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ON DISSONANCE.
169
On reference to the table on page 159, it will be found, that the beats that are not calculated above, are beyond beating distance; but the 32, 24, and 80 beats per second of the first interval, and the 16, 40, and 32 of the second, form very harsh dissonances; and moreover in the second interval, the 16 beats per second will usually be very prominent, as they are between a 2nd and a 3rd partial.
From the table on page 159 we see that thebeats
per second are slightly within or just on the verge of the beating distance. In the first Interval, thebeats per second will produce a harsh discord, as will also the 24 per second, though as they only arise between soft 5th and 6th partials, they have no very great intensity. The inversion is the worse of the two, thebeats per second between a 3rd and a 2nd partial, forming a bad and some­what prominent dissonance, which is made still worse by the 12 and andbeats per second higher up.
As already remarked, the above results must be modified for Compound Tones, which do not possess all the first six partials.
(4) Beats arising "between Compound Tones, through the occurrence of Differentials. The Fundamentals being Simple Tones, the con­clusions we arrived at concerning the beats due to the Differentials, generated by simple tones, in the former part of this chapter, at once apply to them. It only remains to ascertain the effects, due to the Differentials, generated by the Overtones.
Differential Tones are only produced when the generators are pretty loud, therefore we shall not go beyond the 2nd or 3rd partial, as those above rarely have any considerable intensity. Moreover it will not be necessary to consider any differentials except those of