508 Mr. R. H. M. Bosanquet on Temperament, 



taining 12 fifths, from/# up to b. The series f$-b is called the 

 unmarked series; the next series of 12 fifths up is affected with the 

 mark (/), the next series of 12 fifths up with (//), and so on ; the 

 first series down below the unmarked series with the mark (\), 

 the next series down with (\\), and so on. Thus \e is 8 fifths 

 down from c, and c-\e is approximately a perfect third. The 

 error of the third c-\e is about -4^- of an E. T. semitone when 

 the fifths are perfect. 



This notation is suitable for employment with written music. 

 The following passage is an example : — 





• r 



The interval g-\f is a close approximation to the harmonic 

 seventh; /a\)-f$ is rendered very smooth by the employment 

 of the same interval. 



A harmonium has been constructed on which such passages 

 can be played, the form of the fingering being the same in 

 all keys. 



The notation is also useful for the discussion of some systems 

 of historical interest. Thus we have a scale of F in Mersenne 

 (1636) with eighteen notes to the octave, This possessed the 

 following resources : — 



Major chords of c-f-b\)-e\), 



„ \e-\a-\d-\g, thirds to the above, 



,, /a\)-/d\)-/g'\) y thirds below c-f-b\}. 



Minor chords of c-f-b\}-e\}j 



)} \e-\a-\d-\g, thirds to the above, 



* „ \c#-\f#-\\b } thirds to \a-\d-\g. 



We have here the two forms of second of the key, g and \g, 

 differing approximately by a comma. This double form appears 

 in all good attempts at systems with perfect fifths. 



Principle of " symmetrical arrangement." — If we place the 

 E. T. notes in the order of the scale, and set off the departures 

 of the notes of any system at right angles to the E. T. line, sharp 

 departures up and flat departures down, we obtain the positions 

 of a symmetrical arrangement. (A diagram was exhibited with 

 a symmetrical arrangement of the notes of General Thompson's 

 enharmonic organ.) This symmetrical arrangement is the prin- 

 ciple of the keyboard of the harmonium above referred to. The 

 following series of intervals lie on characteristically placed straight 

 lines in a symmetrical arrangement. 



