TEMPERAMENT. 175 



APPENDIX I. 

 BOSANQUET'S GENERALISED KEYBOARD. 



IN the enharmonic harmonium exhibited at the Loan Collec- 

 tion of Scientific Instruments, South Kensington, 1876, there 

 is a keyboard which can be employed with all systems of 

 tuning reducible to successions of uniform fifths ; from this 

 property it has been called the " generalized " keyboard. It will 

 be convenient to consider it first with reference to perfect 

 fifths ; it is actually applied in the instrument in question 

 to the division of the octave into fifty-three equal intervals, 

 the fifths of which system differ from perfect fifths by less 

 than the thousandth part of an equal temperament semitone. 

 It will be remembered that the equal temperament semi- 

 tone is the twelfth part of an octave. In the present notice 

 the letters E. T. are used as an abbreviation for the words 

 " equal temperament." 



The arrangement of the keyboard is based upon E. T. 

 positions taken from left to right, and deviations or depar- 

 tures from those positions taken up and down. Thus the 

 notes nearly on any level are near in pitch to the notes of an 

 E. T. series ; notes higher up are higher in pitch ; notes lower 

 down lower in pitch. 



The octave is divided from left to right into the twelve E. T. 

 divisions, in the same way, and with the same colours, as if 

 the broad fronts of the keys of an ordinary keyboard were 

 removed, and the backs left. 



The deviations from the same level follow the series of 

 fifths in their steps of increase. Thus G- is placed ^ of an 

 inch further back, and -^th of an inch higher than C ; D 

 twice as much ; A three times, and so on, till we come to C', 

 the note to which we return after twelve fifths up ; this note 

 is placed three inches further back, and one inch higher than 

 the C from which we started. 



