1864.] 



on Instruments with Fixed Tones, 



95 



The following symbols always represent the fractions, and are called by 

 the names written against them : 



1 . Following a Note, 



135 



= — — = sharp, or greater limma. 

 128 



b = ^-5? = flat, or hypolimma. 



X = . Jf = double sharp ; bl? = [? . b = double flat. 



2. Preceding a Note. 



4- 81 



t = — = acute, or comma. 

 80 



J = — - = grave, or hypocomma. 

 63 



z = — • = septime (an inverted 2) . 

 64 



^ 32805 ^ 1.001129150390625 = schisma. 

 " 32768 



It =: = 0-99887212315 = hyposchisma. 



The name and pitch of the tones represented by any such notes as 



. ^ ,80 135 25 



tct = grave c sharp = _ . c . — = — c, 



MJ. , n . S\ 128 24 



= acuteeflat =-...— = 



and the ratio of their pitches to the corresponding notes in the scale of C major 

 is therefore precisely indicated. In ordinary musical notation on the 

 staff, it is only necessary to prefix the signs t, 3, If, to those already 

 in use. These symbols suffice for writing any tone whose index is the pro- 

 duct 2"". 3". .5^. 7'^ (see Tables I. and III.). For equally tempered tones, when 

 it is necessary to distinguish them, the sign || is prefixed to the usual names, 

 and read equal." Since 



11^ : c = 2M = 0-998871384584 x f, 



and 



J^:c = 0-99887212315 x f , 



we may without sensible error consider \\g = \^g, and hence represent the 

 equally tempered scale 



0, \\d, \\c^, We, \\f, \\f^, Wff, \\a^, \\a, \\bb, \\b by 



c, Te^, V i-e, %f, Vt/it; IV.'/; T^^^, ]k't«; V^7, ivn^'. 



In calculating relative pitches or intervals, and in all questions of tern- 



