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Considering in the first place the distributions of the Major Triads, it is obvious that no such Triad can be injured by differential tones if the intervals of which it consists occur in Tables I or II above. For the Differential of each Interval in Table I only dupbicates one or other of the Constituent Tones of such interval; while the Differential Tone of each interval in Table II will either coincide with, or duplicate the tone that must be added to that interval, to make it a Major Triad. On the other hand, those Triads which contain either of the intervals in Table DH, must be disturbed more or less by their differentials: for in the first place, the differentials are foreign to the scale, and will consequently sound strange and disturbing; and secondly, they may produce audible beats with the third tone of the Triad or one of its overtones, as for example,
in which the s1 will dissonate against the fe1.
Both the rules concerning the widening of the Consonant Intervals, and the Differentials generated by such Intervals, therefore, teach the same fact, viz.: that in selecting the most harmonious distributions of the Major Triads, the following intervals must be avoided.
The Minor Tenth.
The Thirteenths.
On examining all the possible distributions of the Major Triad, within a compass of two octaves, and rejecting those that contain either a Minor Tenth or a Thirteenth, the following Triads appear the more harmonious, the differentials being shown below: