly. For, however neatly this might be 

 managed, expression or artistic rendering would be unattainable. Yet 

 it is remarked, " The performers would merely require a little drilling 

 and practice together." 



Logarithms may be piled and compiled to define scales, but it is 

 not so easy to reconcile the conflicting principles that appear in actual 

 composition. The musician baffles the mathematician, who fails to 

 follow him in his operations, as proved by the hitherto unnoticed dis- 

 crepancies between melodic and harmonic proportions herein demon- 

 strated. Although the composer's notation is not an exact statement, 

 the performers do not experience practical difficulties : the intention is 



