HANDBOOK OF ACOUSTICS - online book

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190
HAND-BOOK OF ACOUSTICS.
equal, the roughness of this interval will depend upon its position in the musical scale; such roughness becoming greater as we descend, and less as we ascend. Two reasons may be assigned for this; in the first place, the upper partials of low tones aro usually stronger than those of higher ones, and consequently, when they beat with one another the beats are more intense, thus producing a harsher effect; secondly, partials that beat with one another in the lower part of the musical scale may be beyond beating distance in the upper part. To illustrate this fact, which of course applies to other intervals, we will take two or three cases of Fifths in different parts of the musical scale.
Now from the table on page 159, we know That 128 beats per second, in the neighbourhood of C2 = 1,024, is only just within the beating distance; consequently we may conclude that fifths above middle C having the constitution assumed above, are devoid of all roughness whatever.
From the table of page 159, we see that 32 beats per second in the region of C = 256 form a somewhat harsh dissonance. In fact, when C2 and Gr2 are strongly sounded on a harmonium, the harsh effect produced is due to the dissonating partials C and D, and consequently this harsh effect is about the same as that obtained by softly sounding the C and D digitals together,a matter which can be easily put to the proof.
The above, therefore, explains the fact, that while an Octave may be played anywhere in the Musical Scale, a Fifth cannot be well used below a certain limit. On the other hand, we see that speaking generally, a Fifth is a perfectly consonant interval, when taken above middle C ; we might therefore term this, the limit of a perfectly consonant Fifth on the Harmonium, Pianoforte, and stringed instruments in general.