1 78 On Temperament or the Division of the Octave. 



a result of experience, I am satisfied that 24 will be sufficient 

 for all practical purposes. Probably Smith's system of fifths 

 and thirds beating equally in opposite directions would be best to 

 begin with. 



The large harmonium was tuned according to the division of 

 the octave into 53 equal intervals. For the details of the 

 tuning and the specialization of the notation in the system of 

 53, I must refer to the ' Transactions 3 of the Musical Associa- 

 tion. The compass of the key-board is 4J octaves ; and the 

 keenness of the tone, the perfect standing in tune, and the ge- 

 neral completeness of the instrument have enabled me, during 

 the two years it has been in my possession, to obtain a consider- 

 able familiarity with one of the most important of the approxi- 

 mately just systems. 



The fifths of the system of 53 being practically perfect, the 

 thirds by 4 fifths up are practically Pythagorean thirds. The 

 contrast between these and the approximately perfect thirds may 

 be called startling. 



With the view of having an instrument which should be less 

 troublesome to take to pieces for removal, and also with a view 

 to obtain a negative system on the key-board, a small organ was 

 subsequently constructed with a generalized key-board of three 

 octaves in compass, 48 keys per octave and two stops, the one 

 tuned to the positive system of perfect thirds, and the other to 

 the mean-tone system. The mean-tone system has only 36 

 pipes per octave. The pipes are metal stopped diapasons ; and 

 their accurate tuning is effected by stoppers of a peculiar con- 

 struction, containing an internal slider worked by a projecting 

 screw, which may be regarded as a fine adjustment. The ar- 

 rangement is of a general character, which is susceptible of ex- 

 tension ; and all the working parts can be got at quite easily, 

 which is not the case with the harmonium. This organ, as well 

 as my tuning- machine, the great harmonium, and an ordinary 

 organ, have been built for me by Mr. T. A. Jennings, whose 

 exceptional mechanical skill alone has enabled me to prosecute 

 these investigations with any success. 



For any further details I am obliged to refer to the two 

 papers above quoted. I have here endeavoured to give a general 

 summary of my investigations, avoiding technical details. The 

 points I specially wish to direct attention to are : — the ques- 

 tion of melodic sequences; the unsuitability of just systems 

 for ordinary music, and the desirability of writing specially 

 with a view to their employment; and the suitability of nega- 

 tive systems for ordinary music ; but especially it is most de- 

 sirable that it should be felt how worthless theoretical ideas 

 about the properties of musical sounds are when unaccompa- 

 nied by practical study. 



