422 - REPORT OF NATIONAL MUSEUM, 1900. 



some of his coincidcnce.s between other scales and the harmonic scale 

 can be exphiined in other and simpler ways. Writers less careful than 

 Hclniholtz have made the assumption that these harmonics and the 

 constitution of the ear must hav'e guided primitive musicians to a sub- 

 stantially harmonic scale; and one writer has even maintained that 

 instruments corrupted the taste of men. But as j^et there has been 

 no such body of facts collected in support of this assumption as need 

 delay one following out the other theory. Of course the knowledge 

 of the scales is only a stepping-stone to the understanding of the music 

 and something of the life of a people; so some day the materials worked 

 into shape by the physicist may be built into a fairer structure by the 

 psychologist. 



The broad fact which underlies all study of scales was recognized by 

 the Greek musician Aristoxenus three centuries before the Christian 

 era. He pointed out that the voice, in speaking, changes its pitch by 

 insensible gradations, while in singing it moves mostly by leaps. We 

 recognize the same fact when we say that a singer follows a scale^ but 

 do not say it of a speaker. The one, to use the common figure, ascends 

 or descends a ladder or staircase; the other follows a continuous slope, 

 and may never step twice in the same place. Now, it is quite possible 

 that in a song the voice may alwa3^s move by leaps, and in repeating 

 the song always take the same leaps as closely as can be observed, yet 

 never strike a note which it has struck before; just as one may toss 

 a stone up and down on a hillside, marking each time where it lands, 

 and after a hundred tosses finds it had not landed twice at quite the 

 same level, or in striding up and down hill may never plant his foot 

 twice at the same level. I think this was the character of the songs 

 of the first stage and of nuich primitive song to-day, though the 

 evidence is too scanty to lie conclusive. 



However this may be, it is certain that uiost peoples who have attained 

 any moderate degree of civilization have attempted to limit the num- 

 ber of steps to be taken by the voice in any song between the highest 

 and lowest note, and to fix these steps by rules, so that man}' men 

 ma}' learn them and be in substantial agreement. Various old writers 

 give the rules in vogue among Greek theorists; in the last century 

 Amiot described the Chinese rules, while in the last two decades the 

 rules of Arab, Hindu, Japanese, and Siamese musicians have been 

 made accessible. The most familiar rules, as is well known, depend 

 on that law of vibrating strings which is followed by a violinist in his 

 fingering — namely, that the frequency of vibration of parts of any 

 stretched string is inversel}'^ as the length of the parts, provided the 

 tension does not change. Our latest rule, historically derived from 

 one of the many Greek and Arab rules by subdividing the whole tones, 

 so giving twelve steps to the octave, is embodied on the neck of a guitar 

 Of mandolin; h(M-«> it is obvious that the successive stopping points as 



