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192 CONSONANT TRIADS. [IX. §99. |
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concord. If so, the triad itself is consonant. In order to determine all the consonant triads within an Octave above the fixed bottom note, we must assign to the middle and top notes every possible consonant position with respect to the bottom note, and reject all such positions as give rise to dissonant intervals between those notes themselves. The remaining positions will constitute all the consonant triads which have for their lowest note that originally selected. The intervals at our disposal are, for the middle note from the Minor Third to the Minor Sixth, and, for the upper note, from the Major Third to the Major Sixth.
In the annexed table1 the possible positions of the middle note with respect to the bottom note are shown in the left-hand vertical column, the name of each interval being accompanied by its vibration-fraction. The possible positions of the top note are similarly shown in the highest horizontal column. Each space common to a horizontal and a vertical column contains the vibration-fraction of the interval formed between the simultaneous positions of the middle and upper notes named at their extremities. When this interval is dissonant its vibration-fraction is enclosed in a square bracket. When it
1 Copied with slight modifications from Helmholtr's work. |
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