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THE PHONOGRAPHIC METHOD                         61
question is, whether a given primitive music recognizes in performance intervals other than those of the diatonic scale. That this question is not an unreasonable one appears from the fact that in music in regard to which we have other avenues of information than records of its products (e. g. theory, instrumental design), adiatonic intervals form a recognized element. That it is an unanswerable one in so far as we depend upon observations of performance taken down in the common notation appears from the facts (1) that whatever any given interval of a primitive performance may be in reality, when written in the chro­matic symbolism it appears as one or another multiple of a (tempered) semitone, and (2) that every multiple of a (tempered) semitone is an interval of the (tempered) diatonic scale.
It may, indeed, be argued that adiatonic intervals are refinements of intonation which cannot reasonably be expected in the music of the unhistoric races. But this argument is based on premises the proof of each of which, if derived at all from musical practice, itself demands more exact observation than can be recorded in the common notation. For a given span in pitch will be a refinement of notation to a given performer only when another interval nearly like it is already known to him, and an impracticable refinement of intonation only when the two are to his musical sense hardly to be distinguished. The assertion, therefore, that all adiatonic intervals are impracticable refinements of intonation to primitive performers rests upon the assumptions (1) that they recognize diatonic intervals, and (2) that any interval intermediate in size to these will be too near its neighbors in the diatonic series to maintain a separate existence in the primitive fancy. The inquiry into the first of these assertions — whether diatonic intervals are recognized by primitive performers — is the same as the inquiry condemned on this assumption, viz., whether they recognize other than diatonic intervals. No evidence whatever, either upon this point or touching the ultra-dia­tonic refinement of the primitive musical sense, will be contributed by any observations of performance recorded solely in the common notation. Records of the nearest diatonic intervals to those which are actually formed by the tones of given textures have no bearing at all on the
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