HAEMOFT IN MUSIC. 103 



are likewise capable of beating, and hence producing 

 roughness in the chords. Suppose a perfectly just major 



third c' e' S=^ (ratio of pitches, 4 to 5) is sounded on 

 the siren, or with properly-tuned organ pipes, or on a 



violin;^ then a faint C ^^^^ ^ two octaves deeper than 

 the c' will be heard as a combinational tone. The same 



C is also heard when the tones e' g' m=^ (ratio of 

 pitches 5 to 6) are sounded together.^ 



If the three tones c\ e\ g\ having their pitches precisely 

 in the ratios 4, 5, and 6, are struck together, the com- 

 binational tone C is produced twice ^ in perfect unison, 

 and without beats. But if the three notes are not 

 . exactly thus tuned,'* the two C combinational tones will 

 have different pitches, and produce faint beats. 



The combinational tones are usually much weaker than 

 the upper partial tones, and hence their beats are much 

 less rough and sensible than those of the latter. They 

 are consequently but little observable, except in tones 

 which have scarcely any upper partials, as those produced 

 by flutes or the closed pipes of organs. But it is indisput- 

 able that on such instruments part-music scarcely presents 

 any line of demarcation between harmony and dyshar- 

 mony, and is consequently deficient both in strength and 

 character. On the contrary, all good musical qualities of 

 tone are comparatively rich in upper partials, possessing 



* In the ordinary tuning of the English concertina this major third is 

 just, and generally this instrument shows the differential tones very \yell. 

 The major third is very false on the harmonium and piano. — Tr. 



2 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— Ta, 



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

 from the fifth d ^'.— Tr. 



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

 sequent effect may be well heard. — Tb. 



