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16                                           HOPI SONGS
sixths. In No. 6 a divided fifth is combined with an undivided third. The combination of divided intervals is illustrated in Anonymous II by superposed fourths; in Coyohim-katcina, by a fourth (extended by a minor third) over a fifth; in Shiashtasha, by a fifth lapping two others superposed; in Anoshkaey, by a fifth lapping a fourth and a fifth superposed; in Jakwaina, by superposed fifths; in Sumyacoli, by doubly lapped fifths. Thirds and fourths are balanced in No. 3, No. 6, Anonymous I, Haikaya, and elsewhere. Maihai-katcina illustrates the extension of a fifth (fourth) to a sixth by a balanced fourth, and the lapping of fifths.
The figures thus elaborated are used as themes; repeated in varied forms (Malo-katcina); shifted in pitch, as well through a minor third (Snake Song No. 6, Anoshkaey) as through the fourth above noted; and in particular ex­panded (Anoshkaey and Haikaya). The main figures may be preceded by an introduction, separated by interludes, and followed by a finale. The introductions are apt to present anomalies of form, and by sug­gesting that the singer is laying his course in the song emphasize its freedom of structure. Through their rehearsal of important notes the finales represent clotures in overture form. The general course of the melodies is downward, both within the individual figures and from figure to figure, the rate varying from the gradual descent of Snake Song No. 6 to the notable plunges of Malo-katcina, Maihai-katcina, and Shiashtasha. Snake Song No. 1 and Anonymous Nos. I and II keep their general level throughout, and Qoyohim-katcina and Jak­waina return to the initial tract after a climax. The singers often attain their highest notes by an approach (Qoyohim-katcina: D', C", D'") or a flourish also (Shiashtasha, Jakwaina), and in descending like­wise often overrun (Anonymous I).
The partial change in the pitch of repeated phrases, which has already been seen to resist explanation by modulation, is the most noteworthy formal feature of this music. De­fining a musical figure as a combination of notes determinate in their relations of pitch, sequence, duration, and emphasis, this process may
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