380 SGienthfiG Proceedings, Royal Dublin Society. 



the tonic and submediant chords of the original key are vertical, 

 its dominant harmonies sloping to the right, and its sub-dominant 

 harmonies to the left. 



In the first sharp key all these positions are shifted through 

 sixty degrees to the right, and in the first flat key they lean sixty 

 degrees to the left. 



Thus aa' bb' and cc' are the directions of the sub-dominant 

 tonic and dominant chords in the original key (compare with 

 Figure 2). In the first sharp key the directions become cc' for the 

 tonic, aa' for the dominant, and bb' for the sub- dominant ; and in 

 the first flat key they become aa' for the tonic, bb' for the domi- 

 nant, and cc' for the sub-dominant. 



When music passes iato the first sharp key, the chords v/hich 

 before were the L D M and S chords of the original key become 

 respectively the R F L and D chords of the new key, see Figure 

 2. It is often desirable to distinguish between these very 

 different uses of the chords, which may be done by adding a hook 

 round the bottom of the symbol when it belongs to the first sharp 

 key. Similarly a loop may be added to the symbol of chords 

 common to the original key and the first fiat key when used in 



in the latter, e.g., the same three notes would be denoted by I 



when used for the D chord of the original key, by when 



used as the F chord of the first sharp key, and by I when used 

 as the S chord of the firsl; fiat key. 



