90 ON THE PHYSIOLOGICAL CAUSES OF 



musical tones sufficed to determine a preference in favour of 

 progressions though certain determinate intervals. When an 

 upper partial tone is common to two successive tones in a 

 melody, the ear recognises a certain relationship between them, 

 serving as an artistic bond of union. Time is, however, too 

 short for me to enlarge on this topic, as we should be obliged 

 to go far back into the history of music. 



I will but mention that there exists another kind of secondary 

 tones, which are only heard when two or more loudish tones 

 of different pitch are sounded together, and are hence termed 

 combinational. 1 These secondary tones are likewise capable of 

 beating, and hence producing roughness in the chords. Suppose 

 a perfectly just major third c' e' wr~f~ (ratio of pitches, 4 to 5) 

 is sounded on the siren, or with properly tuned organ pipes, or 



/vs. 



on a violin ; 2 then a faint C Sg==p two octaves deeper than the 



-ic 

 c' will be heard as a combinational tone. The same C is also 



heard when the tones e' g' ^b -L (ratio of pitches 5 to 6) are 



sounded together. 3 



If the three tones c', e', g', having their pitches precisely in 

 the ratios 4, 5, and 6, are struck together, the combinational 

 tone C is produced twice 4 in perfect tinison, and without beats. 

 But if the three notes are not exactly thus tuned, 5 the two C 



1 These are of two kinds, differential and summational, according as their 

 pitch is the difference or sum of the pitches of the two generating tones. 

 The former are the only combinational tones here spoken of. The discovery 

 of the latter was entirely due to the theoretical investigations of the author. 

 TK. 



2 In the ordinary tuning of the English concertina this major third is just, 

 and generally this instrument shows the differential tones very -well. The 

 major third is very false on the harmonium and piano. TR. 



3 This minor third is very false on the English concertina, harmonium, or 

 piano, and the combinational tone heard is consequently very different from the 

 true C. TK. 



* The combinational tone c, an octave higher, is also produced once from 

 the fifth c' g'. TR. 



5 As on the English concertina or harmonium, on both of which the con- 

 sequent effect may be well heard. TR. 



