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178                                         HOPI SONGS
Observed and Tidied courses superposed.
cidence with a semitone of the chosen key. The accompanying dia­gram superposing the observed and noted courses of the song shows that in eliminating the looseness of texture in which its specific musical charac­ter resides, recurrent notes at e', d', b, and a, approximately equidistant from two diatonic levels, were either referred to one of these or ignored. By this process any sequence of pitch or other variable may be recast as a diatonic air, and a less distortion will commonly suffice. The accompanying chart of the middle region of the northern heavens was traced from a small map, laid off into twelve equal spaces repre­senting an octave of semitones and marked with a line connecting the brightest stars. The curve at once suggested a diatonic melody with a keynote at about 10° north declination, — y and fi Pegasi, which were not in the original choice, offering themselves for a tonic close. As in the Hopi song, so here a single step of the scale (d' in the heavens, de
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