Mat 29, 1908] 



SCIENCE 



845 



homophonie music and early melodic com- 

 position. On this explanation the basis of 

 melody is purely that of rhythm and 

 rhythm based on a scale of intervals. The 

 scale of intervals in turn is based on a 

 recognition conscious or subconscious of the 

 compound character of musical tones and 

 of 'the existence in tones of different pitch 

 of partials of the same pitch. This calls 

 for a degree of musical insight and dis- 

 crimination which it is difficult to credit to 

 a primitive art. It is in reality the skill 

 of the highly trained musician, of a musi- 

 cian trained by long experience with 

 sounds which are rich and accurate in 

 quality. This power of analysis goes 

 with supreme skill rather than with the 

 early gropings of an art. 



After having developed a theory of 

 harmony and discord based on elaborate 

 experimental and mathematical investiga- 

 tions, which was remarkable in bringing 

 together three such diverse fields as physics, 

 physiology and esthetics, he relegated it to 

 the minor application of explaining the 

 use in modem music of an already exist- 

 ing and highly developed musical scale, 

 and sought an explanation of the earlier 

 use of the scale in melody and its original 

 invention in a principle which is very far 

 from possessing either the beauty or the 

 convincing quality of his earlier hy- 

 pothesis. He was forced to this by the 

 priority of melodic or homophonie composi- 

 tion. He saw in melody only a succession 

 of notes, no two existing at the same time, 

 and therefore incapable of producing 

 harmony or discord in a manner such as 

 he had been considering. 



It is true that melody is written as a 

 pure succession of discrete notes, one be- 

 ginning only when the other has ceased. 

 It is true also that melody is so sung and so 

 produced on a homophonie instrument 

 such as the voice, flute, reeds or on 

 stringed instruments. This is peculiarly 



true of the voice, and it is with the voice 

 that one naturally associates the earliest 

 invention of the scale. But while it is 

 true that the earliest song miist have con- 

 sisted of tones produced only in succession, 

 it is not necessarily true that such sounds 

 were heard as isolated notes. A sound 

 produced in a space which is in any way 

 confined continues until it is diminished 

 by transmission throygh openings, or is ab- 

 sorbed by the retaining walls or contained 

 material to such a point that it is past the 

 threshold of audibility, and this prolonga- 

 tion of audibility of sound is under many 

 conditions a factor of no inconsiderable 

 importance. In many rooms of ordinary 

 construction the prolongation of audibility 

 amounts to two or three seconds and it is 

 not exceedingly rare that a sound of 

 moderate initial intensity should continue 

 audible for eight, nine, or even ten seconds 

 after the source has ceased. As a result of 

 this, single-part music produced as suc- 

 cessive separate sounds is nevertheless 

 heard as overlapping, and at times as 

 greatly overlapping tones. Each note may 

 well be audible with appreciable intensity 

 not merely through the next note, but 

 through several succeeding notes. Under 

 such conditions we have every opportunity 

 even with single-part music for the produc- 

 tion of all the phenomena of harmony and 

 discord which have been discussed byHelm- 

 holtz in explanation of the chordal use of 

 the musical scale. In any ordinarily bare 

 and uncarpeted room, one may sing in 

 succession a series of notes and then hear 

 for some time afterward their full chordal 

 effect. 



All the arguments that Helmholtz ad- 

 vanced in support of his hypothesis that 

 the musical scale was devised solely from 

 considerations of rhythm and founded on 

 a repetition of faint upper partials, hold 

 with equal force in the explanation here 

 proposed. The identity of partial tones in 



