172 LECTURES TO SCIENCE TEACHERS. 



ways. Several other notes have alternative fingerings, so 

 that I hope to manufacture reed instruments with which we 

 can get, in many keys if not in all, true intonation. We do 

 not require it in all keys with the clarionet, because as you 

 are aware, players use different instruments for different 

 keys. There is the B flat clarionet, which is useful for the 

 flat keys ; to play in sharp keys there is the A ; and there is 

 also a C clarionet, though it is less used. In this way, by 

 having just intonation for one or two keys on either side of 

 the natural key, I believe we shall arrive at more perfect 

 results. It is very desirable it should be so, and I hope 

 we shall be able to carry it out. I will here conclude the 

 talking part of the lecture, but the most important part you 

 will all agree with me will be the description of his new 

 harmonium which Mr. Colin Brown has so kindly under- 

 taken to give us. Before playing he wishes i to explain 

 the system on which the keyboard is arranged. 



Mr. BROWN. The construction of this instrument arose 

 from a series of experiments in analysing a musical sound. 

 It is mathematically and musically correct, and contains 

 neither compromise nor approximation of any kind from 

 beginning to end of the fingerboard. The octave consists 

 of seven digitals, with one added for the minor scale. It 

 involves no complicated calculations, for there are only seven 

 musical relations or differences on the keyboard, and these 

 require neither decimals, nor logarithms nor equations, to 

 express them. 



The scales run horizontally along the instrument, the 

 keys across it, scales and keys being at right angles. The 

 progression of fingering the scale in all keys is the same, and 

 as no extra digitals, such as the five black upon the common 

 keyboard, are required to play chromatic tones, this finger- 

 board is called the " natural fingerboard." l 



Instead of beginning where, as Dr. Stone pointed out, is 

 usual, with the larger intervals of the scale, as the octave 

 and fifth, I have begun at the other end of the scale with the 

 first elements 8 : 99 : 1015 : 16. 



Though the larger intervals of the scale are relatively in- 

 commensurable, by starting with these primary relations we 

 find that every interval is accurately produced from them ; 

 1 See Appendix II., kindly contributed by Mr. Colin Brown, 



