OAT TEMPERAMENT. 17? 



With the system of perfect fifths the interval, C C', is a 

 Pythagorean comma. 



With the same system, the third determined by two notes 

 eight steps apart in the series of fifths (C C 7 ), is an 

 approximately perfect third. 



With the system of fifty-three the state of things is very 

 nearly the same as with the system of perfect fifths. 



The principal practical simplification which exists in this 

 keyboard arises from its arrangement being strictly according 

 to intervals. From this it follows that the position relation 

 of any two notes forming a given interval is always exactly 

 the same ; it does not matter what the key-relationship is, or 

 what the names of the notes are. Consequently, a chord of 

 given arrangement has always the same form under the finger ; 

 and as particular cases, scale-passages as well as chords have 

 the same form to the hand in whatever key they are played. 

 A simplification which gives the beginner one thing to learn, 

 whereas there are twelve on the ordinary keyboard. 



The keyboard has been explained above with reference to 

 the system of perfect fifths and allied systems ; but there is 

 another class of systems to which it has special applicability 

 the mean-tone and its kindred systems. In these the third, 

 made by tuning four fifths up, is perfect, or approximately 

 perfect. The mean-tone system is the old unequal tempera- 

 ment. The defects of that arrangement are got rid of by the 

 new keyboard, and the fingering is t remarkably easy. The 

 unmarked naturals in the diagram present the scale of C 

 when the mean-tone system is placed on the keys. 1 



1 For further details on this important subject readers are referred to 

 the forthcoming work An Elementary Treatise on Musical Intervals 

 and Temperament, with an account of an enharmonic harmonium 

 exhibited in the Loan Collection of Scientific Instruments, South Ken- 

 sington, 1876 ; also of an enharmonic organ exhibited to the Musical 

 Association of London, May, 1875, by K. H. M. Bosanquet, Fellow 

 of St. John's College, Oxford. London : Macmillan and Co., 1876. 



VOL. II. 



