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WEAD. 
duplicates and one of them useless; so a five-tone scale results; 
but the series is sometimes continued to give a seven-tone 
scale ; our tuners complete the cycle to get a twelve-tone scale ; 
and the Arabs carried the series still further. In one country 
the origin of the five-tone scale seems to have been forgotten, 
and the Octave now has five equal steps. 
The ancient Greek scales are not certainly known in all 
respects, but the general statement is that the early lyre had 
four strings, the outer ones tuned at the interval of a Fourth, 
as A down to E, while the intermediate strings had various 
tunings; the important thing to notice is that the unit was 
not the Octave, but the Fourth, then called a Tetrachord. 
Later, other similar units were added to make one or two 
Octaves. This addition of Fourths lasted through the Middle 
Ages, and a curious survival of it remains today in the Ger- 
man notation ; two Fourths up from C brings us to B-flat, but 
the Germans call the note B, and use IT for our B. 
The addition of unit-intervals, like our Octave or the Greek 
Fourth, may be carried out with smaller units; thus, an Arab 
rule is based on a lute or guitar with two strings tuned to give 
some small interval, perhaps a fraction of a tone; move a, fret 
or bridge along under the string of lower pitch till its note is 
in unison with that of the higher; press the higher string at 
this fret and locate a new fret along the first string; and so 
continue as far as desired: the result will be a step-by-step 
scale of equal steps, and their sum may or may not chance to 
fill exactly some recognized large interval as a Fourth or 
Octave. 
The most common principle of scale-building is based on a 
stretched string, called by the medieval writers a monochord : 
and every one knows how easy it is to produce a succession of 
tones by shortening the string, preferably by frets, as on a 
guitar. While ordinarily this successive shortening is made 
to give a harmonic scale, there are numerous old instruments 
that show, and various rules that direct, the placing of these 
frets at equal linear distances; hence arises still another 
scale, — one whose steps increase as the pitch rises; so if the 
