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166 THE 'BEATING DISTANCE: [VIII. § 79. |
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tones only when they are within beating-distance of each other |
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It follows from what was shown at the end of Chapter VII that the same beating interval will give rise to very different numbers of beats per second according as it occupies a low or high position in the scale. Such an interval, e.g. a whole Tone, becomes palpably less dissonant as it is successively raised in pitch. Accordingly the beating-distance which for tones of medium pitch we have roughly fixed at a Minor Third, must be supposed to expand somewhat in low and correspondingly contract in high regions of the scale.
The general partial-tone series consists of simple tones which, up to the seventh, are, mutually out si beating-distance: above the seventh they close in rapidly upon each other. In the neighbourhood of 10, the interval oetween adjacent partial-tones is about a whole Tone; near 16, a semi-Tone; higher in the series they come to still closer quarters. These high partial-tones are therefore so situated as to produce harsh dissonances with each other. Where they are strongly developed in a clang, there
1 It will be shown in the sequel [§§ 89—92] that dissonance may, in the case of simple tones forming intervals wider than a Minor Third, arise from beats other than those here under conÂsideration. |
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