34 BUREAU OF AMERICAN ETHNOLOGY [BULL. 80 
lengths. In all these groups we note that songs with a large compass 
frequently have a predominance of small intervals (one, two, three, or 
four semitones), while songs with a small compass contain an unusu- 
ally large number of larger intervals (five or more semitones). 
GraPHic REPRESENTATION oR “ Prots ” 4° 
Five classes, or “ prevailing types,” were noted in the plots of the 
Sioux songs. The first two are general throughout the songs and 
do not appear to be connected with any particular idea. These two 
classes or types appear also in the present series, and for comparison 
the Sioux songs selected as represen- 
tative of these classes are here re- 
printed together with similar songs 
of the Mandan and Hidatsa (fig. 2). 
The present series contains no 
songs of sadness, which constituted 
Class E of the Sioux songs. Classes 
C and D comprised songs expressing 
positiveness or self-confidence, and 
songs connected with animals, each 
class showing a peculiarity of out- 
Bee. Gt ee. Bull. 80, No. 20. line. Songs of similar nature in the 
US eet be fis apres eon present series show somewhat simi- 
lar characteristics. It is not the in- 
tention, however, to attribute undue importance to a connection be- 
tween the idea of a song and a certain outline. 
In order to present this subject in a form which is more con- 
venient for observation the coordinate lines, shown in figure 2, are 
omitted and the plots are reduced in size (pls. 11, 12). A descending 
484 form of graphic representation, or “ plotting,’ of melodies was devised by the 
writer in order that the trend of Indian melodies might be more apparent to the eye 
than in the musical transcriptions. The general method employed is similar to that 
used in showing graphically the course of a moving object. The loci of the object at 
given periods of time are determined and recorded, the several positions being connected 
by straight lines. In any use of this method the interest centers in the several points 
at which the object is located, it being understood that the lines connecting these points 
are used merely as an aid to observation. In the present adaptation of this method the 
pitch of the accented tones in a melody is indicated by dots placed at the intersections 
of coordinate lines, the horizontal coordinates representing scale degrees and the vertical 
coordinates representing measure lengths. These dots are connected by straight lines, 
though the course of the melody between the accented tones would, in many instances, 
vary widely from these lines if it were accurately plotted. The use of accented tones 
exclusively in analyzing these songs has already been employed, the structure of the 
melodies being determined by the pitch of contiguous accented tones (see Table 8, foot- 
note). Since the sole purpose of these plots is to show the trend of the melodies, it 
seems permissible to omit from the representation not only the unaccented tones, but 
also a distinction between whole tones and semitones in progressions and a distinction 
between double and triple time in measure lengths. 
