INSTRUMENTS FOE EXPERIMENTS ON SOUND. 141 



ratios would have produced "by a geometrical method those 

 beautiful figures projected on the screen. The principal 

 ratios are : 



2 to 1 



the octave 

 fifth 

 fourth 



major third . 

 minor third . 

 major tone . 

 minor tone . 

 major semikne 



I haye also written down in small figures below (I do not 

 wish to confuse you with them to-day, as I shall have to say 

 more about it to-morrow), the ratio of the comma, a compu- 

 tational interval, 81 to 80 : this at present I will pass over. 



FIG. 2. Moiiocluuxl. 



I will now proceed to show the monochord and the different 

 ways of using it. There is in the South Kensington Museum 

 an old monochord by Broderip and Longman, which 

 was intended for persons to tune their harpsichords. It 

 consists of a small string with definite marks placed under 

 it to which you can set a fret or stop to check the vibrations. 

 There is also a little harpsichord "jack" by the side, a 

 piece of quill, the predecessor of the pianoforte hammer, by 

 which the string was plucked. Here I have a monochord 

 a metre long divided into decimetres and centimetres with 



