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WEAD. 
should have such steps the two notes are not taken in succes- 
sion; our chromatic scale is ordinarily a store-house out ot 
which a few notes are selected for use in a melody ; and one 
can strike all the 12 keys in the Octave, yet use only the large 
steps of Fourths and Fifths. I have never met in Oriental 
music such a series of small intervals as the long chromatic 
passage in “ Carmen,” in the air “Love a vagrant is.” On the 
other hand, it is well known that much Oriental and even 
classical music has a 7-tone scale with the large step of an un- 
divided minor Third, three semitones. 
Some relations of non-harmonic scales 1 have stated in 
more formal shape in a published paper and may be allowed 
to quote from it. 
“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 continu- 
ous slope, and may never step twice in the same place. Now, 
it is quite possible that in a song the voice may always 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 much 
primitive song today, though the evidence is too scanty to be 
conclusive. 
“'However this may be, it is certain that most peoples who 
have attained any moderate degree of civilization have at- 
tempted to limit the number 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 many men may learn them and 
