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56                                          HOPI SONGS
but as they stand involve two theoretic elements, — interpretations of the original comparative observations first in terms of higher and lower in pitch, and second in terms of a scale of approximate fourteenths of a tone.
In the common notation of music, the sequence of lines and spaces taken from below upward has the significance of the diatonic series of intervals from low to high.1 The separate systems of lines, or staves, are always fivefold, with extensions on occasion (leger lines), their dia­tonic meaning being indicated by writing at the left hand end of one of the lines the symbol (clef) for the step which that line signifies. The chromatic and enharmonic subdivisions of the diatonic order are left to be indicated by accidentals. For the expression of the much more minute scale of fourteenths of a tone made the basis of these records, without the employment of any accidentals, I have adopted the follow­ing modifications of the historical notation. Equal distances up and down in the page indicate equal intervals in the corresponding direc­tions in pitch. Thus the equidistant horizontal lines, instead of indi­cating the sequence of every other diatonic step (and hence including sometimes a major third between adjacents and sometimes a minor third), indicate a sequence of equal intervals. Every other line is drawn heavier, these signifying the sequence of the tempered semitones (100c) incorporated in the notes of the harmonium. The intermediate lines represent the intermediate quarter tones : (50c). The number of lines in a connected system or staff is not limited. The symbol for the
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