A complete view of Acoustical Science & its bearings on music, for musicians & music students.

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The number of beats produced in each of these four intervals is 32 per second, and therefore if harshness of discord depended on rapidity of beats alone, these intervals should be equally discordant. But as every one knows, they are not; in fact, if, as we suppose, the tones are simple, the last two will have no trace of harshness whatever. Thus the number of beats per second, necessary to produce a certain degree of discord, varies in different parts of the scale of musical pitch, diminishing as we descend, and increasing as we ascend. Similarly the Beating Distance becomes greater, as we get lower in pitch, and contracts as we go higher.
The following are Mayer's determinations of the beating distance between Simple Tones, in various parts of the musical scale. The first column gives the name of the Simple Tone; the second, its vibration number; the third, the number of beats generated between the simple tone given in the first column, and another simple tone at Beating Distance; the fourth, the Beating Distance approximately expressed in musical language,—in other words, this column shows the smallest consonant interval in the region of the tone given in the first column. It is difficult to fix the points of greatest discord, but we should probably be not far wrong in placing it at somewhat less than half the Beating Distance; or throughout the greater part of the scale, at about a semitone.