LIMITS OF AUDIBLE SOUND. 6$ 



mental or lowest tone quite distinct from all the others, as a simple 

 pendular vibration. As the result of a great number of experiments he 

 found that ears differed very much as to what was really a musical 

 tone, defining that to be one in which we hear no throbs, but only a 

 continuity of sensation. He has also published a work on the limits 

 of sensational power, and. in fact, that was his great point, to deter- 

 mine the limit of continuity of sensation. He found that he himself 

 could hear continuous tone from as few as 14 vibrations to the second, 

 but that most ears perceived sensation to be continuous when the 

 number of vibrations reached 23. Therefore, somewhere between 14 

 and 23 vibrations must be fixed as the lowest limit of continuous 

 simple pendular vibrational tone produced in the human ear, as far 

 as it has yet been investigated. He also has gone very much into 

 the question of the upper limits of tone, but his especial investigations 

 were to determine the smallest amount of error in a melodic interval, 

 which the most practised ears could hear. For this purpose he made 

 use of some of these instruments of Herr Appun, of Hanau. There is 

 one which gives a complete series of partial tones up to the 32nd, and 

 there is another one in the next room which gives tones from 128 to 

 256 vibrations, proceeding by two beats at a time. With that instru- 

 ment Herr Preyer experimented, and the investigation has a very 

 important bearing on the method of representing just intonation by 

 means such as that of Mr. Bosanquet, who uses an approximative 

 scale, obtained by dividing the octave into 53 equal parts, which I 

 consider to be really perfect enough. I have not calculated all Herr 

 Preyer's results out completely, but I may state that no ear seems to 

 detect an error in an interval melodically not in a chord which 

 amounts to the hundredth part of an equal semitone, but that the 

 fiftieth part (double that) may be detected by very fine ears indeed. 

 With regard to just intonation and key-boards, I may say that key- 

 boards like Mr. Brown's and Mr. Poole's (which is very good if we 

 reject the natural sevenths), go upon the principle of carrying out 

 a series of tones proceeding by perfect fifths, in three columns, 

 so to speak, each column being a comma lower than the preceding. 

 Gueroult uses only two. Gudroult and Helmholtz's plan is the one 

 Dr. Stone said I wanted to simplify, using a single key-board by 

 means of compound stops, and that was the instrument which was to 



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