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THE ROTE-SONG OF THE HOPI                        15
is tlie first principle of scalar performance. It is as if from any given tone there were to these singers a comparatively narrow but not very intense field of attraction at the octave, others stronger but perhaps more diffused at the fifth and fourth; and at the sixths and thirds such confused and spreading attractions as might be expected from centres elongated but perhaps not clearly separable to the ear, — as a double star may be to the eye. The prominence of sixths is an unex­pected feature, and in the form of a sequence of major thirds (Snake Songs Nos. 2 and 3, Jakwaina) unpromising diatonically. These approximate ideals of vocal transition await incorporation in an indi­vidual melody to receive exact determination, and then not individ­ually but collectively in the form of the frequent precise adjustments of texture which are so great a surprise in view of the fluctuating and alternating intervals beneath which they are hidden.
Three complementary methods of composition are sug­gested throughout the songs, whose movement may be conveniently described in terms of this hypothetical psy­chology of their invention. Assuming the singer in executing any step of his melody to be guided by another tone than those he leaves and reaches, such an auxiliary note may lie beyond his goal, beyond his start, or between the two. His movement may in the first case be called a division of the interval start-auxiliary; in the second, a combination of the interval start-goal with the interval auxiliary-start; and in the third case, a balance of the interval start-goal upon the auxiliary. The division of an interval by a goal near the auxil­iary may be called a movement of approach. The particular case of combination in which an interior note of a divided interval becomes an extreme of another may be called lapping. The balance of an interval upon a coming auxiliary note near its goal may be called over­running. Steps in general thus interpretable group themselves, by repetition, rests, or changes of measure, into movements within which the singer often revisits the pitches touched. The chief movement in Snake Songs Nos. 1 and 8 appears a simple division of a fifth; those of No. 3, Malo-katcina, and Haikaya, in the main simple divisions of
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