Polytechnic Association. 815 



In the division of scale into fifty-three parts or commas, the differ- 

 ence between these notes is measured by two commas. 



In order to ascertain the true intervals required in the thirteen 

 keys used, I have prepared a table (portions of this table were pre- 

 sented on the black-board), in which the major tone interval is meas- 

 ured by forty-five, the minor tone by forty, and the so-called semitone 

 interval by twenty-four ; and for comparison these intervals are also 

 measured by nine, eight and five respectively. 



By this table it is shown that, to make seventeen perfect intervals, 

 with the tonic in thirteen different positions, forty-six different sounds 

 within the octave are required. If the correct intervals, measuring 

 only five tones and two semitones in thirteen keys, are used, twenty- 

 nine different sounds will suffice. 



Many attempts have been made to construct musical instruments, 

 played by keys, which would give true intonation with every change 

 of the tonic. Among the organs actually constructed in which this 

 plan has been partially carried out, may be mentioned those devised 

 by the Rev. Henry Liston, of Scotland, in the early part of this 

 century ; that of Col. Thompson, of England, and that of Messrs. 

 Alley and Poole, of Newburyport, Mass. Neither of these instru- 

 ments has met with general approval. 



I have devised a plan for bringing into use all the true sounds 

 required for each tonic, by one motion, and so quickly, that the change 

 may be made during the progress of any piece resembling in its 

 movement ordinary church music. It may be applied to the melo- 

 deon, by the introduction of extra reeds ; to the organ without increas- 

 ing the number of pipes ; and to the ordinary piano. No alteration 

 in the key boards is required, since the change from one tonic to 

 another is effected, by moving a single lever operated by the hand or 

 foot. The mechanism required is somewhat complicated, and differs 

 radically from any hitherto employed. 



The pleasure to be derived from the use of such an instrument 

 would be unalloyed, were there not a serious defect in the harmony 

 belonging to one note of the true scale, which, in stringed instruments 

 of violin class and wind instruments like the sliding trumpet and 

 trombone, can be easily remedied ; yet it is doubtful whether the 

 remedy does not produce a confusion more to be dreaded than discord. 

 I allude to two of the chords used with the supertonic. It is gene- 

 rally supposed that the fifth to the supertonic, is identical with the 

 submediant ; for example, in the natural key of C, the fifth to D is 

 supposed to be A, yet it can be demonstrated that the true D and the 



