714 HERMANN VON HELMHOLTZ. 



unpleasant, because every intermittent excitement of any nervous 

 apparatus affects it more powerfully than one that lasts unaltered. 

 Consonance is a continuous, dissonance an intermittent sensation of 

 tone." The disagreeable effect depends in part upon the number of 

 beats, in j)art upon the interval between the notes which produce them, 

 being greatest when the rapidity of the beats is neither very large nor 

 very small, and when the interval between the two notes is not great. 

 In applying this theory it is necessary to take into account not only 

 the beats between the two fundamental notes, but also those due to two 

 series of secondary sounds by which they may be accomi^anied. The 

 presence or absence of one of these — the so-called ui)per harmonic par- 

 tials — depends upon the way in which the note has been obtained. 

 They produce the differences of quality w^hich distinguish one musical 

 instrument from another. They are also the basis of our appreciation 

 of the closeness of the relationship between the notes they accompany. 

 The want of perfect consonance between compound notes is attributed 

 to beats between those members of the two groups of sound which are 

 not very ftxr apart on the scale. The growing importance of these 

 beats, as the intervals become less and less consonant, was traced with 

 wonderful ingenuity. 



This theory alone wonld be insufQcient to account for a percei^tion 

 of want of consonance between two iJure notes unaccompanied by 

 partials. To explain this recourse was had to a second series of 

 attendant sounds, the most important of which had been discovered 

 in 1745 by Sorge, a German organist, and was well known as 

 Tartini's tone. Von Helmholtz proved that such notes would arise 

 when the vibrating body was set in somewhat violent motion, provided 

 that the resistances offered to equal displacements in opposite directions 

 were unequal. Of course the air, which transmits the sounds to the 

 ear, does not possess this property. On the other hand, the drum skin 

 of the ear, to which the aerial vibrations are communicated, is not sym- 

 metrical, being bent inward by the little " hammer " bone. Von 

 Helmholtz, therefore, concluded that it is probable that Tartini's tone 

 is due to this membrane. From his point of view it is subjective, in 

 the sense that it is produced within the organism, though it originates 

 in the auditory apparatus, and not in the brain. It is, if one may use 

 the phrase, the rattling of the machinery of the ear. 



Having thus accounted for the production 'of secondary sounds by 

 tones, which were themselves unaccompanied by partials. Von Helm- 

 holtz explained our sense of the dissonance of inq^erfect intervals, when 

 produced by such pure notes, by beats due to the combinational tones. 



But, though he maintained that these theories exj)lained the physical 

 "reason of the melodic relationship of two tones," the author of the 

 " Tonempfindungen " was careful to point out that the i)rinciples he 

 enunciated had not always determined the construction of the scale, 

 and do not determine it everv where now. The selection of a series of 



