OF ARTS AND SCIENCES. 501 



It appears from these figures that in no case is there a deviation of 

 as mucli as one vibration per second in the scale as given by the organ 

 from the true isotonic scale. It will also be observed that in each of 

 the three series the errors in the upper portion of the scale are all 

 negative, though this is probably accidental. The instrument was 

 presumably tuned from a fork of approximately 536 vibrations per 

 second. 



There is a certain interest attaching to the foregoing measurements 

 from their bearing on the origin and nature of the musical character- 

 istics of different keys. It has always been difficult to account for the 

 existence of such differences upon an equally-tempered instrument; 

 and a favorite way of explaining it has been to suppose that the actual 

 scale is not really an isotonic one, but that the scale of the tuner, as 

 carried in his mind and secured on the instrument, is such as to give 

 values to different notes that will really preserve their characteristics 

 to the various keys. It is hard to understand how this can be the 

 case when one considers the methods used by a tuner ; and our own 

 results, as do also those of Mr. Ellis, lead to the conclusion that the 

 impression in question is an incorrect one. What is true of the cabinet 

 organ and piano must also be true of other keyed instruments, as any 

 noteworthy differences between instruments professing to be tuned to 

 the same isotonic scale would immediately be noticed. 



Helmholtz suggests that with stringed instruments diff'erences of 

 key may arise from the use of open or closed strings, or closed strings 

 of different lengths, and, while denying the existence of such key-ditfer- 

 ences upon the organ, admits them to exist with the piano, and con- 

 siders that they are there produced by difference of fingering, according 

 to the position on the keyboard of the keys struck. 



In order to test this, the following experiment was tried. Three 

 pianos were taken, all of the same make and pattern, and of as nearly 

 the same quality and loudness of tone as possible. The three instru- 

 ments were originally at the same pitch. One of them was raised in 

 pitch throughout the whole scale by half of an isotonic semitone, and 

 a second was lowered by the same amount, while the third remained 

 unaltered as a standard of comparison. Hence, the pianos of highest 

 and lowest pitch were a semitone apart ; that is, the scale was, so to 

 speak, shifted upward by one key in one instrument with reference to 

 the other. Hence, chords played upon the same notes of the key- 

 board would be of different pitch, although in the same musical key. 

 On the other hand, chords composed of notes of exactly the same 

 absolute pitch in the different instruments would be in different rau- 



