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62 HOPI SONGS
question as to whether or no it is these diatonic intervals which are aimed at therein. Nor have records exhibiting only the distinctions of pitch which separate the diatonic intervals any bearing at all on the question as to how much smaller pitch distinctions are appreciable by the performers in question. To answer these queries from observations of musical practice, there is needed a system of notation which permits at once the registry of adiatonic intervals and of smaller pitch distinctions than the diatonic semitone. In truth, the opinion that the more natural music of the unhistoric races is always diatonic, adiatonic intervals being artificial products found among more civilized peoples only, may rightly at present be held in suspicion, seeing that the apparatus on which we are mainly dependent in the study of their music (the historical system of notation) is such as reveals diatonic intervals, and diatonic intervals only, in any textures of tone whatever to which it may be applied. The theoretic bearing of exacter observations than can be expressed in the common notation appears from these considerations to justify an effort like the present to record them.
The question as to the truth of the following notations to the actual course of tone of the phonographic perform ance from which they were made is the question as to the proportion of cases in which a note of the reproduction is represented by that sign in the notation which stands for the nearest fourteenth tone to that note. I myself feel great confidence that the great majority of those notes represented in the notations either' as identical with or as about a seventh tone away from the harmonium semitones were in reality nearer these than any other steps of the fourteenth tone scale. In regard to the notes represented as a fourteenth tone from the semitones, while I have an equal confidence that the interval was generally much less than a seventh tone, I recognize that the fatigue involved in trying to hear what manner of difference this small discrepancy might be makes these judgments much more uncertain. In like manner I have a considerable though a less confidence that the notes appearing in the notations at three fourteenths distance from the harmonium semitones were in gen-