816 Transactions of the American Institute. 



true A do not harmonize. The intervals between these sounds are a 

 minor tone, a semitone, a major tone and a minor tone, measured by 

 thirty commas, while the true fifth is measured by thirty-one 

 commas, and contains two major-tone intervals. The other 

 doubtful chord is the supertonic and subdominant, or the 

 sounds D and F of the natural key; this is the only instance 

 in the true diatonic scale where a minor tone and a semitone 

 form a minor third measured by thirteen commas, the other minor 

 thirds being measured by fourteen commas. The effect of this com- 

 bination is not so displeasing as that of the supertonic and the sub- 

 mediant. Moreover, when the submediant of a major mode becomes 

 the tonic in the relative minor mode, the supertonic of the major key 

 is a comma more acute than the true fourth of the minor mode. This 

 could be remedied by the introduction of a new sound in the scale 

 one comma higher than the submediant in one case, and a comma 

 lower than the supertonic in the other, which would require an addi- 

 tional key or pedal to bring each sound into use ; but the query arises, 

 "What would be the effect of introducing this A 1 when every other 

 note and chord demands the true A generated from the tonic C ? The 

 answer can only come from those who are favored with educated ears 

 highly sensitive to discords. It is for this class more especially that 

 enharmonic instruments will be made. Very few, however, even of 

 those who are not musicians, are unaffected by a "concord of sweet 

 sounds." Pure harmony, unaccompanied by words, has the power of 

 exciting and controlling human emotions. When invention has per- 

 fected instruments which will answer the human touch in true intona- 

 tions, their introduction and general use will only be the work of time. 

 Dr. Yan der "Weyde commented on the paper of the President, and, 

 confirmed the position maintained in it by demonstrating mathemati- 

 cally that the interval between the second and the sixth of the dia- 

 tonic scale, if perfectly tuned, is less than a fifth, and, therefore, hot 



a chord. 



Adjourned. 



